HIGH RESOLUTIONATOMIC-BEAM-LASER SPECTROSCOPY

OF EUROPIUM I AND DYSPROSIUM I

G. J. ZAAL

VRIJI: UNIVI-:RSITI:IT AMSTÜRDAM

HIGH RESOLUTIONATOMIC-BEAM-LASER SI'liCTROSCOPY

OF EUROPIUM 1 AND DYSPROSIUM I

ACADKMISC1 IPROl- FSCHRll-T

tcr verkrijging van dc graad vandoctor in de wiskunde en natuurwetenschappen

aan de Vrije Universiteit te Amsterdam,op gezag van de rector magnificus

dr. D. M.Schenkeveld.hoogleraar in de faculteit der letteren,

in hel openbaar te verdedigenop donderdag 22 maart 1979 te 13.30 uur

in het hoofdgebouw der universiteit.Dc Boclelaan 1105

door

GHRARDUS JOSEPHUS ZAAL

geboren te Amsterdam

Promotor : Prof.dr. J. Blok

Copromotor : Dr. W. Hogcrvorst

typewerk en lay-out : Gerrio Rijnsburger

verzorging figuren : A. Pomper, G.J. Schut

en W.C. van Sijpveld

druk : Krips Repro - Meppel - 1979

STELLINGEN

1. De door Muller c.s. berekende waarde voor de isotopie-

verschuiving van 1 5 3Eu ten opzichte van 1 6 1Eu in de

spektraallijn 564,6 nm is onjuist.

W. Muller, A. Stendel, H. Walther; Z.Physik \_83_ (1965) 303

2. Enkele spektraallijnen van dysprosium worden door Ross

ten onrechte als grondtoestandsovergangen gekarakteri-

seerd.

J.S. Ross; J.Opt.Soc.Am. 62 (1972) 548

Dit proefschrift, hoofdstuk VI

3. De ontwikkeling van een Röntgen- of gamma-laser leidt

onvermijdelijk tot de ontwikkeling van nieuwe wapens.

4. Het verdient aanbeveling de toepassingsmogelijkheid van

isotopenseparatie met behulp van lasers voor de bewerking

van radioaktief afval nader te bestuderen.

5. Bij innovatie van het Nederlandse bedrijfsleven dient

meer aandacht te worden geschonken aan optische techno-

logie.

6. Menig aktiegroep is meer reaktiegroep.

7. De bescherming van de burger tegen organisaties zoals

particuliere bewakingsdiensten dient wettelijk geregeld

te worden.

8. De bewering dat individualisering in het basisonderwijs

le id t tot opheffing van het leerstof jaarklassensysteem,

is in zijn algemeenheid niet j u i s t .

Innovatieplan Basisonderwijs -

Advies van de Innovaciekommis.sie HasisHchool

Staatsuitgeverij, 's-Gravenhajju, 1978

9. Een laser-experiment is niet altijd een licht experiment.

22 maart 1979 G.J. Zaal

r

C O N T E N T S

I. INTRODUCTION AND SUMMARY 1

II. THEORY AND INTERPRETATION OF EXPERIMENTAL 5

RESULTS

U . I . I NTUOliUCTION 5

II . 2 . ISOTOPE Sll I FT <•

I I . 2 . 1 . General i>

It. 2. 2. Mass-effect. 7

I I . 2 . 3 . Field-off ei-1 JO

I 1 . 2.A . S e p a r aL i o n of exp e r i m e n t a l IS into MS

and FS 11

I t . 2 . 5 . D e t e r m i n a t i o n o f <•• • r ' •• f r o m t l i e f i e l d

shift 13

I1 . 2 . 6 . S e p a r a t i o n of f, • r? • into volume and

de f o r m a t i o n effect 14

1 1 . 3 . H Y P E R F I N E S T R U C T U R E 16

1 1 . 3 . I . E lementary theory of hfs 16

1 1 . 3 . 2 . E f f e c t i v e o p e r a t o r s 18

1 1 . 3 . 3 . P a r a m e t r i z a t i o n of the h f s - c o n s t a n t s 21

11. 3 . 4 . (i y p e r f i n e a n o m a I y 2 3

1 1 . 4 . T R A N S I T I O N P R O B A B I L I T Y AND SELECTION RULES 24

11.5. DETERMINATION OF HFS-CONSTANTS AND IS FROM A

SPECTRAL LINE 26

III. EXPERIMENTAL PROCEDURE 30

II I . 1 . INTRODUCTION 30

111.2. THE DYE LASER 31

111.2.1. Operation 31

111.2.2. Dyes 35

II1 . 2.3 . Stabi lity 36

111. 3. FREQUENCY CALIBRATION 37

I 11 . A . THE WAV E LE NG TH -ME TE R 4 1

111.5. ATOMIC BEAM APPARATUS 43

111.5.1. General 43

1 1 1 . 5 . 2 . T h e , - i p p a r a ! u s 4 4

1 I I . 5 . 3 . 1) o p p ] i' r - b r o ;nl o n i ii j ; 4 6

I I 1 . 5 . 4 . S t r a y l i ^ l i t r u d m i i n n 4 8

111.6. DATA TAKING 49

111.7. DATA ANALYS1S 51

IV. TEST AND CALIBRATION EXPERIMENTS UN Na AND In 54

IV.I. INTRODUCTION 54

IV. 2. SuIHUM EXPERIMENTS 54

1V.2. 1 . Calibration of interferometers 54

I V . 2 . 2 . Sensitivity of the 1 a s er- a t o m i c-b e a m

setup 57

IV. 3. HFS- AND IS-MEASUKEMENTS IX THK In 1-Sl'ECTKL'M 59

IV.3.1. General 59

IV.3.2. Measurements 60

IV . 3.3. Results and dis> ussion 61

V. HFS AND IS IN THE Eu I-SPECTRUM 6 4

V.I . INTRODUCTION 64

V.2. EXPERIMENTAL RESULTS 65

V.3. DISCUSSION 69

V.3.1. Hyper fine structure of the excited

states 69

V.3.2. Isotope shifts 80

VI. HFS AND IS IN THE Dy I-SPECTRUM 85

VI . 1 . INTRODUCTION 85

VI. 2. EXPERIMENTAL RESULTS 87

VI.3. DISCUSSION 95

VI.3.1. Isotope shifts 95

VI.3.2. Hyperfine structure of the excited

states 99

C H A P T E R

INTRODUCTION AND SUMMARY

The study of optical spectra has stimulated the development

of quantummechanics and significantly contributed to a

better understanding of atomic and molecular structure. Several

nowadays classical phenomena wore discovered in atomic

spectra first.

The discovery of the finestructure of a spectral line e.g.

led to the introduction of the concept of electron spin and

the observation of the hyperfine structure to the introduc-

tion of the spinning nucleus having magnetic and electric

moments. The dominant hyperfine interactions are the mag-

netic dipole and electric quadrupole interactions.

From measurements of hyperfinestructure splittings in

spectra nuclear spins, magnetic moments and values of

electric quadrupole moments were deduced, stimulating the

development of nuclear theory.

In 1932 Urey c.s. [URE 32] studied the hydrogen spectrum

and obtained the first experimental evidence for the ex-

istence of a second hydrogenlike atom: the isotope deute-

rium. Very weak spectral lines shifted towards shorter

wavelengths compared to the lines of normal hydrogen were

observed.

The so-called isotope shift could be explained by assuming

different masses for the two isotopes. However, isotope

shifts of many of the heavier elements could net be ex-

plained by mass differences only. Contributions from dif-

ferences in charge distribution of the nuclei had to be

taken into account too. Isotope shift measurements nowadays

provide a very suitable moans for the study of changes in

charge distributions between isotopes.

The resolution in most classical optical measurements of

atomic spectra has been limited by tne Dopp]urwidth of the

spectral linos, often obscuring the hyper finest, ructuro or

isotope shifts. The Dopplorbroadening could be reduced

with the introduction of atomic beam light sources. The

collimation ratio however, v/as limited for reasons of in-

tensity, since classical spectrometers only accepted light

emitted in small solid angle;;. Thus an increase in resolu-

tion often meant a loss in sensitivity.

Resolution nnd sensitivity of hyperfinestructure experi-

ments were strongly improved witli the introduction of

radiofrequency techniques. Atomic beam magnetic resonance

methods were developed for the study of the hyncrfine-

structure in atomic ground states of stable and radio-

active isotopes, whereas optical double resonance and op-

tical pumping methods became available for the study of

excited states. Also the study of coherence properties of

excited states of atoms in magnetic fields provided a

powerful now method, the level-crossing technique, for

high resolution experiments. The resolution in all these

types of experiments is in principle determined by the

natural linewidth.

No such progress v/as made in the study of isotope shifts.

The development of lasers, in particular tunable dye

lasers, has led to a renewed interest in atomic and mol _-c-

ular spectroscopy. The striking features of dye lasers,

the spectral purity, tunability, high intensity, coherence,

polarization and low divergence, make this type of lasers

a nearly ideal light source for high resolution optical

spectroscopy.

Experiments, in which both hyperfinestructure and isotope

shifts are measured with high accuracy, are possible now.

In atomic-beam-laser spectroscopy, which is the subject

of this thesis, the absorption of laserlight I y an atomic-

beam is studied. The absorption of ]iqht is detected

through the fluorescence light emitted immediately after

the absorption. It is possible to study ijb.sorptjon

spectra almost devoid of inhomogeneous broadening by using

well collimated atomic beams in >i configuration with laser

beam and atomic beam perpendicularly. This setup enables

the measurement of hyperfinestructure and isotope shifts

at tiio same time, preserving Hie poss i bi ) i ty of detection

of very small quantities of atoms or weak transitions.

In this thesis laser-atomic-bcam experiments on the rare

earth elements europium and dysprosium are described.

Results of hyperfinestructure measurements will be given

and discussed with the help of an effective operator for-

malism. Isotope shifts will be evaluated and the variation

in nuclear parameters such as changes in nuclear charge

radius and nuclear deformation between isotopes of the same

element will be extracted.

In chapter II the theory of hyperfinestructure and isotope

shjft is reviewed. The evaluation of the change in nuclear

charge distribution and nuclear deformation between isotopes

from observed isotope shifts is outlined. The effective

operator formalism for the analysis of the hyperfincstruc-

ture is presented.

The experimental arrangement is described in chapter III.

The principles of dye laser operation as well as laser

performance are given. Problems arising in the experimental

procedure, such as frequency calibration of the dye laser

scan and wavelength readout are discussed and the atomic

beam apparatus is described.

The laser-atomic beam setup was tested on indium and sodium.

The test-experiments are described in chapter IV.

Frequency calibrations of dye laser scans wore per/ormed on

absorption lines of these elements. The sensitivity of the

setup could be determined from experiments on the sodium

D-lines. For indium the magnetic hyperfinestructure split-

ting in the 'Si_-cxci ted state was measured, as was the

isotope shift between l; Tn and ' '• In in the transition at

451.1 nm. From the observed isotope shift the change in

nuclear charge radius was calculated.

In chapter V measurements of hyperfinestructure and isotope

shifts in 8 transitions of the spectrum of europium 1,

connecting the 4f'6s ground configuration with the first

excited 4f'6s6p configuration, are described. Accurate

values for hyperfinestructure and isotope shifts were ob-

tained for the isotopes •' • Eu :<nd ' Eu. The h/perfine-

structuro analysis of the excited states is presented. The

influence of configuration mixing on tile isotope shift

is studied and the difference in nuclear charge distribu-

tion determined.

In the last chapter laser absorption measurements on the

dysprosium I-spectrum are described. Isotope-shift values ..ci

obi- jined for all lines investigated, allowing the calcula-

tion of the variation in nuclear charge distribution and

in nuclear deformation between the Dy-isotopes.

The hyperfinestructures of '' !Dy and :' 'Dy were determined

in a number of excited states, permitting an analysis with

the effective operator formalism.

The nuclear quadrupolc moments of '' '• Oy and :' 'Dy were

evaluated.

C H A P T E R I I

THEORY AdD INTERPRET;nor,1 01 EXPERIMENTAL RESULTS

11.1 INTRODUCTION

The development of sprctrosropic instruments with high

resolving power at the end of the nineteenth century led to

the discovery of hyperfine structure (hfs) in many atomic

spectral lines. Michelson [MIC 0 1], Fabrv and Perot [TAB 97]

and Lummer and Gehrke [LUM 03] found that many atomic tran-

sitions displayed not only a finestructure, but, that in

fact each fine^tructure ]ine consisted of several closely

spaced components. Whereas the finestructure splitting is

in the order of 10-10' GHz, the hyperfine structure split-

ting is m the range from 10 MHz to 10 GHz.

The finestructure could be explained with the introduction

of the electron ?pin and is the result of the interaction

between the spin and the orbital motion of the electrons.

In 1924 P.'iuli [PAU 24} explained the hfs with a magnetic

coupling between the atomic nucleus and the electrons. If

the hfs was caused only by a magnetic hyperfine interaction,

the separation between the hyperfinc levels should follow a

regular pattern, the Lande-interval rule [CAS 36].

Deviations from this rule were found for the first time by

Schuler and Schmidt [SCH 35] in Jie hfs of europium.

Casimir rCAS 36] showed that the experimental results could

be explained by taking into account an electric quadrupole

interaction between the electrons and the nucleus. In very

accurate atomic-beam-magnetic-resonance (ABI'.R) experiments

even higher order multipole interactions such as magnetic

octupole and electric hexadecapole interactions were demon-

strated .

In 19 32 it was observed by Urey and coworkers [URE 32] that

in the hydrogen spectrum every line was accompanied by a

week satellite shifted towards a higher frequency. This

observation could not be explained in terms of magnetic or

electric interactions. However, the intervals between the

satellites exactly fitted the Rydborg formula for mass num-

ber M = 2 , which unambiguously demonstrated the existence of

deuterium. The shift between main component and satellite

was called "isotope shift". It was later shown to be a

general feature in spectra of elements with several isotopes.

In section II.2 the isotope shift will be discussed in more

detail, whereas the hyperfine structure is subject of sec-

tion 3. Transition probabilities and selection rules of

atomic transitions are presented in section 4. Often a com-

bination of hfs and IS is experimentally observed in a single

spectral line. In section r< of this chapter a general method

is outlined for the interpretation of complex spectra.

II.2. ISOTOPE SHIFT

11.2.1. General

Different isotopes absorb light at slightly different fre-

quencies. For a given pair of isotopes this difference is

called the isotope shift (IS). Without loss of generality

in the following it is assumed that the isotopes have no

hyperfine structure.

In order to evaluate the IS in a spectral line, the energy

shift of both levels involved in the transition must be

calculated. As a reference level the finestructure term

energy of an atom with a point ,.ucleus of infinite mass is

considered. The non-relativistic Hamiltonian for a neutral

atom with Z electrons can be approximated by:

// = —^- y p 2 - y — + y -^- + y r 1' s' (2-0me i i ri i/j ri.i i

The sum is over all electrons in the atom, p\ is the momen-

tum of the i t l electron, m the electronic mass and e the

electronic charge. The first term in (2-1) is the kinetic

energy-operator of the electrons. The second and third term

represent the potential energy duo to the monopole electro-

static interaction between the nucleus and the electrons,

and the electrostatic interactions among the electrons re-

spectively; r. = |r.| with r. the position coordinate of the

i t l electron and r. . = j r". - r". \ the distance between elec-

tron i and electron j. The last term in (2-1) represents

the spin-orbit interaction, where 1^ is the angular momen-

tum, s. the electron spin and 5. the spin-orbit interaction

constant.

Any effect due to the finite mass or size of the nucleus is

neglected in this Hamiltonian. If these effects are taken

into account, the finite mass gives rise to the mass isotope

shift and the finite nuclear size to the field isotope shift.

II.2.2. Mass-effect

When the finite nuclear mass is taken into account, the

nucleus no longer is the centre of mass of the atom. There-

fore the energy of the electrons has to be corrected for the

motion of the nucleus around the centre of mass. This results

in a correction AE to the energy equal to the recoil kinet-

ic energy of the nucleus:

AEM " 4 ^ ' (2"2)

where M is the nuclear mass and pN the nuclear momentum.

Since in the centre of mass system

with p. the momentum of electron i, the correction AE . can

be expanded and combined with the kinetic energy of the

electrons.

Then:

A E = < % ( i + J)Xp 12> + < ± I P'i-P^. (2-4)c i i*j

The quantity •~ = m~ + M ^s defining the reduced mass \t.

The first term in (2-4) gives rise to the so-called

"normal- mass shift" (NMS) and the second term to the speci

fic mass shift (SMS).

Since the reduced masses of isotopes with atomic mass num-

ber A and A' are slightly different, this results in an

unequal shift of the term energies and consecutively in a

frequency difference in the transition frequency \>. This

frequency difference Sv ,,s can be calculated exactly:

. AA1 Ar A mo A'-A ., A'-A . _ - ,6v = v ~ v = * = » (25)

m is the proton mass.

The NMS is always positive, which means that the absorption

line of the heavier isotope is shifted towards higher fre-

quencies.

The specific mass shift originates from non-vanisbing pair

correlations in the momenta of electrons. It can be positive

or negative depending on the coupling of the electrons. The

SMS shows the same dependence on nuclear mass as the NMS,

as is evident from (2-4), and is therefore also proportional. A'-At O-A^~ :

" MSMS

M can be expressed as [VIN 39]

mM S M S - 2 5 T R k ' ( 2 ~ 7 )

p

where R is the Rydberg constant. Vinti's factor k is a

linear combination of products of integrals of the typo

= [ Rnl(r)(D (1-1)

dr r n'l-R ,,_, (r) r-dr .

(2-8)

The radial part of the electronic wavefunctlon R (r) is

normalized according to

Rnl(r)|2r2dr = 1 .

For transitions between states of pure LS-coupling, the

value of M_M_ does not depend on the quantumnumber J [VIN 39].

Hartree-Fock calculations [BAU 74] yield values for <$'-> s

which are small for pure s-p and s2-sp electronic transitions,

when compared with ^v^-.g. This is in qualitative agreement

with experimental results.

If the evaluation of nuclear parameters from isotope shifts

is emphasized, experiments are preferably performed on spec-

tral lines involving these pure s-p or s2-sp transitions.

The SMS can be roughly estimated [HEI 74] resulting in:

6vSMS = ( - 3 ± "9)l5vNMS f o r n s~ nP transitions (2-9)

6vSMS = * ° * #5'fivNMS f o r ns'?~nsnP transitions (2-10)

However, transitions in which a nd- or nf-electron is in-

volved, can result in SMS considerably larger than the

corresponding NMS.

_2

Because of the A dependence, mass effects will be compara-

tively small in heavy elements.

II.2.3. Field effect

The field effect is due to the finite nuclear charge distri-

bution. Consider e.g. a homogeneously charged spherical nu-

cleus with radius R. The electrostatic potential outside theZe?-nucleus will be V = ——-. Inside the nucleus the potential

deviates from the Coulomb potential. A sketch of the poten-

tial for two isotopes A and (A+l) differing by •• R in nuclear

radius is shown in fig. II.1. The smaller nucleus has the

larger potential. It may thus be seen, that the finite nu-

clear charge distribution diminishes the binding energy of

the electrons, though more pronounced in the case of the

heavier isotope, through the overlap of their wavefunctions

with the nuclear volume. Because changes in the nuclear

charge distribution arc; noticeable only inside the nucleus,

this effect is important only for s-electrons, or to a far

less extent pj,-electrons, as they have non-zero wavefunctions

at the nucleus.

A change in the deformation of the nucleus has a similar

effect on the electron binding energies as a change in

volume. The resulting isotope shift in a spectral line i

!«¥•

Fig. II.I. Potential energy V of an electron in the

field of a spherical uniformly charged nucleus.

10

<Sv. ' due to changes in nuclear volume and shape induced

by changing the neutronnumber, is called the "field .shift"

(FS).

The FS is connected with the change of the nuclear charge

distribution by [HEI 74]:

= E.f(Z) (2-11)

where i\<r?-> is the mean-square nuclear charge radius.

Contributions of higher charge moments are small and have

been neglected in (2-11) [LEE 73]. The electronic factor

E. is proportional to the change of the total non-relativis-

tic electron-charge density A|iji(O) |2 at the nucleus in the

transition i

E =i (2-12)

where aQ is the Bohr radius. f(Z) accounts for the relativ-

istic correction to &\ip(0)\2 as well as for the influence

of the finite nuclear charge distribution on the Dirac

electron wavefunction.

f(Z) =5/2

unif.(2-13)

—with A = r = 1.20 fm and C A A'

0 unif.the theoretical iso-

tope shift constant for a uniformly charged nuclear sphere

of radius R = rQ A . This constant has been tabulated

by Babushkin [BAB 63] for stable isotopes.

II.2.4. Separation of experimental IS into MS and FS

The total IS in an optical transition i is the sum of the

three terms (2-5), (2-6) and (2-11):

11

AA' (2-14)

For light elements (Z < 30) the field shift is generally

negligibly small. In heavier elements (Z > 58) the field

shift is predominant. In the intermediate region mass shifts

and field shifts are roughly of the same order of magnitude.

6<r2> can be calculated from measured isotope shift values

with the help of (2-14). This requires a separation of MS and

FS.

When three independent isotope shifts in several optical

lines have been measured, the consistency of (2-14) can be

checked and MS and FS separated using a so-called "King

plot" [KIN 63]. For two lines i and j it follows from (2-14)

that:

where M. =M. I1.

J j AA1 { - j

. When the modified isotope shift

o AA' AA'A'-A

(2-16)

for all possible pairs A, A' is plotted against the corre-

sponding quantity for another line, the points shouldJ Ei

fall on a straight line (King line) of slope — and inter-im Ei I EJ E:

cept M. - M. — I. By inserting the numerical value of —--

I -' j J * in the expression of the intercept, a pure mass shift J

quantity is obtained. If the factor M. is known for one line,

then the mass shifts in other lines can be calculated. The

NMS can be calculated with (2-5). In a pure s-p or s2-sp

transition the SMS estimates are given by (2-9) and (2-10)

and then also SMS in other transitions can be evaluated.

The field shift is then easily obtained by subtraction of12

the mass shift from experimental IS-values.

II.2.5. Determination of >5<r2> from the field shift

The field shift is equal to the product of a purely elec-

tronic part E.f(Z) and a nuclear part ^••r?> (see (2-11)).

Therefore &<r2> can only be determined by evaluating the

electronic part of the field shift. f(Z) is a known function

(see (2-13)) and can be calculated in a straightforward

way. The methods used to determine E. are partly empirical

[HEI 74].

When in a ns-np transition the small contribution of the

Pi-electron is omitted, the change in the total non-relativ-

istic electron-charge distribution at the nucleus 4 ! i;> (0)"! 2

can be calculated as a fractional part of the electron-

charge density |i^(0)j2 :

The factor (3 accounts for the change in the screening of

the inner closed shell electrons from the nucleus, when the

outer electron jumps from a ns to a np-orbital. 3 can be

obtained from Hartree-Fock calculations [WIL 72], [COU 73].

The error in 3 is supposed to be a few percent.

For other types of transitions, e.g. ns2-ns np, A|I|I(0)|? r_

can be calculated with a screening ratio y:

* ( 0 )

2ns

-**, (2-18)

which again is known from Hartree-Fock calculations. In this

case |iJ)(0)|2 is the electron-charge density for a singly

ionized atom.

For an outer ns-electron |!i>(0)|2 can be calculated from theII S

13

magnetic hfs-splitting of an atom or ion, as is obvious

from (2-39) and (2-41). A value for |(H0)|2 can also be

calculated from the ionization potential of an atom or ion

[WYB 65]. The ionization potential energy determines the

binding energy of the ns-electron. From the latter energy

the hfs-constant a can be calculated through the Fermi-

SegrS-Goudsmit formula [KOP 58].

IX.2.6. Separation of &<r?-> into volume and deformation effect

The fieJd shift given in (2-11) is proportional to f,--r?>.

As mentioned in section II.2.3, there are two effects, which

give rise to changes in 6<r2> and hence contribute to the

isotope shifts of a spectral line: the volume effect and

the deformation effect.

The change in 5<r2> . due to the volume effect can be com-

pared with predictions of the liquid drop model. The change

in the mean-square radius <5<r2> . , of an incompressible,

uniformly charged spherical nucleus is given by:

*A<*2>unif - I V TT ' (2"19)

with R =1.20A fm. However, experimental isotope shifts

in non-deformed nuclei yield appreciably smaller values than

those predicted by this liquid drop model. Comparison of

experimental values of 5<r2> . with 6<r?> ., gives:c vol unit '[BOD 59]

5<r2>p = ^ - = 0.65(10) (2-20)

5<r?> .,u in f

This is the so-called isotope shift discrepancy, demonstrat-

ing that the expansion of the nuclear charge distribution

of a spherical nucleus on the addition of neutrons is less

than the value predicted by the liquid drop model.

In the case of a deformed nucleus, the nuclear shape can be

14

expressed as:

= R Q{I (2-21)

R» is the average radius,U

V

A \iare deformation parameters and

Y V { 9 , $ ) is a spherical harmonic. Assuming only quadrupole

deformations (A =2) (2-19) represents a quadrupoloid. In the

intrinsic coordinate system it is convenient to use the pa-

rameters (•: and y. The mean-squared deformation •<?,?:• of the

nucleus is defined by

'2,/(2-22)

The asymmetry parameter y describes triaxial shapes.

When a uniformly charged nucleus with constant volume and

density is deformed, it's second radial moment up to second

order is given by:

<5<r2> = 47 (2-23)

Contributions to 6<r2> due to the asymmetry parameter y

have been neglected in this expression.

Combining the results of volume and deformation effect, the

mean - square nuclear charge radius can be written as:

6--1-2 > A A 'unif 4-i 0

(2-24)

As 6<p,z> is the only unknown quantity in (2-24), it can be

evaluated from the experimental value of

15

II.3 HYPERFINE STRUCTURE

11.3.1. Elementary theory of )ifs

A first contribution to the hfs of an atomic fincstructure

level is originating from the coupling of the magnetic

dipole moment ii. of a nucleus with non-zero nuclear spin 1

with the magnetic field II' (0) produced by the electrons at

the nucleus. The interaction Hamilton!an is:

/;M] = -1., .11,(0) . (2-25)

The magnetic field at the nucleus is produced by the orbit-

al motion as well as the spin dipole moments of the electrons

and can be linearly related to the total angular momentum of

the electrons J. The nuclear magnetic dipole moment can be

written as:

where \i is the nuclear magneton and g1 the nuclear g-factor.

When only diagonal elements in I and J are considered /.'

can be replaced by an equivalent operator:

//... = h AI.J . (2-27)

A is the magnetic dipole coupling constant and is equal to

Vx 11,(0)

h I J-> •> ->

In the I IJFM> representation, where F = I + J is the total

angular momentum and M is the eigenvalue of F , the result-

ing energy contribution is:

EMl = IT K' ( I - hl J - h) (2-28)

with K = F(F+1) - 1(1+1) - J(J+1) .

16

The electric quadrupole coupling as a second contribution

to hfs is caused by an interaction between the nuclear

quadrupole moment Qj and the electric field gradient %j(°)

at the site of the nucleus. The interaction ilamiltonian is

the scalar product of a nuclear (Q' ) and electronic (q'j)

second rank tensor:

CJ'l • (2-29)

For matrix elements diagonal with respect to I and J (2-21)

reduces to:

21(21-1)J(2J-1)

where B=e2Q-q,(0) is the electric quadrupole coupling

constant.

Then the energy contribution is:

hB_ _ hB (/2)K(K+l)2I(I+l)J(J+l) .EE2 " 1 I(2I-1)J(2J-1) ' (I ' 1( J '

The total hfs-energy of a free atom is the sum of the

energies (2-28) and (2-31), which results in the well-known

Casimir formula:

P _ hA hB(3/2)K(K+I)-2l2 4 I(2I-1)J(2J-1) U-J-i;

As an example the hfs-splitting in the ground state of

l63Dy With I = 5/2 and J = 8 is shown in fig. II.2. The

total angular momentum F ranges from 11/2 to 21/2. A and B

factors of Childs were used [CHI 70].

It is not difficult to prove with relation (2-32) that the

centre of gravity of a finestructure level remains un-

changed in the presence of a hyperfine structure.

17

OH.

:.» i.f

Fig. II.2. HFS levels of the ground state of 1&3Dy.

A(163Dy) = 162.754 MHz, B(IC>3Dy) = 1152.869 MHz.

II.3.2. Effective operators

Relation (2-32) is commonly used for the calculation of hfs-

constants from the experimentally observed hyperfine split-

tings. A more fundamental approach is required to interpret

the values for these constants. The Hamiltonian for the

interaction of the electrons and the nucleus can be expanded

in scalar products of multipoles of rank k [SCH 55]:

U = T(e)k.T(n)k T(e)°.T(n)° + //his

(2-33)

k k

where T(e) and T(n) are spherical tensor operators of rank

k representing the electronic and nuclear part of the inter-

action. Because of invariance under parity operation, terms

with even k-values represent electric, those with k odd

magnetic interactions. The monopole term (k=0) represents

18

the Coulomb interaction of the electrons with the spherical

part of the nuclear charge distribution. It is part of the

finestructure Hamiltonian (2-1) and is of no further impor-

tance for the hyperfinesplitting. The k=l term describes the

magnetic dipole hfs. The second order term of //. f , is the

electric quadrupole operator. Higher order terms will be

neglectedi because their contributions are roughly at least

a factor 10R smaller.

The hyperfine interaction depends strongly on values of the

electronic wavefunctions in the neighbourhood of the nucleus.

The velocities of the electrons in this region are not small

compared to the velocity of light and therefore the electrons

should be described with relativistic Dirac wavefunctions.

However, the matrix elements of the true Hamiltonian //, ,hfs

between LS-coupled relativistic eigenfunctions can be shown[SAN 65] to be equal to the matrix elements of an effective

ef fHamiltonian tf , between non-relativistic LS-coupled states.This effective Hamiltonian turns out to be of the same form

as (2-33). The effective operator not only accounts for rel-

ativistic effects, but also for polatization effects and

configuration interactions.

The hfs of an atomic finestructure state is commonly de-scribed in the |IJFM> representation. The first order expec-tation values of //. , are:

hfs

E p = <1JFM| h f 8|UFM> = I (-DJ+I+F{]J J} <J|]T(e)ki|j><l!|T(n)kpT>

k=1 (2-34)

The quantity in the brackets is a 6-j symbol. The reduced

matrix elements are independent of the magnetic quantum

number M. The degeneracy in F is removed by the hyperfine

interaction and the F dependence is entirely contained in

the 6-j symbol and a phase factor.

19

It is convenient to introduce parameters A(J) using the

stretched state (M =1, M = J ) :

A, (J) = <Il|T(n)k|H •<JJ|T(e)k|jJ- , (2-35)

which can be related to the reduced matrix elements of

(2-36) by application of the Wigner-Eckart theorem:

The expression in the parentheses is a 3-j symbol.

<Il|T(n) |ll> is defining the magnetic moment \i , whereas

the nuclear quadrupole moment Q = — <II | T (n) -" | II> .

Combining (2-34), (2-35) and (2-36) and using explicit

formulas for the 6-j and 3-j symbols (2-32) is obtained when

A (J) = AIJ and A9(J) = kB is substituted.

The magnetic dipole constant A and the electric quadrupole

constant B are then related to the effective tensor opera-

tors T(e)1 and T(e)2 through the reduced matrix elements:

T -1

~ [J(J+D (2J+1) ] 5<j||T(e) ! i|j* (2-37a)

and

2J(2J-1)(2J+3)(2J+2]

(2-37b)

The expressions for the electronic tensor operators take on

the explicit forms [ARM 71 ]:

T(e)1 = 2lJo j

(2-38b)

20

In these expressions 1. is the orbital angular momentum of

the i11 electron, sy. t.he electron spin and c\? resp. cV4 the

modified spherical harmonics of second resp. fourth order.

<r. > represents radial integrals of the type fR(r)-r,R(r)r?dr,i r y

where R(r) is the radial part of the electronic wavefunction.

The summation extends over all electrons in open shells.

The first term in (2-38a) accounts for the orbital magnetic

hyperfine structure. This contribution is caused by the mag-

netic field at the nucleus generated by the orbital motion

of non-s electrons. The second term in (2-38a) is the spin-

dipole contribution, due to the intrinsic spin dipole moment

of the electrons producing an additional field at the nucleus.

The last term represents the Fermi-contact interaction for

s-electrons.

-3In the non-relativistic limit the radial integrals <r. >„,,

-3 -3 L O l

<r. >., and <r. >n_ are equal and reduce to the single

value <r. > . (1 > 0 ) . For s-electrons the integral <r. >._

has the following non-relativistic limit: <r. >._ = 4u iS<r>.

The integrals <r; >.„ and <r. >. are purely relativistic

and will both vanish in the non-relativistic case i.e. the

quadrupole interaction is entirely orbital in character.

11.3,3. Parametrization of the hfs-constants

Since it is difficult to calculate the radial integrals in

(2-38), they are often interpreted as free radial parameters,

which can be determined from a fit to experimental hfs-data.

It is convenient to define single-electron hfs parameters,

related to the radial parameters given in (2-38) in the

following way:

a,0(i) = j y vB <ri' >]Q (2-39a)

a, . (i) =2-4- p., <r73>. . (2-39b)

b u(i) = e^ Qx <rT3>kl (2-39O

21

-3

The radial parameters <r >, can also be estimated in aklway when the

known [BOR 65]

semi-empirical way when the finestructure constant f,. is

0.17114 F k lU,Z e f f) g-^j a ^ cm (2-40)

F,. and H are relativistic Casimir-correction factors

[CAS 36] tabulated by Kopfermann [KOP 58]. Ztiff is the

effective charge number. Z,.. = Z-4 for p-electrons/ Z-ll

for d-electrons and Z-35 for 4 f-electrons [ARM 71].-3

The parameter <r.(s)> corresponding to an unpaired s-electron is correlated to the density of the s-electron at

the nucleus i|),(0) and can be estimated as:

~3 (l-fi)(l-E) (2-41)

F, & and c are relativistic correction factors [KOP 58].

A parametric expression for the hfs-constants A and B can

only be obtained from an evaluation of the reduced matrix

elements in (2-37) which requires accurate values of the

wavefunctions.

The angular momenta of electrons in e.g. the unclosed

4 f-shell of rare earth elements are not purely LS coupled

as is convenient for the application of effective operator

techniques.

The breakdown of LS coupling can be accounted for by an

expansion of the actual wavefunction for a particular state

as a linear combination of pure LS-states. The expansion

coefficients can be obtained from a parametric finestructure

calculation. Using adjustable parameters for the radial

integrals and the finestructure coupling constants in a non-

relativistic calculation of the finestructure level energies

with (2-1) the calculated energies can be fitted to the

experimental values. In i-hi<? fitting procedure not only

22

the energies are determined, but also the corresponding

eigenfunctions.

The reduced matrix elements in (2-35) could be evaluated

with the computer program "AUFSPA" * [CLI 78]. With accurate

wavefunctions as input this program calculates the angular

part of the reduced matrix elements of all hfs-operators

in (2-36) in order to obtain the angular coefficients of

the one-electron hfs-parameters in the parametric expres-

sion.

When a sufficient number of hfs-constants A or 13 are known

experimentally, the hfs-parameters can be determined from

a least-squares fit of the parametrized expressions to the

experimental values.

11.3.4. Hyperfine anomaly

From (2-21) it is obvious that the magnetic hfs-constant A

is the product of — with a purely electronic factor. This

implies for the hfs-constants A(l) and A(2) of a given level

for two isotopes of the same element, that the following

relationship should hold:

A(l) u (1) 1(2) g (1)— __i _ _i (2—42)

A{2) Mj.(2) 1(1) gI(2)

assuming the electronic quantities to be equal.

The same argument holds for B. and:

B(l) QT(l)— . (2-43)

B(2) Qx(2)

Although (2-4 2) is valid to a rather high degree of accuracy,

experimentally deviations have been found, which can be

expressed in terms of a magnetic hyperfine anomaly ]A2 for

a certain level:

* "Aufspa" was kindly supplied by H. llrund (Ilanmwur).

23

gT(2)i 1 , (2-44)

A(2) gx(l)

where 2 is the heavier isotope. The anomaly generally is

smaller than 1 %. Hitherto no hyperfine anomaly has been

measured for the electric quadrupole constants.

Hfs anomalies cannot be explained with (2-33) , as it is

assumed that the hfs-Hamiltonian can be written as a product

of two terms. But, since the nucleus has a finite extension

nuclear and electronic coordinates are no longer independent.

When the electron is inside the nucleus, the electronic wave-

functions may vary slightly from one isotope to the other-

This change in wavefunction is important only for s-electrons

(and p^-electrons) since only they have non-vanishing elec-

tron densities at the nucleus. So, hfs anomaly is a clear

indication, that s-electrons do contribute to the magnetic

dipole interaction. The contribution to *A2 due to a differ-

ence in the nuclear charge distribution is known as the

Rosenthal-Breit effect. In the semi-empirical calculation of

the one-electron hfs-constant (2-41) this effect is account-

ed for by the correction factor (1-5) [KOP 58]. The contri-

bution due to a difference in the distribution of nuclear

magnetism over the nuclear volume is called the Bohr-

Weisskopf effect. In (2-41) allowance for this effect is

made for by the factor (1-e).

II.4 TRANSITION PROBABILITY AND SELECTION RULES

The emission or absorption of radiation by atoms is predomi-

nantly of an electric dipole character, which means that the

parities of the two states involved must be different.

In the absence of hfs the probability of absorption or

emission of radiation, due to a transition between the

levels -yj and y'J' is often expressed in terms of the line-

24

strength. The linestrength is defined as:

S(YJ^Y'J') = I \<yJM\P\ylJ'M'>\' = | - yJ || P || y ' J ' >\ 'M M < (2-45)

P = -e Jr. is the electric-dipole operator.i

In the LS-coupling scheme the square root of the linostrength

is given by:

-YSL||P||7'S'L'-

(2-46)

Since 5(S,S') appears in (2-44) the selection rule AS=0 must

be obeyed. From the properties of the 6-j symbol the follow-

ing selection rules can be derived.

AL = 0, ±1 and AJ = 0, ±1 (the transition J=0*-->J=0

is excluded)

The J-selection rule is independent of the coupling scheme.

The selection rules on S and L are not absolute, since they

depend on the type of coupling. A departure of LS-coupling

will lead to a breakdown of these selection rules.

The transition probability is directly related to the natural

lifetimes of lower and upper state. Since the lower state is

stable for the transitions studied in this thesis, the tran-

sition probability is completely determined by the lifetime

of the excited state. For radiation in the visible region it

typically has values in the region 10~8 - 10~9 sec. The

natural lifetime of the excited state results in a natural

linewidth of a spectral line as a consequence of the uncer-

tainty principle. In high resolution absorption experiments

this linewidth can be observed.

25

The relative intensities of electric dipole transitions

between two hfs-multiplets can be calculated in the JIF-

coupling scheme in a way analogous to the calculation of

relative intensities of transitions between two LS-coupled

multiplets if the correspondance

S -• I, L •> J and J • F

is made. The selection rules become:

AI = 0, AJ=0, tl, AF = 0, ±1 (but not 0—0)

The relative intensities of transitions between two hfs-

multiplets have been tabulated for many values of I and J

by Kopfermann [KOP 58].

II.5 DETERMINATION OF HFS-CONSTANTS AND IS FROM A SPECTRAL LINE

The structure of a spectral line determined in an absorption

experiment can be attributed to transitions between the hfs-

levels of the excited and the ground states of the different

isotopes present in the absorbing medium.

The derivation of IS and hfs-constants from observed spectra

is outlined next on a transition in the spectrum of Dy I.

Hfs-spectra, especially of rare earth elements can be rather

complex, as is shown in the transition at 597.4 nm between

two finestructure levels with J =8 of dysprosium (see fig.

II.3). Since hfs-splittings in this spectral line are larger

than the electronic frequency scanning range of the dye

laser (see section III.2) the complete spectrum is obtained

from several overlapping scans. Finer details are measured

in more restricted scans as is shown in fig. II.3. for two

parts of the spectrum. A natural sample of dysprosium contains

seven isotopes with mass numbers 156,158,160,161,163 and 164.

26

_ . -znz e»i2(El*-Z/Cl COIV\

-ZlLi 101- ziu cm -

i"-4'» '?'I •- II!

l i .<

0.05

0.09

IS 03

2.29

O

18.8

8

(M r 28.1

8

27

The natural abundances and the nuclear spin values of the

seven isotopes also are denoted in the figure. Contribu-

tions from the various isotopes are indicated and the

values of the total angular momentum of ground and excited

state for the odd isotopes are given. The upper value

belongs to the excited state. The peaks in the reference

spectrum were generated with an interferometer (see section

III.) and serve as a frequency scale. Peak distances are

75 MHz.

The even-even isotopes have nuclear ground state spin 1 = 0,

which implies they have no hfs and contribute only a single

component to the hfs-pattern. The two strongest components

can now be assigned to the most abundant even-even isotopes.

The two odd isotopes exhibit hyperfine splittings, because

of their half-integral spin 1 = 5/2. Since J > I both ground

and excited state will have (21+1) =6 hyperfine levels (see

fig. II.2). Hyperfine transitions between ground and excited

state obey the selection rule i\F = 0, ±1 (see section II.4).

For this reason the line will split up into 16 components

for each odd isotope. Together with the 5 single components

of the even-even isotopes, the spectral line 597.4 nn will

be composed of 37 components. The relative intensities of

the hyperfine components belonging to the odd isotopes can

be used for identification.

Large J hfs-components with AF = 0 have the highest intensity

if the transition is of AJ=0 type. The calculated relative

intensities do not exactly agree with the measured inten-

sities. Probably due to saturation effects and hyperfine

pumping weaker components are somewhat enhanced in the

experiment. But the overall trend remains as expected. This

criterium allows an initial identification of the next

strongest components belonging to the hfs of 1&1Dy and I63Dy.

The observed hyperfine pattern originates from the hfs of

the two combining states. 4 parameters for each isotope are

sufficient to interpret this pattern, whatever the number

28

of components. These 4 parameters are the hfs-constants

A , B , A and B of ground- and excited states,gs gs exc oxc J

The hyperfine splittings of the groundstate of 1 G IDy and1 6 3Dy are very accurately known from atomic-beam-magnetic-

resonance (ABMR) measurements [CHI 70]. Starting with an

initially identified component e.g. IG3Dy 10/2 > 19/2 the

positions of the components 16SDy 21/2 '19/2 and l'"Dy

17/2 * 19/2 can be found with the groundstate hyporfinc

splitting.

By selecting suitable pairs of components hyperfine split-

ting of the excited state can be separated out from the

identified components. The separation Av.9 of two hyperfine

levels F. and F_ is given by (compare with (2-32)):

K.-K- 3B[K, (K.+l) - K,(K,+ 1)]Av.9 = A -! ^ + ! ! s i (2-47)

2 8IJ(2J-1) (21-1)

where K = F(F+1)-I (I+D-J (J+l) .

Approximate values of A and B can je deduced and

successively all components belonging to l s 3Dy can be

identified. From these approximate values the hfs-constants

A (161) and B (161) can be estimated using the ground-

state ratios A (163J/A (161) and B (163)/B (161).

gs gs gs gs

Identification of the 1 6 1Dy components is then straight-

forward. Three peaks will be left. They can be assigned to

the less abundant even isotopes with mass numbers 160, 158,

156.

Finally a computerprogram is used to fit the experimental

hyperfine splittings by varying the hfs-constants of the

excited states for 1 6 1Dy and ' 6 3Dy independently.

The IS between the even isotopes are given by the frequency

separations of the corresponding components, while for l s lDy

and 1 6 3Dy the positions of the centres of gravity of the

hyperfine components of each isotope have to be determined first.

29

C H A P T E R III

EXPERIMENTAL PROCEDURE

III.I. INTRODUCTION

Atomic transitions can bo studied with ultra high resolution

in a light absorption experiment with the laser-atomic beam

technique. In this chapter the experimental procedure is

presented. In fig. III.l. the experimental set-up is shown

schematically. Two dye lasers can be pumped with an argon-

ion laser; one dye laser is tunable in the wavelength region

560 - 630 nn), whereas the second dye laser can be tuned in the

region 435 - 470 nm.

IYE LASER?

POAEfl SuPP^| INTI-NSlTlJCONTROILC

Fig. 111.1. Scheme of the experimental setup; M: mirror; S: beamsplitter;

LN-trap: liquid nitrogen trap; PD: photodiode; PM: pholomultiplier.

30

The dye laser wavelength is measured with a flichelson type

interferometer. Linearly polarized light of the continuous

wave (c.w.) dye laser is intersecting an atomic beam at

ri.ght angles. The frequency of the laser is swept over the

absorption profile of an atomic transition and fluorescence

light from the atomic beam is detected with a photomulti-

plier and recorded. Laser scans are frequency calibrated

with a Febry-PS'rot interferometer and a spectrum analyzer

is used to monitor single frequency operation of the laser.

In the following sections the different parts of the setup

will be described in more detail. In section 2 the dye

laser and its performance will be discussed. The frequency

scale calibration is treated in section 3. In section 4 a

description of the wavelength meter is given and section 5

deals with the atomic beam apparatus and production of

atomic beams. In the last two sections finally the data

taking and analysis are considered.

III.2. THE DYE LASER

III.2. I. Operation

Tunable light for atomic absorption experiments was pro-

duced with c.w. dye lasers (Spectra Physics 580 A). The

principles of dye laser operation have been discussed exten-

sively by several authors [SCH 73, SHA 75, SNA 73], there-

fore only a brief description will be given here.

This dye laser employs a free flowing jet of dye solution

as a gain medium. The dye molecules are pumped with an Ar -

laser from the electronic ground state to the first excited

electronic singlet state (see fig. III.2a.). Because of the

high density of vibrational-rotational levels of the complex

dye molecules and because of Doppler-broadening, the elec-

tronic energy levels are considerably broadened. Due to very

31

>•0aLJ

u

single

oOsorp-tlon

—

It states 1 triplet states

111

1 —

11

- V ••-V— I

-^-~)1tluorev , -~cence 1

absorption

f,«1ns I ^^

^^-fphosphorescence

IIIII

Fig. III.2a. Energy levels of an organic dye with radiative (solid lines)

and non-radiative (wavy line) transitions.

fast (~10~12 sec) radiationless intramolecular relaxation

down the rotational-vibrational ladder, after a few nano-

seconds the system will decay from the lowest vibrational

level of the first excited electronic state to an excited

rotational-vibrational level in the electronic qround state.

This results in a fairly broad fluorescent band ( ~ 100 nm)

shifted towards longer wavelengths compared with the absorp-

tion band. Stimulated emission can be generated in almost

the complete fluorescent band, except for the region where

fluorescent and absorption band overlap (see fig. III.2b.).

Due to electronic singlet-to-triplet intersystem crossings

from the excited singlet state (see fig. III.2) a metastable

triplet state will be populated. This can seriously impede

laser action, since the absorption band starting at this

triplet state overlaps the fluorescence band from the

excited singlet state to the ground state. Accumulation of

32

losing region

450 500 550 600 650 700wavelength Inm)

Fig. III.2b. Absorption and fluorescence band of the organic dye

Rhodamine 6G.

molecules in the metastable triplet state is prevented by

pumping the dye solution at high speed through the lasing

region.

Light of the Ar -laser is focussed into the ribbon-shaped

dye jet localized in the focus of a folded three mirror

cavity [KOG 72]. A schematic view of the dye laser optics

if given in fig. III.3.

outputfnirror tnterfemncQ

filter PZT-crystal

x 7 / toidmg\^J mirror

PZT - crysta

Fig. 111.3. Schematic view of the dye-laser cavity PZT-crystal: piezo-

electric crystal.

33

The output power of the laser is channelled into a small

lasing bandwidth with intracavity frequency selective ele-

ments. Three such elements determine single frequency oper-

ation. Coar wavelength tuning is accomplished with a

wedge-like interference filter, which limits the laser band-

width to less than .05 nm. A plane parallel glass plate,

acting as a fine tuning etalon with a free spectral range

(fsr) (see section III. 3) of 1 nm or about 800 G\lz, further

reduces the bandwidth to about 10 GHz. The laser cavity

itself also is an interferometer. Duo to its length of 38.5

cm the free spectral range will bo 390 MHz. This will be re-

flected in the dye laser output frequency. Single frequency

(s.f.) operation finally is achieved with a piezo-electri-

cally tunable, temperature-stabilized Fabry-Perot etalon

(fsr 75 GHz). The output frequency can be scanned continu-

ously by simultaneously applying a linear ramp voltage to

piezo-electric (PZT) crystals of output mirror and main

etalon.

To maintain s.f. operation all frequency selective elements

have to remain in tune (see fig. .111.4.). Continuous s.f.

scanning is possible over a range of about 3 GHz, limited

by the finite extension of the output mirror PZT. The

linear ramp voltage approximately gives a linear frequency

Fig. III.4. Transmission curves of FIW IUNING /~\ FSR-900O«

the dispersive elements. The 581 A § ~

etalon and the cavity can be electroni- ? **

cally scanned. For single frequency « J L /MAIN E1ALON

output a l l transmission maxima must 390MH1coincidc- _JJ_] u .LIILLJJ.

lASfcR CU'PU!

34

scale which, however, is not sufficiently linear for

precise calibrations (see section 3).

HI.2.2. Dyes

Two dyes were used in the experiments described in this

thesis: Rhodamine 6G for the wavelength region 560-630 nm

and Stilbene 3 for the region 435 - 470 nm. For the blue

region at first another dye, Coumarine 2, was tried. Because

of high lasing threshold and poor photochemical stability

efforts to use this dye were not very successful.

The Rhodamine dye laser was operated with a 2 • 10" moles/

liter solution of Rhodamine 6G in cthylene glycol. This laser

is pumped by the 514.5 nm Ar -laser line. With a pumping

power of 2 W single frequency output powers of over 50 mW

could be achieved at 590 nm (see also fig. III.5.). The

active medium used in the second dye laser was a 1.3* 10"3

moles/liter solution of Stilbene 3 in ethylene glycol. This dye

has to be pumped with U.V. light. Stilbene 3 is stable, has

a low lasing threshold (~ 350 mW U.V.) and a large tuning

RHODAMINE 6G

2W.5U5nm

5/u 9 6 55o W O B I B 57D!nm).wiveltnglh

Fig. III.5. Single mode dye-laser output power. The dye Rhodamine 6G was

pumped with 2.0 W at A-5I4.5 nm; Stilbene 3 was pumped with 1.2 W U.V. at

350-360 nm.

35

r

range. S.f. output power of approximately 10 mW has been

achieved at a total pumping power of 1.2 W (see also fig.

III.5.) at wavelengths near 360 nm of the Ar -pumplaser.

III.2.3. Stability

ur. Intensity stability

The output power of the dye laser is not a priori stable

during a frequency scan. Even with an intensity-stabilized

Ar -pump laser, the dye laser output may vary considerably

{ > 10 % ) . This can be caused e.g. by sliyht changes in the

alignment of the laser cavity during a frequency scan due

to imperfections of the PZT-crystals. However, the dye laser

power could be intensity stabilized. By reflecting a frac-

tion of the dye laser light onto a photodiode, which is part

of a servosystem controlling the Ar -laser output power

(see fig. III.l.), a stability of better than 1 % could be

achieved.

b. Frequency stability

The various contributions to frequency instabilities and

the resulting linewidth broadening of a dye laser have been

estimated e.g. by Hercher c.s. [HER 73]. Their conclusion

was, that the observed linewidth Av is ultimately determined

by variations in the optical length L of the cavity accord-

ing to:

where v. is the laser frequency.

A variation of 10~8 m in the optical length of the 3P.5 cm

resonator length, corresponding e.g. to a temperature change

of .05 C, results in a frequency shift of 13 MHz.

Although the laser cavity is constructed with quartz rods

(thermal expansion coefficient .55 * 10~6 K - 1 ) , perturbations

36

r

in the optical length of this size may arise from vibrations

of resonator components caused by mechanical or acoustical

noise, by refractive index variations in the dye jet due to

temperature changes in the dye solution, or by sudden tempe-

rature and pressure variations in the air surrounding the

laser. In order to optimize the frequency stability a number

of precautions were taken. The dye lasers were rigidly

mounted onto a heavy granite slab, resting in a sandbox.

The Ar+-pumplaser was mounted on a separate table. This

construction was chosen as the high flow rate in the water

cooling circuit of the plasma tube of the Ar -laser can be

a considerable source of mechanical vibrations.

The dye lasers were insulated from air currents and acousti-

cal vibrations by enclosing the cavity in a sound insulating

box.

These precautions also fairly well suppressed "mode hopping"

of the laser frequency to a neighbouring cavity-mode. S.f.

operation and mode hoppings were visualized with an optical

spectrum analyzer with a fsr of 2 GHz.

With Rhodamine 6G effective laser linewidths of about 7 MHz

were common, whereas with Stilbene 3 a slightly broader

linewidth of 10- 15 MHz was obtained.

A more active form of frequency stabilization is possible

by locking the laser frequency to a transmission resonance

of an ultra-stable external Fabry-Perot cavity [BAR 75,

GER 76]. Linewidths of less than 1 MHz have been obtained

in this way. For the experiments described in this thesis,

such small laser linewidths were not strictly necessary,

since most spectral lines studied in this work could be

resolved completely.

III.3. FREQUENCY CALIBRATION

In the observed high resolution spectra the frequency

37

differences between absorption peaks had to be determined

accurately. As was pointed out in section III.2., a linear

ramp voltage applied to the PZT-crystals of the laser

cavity gave only approximately a linear frequency scale

( 5 % ) . This is not sufficient for precise calibrations.

Therefore laser frequency scans were analyzed by passing a

fraction of the laser light through a confocal Fabry-Perot

interferometer.

The interferometer was composed of two concave mirrors

separated by a distance d, equal to their common radius of

curvature r. This type of interferometer shows interferences

after a double passage of the light [HER 68] (see fig.

III.6a.). The distance 4v. , between two adjacent interfer-

ence fringes, called the free spectral range (fsr) is given

by:

cvfsr 4d '

where c is the velocity of light.

The finesse F of an interferometer is defined as the ratio

of the fsr and the full width at half maximum (FWHM) of the

Fabry-Perot peaks:

Av ,F = t S r . (3-3)

FWHM

The finesse F of a spherical mirror cavity can be attributed

to reflectivity of the mirrors (reflection finesse F £])

and to irregularities in their surfaces (surface finesse

Fsurf>-A relation for F f in terms of the reflectivities R andR_ of the two mirrors is given by Hercher [HER 68]:

F-fi = T T ^ ; • (3"4)

38

Fig. III.6a. Ray path in a spherical mirror Fabry-Perot interferometer in

the paraxial approximation.

He also estimated the surface finesse to be

surf * 2 ' (3-5)

where the number m is a measure of the surface flatness

across the detector aperture, given by — (X is the wave-

length) .

At first experiments were performed with a 1 meter long

interferometer giving interference maxima every 75 MHz

(see fig. III.6b). Two Nilo-36 bars having a low thermal

expansion coefficient (< 1.5 * 10~6 I'"1) served as spacers.

Fig. III.6b. Transmission curves of the Fabry-Perot interferometers.

39

This Fabry-Pe'rot interferometer was used off-axis, enabling

the input mirror also to be used as output mirror. The two

mirrors had different coatings with reflectivities of

80-90 % and > 99 % respectively, resulting in a reflection

finesse of F - = 24 at 600 nm. The overall flatness of therefmirrors according to factory specifications was better than

A/10. From the experimental finesse F = 11 at 600 nm, it

was concluded that F is mainly due to F . with m fa 22.e x p J surf

Because of the broad band coatings of the mirrors, this

interferometer could be used over the region 420 - 650 nm

without changing mirrors.

The interferometer was placed in a thermally insulated

housing to reduce long term drifts due to atmospheric pres-

sure or temperature changes. From a comparison of spectra

recorded at different times, the thermal drift could be

deduced to be less than 4 MHz/min., which significantly

contributes to the experimental error.

For this reason an improved confocal Fabry-Perot interfero-

meter having a .5 m long super-invar spacer (linear expan-

sion coefficient < 3.6 * 10~7 C"1) was installed. This

interferometer was placed in a closed airtight housing,

which could be evacuated and temperature stabilized. The

thermal drift was less than 1.5 MHz per 30 min. Two differ-

ent mirror sets (reflectivities > 99.5 %) were used for the

spectral regions 4200 - 5200 nm and 5500 - 6500 nm respec-

tively. This results in a reflectivity finesse of 300. The

experimental finesse was too high to be measured with the

dye laser. Scanning the dye laser frequency, the widths of

the Fabry-Pe'rot resonances were completely determined by

laser jitter (see fig. III.6b).

The fsr of the interferometers were calibrated on well-known

hyperfine structures of atomic ground states. In the Rhod-

mine 6G-region the transition 32S, - 32P, of sodium at

589.6 nm with well-known ground state splitting [BEC 74]

40

was used. In the blue spectral region the • P.,, - ?S,J/2 '/2transition of indium at 451.1 nra was studied (see chapter

IV) . The ?-P3 ,,-state has been measured accurately by atomic

beam magnetic resonance methods [ECK 57]. The fsr of the

75 MHz and 150 MHz interferometer were measured regularly

with an accuracy of 50 - 75 kHz.

111,4. THE WAVELENGTH-METER

The laser .linewidth (~ 10 MHz) is of the same order of

magnitude as the natural linewidth of an atomic transition,

generally in the 1 - 100 MHz range. In high resolution laser-

atomic beam experiments the problem of tuning the laser on

these narrow transitions can only be solved with the help

of an accurate wavelength meter. Since the automatic laser

scan is limited to about 3 GHz and the offset of the scan

can be varied over some tens of GHz, an accuracy in the

order of .01 nm or 10 GHz is required for this purpose.

Several solutions are possible e.g. a monochromator with

very high resolving power, which is rather expensive how-

ever; a set of precision Fabry-PSrot reference etalons

[BYE 77]; a sigma-meter [JUN 75], a very sophisticated

solution of measuring the wavelength with a polarization-

sensitive interferometer; or the technique of a fringe

counting Michelson interferometer [HAL 76, KOW 76].

The latter method was adopted in the experiments described

in this thesis. The Michelson interferometer, which is very

similar to the setup of Hall and Lee [HAL 76], is shown

schematically in fig. III.7. The wavelength meter compares

the unknown dye laser wavelength with the accurately known

wavelength of a He-Ne laser (632.17 nm).

The He-Ne laser lightbeam is split up by a beamsplitter

into two beams. In both paths the beam is reflected parallel

to itself by corner -rube prisms. The reflected lightbeams

are combined again in the beamsplitter to interfere.

41

—1 I —1 r

. I I - I :"1

lu |

]

rcr~i>i

LJ

/ •

Fig. III.7. The wavelength meter.

M: mirror; S: beamsplitter; PD: photodiodp; C: cornercube.

As the corner cube prisms are mounted on a carriage, a

translation of the carriage shortens one lightpath and

lengthens the other. Viewed from the photodiode-detector,

these moving prisms act as a phaseshifter between the two

lightbeams, resulting in interference fringes.

Light from the dye laser is directed into the interfero-

meter in such a way, that it follows exactly the same path

as the He-Ne laserlight but in opposite direction.

The central interference fringes of dye laser and He-Ne

laser are monitored with two detectors. The fringes are

simultaneously counted in two counters. The counting rates

of this interferometer (in the audio frequency range) are

linearly related to the wavenumbers of the input radiation.

So, when the number of fringes counted for the unknown wave-

length reaches the preset number 6 32817, the other counter

monitoring the He-Ne laser fringes, will digitally display

the wavelength of the dye laser.

42

The corner cube prisms relaxe the requirements for reflec-

tor alignment compared with ordinary mirrors. They also

minimize the effect of vibrations. The corner cube prisms

are mounted on a carriage, moving uniformly and smoothly

along a 25 cm long, cylinder bearing slide driven by a

spindle. This spindle is driven by a reversable dc motor.

An electronic gate excludes counting at the turning points

of the carriage motion, because in this region the motion

is non-uniform.

With a laser power of about 100 11W the signal-to-noiso ratio

was sufficient, enabling partial fringe counting with a

phase-locked * 10 frequency multiplier. This resulted in an

increased sensitivity. The precision of the wavelength

meter was ± 1 count, whatever the total number counted.

This precision was determined with the He-Ne laser beam

both as reference and as unknown laser beam. The accuracy

was determined by the He-Ne laser in the setup, which could

not be operated single mode. An overall accuracy of .001 nm

or 1 GHz was verified by measuring the wavelengths of the

argon-laser and the Na-D-lines. The accuracy can be further

improved with a frequency stabilized He-Ne laser.

III.5. ATOMIC BEAM APPARATUS

III.5.] General

In section III.2 it was noted, that the dye laser light was

nearly monochromatic (Av. « 10 MHz). To fully exploit this

high resolution light source, any linebroadening mechanism

in the atomic sample has to be eliminated.

A well-known solution to this problem in atomic spectroscopy

is the use of atomic beams. Kuhl [KUH 71] e.g. investigated

the 466.2 line of europium by means of an atomic beam inside

a spherical Fabry-Perot interferometer. In his review arti-

cle on atomic beam spectroscopy Jacuinot [JAC 76] gave

various reasons for the use of collimated atomic beams in

43

high resolution experiments. Three main reasons can be

quoted. Firstly, since all atoms travel in about the same

direction, collisional broadening is eliminated. Secondly,

the Doppler-broadening in an orthogonally excited atomic

beam is determined only by the width of the atomic beam

(see section III.5.2.) and finally the atomic beam tech-

nique is attractive because of its wide applicability: it

may be used for nearly all elements and includes the possi-

bility of experiments on radioactive isotopes.

III.5.2. The apparatus

The atomic beam apparatus* consisted of an aluminum oven

and detection chamber, a stainless steel tube connecting

these two and a vacuum system {see fig. III.8). Oven chamber

and detection chamber had separate pumping systems. In the

detection chamber a liquid nitrogen-cooled beam stop further

reduced the vacuum pressure. Pressures obtainable in the

system were better than 10~6 mm Hg. A valve was inserted

in between the two chambers, so the vacuum in the detection

chamber could be maintained, while installing an oven in

the oven chamber. The oven could be reproducibly positioned

in the oven chamber, enabling fast loading of the apparatus.

The ovens were made of stainless steel or tantalum and were

provided with a slit or a snout to reduce the amount of

material required to produce an atomic beam [GIO 60]. The

oven was heated to a temperature sufficiently high for the

production of an atomic beam (see table III.l). The heating

element was a tungsten filament just in front of the oven

slit. A positive high voltage was applied to the oven with

respect to the filament and by means of electron bombardment

Th.'inks t » U . F . I . . Kood;i and l i i s c o - w o r k e r s f rom I IK- m e c h a n i c a l w o r k s h o p ,

e s p e c i a l l y . 1 . V e r b l . i u w , f o r t h e c o n s t r u c t i on of many p . i r i s of t h e i -xper i inent . i 1

s e t u p .

44

PMT

fs r.:.

r:TO.PUMP

OVEN-CHAMBER

t O l P U M P •*•""

OET ECTION-CHAMBER

PMT

,- 1,- ATOMIC-BEAM

LIQUID N2

0 .PUMP

Fig. I I I . 8 . The atomic beam apparatus.

Side view and cross sect ion. L: lens; M: mirror.

r

the oven was heated to temperatures of 2000 C or more. Tor

low temperatures (< 500 C) the radiation from the hot filament

alone suffices. In that case the oven temperature could be

measured with a thermocouple. The oven was mounted inside

a water-cooled stainless steel reflector to restrict heating

loss and also to serve as a first light ha: 21e. A second

liyht baffle was positioned at the exit of the oven chamber.

III.5.3. Doppler-broadening

The atomic beam is collimated with a slit positioned just

in front of the interaction rcyion, where the atomic beam

is excited orthogonally by the laser beam. The divergence

of the atomic beam after collimation is:

d1

(3-6)

(see fig. III.9.), where d is the width of the collimator

slit and 1 the distance between oven and slit. The inverse

of the divergence is called the collimation ratio.

The velocity component of an atom perpendicular to the

atomic beam in the direction of the laser beam is v sin 6,

where v is the velocity along the atomic beam axis. The

Doppler shift 5vD in the absorption frequency of an atom

due to this velocity is:

6VD = V0 c (3-7)

Fig. III.9. Collination

of the atomic beam.

46

where vQ is the unshifted frequency and c the velocity of

light.

Since the velocity distribution in the atomic beam is

Maxwellian, these shifts in the absorption frequency result,

after integration over all velocities, in a Gaussian absorp-

tion line profile. The full width at half maximum is approx-

imately equal to the difference in absorption frequencies

between atoms with velocities in opposite directions along

the laser beam axis equal to the mean scalar velocity 11. :

sin o « £ (3-8)

where /ii p sin 0/2 (3-9)

is used with JJ = (2 RT/M) '2 the most probable velocity in

the oven.

The Doppler width of the atomic beam should be less or of

the same order of magnitude as laser linewidth (~ 10 MHz)

and natural linewidth (1 - 100 MHz). In the apparatus de-

scribed here, the width of the collimator slit is d=2 mm

and the distance between oven and slit 1 = 60 cm. This re-

sults in a collimation ratio of 300. In table III.l. the

Doppler-broadening at a wavelength X = 500.0 nm is given

for the elements studied in this work.

Table III. 1

element

vapor pressure

temperature K

Doppler width

mmHg

(MHz)

[Nes 63]

Na

lO"1

628

4.5

In

10-1

894

2.4

En

10-'

975

2.2

Dy

1270

2.4

47

III.5.4. Stray light reduction

In the laser-atomic beam experiments fluorescence light,

originating from the atomic beam, was detected with a photo-

multiplier in a direction perpendicular to both atomic and

laser beam. In the course of the experiments two photo-

multiplier tubes were used. EMI 9789Q and EMI D 307. Both

have a bialkaline cathode. The solid angle detection effi-

ciency was doubled with a spherical mirror (see fig. III.8.)

to about 10 %.

For detection of low concentrations of atoms (e.g. radioactive

atoms) or weak spectral lines the amount: of stray light had

to be reduced. Stray light, which produces an unwanted back-

ground illumination of the photomultiplier, is mainly orig-

inating from the oven heating filament and the laser.

As a general precaution the detection chamber had been

blackened completely with a velvet coating and the optical

collection system had been enveloped with a blackened box.

The oven stray light could be eliminated almost completely

with a slit at the exit of the oven chamber and with the

collimation slit positioned just in front of the interaction

region.

Laser stray light is produced by scattering on entrance and

exit windows of the detection chamber. Therefore long side

arms were used, in which several light baffles could be

placed.

Backscattering of laser light from the exit window into the

detection chamber was prevented with a Wood's horn (see

fig. III.8.).

To discriminate against light not produced in the interaction

region, the fluorescence light was spatially filtered with

a lens and slit system. Only the interaction region was

imaged onto the photomultiplier. Despite all precautions

some stray light was still left because of imperfectness

of the components. Stray light due to the oven heating

filament amounted to a few hundred counts per second,

48

measured with the photon counter.

Multiplier noise of the uncooled photomultiplier was about

900 cps. The main contribution to the background arose from

stray light of the laser beam amounting to a few ten thou-

sands of counts per second, depending on intensity and

wavelength of the laser light.

III.6. DATA TAKING

Experiments were performed with the photomultiplior either

in the current mode or in the photon-counting mode.

In the current mode the anode current of the photomultiplier

was amplified and recorded directly (sec fig. III. 10.).

A)

ATOMICBEAM N

'L J GEN!

CURRENTAMPLIFIER

FABRY-trom

PEROT NT

Y,

~—»

EC

i

B)

ATOMICBEAM .

LASERCONTROL

S11RJ_

AMPLIFIER /DISCR

STOP I 1

PULSE GEN

iPHOTON

COUNTER - DAC

r '\.,.

f rom »• *•FABRY-PEROT INT L

Fig. 111.10. Block diagram of the electronics.

a) current node

b) photon counting mode

PMT " photomultiplier tube; DAC « digital-to-unalofi-converter;

HVS = high voltage power supply.

49

The voltage ramp, which generates the frequency sweep of

the laser, generated a signal for the x-coordinate of the

recorder too. Simultaneously the photodiodc signal from the

Fabry-Pe'rot interferometer was registrated on the X-Y Y,,

recorder.

The photon-counting system consisted of an Ortec preampli-

fier, an Ortec amplifier/discriminator and a 100 MHz coun-

ter* with analog output (see fig. III.10.). The counting

time was determined by a pulse generator. The pulses of

this generator were counted in a preset binary counter and

the digital-to-analog-converter (DAC) delivers a ramp volt-

age, which was applied to the PZT-crystals of the dye laser.

In this way the dye laser frequency was scanned in discrete

steps.

It was also possible to perform data acquisition under

computer control with a Nuclear Data ND 50/50 computer

facility (see fig. III.11.).

The ND 50/50 system included a 4k PDP--8L computer interfaced

with a HP 3000 computer. The PDP-8L provided a startpuls for

the pulse, generator and subsequently the ramp voltage which

drove the laser sweep. The pulse generator also incremented

the channel number of the ND-memory. Photomultiplier signal

and Fabry-Perot calibration signal were simultaneously dig-

itized in an analog-to-digital-converter (ADC). The data

were stored simultaneously in a 4k 24 bit ND-memory and were

afterwards written on disc or magnetic tape of the HP 3000.

The ND-memory could be divided into four parts. Two parts

(Ik each) for storing the two measured spectra and two

parts (Ik each) for summing the spectra in case several

scans were made successively. The content of the ND-memory

was visualized on a display unit used to monitor the exper-

iment. The ADC allowed complete laser sweeps to be finished

*Tl i a : ik s u> . 1 . Knul a n d h i s c o - w o r k e r s for i b e c u n s i n u ' t i o n of t he f l t ' c t r o u u - s .

50

AMPLDISCR

COUNTER QEN

F»8RV-PEROT INT

ND SCHSO

|_ sto

L _ .... A

Fig. III.II. Block diagram of the electronics with computer controlled

data acquisition.

PMT * photomultiplier tube; PC = photon counter; DAC • diRital-to-analog-

converter; TTY • teletype; DPC • single/dual parameter AL'C control;

HVS - high voltage power supply.

in a minimum time of .2 sec.

III.7. DATA ANALYSIS

The fluorescence spectra stored on disc or magnetic tape

were analyzed with a computer program. In this program the

accurate peak positions and peak areas were determined with

a fitting procedure.

In general the experimental lineshape is a Voigt function:

51

P(w) = f F. (w) F_U+w -u)dw (3-10)L U U

where u>Q is the central frequency. F(u>) is the convolution

of a Lorentzian F. (to) (homogeneous line brondening: natural

linewidth) and a Gaussian FG (n>) (inhomogeneous broadening:

Doppler broadening and laser linewidth).

Since it is not possible to give a simple mathematical

expression for numerical evaluation of the Voigt function,

in the fitting procedure it was approximated by the follow-

ing modified dispersion function:

f(x) = l- . (3-11)l+ax2+bx''+cxfl

The three parameters a, b and c fixed the curve shape.

The heights of the individual peaks were taken as addition-

al variable parameters.

From the peak spacings in the Fabry-Perot spectra a relative

frequency scale was obtained for the fluorescence spectra.

Since the Fabry-Perot peaks were not equidistant due to

alinearities in the laser sweep, a least squares fit of the

experimental Fabry-Perot peak positions with a second degree

polynomial was necessary.

From spectra registrated with the X-Y Y recorder relative

peak spacings were determined manually with respect to the

Fabry-PSrot calibration peaks.

Once the relative peak spacings were determined and the

peaks identified following the procedure outlined in chapter

II, section 4, a least squares computer program fitted the

experimental hyperfine splittings of the excited state by

varying the hyperfine structure constants A and B forJ 3 IC exc excall isotopes independently.

A straightforward test of the results was possible. From

the measured spectra also the hyperfine structure of the

52

atomic ground states could be determined and compared with

results from ABMR-experiments.

53

sC H A P T E R IV

TEST AND CALIBRATION EXPERIMENTS ON Na AND In

IV.I. INTRODUCTION

In this chapter laser-atomic-beam experiments on sodium and

indium are described. The experiments on the Na D-lines

were performed partly to calibrate the Fabry-PSrot interfer-

ometers used in the course of this work (see section III.3.)

and partly to test the sensitivity of the experimental

setup.

The purpose of the experiments on the transition A =451.1 nm

of indium was to calibrate the interferometers in the blue

spectral region as well as to determine the hfs-constants

of the excited 2Sj,-state and the IS between the two iso-

topes 113 and 115 in this transition.

IV.2. SODIUM EXPERIMENTS

IV.2.1. Calibration of interferometers

The Fabry-Perot interferometers were calibrated on the D-

lines of Na for the wavelength region 560 -630 nm. Part of

the level scheme of Na I is shown in fig. IV.1. Due to the

nuclear spin 1 = 3/2 the 2S,-groundstate and 9P, -excited

state are split up into two hyperfine levels with total

angular momentum F=l and F = 2. There are 4 hyperfine levels

in the 2P 3 -state (F= 3,2,1,0). The known hyperfine split-

tings are denoted in this figure too. The four allowed

transitions according to the selection rule AF = 0,±l, be-

tween hyperfine components of the 2S^- and the 2P^-state

54

3/2.

T1/2.

D2

589.0 nmr

ID,|589.6nm

1= 3/2\ 1772 MHz

F = 3

/ 59 MHz = 2•4: 34 MHz = 1

\ 15 MHz =o

s. 192 MHzF = 2

Fig. IV.I. Part of the level scheme of Na 1. The allowed hyperfine

transitions belonging to the D -line are indicated.

are indicated. These four transitions form the D -line of

sodium (589.6 nm).

A typical result of a laserscan over this D -line is shown

in fig. IV.2. The recording of the photomultiplier signal

obtained from the atomic beam fluorescence as a function

of the laser frequency, contains four components as expected

and is shown in the upper part of the figure. The interfero-

meter signal is given in the lower half of the figure. From

a number of such recordings the fsr of the interferometers

were determined with an accuracy of 50 - 75 kHz using the

accurately known hyperfine splitting of the Na-ground state

[BEC 74].

As an example of the resolving power of the method in fig.

IV.3. part of the D -line, which belongs to the transition2S, (F = 2) -* 2P,, (F' =1,2,3) is shown. The hfs of the ex-'s Di 2

cited state is completely resolved and the recorded line-

width is mainly due to the natural linewidth of 10 MHz

[ERD 721.

55

Fig. IV.2. Experimental recording of the hfs of the Na-D line. The

transmission peaks of the calibration spectrum were obtained with a

.5 m long confocal Fabry-Perot interferometer.

Fip,. IV.3. Part of the Na-D2 line.

(Transitions 2s, . (F»2) -• 2P (F'=l ,2,3)).

56

IV.2.2. Sensitivity of the Laser-atomic-beam setup

The absorption of light by atoms in the atomic beam can be

detected with several techniques. Jacquinot c.s. [JAC 73]

proposed a detection technique using the deflection of an

atomic beam by the pressure of resonant light. The same

group in Orsay [HUB 75] developed a method, which is based

on the detection of optical pumping, which occurs when a

laserbeam is tuned to the frequency of one of the hyperfinc

components of the D-lines. They wore able to perform high

resolution spectroscopy of the D-lines of radioactive sodium

isotopes using inhomogeneous magnets for the detection of

optical pumping. This method is especially suited for

alkali-like atoms.

In our experiments the absorption of light was detected by

observing the intensity of the fluorescent radiation, emit-

ted immediately after the absorption. The sensitivity of

the setup was tested by decreasing the temperature of the

oven, which produced the Na-atomic beam. Absorption of

light tuned to the Na-D -line could still be observed at

temperatures as low as 120-130 C, corresponding to a vapor

pressure of ~10~6 torr in the oven.

This temperature can be related to the number of Na-atoms

present in the interaction region. The number of atoms I

passing the interaction region is given by [RAM 56]:

u A AI = 1.118 * 102? 1—£ atoms/sec , (4-1)

i7 /FIT

T=400K is the temperature of the oven, M = 23 the molecular

weight, 1 = 60 cm the distance between collimation slit and

oven, A =2 * 10~2 cm2 the area of the collimation slit,

A = 7-5 * 10"3 cm2 the source aperture, p= 10 ~6 torr theS ~ *"

source pressure and M the molecular weight. This results

in a number of 4.9 * 106 atoms passing the laserbeam each

second.

57

The average velocity v. in the atomic beam is [RAM 56]:

vb = | / 27'M

R^ = 714 m/sec (4-2)

where R is the gas constant. The resulting beam density is

3.4 * 103 atoms/cm3, corresponsing to 7 atoms in a volume of

2 mm3, which is about the interaction volume.

An atom will cross the laserbeam (diameter 1 mm) in 1.4

\isec. When the atoms are excited by the strong resonant

radiation of the laser, the transition will bo saturated

and the atoms spend about half their time in the upper

state. Since the lifetime of the 3?Pv-level of Na I is:

T(3 2P.) = 16.4(6)nsec [ERD 72], this corresponds to more

than 40 excitations of a single atom during the interaction time

The mean spontaneous emission rate will be 3 • 107 sec"1.

When the transition 2S,(F = 2) - 2P,(F" =1) is considered

and the statistical weight 3/8 of the F = 2 level is taken

into account, 1.3* 108 photons/sec are randomly emitted.

The number of detected photons is determined by the col-

lection efficiency (10 %) and the quantum efficiency (3 %

at 590 nm) of the bialkalic photomultinlier. The expected

number of photon-counts amounts to 3.9 * 105 counts/sec.

However, optical pumping has been neglected in this calcu-

lation. This means that it is assumed that all atoms excited

to the 2Pj,(F' = 1)-state will decay again to the original

state 2S;JF = 2). But a decay to the 2S^(F= 1)-state is also

possible and then the atom is lost for further absorption-

reemission cycles. Due to this optical pumping effect the

number of photons will be a factor of 10 smaller, resulting

in ~4 * 10'1 expected counts per second. This number is about

equal to the number of background counts due to stray light

of the laser and photomultiplier dark current, as was al-

ready mentioned in section III-5.

The detection sensitivity will be even higher for blue

spectral lines, since the quantum efficiency of the photo-

58

multiplier is much higher then (20 % ) . The beam density at

the interaction region can be further reduced by increasing

the collection efficiency with an elliptical reflector.

The laserbeam and the atomic beam must intersect orthogo-

nally in one focus of the reflecting ellipsoid and the

photomultiplier has to be positioned in the second focus.

In this way Greenlees c.s. obtained a collection efficiency

» of 46 %, enabling the use of photonburst methods [GRE 77].

The sensitivity can then be made 400 times greater. Experi-

ments can then be performed with atomic fluxes as low as

10 atoms/sec crossing the laser beam. This sensitivity is

particularly useful in the study of radioactive atoms. For

the experiments described in this thesis such a high sensi-

tivity was not necessary. For further experiments an ellip-

soidal reflector will be installed however.

IV.3. HFS- AND IS-MEASUREMENTS IN THE In T-SPECTRUM

IV.3.1. General

The blue dye laser setup was tested on the 5 s7 5p(-'P3/9 )-

5s26s(?-SL) transition at a wavelength X = 4 51.1 nm in nat-

ural indium.

A natural sample of indium contains the two isotopes 113

(4.2 %) and 115 (95.8 % ) . Both isotopes have a nuclear

ground state spin I = 9 / 2 , giving rise to four hyperfine

levels in the 2P, -state (F= 3,4,5 and 6) and two levelsihin the ?SL-state (F=4 and 5) (see fig. IV.4.). The hyper-

ifine structure of the 'P>, -state has been studied with

i?atomic beam magnetic resonance techniques and very accurate

values of the hfs-constants for the two isotopes are known

[ECK 57]. The hfs of the ?S,,-state of ] ] r'In has previously

been measured with interferometric techniques using atomic

beam light sources [DEV 53]. An indication of the value of

the isotope shift has been obtained by Jackson [JAC 57],

who measured the displacement of the strongest hyperfine

59

L5s26sJ Vi4 51.1 nm

T<

410.1 nm

•6•5•4

•3

5

• 4

Fig. IV.4. P a n of Llie level scheme of In 1.

transition ?P,, (F = 6) - ?S,(r=5) in a sample of indium•V? -2

enriched to contain about 50 % of the isotope 113.

IV.3.2. Measurements

The atomic beam was produced by heating a tantalum oven to

a temperature of 1300K. At this temperature about 7 % of the

atoms will be transferred to the ?P 3 , -state, which is

situated 2200 cm"1 above the ?P,-ground state.'2

The frequency of the laser was swept over the absorption

profile of the transition and fluorescence light from the

atomic beam was recorded. Simultaneously the signal from

the Fabry-PSrot interferometer was recorded. Due to the

large hyperfine splitting of the 7S,-state and because of

the limited range of the laser sweep (3 GHz) overlapping

scans had to be made to cover the complete spectral region

of interest. A 2 GHz spectrum analyzer was used to monitor

this procedure.

60

An example of a complete recording of the transition

\ =451.1 nm is shown in fig. IV.5. The six possible hyper-

fine transitions of both isotopes are completely resolved

and are indicated. The registration time for one scan was

about 2 minutes. The experimental linewidth of 2 5 MHz could

mainly be ascribed to the natural linewidth of 22 MHz for

the transition [ERD 76].

—

—

t

rin

I"3O0MHZ

113 J\^ J K /

t

|

\\

T

i

y

T10

Indium I[ X - 451.1 nm |

I 4.68 GHzL

It

AJ

300 MHz

V

if) 1

1ft

Fig. IV.5. Hyperfine s p l i t t i n g and isotope shift in the 5s?5p(?P ) -

5 s 2 6 s ( 7 s 1 / ) t rans i t ion (A-451 . I nm) in In 1.

The two isotopes 113 and 115 are indicated. The frequency scale is interrupted

in between the two groups of components and is different for both sroups.

IV.3.3. Results and discussion

Spectra of the type of fig. IV.5 were analyzed to derive

values for the fsr of the calibration interferometers by

comparing the observed hfs of the ?P, . -state with the well-•V?

known s p l i t t i n g [ECK 57].

With interferometers ca l ibra ted in t h i s way the magnetic

dipole in te rac t ion constant A of the 2 S^-s ta te was deter -

mined from the same spectra to be 1684 (3) I"H?. for ] 1 s in .

61

1680(3) MHz for 113In. The main contribution to the error

arose from uncertainties in the mapping of overlapping

scans.

The value of A(115) is in good agreement with the value

of 1688(3) MHz calculated from the hyperfine splitting

measured by Deverall c.s. [DEV 53]. Recently the hfs of the2Sj.-state of 113In and n''In have been remeasured by Noyzen

[NEY 79] in a pulsed laser experiment. Iiis result A(113) =

1681.8(8) MHz and A(H5) =1685.2(6) MHz confirm our experi-

mental hfs-constants.

The isotope shift 6v (113-115) was determined to be 255.4(5)

MHz. Jackson [JAC 57] measured a frequency distance 261(15)

MHz between -?P, . (F = 6) - •''S, (F1 =5) of the two isotopes.

This latter value is in good agreement with our value for

the same displacement 257.5(1.0) MHz.

The measured IS could be separated into a mass and field

shift. The normal mass shift was calculated with (2-5):

6vN.{s = 55.7 MHz. The specific mass shift for the ns-np

transition was taken (0.3± 0.9) times the normal mass shift

(see (2-9)). The total mass shift in the case of indium

amounted to 70(50) MHz, resulting in a field shift

Sv =185(50) MHz. The error is completely due to the un-

certainty in the SMS.

From <5v_g the change in the value of the nuclear charge

distribution 6 <r? > was calculated with (2-11), (2-12) and

(2-13). This calculation required an evaluation of the elec-

tronic part E of the field shift, given in (2-12). This

factor E depends on A | i|i (0) | '' , > the difference in the

total non-relativistic electron-charge density at the

nucleus between initial and final state of.the atom.

A 11(1 (0)| was calculated with the help of (2-17). Theii s — n p

value $=1.1(1) was adopted for indium. It was extracted

from the screening factors yiven in table A in the paper

of Heilig c.s. [HEI 74]. |ijj(O)|'" was calculated from the

experimental A-factor (see section II. 2.5.) of the 7SX-'2

62

level with gx =-1.22976 [TIN 53], resulting in 1.706 a~ '

With this value E=.12O3 was obtained. f(Z) (see 2-13)

has been calculated with C^ ! ?"''''= 65 (5) * 10~3 cm"1 FBAB

63].

Thus 5<rz> becomes 187(60) * 10"! fm? , which is in good

agreement with the accurate value 191.3 • 10~! r.m? obtained

from muonic X-ray transitions [L'NG 74 1.

63

C H A P T E R V

IIFS AND IS IN THE Eu I-SPECTRUM

V.I. INTRODUCTION

The transitions from the ground state 4f/6s? HS/, of euro-

pium I to the levels of the configuration 4f/6s6p have been

subject of many spectroscopic investigations. As early as

1935 Schiller anr1 Schmidt [SCH 35] determined from the hyper-

fine structure (hfs) of some of the transitions the nuclear

ground state spins of both stable isotopes 151 and 153

(natural abundances 47.8% and 52.2%) to be 1 = 5/2.

They showed for the first time, that a quadrupole interaction

contributes to the hyperfinesplitting.

The hfs of the ground state was studied with the atomic

beam-magnetic-resonance technique by Sandars c.s. [SAN 60]

resulting in precise values for the hfs constants. Because

of the spherically symmetric charge distribution of a half-

closed 4f-shell (and a closed 6s?-shell) in pure Russell-

Saunders or LS-coupling, no hfs was expected. The observed

hfs of the ground state could be explained by assuming

deviations from pure LS-coupling and by taking into account

relativistic effects [EVA 65].

The hfs of excited 4f76s6p-levels has been measured e.g. by

Miiller c.s. [MUL 65], Kruger [KRU 72] and Kuhl [KUH 71] by

means of interferometric methods and by Lange [LAN 75] and

Champeau c.s. [CHA 73] with the level crossing technique.

Using the experimental data of Muller c.s. [MUL 65],

Bordarier c.s. [BOR 65] analyzed the hfs of these levels

with the effective operator formalism (see chapter II.3.2.).

64

Lange [LAN 75] showed that the agreement between calculated

and experimental A(151)-factors could be improved by taking

into account configuration interactions. He repeated

Bordarier's analysis with wavefunctions constructed by

Smith c.s. [SMI 65] from an analysis of finestructure data.

Champeau c.s. [CIIA 73] showed this to be valid for the

B(151)-factors as well.

Hitherto the hfs constants of ' r>' L"u of all levels but one

(z GP3 / ) had been measured. Tor ' '• !Eu a considerably less

complete picture was available, mainly due to the small hfs

of this isotope. Isotope shifts (IS) have been measured by

Brix [BRI 52], Krebs c.s. [KRE 61], Miiller c.s. [MUL 65]

and Heinecke c.s. [HEI 70], but for some transitions data

were still lacking. Moreover the existing data showed some

discrepancies. To clarify the situation there was some need

for additional and more accurate isotope shift-data.

In this chapter results of a high resolution laser-atomic-

beam experiment will be presented. All allowed transitions

from the ground state in the wavelength region 435 - 630 nm

were studied. Prom the experiments the hfs-constants of the

upper levels for both isotopes as well as the IS were de-

termined. The results are presented in section V.2. In the

last section of this chapter the results are compared with

results of other experiments and the parametrization of the

hfs-constants is discussed. Also the calculation of S<r2--

from IS-data is given.

V.2. EXPERIMENTAL RESULTS

In the high resolution laser-atomic-beam experiment 8 al-

lowed transitions from the ground state were studied (see

fig. V.I.). Since dye-laser operation was limited to two

spectral regions (435 - 470 nm and 560 - 630 nm) two spectral

lines (A =686.5 nm and A =710.6 nm) could not be investi-

gated in this work. Examples of completely recorded transi-

65

E (cm-')22000

20000

HOOO

16000

14000 6O1.Snm

626.7nm

629,1 nm

564,6 nm

S76,5nm

462,7nm

466,2nm

Fig. V.I. Part of the level scheme for Eu I.

tions are shown in figs. V.2-4.

The weak transition at 629.1 nm is shown in fig. V.2. This

transition is near threshold of single mode Rhodamine 6G

laser action (see fig. III.5.) and the detection efficiency

of the photomultiplier (EMI 97890) was poor in this region.

Nevertheless a good signal-to-noise ratio was obtained. The

duration of a 3 GHz scan was typically about 2 min. Five

overlapping scans had to be made to cover the complete

structure. The linewidth of a single component was 8 MHz,

dominated by the laser linewidth. The transitions in the

blue spectral region are relatively strong (see table V.I.).

The linewidth of the hyperfine components is therefore main-

ly determined by the natural linewidth, as is shown in fig.

V.3. on the transition at 466.2 nm with a linewidth of 30 MHz.

66

Ail

z'til

zi k

153 153

1

Hi m i « i " • ! • -»-*

M i l M t

f|

JJl . . __jl -

155 153

M t MJ

JI

151

1 ,

JEuropiumA=629.1nm

151

"l 1 "

300 MHz

I151

15

; ";

1.

' f

ll

151

- j i J

t t 1 *

1

' hJ.I,

'•>i 161

• ' ' t

„_ *.. 1 A_,

t

151

J4 |J

J_I161

" ~t ~

151o

t

y

Fig. V.2. The transition at 629.1 ran of Eu 1. Five overlapping frequency

scans were made for a complete recording of the spectral line. The hyperfine

components are identified by the mass numbers and the values of the total

angular momentum of ground and excited state. The upper value belongs to the

excited state.

67

Table V.I. The relative oscillator strengths, fQsc r e J, according to

Penkin c.s. [PEN 76J; f is linearly related to the line strength defined

in (2-45). In the last column the experimental lincwidth of a hfs-componunt

in the involved line is given.

\

Inm]

629.1

626.7

601.8

576.5

564.6

466.2

462.7

459.4

osc,rel

1.5

.74

10.6

9.7

4.7

585

794

1000

1 i new id til

[MHzJ

8

8

9

8

8

30

38

44

Europium= 466.2nm 151,!Eu

4

3 4 5

3

2 34

2

12 3

1 0

12 1

-• V

Fig. V.3. The transition at 466.2 nm of Eu I. Peak identification as in

Fig. V.Z.

68

The small hyperfine splitting of the ground state of ]r'3Eu

was not completely resolved in this case.

In fig. V.4. the transition at 576.5 nm is shown, where the

hyperfine splitting is very small. The two structures belong

to the isotopes 151Eu and Ul3Eu respectively, each structure

having 16 components in a frequency region of about 300 MHz.

With a computer program (see III.7.) the accurate peak posi-

tions and peak areas were determined.

The hfs constants A and B of both ground state and excited

state could be calculated from measured hfs splittings with

the help of a least squares fitting program. In all cases

the accurately known hfs constants of the ground states of

the two isotopes could be reproduced very well. The results

for the excited states are given in table V.2. IS data are

presented in table V.9.

V.3. DISCUSSION

V.3.1. Hyperfine structure of the excited states

<:. Convififson of vic'il in

In table V.2. the values of the magnetic dipole and electric

quadrupole coupling constants A and B for the excited states

of 151Eu and 153Eu, as determined from our high resolution

laser experiments, are compared with other values. In general

a good agreement is obtained, with an exception for the

small A-factor of 151Eu for the z r^i/ -level. Our value for

this level differs 5 % from the value given by Lange

[LAN 75].

With Lange's hfs constants a spectrum of the transition at

576.5 nm of 151Eu was generated, which was compared with our

experimental spectrum from fig. V.4. Some differences were

easily observed. E.g. the transitions between levels with

total angular momenta 5 and 4 resp. 5 and 6 (momentum

ground state is 5) do not coincide as predicted with Lange's

values. A clearly broadened peak was observed, with a

69

Fig. V.4. The transition at 576.5 nm of Eu I. Peak identification as in

Fig. V..'.

Table V.2. Exper.mental hfs-constants (in MHz) for the excited states of 1 5 I. 1 5 3Eu.

level

5/2

ZSP 7/2

9/2

111

5/2

5/2

y3P 7/2

9/2

energy

[cm"']

15891

15952

16612

17341

17707

21445

21605

21761

this

-606

-236

664

- 6

-590

-157

-219

-228

AC 151)

work

.8(4)

.5(2)

•9(5)

.2(2)

.7(5)

.2(3)

.1(2)

.9(2)

others

-610(2)

-238.

665

- 6

-591

-157

-219

-230

3(8)

4(3.0)

51(6)

6(1.5)

5(9.0)

0(6.0)

4(3.3)

A(I53)

this work others

-268.6(3)

-106.2(3)

294.9(2) 294.9(3.0)b)

- 2.9(2) - 2.84(3)a)

-263.3(3)

- 69.2(3) 7O(3)C)

- 97.0(4)

-102.4(2)

B(l

this work

65(4)

-203(3)

296(7)

132(3)

-354(4)

78(3)

-295(3)

226(4)

51)

others

Wi(27)e>

-I92(l8)e)

289.5(4.5)b)

131.2(I.O)a)

-354(1 2)b>

72(1 3) c )

-297(9)d>

258(36)b)

»(I5

this vork

166(3)

-506(4)

723(3)

324(3)

-l>19(3)

192(3)

-753(7)

573(8)

3)

others

327.5U.5f>

186(36)c)

a) Lange [LAN 75] and references therein

b) Muller c.s. [MUL 65]

c) Kuhl [KUH 71]

d) Champeau c.s. [CHA 73]

e) Kruger c.s. [KRU 72]

separation between the two components of 6 MHz. Furthermore

the positions of the level crossings of lslEu were calcu-

lated with both sets of hfs constants. The agreement between

Lange's experimental results and these calculations is only

slightly better for Lange's constants. However, the agree-

ment could be improved significantly with the v luos

A = - 6.3 MHz and B=132 MHz. This value of A Is well within

our experimental error.

The parametrization of the hfs-constants of europium in the

effective operator formalism (see chapter II.3.2.) requires

a detailed knowledge of the atomic wavefunctions. Wavefunc-

tions for the intermediate coupling case have been deter-

mined by Bordarier c.s. [BOR 65] in terms of LS-wavefunc-

tions: |4f7(RS)6s6p; SjP,S,PJ>.

The seven f-electrons couple to SS, the two electrons 6s

and 6p couple to !P or P and finally 3S and JP or 3P

couple to 2 S + 1 P j . The z flP, z 8P and z I0P-states belong

to the coupling via the 3P-intermediate state, whereas in

the y 3P-multiplet the 6s and 6p electrons are coupled to

!p (see fig. V.1.).

In his finestructure calculations Smith [SMI 70], also

included configurations of the type 4f7(8S)5d6p and

4fG(7F)5d6s2 and obtained better agreement with experimental

finestructure data. The contributions of pure LS-wavefunc-

tions, belonging to the configurations 4f7(8S)6s6p and

4f7(8S)5d6p, to the actual wavefunctions are given in

table V.3. [SMI 78].

Contributions clue to the configuration 4fs(;F)5d6s? have

been omitted in table V.3.; therefore the sum of the given

contributions is not exactly 1.

These wavefunctions have been used by Lange [LAN 75] in the

analysis of the dipole interaction and by Champeau [CHA 73]

for the guadrupole interaction.

Since there is good agreement between experimental results

72

Table V.3. The expansion

LS-wavcfunctions. The sign

confifiuration 4ff'5d6s? are

coefficients a. of the total wavefunet ion into

indicates the phase. Contributions from the

not s»ven.

level

energy! an"']

O n i°i>

4f76s6p "(1P) 8p

( 1 P ) Cp

(3P) 1 0P

7 (3P) 8P

('P) 8P

(3P) 6P

5/2

15891

-.9274

.0567

.3506

-.1071

-.0341

.0321

.9999

z flP

7/i

15952

-.2 309

-.7820

.0318

.5675

-.0300

-.0889

-.0217

.0526

.9999

9'2

16612

-.3652

-.9161

-.1157

-.0486

-.1005

.0318

.9995

7/'i

17341

-.1179

-.5552

-.1135

-.8080

-.0167

-.0607

.0344

-.0797

.9994

'•[•

bl217707

-.3549

-.0841

-.925.2

-.0384

.0260

-.0921

.9997

21445

.0405

.8487

-.1059

-.0856

-.4123

-.0128

.9106

>• "P

21605

-.0655

.0463

-.8534

.1154

-.0131

.0874

.4170

.0143

.9299

H'2

21761

.0697

-.1473

.8556

.0139

-.0866

-.4193

.9421

obtained in this work and previous results, their parame-

trizations will not seriously be affected. To demonstrate

the accuracy and applicability of the wavefunctions to

describe the hfs, the analysis of the hfs-constants of15'Eu was repeated for the present experimental results.

The A-factors of the investigated levels can be expanded

into a linear combination of five one-electron hfs-parauie-

ters (see II.3.3.).

Ai = a i a l 0 ( 4 f ) + I3i a l 0 ( 6 s ) + Yi + l Si

a o i ( 6 p ) + ci

a i 2

( 5 - 1 )

The c o e f f i c i e n t s a . , . . . / e . d e p e n d on t h e c o u p l i n g o f t h e

73

electrons in the level concerned and wore calculated with

the non-relativistic wavefunctions for these levels with the

computerprogram "Aufspa" (see 11,3.3.).

In (5-1) only the configuration 4f/6s6p has boon taken into

account. Lange showed, that the direct contributions of the

perturbing configurations 4f75d6p and Af.c'5d6s? could be

neglected in the analysis. It is sufficient to account for

the renormalization of the wavefunction within the config-

uration mixing. Even in the case of the y fiP-levcls, where

the contributions of 4f75d6p are considerable (sac table

V.3.), this procedure can be followed. This is due to the

fact that the unpaired s-elcctron gives the most important

contribution to the hfs.

The results of "Aufspa" are presented in table V.4. In a

least squares fit the hyperfineparamoters a (4f), a.. (6s),aOi(6p), and a)2(6p) were varied, whereas the ratio

a 0(6p)/aQ (6p) = -.095 was calculated with Casimir's

relativistic correction factors [KOP 58], assuming the cus-

tomary value of the effective nuclear charge Z ,=7,-4 for

the p-electrons (see II.3.3.). A good fit to the experimen-

tal data was obtained. The values for the hyper fine param-

eters and the calculated A factors are given in table V.5.

and can be compared with Lange"s calculations. In the latter

calculation an effective charge Z = Z-3 for the p-elec-

trons was used. The agreement between experimental and

calculated values in the present analysis is slightly

better.

For the parametrization of the quadrupole hfs-constants

(see II.3.3.) the configuration 4f76s6p as well as the

configuration 4f75d6p have to be taken into account [CHA

73] and 6 parameters are required:

(5-2)

74

.v--1*

ii; V,'4';. K- ratfticients of the one-elect r.m magnetic hf s-p.iramuters.

; •

i

I .2.47 36

•T. O H I 7

-.00094

•:2 326l

-.09951

15952

.92835

-.0)11 1

-.02456

.11906

.134 56

9/2

16612

.71047

.06701

.02924

.19486

-.0)459

z '

7/2

17341

.78344

-.00049

-.0)999

.20)81

-.0)189

•P

5/2

27707

1.07536

-.05002

-.084 39

.05982

.05)25

V.21445

.^1572

,0006 1

-.00428

-.20498

.01703

y P

7/2

21605

.7)647

-.01947

.01846

.0492)

-.00005

9/2

21761

.57109

-.02671

.02R0I

.16770

-.01666

Table V.5. Comparison of the experimental and calculated A(151)-factors.

Also the best fit values of the hfs-parameters are Kiven. All values are in MHz.

level

v2z 8P 7/2

9/2

2 6 p 5/2

y 8P 7/2

9/2

a,0(4f)

a,0(6s)

a^<6p)

exp

-606.8(4)

-236.5(2)

664.9(5)

- 6.2(2)

-590.7(5)

-157.2(3)

-219.1(2)

-228.9(2)

Cd 1C

this work

-597.5

-233.5

653.6

2.0

-585.4

-159.6

-225.8

-236.8

-84(5)

9635(170)

488(21)

787(54)

A(151) ,calc

[LAN 75]

-608.7

-?41. .5

686.7

5.7

-593.7

-147.9

-225.3

-247.2

-72(12)

10080(180)

480(69)

825(150)

75

Unprimed letters refer to the configuration 4f76s6p and

primed letters to the configuration 4f75d6p. The coeffi-

cients a., ... , calculated with "Aufspa" are given in

table V.6.

To reduce the number of free parameters the ratios

b,, <6p)/bQ2(6p), b|, (6p)/b(')2(C.p) and bj, (5d)/b('J2(5d) were

fixed to the values of the ratios of the corresponding

relativistic correction factors [KOP 58]. The ratios

b^,(5d)/b0., (6p) and b^2 (6p) /b{y) (6p) have been fixed with

the help of (2-39c) and (2-40) using relativistic correc-

tion factors and the finestructure constants £ ' = 470 cm"1

C' = 655 cm"1 [SMI 70] and S, = 1227 cm"1 [SMI 78]. Inop opthis way only one free parameter was left: bn9(6p).

In the case of sp-configurations it is well known that

nuclear quadrupole moments derived from the ]P term are

systematically smaller than those derived from the 3P-term.

This can be understood, if one assumes <r~ ' (p) > values to be

smaller for !P-terms than for ?P-terms [LUR 65].

Table V.6. The coefficients of the one-electron quadrupole parameters.

level

energy(cm"1)

"i

H6i

• ci

15891

.07147

.06713

-.00137

.00013

-.00146

.00067

z 8P

7/2

15952

-.12342

-.18791

.00176

-.00032

.00016

-.00160

16612

-.10357

.2634 5

-.00296

.00031

-.00682

.00154

2 *

7/2

17341

-.56155

.09247

.00243

-.0097 3

5/2

17707

-.37865

-.37231

.00326

-.00036

-.00390

-.00179

5/2

21445

-.02649

.09801

-.01244

.00253

-.04129

.01263

y 8P

7/2

21605

-.05301

-.38344

.00697

.00967

.02287

-.04835

9/2

21761

.16597

.29867

.02403

.00732

.07763

.03661

76

Therefore, in his analysis of the B(151)-factors, Champeau

used different parameters b (6p) for the y 8P states and

the z G»RP-states respectively.

Following the same procedure, the fit of calculated and

experimental hfs-constants resulted in:

bo,;(6p) <P = ]042(37) MHz

bO2(6p) 'P = 722 (6) MI If!

The B-factors calculated with those values are shown in

table V.7. and have to be compared with the experimental

values. The agreement is fairly good.

From the parameter bo_(6p)^P the electric quadrupole moment

of the nucleus can be calculated with (2-39c). The value of

<r~3(6p)> was calculated with (2-40). The result is:

15]Q(6p) = 1.09(4) cm-

Table V.7. Comparison of the experimental and ralculated B-factors.

All values are in MHz.

level

5/2

z BP 7/29/2

. *P ?/2

5/2

y 8P 7/29/2

exp

65(4)

-203(3)

296(7)

132(3)

-354(4)

78(3)

-295(3)

226(4)

B(l5l>calc

67.9

-192.6

279.0

1 15.4

-376.2

76.7

-295.3

226.1

77

The quadrupole moment of 15?Eu was calculated using the

ratio of the B-factors in the excited state:

B(151)/B(153) = .394(3) (see next section), resulting in:

1 5 3Q(6p) = 2.77(12) 10" cm- .

These values were not corrected for the Stornhcimcr effect

[STE 66], [STE 67]. The results for the quadrupole moments

are in good agreement with the results of Mullor c.s.

[MUL 65]

1 r>1Q = 1. 16 (8) • 10"-'1 cm?

1 S 3Q = 2.92(20) • 10~pi1 cm"

and Guthohrlein [GUT 68]

1 5 1Q = 1.12 (7) • 10-?l1 cm?

1 5 3Q = 2.85(18) • 10 ~r !< cm?

Miiller c.s. determined the quadrupole moments in an optical

experiment on neutral europium, whereas Outhohrlein derived

his values from singly ionized europium.

The results of the hfs-analysis show that a reasonable

agreement between calculated and experimental hfs-constants

could be obtained. It can be concluded that the wavefunc-

tions of Smith [SMI 78] are indeed sufficiently accurate

to describe the hyperfine structure.

'•. ill;','' i\'','.H:' nipr:i<!Ilj

From the ratios of experimental A-factors of '"'Eu and153Eu and the ratio of the nuclear magnetic momentsUT (151)a Q53) = 2.26505(42) [EVA 65] the hyperfine anomalyI

151^153 c a n kg calculated with the help of (2-44). Results

are given in table V.8.

The major contribution to the hfs anomaly - 5iAlb 3 arises

from the unpaired s-electron, which is most sensitive to

78

Table V.8. The ratios of A and I) factors and the hyperfine anomaly '<J'A''

level

5/2

i aV 1ll

"/2

• f'P ? / 2

5/2

y 8P 7/2

A(15I)/A(I53)

2,259(3)

2,227(7)

2.255(2)

2.14(14)

2.243(3)

2.272(11)

2.259(9)

2.235(4)

(7.)

-.27(13)

-.17(3)

-.44(9)

-.6(7)

-.97(13)

-.31(49)

-.27(40)

-1.33(18)

U(151)/R(I53)

.392(25)

.401(7)

.408(11)

.407(9)

.385(5)

.406(17)

.392(5)

.393(9)

changes in nuclear volume or shape. For a pure s-electron

the hfs anomaly ] 5 1 ] 5 3 which should be equal for all

levels, can be calculated from

1 5 ]A 1 5 3 =s

CX]

s1 5 1 A 1 5 3

ex p (5-3)

A is the contribution to the A-fartor arising from the

contact interaction of the unpaired s-electron. This con-

tribution can be calculated from the product of the hfs-

parameter a ] 0(6s) (see table V.4.) and the corresponding

coefficient p. in the expansion of the A-factor in linear

combinations of the different hfs-parameters given in (5-1)

The levels z 6P 7/ and y 8P 5 , have a very small coefficient

for a (6s) and were therefore omitted from further anal-

ysis. From the remaining levels a mean value 1 5 1A I53 =

.7(2) % was calculated, which has to be compaired with a

value of .65 % from earlier experiments. The error is a

79

gross estimate of the uncertainty caused by the scatter in

the individual anomalies.

The ratios of experimental B-factors are nearly equal and

averaging the values results in: B(15J)/B(153) = .394(3).

This is in good agreement with the ratio of the ground state

values of .393(2) [SAN 60],

V.3.2. Isotope shifis

In table V.9. a compilation of observed isotope shifts in

the transitions 4f76s? - 4£76s6p of europium I is given

Though the present results are an order of magnitude more

accurate, in general a good agreement with existing data was

obtained with an exception for the transition at 564.6 nm.

Table V.9. observed isotope shifts <! v (in Muz) in the spei-irun of I'M 1.

(nm)

629.1

626.7

601.8

576.5

564.6

466.2

462.7

459.4

this work

-3582(2)

-3601(2)

-3552(2)

-3619(2)

-3658(2)

-2804(2)

-2977(2)

-3111(2)

other work

-3510(30)

-3555(9)-3546(9)

-3600(30)

-3621(6)-3249(45)

-2730(^30)

-3150(>30)

-3249(45)-3216(51)

ref

IBR1 52]

[KRE 61 ]

[MU1. 65]

[BRI 52]

[HEI 70]

[MUL 65]

[BRI 52)

(BRI 52]

[KRE 61]

tMUl. 65)

80

This transition was studied by Miillcr c.s. [MUL 65]. They

determined the isotope shift in this transition only from a

frequency separation of 4866(6} MHz between the unresolved

triplets F = 4,5,6 -> F1 = 5 of 1 MEu and F = 3,4,5 > F' = 4

of ir>1Eu. F and F1 are the total angular momenta of ground

and excited state respectively. In the present work the

frequency difference between F = 6 - F1 = 5 of '' 'Eu and

F = 5 -> F1 = 4 of lfllEu was measured to bo 4807 MHz. Since

the hfs-constants are also nearly equal (see table V.2.),

it was also concluded, that null or c.s. must have made a

mistake in the calculation of their IS-value.

The field shift can be calculated from the experimental IS

by subtraction of the mass shift (see (2-14)). Since the

transitions investigated are of the f's-" • f;sp-type, it is

sufficient to consider normal mass shift only (see (2-10)).

A possible contribution from specific mass effects ip in-

cluded in the error.

The IS in the blue spectral lines of Eu I deviates consid-

erably from the IS in the other transitions, which can be

ascribed to the influence of configuration mixing in the

y 8P-states. These transitions will bo considered separately.

The field shift averaged over the remaining spectral lines,

as calculated with relations (2-5), (2-10), (2-14) (with a

small mass shift in the order of 30(15) MHz), is

M H z •

From this result a value for 'S<r?> was calculated in the

following way. From the tabulations of Babushkin [BAB 63]

a value C ., = 149.4 cm"1 was obtained, resulting in a

value f(Z) = 20.76 xlO3 MHz/fm2. In the calculation of the

electronic factor E it is assumed that contributions from

the p-electron can be neglected. Then relation (2-18) holds.

81

A screening ratio 7 = 0.73 was obtained with Hartree-Fock

calculations by Coulthard [COU 73]. The charge density

(0)6 s in f ' 6 s

of the s-elcctron in the configuration

4f'6s belonging to singly ionized Eu II was calculated

using the Eu Il-ionization potential of 11.25 oV as deter-

mined by Sugar c.s. [SUG 65], resulting in a value of

8.11 a^3. This is in good agreement with the value 8.04 aj

given by Brix [BR1 64] and calculated from the magnetic

dipole coupling constant of the s-electron: a.(4f''f>s).

With the value 8.11 a~ ': the electronic factor E = .2953,

resulting in a value

r - • = . 5 9 1 ( 7 ) f n T

between the isotopes ' '• ' ! 'Eu. The error in 'r • does not

account for possible uncertainties in the evaluation of

A' C (0) | r . Our result for .:--r- • is in good agreement with

results from earlier optical experiments [11121 74] (using

the same y) •: <r: • = .571(46) fnv and rontgen experiments

[BOE 74] 6-rr> = .581(33) fnv' .

The isotope shifts in the transitions to '.he y "P-lcvels

can be explained by taking into account admixtures from ttie

configurations 4f7(MS} 5d6p and 4f (7F) 5d6s:.

In transitions involving a state with considerable con-

figuration mixing the specific mass shift and the field

shift can be evaluated with the 'sharing rule1 [BAU 69]

c AA1 _ I- ? . _ , . . AA'

<5v(i) is the IS in the transition to the pure state with

configuration i involved in the composition of the mixed

state, a.2 is the contribution of the configuration i to

the mixed state. In table V.10. the relative contributions

of the three configurations to the y 8P-levels are given,

82

Table V.IO. The isotope shifts (in MHz) after subtraction of the normal mass

shift in transitions to the y flP-levels of europium I. The composition of the

upper levels in terms of three configur.it ions is given.

transition

(nm)

466.2

462.7

459.4

of

f'sp

73.22

74.80

75.86

composit ion

upper level

f7dp

17.75

18.19

18.35

(7.)

f'uV

8.93

7.00

5.78

151-

*VSMS

exp

-2BJ4(I2)

-3008(12)

-il/./UJ)

153

• FS

c a 1 c

-28 30

-3017

-3l3h

together with the experimentally derived sum of specific

mass and field shift (5vS\IS + ].- • "'-"sMS + l'S f o r t h e configura-

tion 4f76s6p was determined from the five spectral lines

with almost pure upper states (- 3626(40) MHz), enabling a

determination of the sum of specific mass and field shifts

in the two admixed configurations from a least squares fit

to the experimental values:

,. 131-153 , cir "A v S M S + F S

( f 6 S'fv5d6p) = - 3990(250) MHz

15 1-153JSHS+FS

(f76s:< • f(5d6s:>) = 6000(620) MHz

The last column in table V.10. was calculated with these

values. The value of 5 VSMS + F " (fV(5s? " f''5d6P' c a n b e

compared with the directly measured values of the IS in the

transitions at 321.0 nm and 306.6 nm between the ground

state and a state of the configuration f75d6p - 3600(150)

MHz and - 4050(300) MHz respectively [SKR 77], Measurements

were also performed [SKR 77] on transitions of the type

4f76s2 -•• 4f5d6s7- resulting in a value of the IS of 5310(90)

83

MHz. It can therefore be concluded that the IS in the blue

spectral lines can be explained quantitatively by assuming

admixtures of the configurations 4f75d6p and 4f65d6s? to the

configuration 4f76s6p.

84

C H A P T E R VI

HFS AND I S IN THE Dy I-SPECTRUM

VI. 1. INTRODUCTION

The element dysprosium (see table VI.1.) has been subject

to many spectroscop.ic investigations.

Conway and Warden [CON 71] measured over 22000 spectral

lines of Dy I and Dy II and used the results for a classi-

fication of the energylevels. The ground state configuration

was determined to be 4 f l n 6 s r .

From a .study of the isotope shifts 5v(lG4-160) in 165

transitions in'the Dy I-spectrum by Ross c.s. [ROSS 7 2 ] ,

Griffin c.s. [GRI 72] were able to designate many levels and

to establish the electronic configurations. In a computerfit

of the finestructure energies v/avefunctions were determined

for the configurations 4f l o6s6p and 4fC)5d6s".

The acquisition of new data in the infrared, obtained with

high resolution Fourier spectroscopy and new data in the

ultraviolet [CAM 73], induced Wyart [WYA 74] to perform a nev;

analysis of the spectrum of Dy I. In his finestructure cal-

culation Wyart fitted 155 energy levels between 7565 cm"1

and 30840 cm"1 with the configurations 4fr)5d6s?, 4f l o6s6p

and 4f 95d 26s. The wavefunctions obtained from this calcula-

tion [WYA 78] are used in the present work.

Table VI.I. Natural composition of dysprosium.

mass nr

relative abundance m

156

.05

158

.09

160

2.29

161

18.88

162

25.53

163

24.97

164

28.18

85

The IS of the two most abundant even-even isotopes 164 and

162 in a natural sample have been measured by Murakav;a c.s.

in 1953 [MUR 53]. Using enriched isotopes in a liquid nitro-

gen-cooled hollow-cathode lamp Striganov c.s. [STR 63]

measured the IS of the five even-oven isotopes in 30 transi-

tions to investigate the differences in nuclear deformation.

They established, that the IS >Sv(156-158) were larger than

the other AA=2- shifts (A is mass number). This was ascribed

to a non-uniform change in the nuclear deformation. Also

with enriched isotopes Dokkor c.s. [DEK 68] measured IS

between all stable isotopes in six Dy-lines. The results were

discussed in terms of the collective model of the nucleus

accounting for nuclear deformation. The behaviour of the IS

in Dy resembles che situation in Sm. For Sm the sudden increase

in IS between 150Sm and 11)2Sm is caused by t.he strong in-

crease in deformation when the 45th pair of neutrons is

added to the. nucleus. In dysprosium this increase was ab-

served between N = 90 and N = 92.

Ross [ROSS 72] measured the isotope shifts i c- *« -1 c c- jjy ±n ^ 5

spectral lines. The results of this measurement were used

to establish the electronic configurations of many of the

energy levels of dysprosium (see above). Recently Grundevik

c.s. [GRU 76] performed pulsed dye laser experiments on an

atomic beam and determined IS of the three most abundant

even isotopes in three Dy I-transitions.

Hfs-studies of Dy I have only been performed for the levels5IC, and

5 I 7 of the ground state configuration 4flo6s?

[EBE 67, CHI 70, ROS 72, FER 74]. The hfs in these states

have been measured with ABMR-methods.

Childs interpreted the experimental results for the stable

isotopes 1c1 — lG 3Qy ^n terms of the wavefunctions computed

by Conway c.s. [CON 71] using the effective operator formal-

ism. Rosein [ROS 72] measured ground state hfs-constants of

neutron-deficient l 53, ] 55 ,2 57[)y ancj axSo performed a theo-

retical analysis of the hfs ^f 161 ,16 3Dv in o r { j e r to derive

86

nuclear moments.

At the start of the experiments, described in this work, the

hfs of excited states of dysprosium had not been investigated

before. However, in the meantime hfs and IS measurements in

some transitions of Dy I have been reported nearly simulta-

neously by several groups [CUT 77, CLA 77, HOG 7a]. The

results were obtained from atomic-beam laser spectroscopy.

In this chapter the results of high resolution hfs- and IS-

measurements in 15 lines of Dy I are reported (section VI.2.1.

In section VI.3.1. the IS-rosults arc compared to earlier1

results. The consistency of the IS-measuremcnts is tested in

a King plot and nuclear parameters '•: • r' • and v -•'•• arc

determined. The hfs-constants of the excited states of :Dy

and ! f> 3Dy are analyzed within the effective operator formal-

ism with the theoretical wavefunctions of Wyart [WYA 74,78].

VI.2. EXPERIMENTAL RESULTS

In a laser-atomic beam experiment 15 lines were investigated

in the wavelength regions 435-470 nm and 560-630 nm.

Only excitations of atoms from the ''I., ground state and ! I 7

metastable states (4134 cm"1) have been measured, since

these two levels were populated sufficiently at the oven

temperature (1500-2000 K) . The Boltzmann-factors at 2000 K

for the three lowest states of the multiplet 4f'"6s;-rr

are given in table VI.2.

Table VI.2. The ' 'Itzmann factors for the lowest .suites of Dy at 2000 K.

term

"18

Sl7

5>6

Icm-']energy

0

4134

70")0

Boltzmann

factor

1.00

.05

<0.01

87

Table VI. 3. Transitions studied in the [)y I-spectrum. The conjps:;•-, i t ion of the

upper level is according to Wyart [WYA 74S7H],

wavelength

<n«0

62S.909

616.843

608.826

601.082

598.856

597.449

569.933

566.44

565.201

563.950

562.749

461.226

458.936

457.778

456.509

energy

[cm

0

4134

4134

4134

0

0

4134

4134

0

0

4134

0

0

0

0

ieve Is

-']

15972

20341

20554

20766

16693

16733

21675

21783

17687

17727

21899

21675

21783

21838

21899

main

''!»,

*H,3K65H7

5K,7K7

5K,7l85H7

SK7

7K,7l8

composition

t.S-component

%

64

30

45

3"

29

32

62

70

44

51

33

62

70

62

33

of upper

CO

6

1

78

1

1

1

91

98

95

0

0

91

98

0

0

level

flosp

(7)

94

99

21

99

99

99

8

1

4

100

100

8

1

97

100

fVs

U)

I)

0

1

0

0

0

1

1

1

0

0

1

1

3

0

In table VI.3. the lower and upper level of the transitions

are given. The excited states are mixtures of the configu-

rations 4flo6s6p and 4fn5d6sr> with a small contribution of

the configuration 4fg5d6s2 in certain cases [WYA 74]. The

excited states are far from being purely LS-coupled, as is

obvious from table VI.3.

Examples of completely recorded spectral lines are shown in

fig. VI.1-4 and in fig. II. 3. Fig. VI. 1. shows the spectrum

of the Dy I-line A=625.9 nm, belonging to the transition

4flo6s2 5I8-4flo6s6p 7 I g . The recording of the transition

peaks of the calibration interferometer is also shown. Since

the nuclear spin of both isotopes lf>1,lfi3Dy is I = 5/2» 15

peaks are expected for each isotope in the spectrum of this

line (see also section II.5.). The total spectrum therefore

88

68

•a]Dis paiinxa ai|l 03 sttuoiaq anjCA jaddn

aAitf oiv sadoiosi ppo ai|] JOJ oiejs pa?T3xs pup punojH jo uirouauioui avjn

aip jo sanii'A aiji pup u«oi[s OJP sadoios; luoaojj ip 3i[j uioaj s

•jaiaiuojajjaiui-z|Uj ^^ ni|i ip in paicjauait oxon tuna ID,ids DDiiDjnjna aip UT squad ai|X

•umisoadsXp iLunieu jo au i | urn 6'5?9"=< a l l l 1° uinjisads iciuaiuiandxH * l ' I A '%M

8 = r

I I I I

15/2

13/21 iU M

i19/

IV

S

117/

M

s113/

13/2

I3

21

/219/2

i i| uN M

15/2

I17/

Tl

3 -

1 I

UI 3 a 5

As

j

contains 35 peaks, which are not all completely resolved.

It must be noted that in all figures the spectra have been

composed from several overlapping frequency scans.

Experimental circumstances were not always the same for all

scans. Laser intensity, atomic beam temperature and signal

amplification varied from scan to scan, resulting in dif-

ferent intensity scales (vertical).

Fig. VI.2. is an example of a transition starting at the

less populated metastable ''Iy-lovel (4134 cm"1). The signal-

to-noise ratio is not as good as for '^Ip-ground state tran-

sitions. The background signal was not constant, caused by

fluctuations in the temperature of the oven. The oven tem-

perature could not be kept constant at the elevated tem-

peratures necessary to observe the small components in the

spectrum. The isotopes 15G,158 D V w e r e not observed in this

experiment.

Further examples of recorded spectral lines in the red and

blue region are shown in fig. VI.3. and VI.4. and also in

fig. II.3.

The measured IS are presented in table VI.4. The hfs-con-

stants in the excited states of 1C]Dy and 'G3Dy are given

in table VI.5.

In the wavelength regions studied in this work, several more

transitions, starting at the 5 I 7 atomic: ground states,

have been reported by Ross [ROSS 72]. xn his table e.g. a

transition at A=464.3 nm, connecting the ground state 5 I 8

with a level at 21529 cm"1, is given, which has not been

classified by Wyart [WYA 74]. In present experiments no

absorption at this wavelength was found although the sensi-

tivity of the setup was sufficient. Also for the transitions

at 611.4 nm, 594.4 nm and 460.0 nm no absorption was

detected.

90

rt t t t t t

W rg

ISOMhJ?

| DYSPROSIUMt t U t t • t

> to in

IICM

s

- n - 1 1P 5>

(f) (0

¥I L

ttft 6i

/ JSOWHi

—AA

Fig. VI.J. Experimental spectrum of the 1" 569.9 tun line of l)y I. Peak

identification as in fig. VI.I, where the lower F-valuc now belongs to the

metastable J * 7 ground state at 4134 cm"1.

91

DYSPROSIUM4589nm

J'8—»J = 7

t t t t t ttnP: Sin

t* t?

300MH;

'fts at t

L

ttS3

<o

;,?tt ft

(O lDi£)tD (OtO

Fig. VI.3. Experimental spectrum of the X»458.9 ran line of Dy I. Peak

identification as in fig. VI.1.

92

f t t t tt

J_N_J_

sts

en (o en c\ rn in rn<O <O <C 10 K><0 (0

3OOMH2

(0(0(0(0

11 j | i; 11oS<o5£ £ io

111 t } tft 11 TM t t tDYPROSIUM

456 5 nmJ=8—<^l=8

10(0 (0 JO

L

3OOMH2

<0 (0<0

I(0 (0 <0 n

Fig. VI.i. Experimental spectrum of the X- 456.5 nm line of Dy I. Peak

identification as in fig. VI.I.

93

Table VI.4. Isotope shifts of the stable l)y-isotopes. All values arc in MHz.

wavelength

(nm)

625.9

616.8

608.8

601.1

598.1

597.4

569.9

566.4

565.2

563.9

562.7

461.2

458.9

457.8

456.5

162-J64

- 962(3)

- 969(3)

418(1)

- 891(2)

- 8b0(3)

- 973(3)

1065(2)

1009(4)

1121(3)

-1013(3)

-1005(3)

1095(2)

1041(2)

- 963(3)

- 9b9(3)

161-

-1036

-1045

473

- 962

- 935

-1059

1179

1113

1234

-1089

-1085

1213.

1145

-1042

-104R

162

(3)

(4)

(2)

(3)

O)(3 ;

<4)

(4)

(3)

(3)

(3)

5(3)

(3)

(3)

(3)

ISOTOPE SHIFTS

158-160

- I026O)

-

-

-

- 924(3)

-1034(3)

-

-

1216(3)

-1073(3)

-

1178(3)

1116(3)

-1029(3)

-IO3<>(3)

156-158

-1518(3)

-

-

-

-1344(3)

-1542(3)

-

-

2003(3)

-1596(3)

-

l%6(6)

1861(4)

-1525(3)

-1541(3)

162-163

-308(3)

-312(3)

77(2)

-2H9(4)

-279(3)

-308(3)

258(4)

243(4)

275(3)

-322(3)

-322(4)

268(2)

254(2)

-310(4)

-312(4)

161-162

-7<>5<3)

-770(3)

4 10(2)

-699(3)

-686(3)

-780(3)

981(3)

929(4)

1026(3)

-803(3)

-801(4)

1007(3)

949(3)

-768(3)

-774(3)

Table VI.5. Experimental hfs-constants (in MHz) for the excited states of

energy

15972

16693

16733

17687

1772720341

20554

20766

21675

21783

21838

21899

main LS-component

7 , ,

5H7

7Kr5 l 97K8

%5K75»75K7

7K9

7 I 8

M.6 . )

-186.9(2)- 64.2(2)

- 88.6(2)

-113.2(3)

-148.0(2)

-200.6(3)- 82.3(2)

-102.6(2)

-101.0(2)

-107.3(2)

-194.7(2)

-163.6(3)

A(163)

261.3(2)

89.9(2)124.0(2)

158.0(3)

207.3(1)281.4(2)

114.0(2)

143.8(2)

141.4(2)

150.3(2)

273.1(2)

229.4(3)

- 315(4)

892(4)

1405(5)

2421(9)

1566(5)

- 183(9)

1155(5)

1647(5)

1838(5)

2001(6)

2122(4)

1297(4)

B(163)

- 349 (6)

939 (3)1479 (5)

2570 (9)

1658 (5)

- 190(10)1237 (5)

1742 (4)

1939 (4)

2115 (3)2235 (3)

1363 (4)

VI.3. DISCUSSION

VI.3.1 Isotope shift

U . Coilllxll'IV'Ot Oj' J V . ' J / i / III

In the introduction of this chanter it has been mentioned

that IS have been measured in a number of spectral lines of

Dy I with conventional interferomctric techniques [MUR 53,

STR 63, DEK 68, ROSS 72] and in some transitions with laser

techniques [GRU 76, CIII 77]. Present results are in good

agreement with IS-data obtained in classical spoctroscopy,

however the accuracy has been improved. Therefore in table

VI.6. a comparison is given only for those transitions where

data from experiments with lasers are available.

h. F.inj j'Lol

The consistency of the experimental IS can be tested accord-

ing to a method due to King (see section II.2.4.). In fig.

VI.5. the modified isotopic shifts (2-16) in nine spectral

lines have been plotted against the same shift in the

spectral line >, =565.2 nm. No significant deviations from

a straight line were observed. For the plot the modified

isotope shifts (2-16) were multiplied by 2/(162*164). The

remaining five spectral lines show the same behaviour, but

are omitted from the figure.

Table VI.6. Comparison of IS-data from present work with other hifih resolution

laser spectroscopic work. All values arc in MHz.

wavelength

(nm)

518.9

565.2

564.0

6v(l62-164)

- 864

- 860

1121(4

1121

-1008(4

-1013

(8)

(3)

• 5)

(3)

.5)

(3)

ISOTOPE

6vfl6O-162)

- V38

- 935

1235

1234

-1090

-1089

(8)

(3)

(6)

(3)

(6)

(3)

SHIFTS

6v(162-163)

-283(8)

-279(3)

6v(161-162)

-677(8)

-686(3)

ref.

[CHI 77]

this work

[GRU 76]

this work

iGRU 76]

this work

95

IS »•M00MH2

Fig. VI.5. King plot for several Dy-lines. The modified IS were multiplied

with 2/(162 * 164).

The transitions can be divided into two groups. The first

group consists of transitions between the ground state

configuration 4flo6s2 and the configuration 4f10Gs6p and

has negative IS. The second group includes the transitions

between 4flo6s2 and 4f95d6s2 and show a positive IS. The

line A=608.8 nm corresponds to a transition from the ground

state to an excited state with configuration 4f95d6s2,

strongly admixed with the configuration 4flo6s6p (see table

VI.3.).

The King plot also allows for a separation of mass and field

shift. For a pure s2-sp transition, the specific mass shift

can be estimated with (2-10).

SMS and PS in the spectral lines can be determined from the

slope and the intercept of King lines. A comparison of the

transitions with negative isotope shifts, taking the transi-

tion A = 456.5 nm as the common line in the King plot, yields,

96

that the approximation (2-10) is reasonable indeed in most

cases. The calculated SMS did not differ more than half the

NMS from zero, taking into account experimental errors.

However, the transitions > =601.1 nm and X =598.9 nm, whose

upper levels also belong to the 4f'n6s6p-configuration,

show significant deviations from this approximation and for

this reason they were omitted from the calculation of the

FS averaged over the transitions of the flos?-flosp type.

Thus averaged FS are given in table VI.7.

Table VI.7. Averaged Field Shifts 6v_ obtained from 4f 106s? - 4floftsbp-

transitions.

156-158

158-160

160-162

161-162

162-163

162-164

6 vFS [MHz]

-1569(30)

-1065 (19 )

- 1 0 B I ( 2 l )

-792(15)

-325(12)

-996 (28 )

f. < r? >

t h i s work

.191(15)

.130(10)

.132(11)

.097 (8)

.040 (3)

. 1 2 1 ( 1 0 )

[fin- 1

[HE1 7A]

.204(32)

.139(22)

.138(22)

.040 (7)

.129(20)

6 ' B? >

.0052(15)

- . 0008 (10 )

- . 0 0 0 5 ( 1 1 )

.0027 (8)

- . 0 0 2 8 (3)

- . 0 0 1 6 ( 1 0 )

Vhe CMS flv^l"16'4 and FS 6v'|'4"162 for the transitions

4f!06s2-4f95d6s2 were estimated from King-lines, where once

again the spectral line \= 456.5 nm was taken as the

reference line:

6vSMS= " 505<25> M H z

1540(50) MHz

Hartree-Fock calculations [BAU 74] yield SMS of -900 MHz

for the Dy I-transition 4flo6s2 5I - 4f95d6s2 7K. However,

these calculations are believed to reproduce the experimental

97

values to within a factor of two, so the difference is not

astonishing.

a . C a l c u l a t i o n o % ' ?ir< •'•-.'.'' ; /;'.•.". '• /•••

The IS in 4f'°6s'-4f'06s6p-transitions have been used to

evaluate the differences in the moan-square nuclear charges

radius 6<r?> between the Dy-isotopes.

Hereto the electronic part of the FS, E.f(x) (see 2-J1),

must be calculated. This was done with the help of (2-18)

The electron-charge density | <i>{0) | j?H of the 6s-cloctron in

the configuration 4flfl6s of Dy II was determined from the

Dy II-ionization potential [SUG 65] and resulted in

|iJ/(0) |? = 9.05 a Q3. The screening ratio Y was estimated

to be .73 [HEI 74]. The value of f(z) for the isotopes

l62,i64Dy w a s obtained with c!f2'1G'' = 182.5* 10"3 cm"' andu n i 1"

becomes: f(z) = 25.96 GHz/fm?.

The constant c 1 6?~ 1 G M was intrapolated from the table given

by Babashkin [BAB 6 3]. The result of the calculation of the

electronic factor is E^f(z) = 8.2 GHz/fnr-, giving a value

6<r2> = .121(10). The error accounts for the uncertainties

in the procedure.

In table VI.7. the values of s~-r?-- are compared to the

values given by Heilig and Steudel [HEI 74], showing a good

agreement.

The change in the mean-square radius of the even isotopes

froin 1 5 8Dy to Ifl''Dy is largely due to a change in nuclear

volume. For the isotopes ' 62"l r>)(Dy &<r?->, due to the volume

effect, calculated with r = .65 (see (2-19), (2-20)), was

equal to .137 fm? . Witheq. (2-24) differences in nuclear defor-

mation parameters <5<S?> were obtained. They are given in

the last column of table VI.7. The values of S<t±7> differ

only significantly from zero between ' 5 6Dy and ' 5 aDy. This

larger difference in deformation causes the larger isotope

shift values between 1 5 GDy and ! 5 BDy compared to other

isotope shifts between even-even isotopes.

If the irregularity in 6<r?> for the isotope pairs l c l» 1 G~Dy

98

r

and H"'2,]6"5Dy (odd-even staggering) is assumed to be a

purely deformation effect, then deformation parameters are

obtained which are different from zero. This reflects the

presence of an unpaired neutron in the nuclei of these odd

isotopes.

VI.3.2. Hyperfine structure of the excited states

Comrai'i-noH o/ i'^nu! tr,

In table VI.8. hfs-constants from present work arc compared

with results obtained by Childs c.s. [CHI 77] and Clark c.s.

[CLA 77], who also applied the atomic-bcam-laser technique

to study some transitions. Good agreement is obtained,

especially with the very accurate results of Clark c.s.

This group used an ultrastable He-Ne laser to stabilize

their reference Fabry-Perot interferometer.

Table VI.8. Comparison of hfs-constants (values in MHz).

energy

16693

16733

17687

17727

main

LS-component

- 5H 7

3K 8

7 K 7

A(161)

- 64.8 (3)

- 64.286(17)

- 64.2 (2)

- 8 8 . 6 5 7 ( 1 4 )

- 88.6 (2)

-112.874(16)

-113.2 (3)

-148.004(13)

- " . 8 . 0 (2)

A(I63)

90.1 (3)

89.858(17)

89.9 (2)

123.998(14)

124.0 (2)

158.054(16)

158.0 (3)

207.295(13)

207.3 (2)

BO 6

879

892.2

892

1401.3

1405

2432.3

2421

1561.0

1566

1)

(17)

( 9 )

W( 9 )

(5)

( 9 )

(9 )

( 9 )

(5)

B(I63)

927

943

939

1481

1479

2575

2570

1652

1658

(17)

2 (9)

(3 )

2 (9)

(5 )

1 (4)

( 9 )

2 (9)

(5)

r e f

[CHI

[CIA

this

[CLA

this

[CLA

this

feuthis

77]

77]

work

77]

work

77]

work

77]

work

b. l'avameti'i:%abion of the A-fries Lorn

The LS-coupled wavefunctions derived by Wyart [WYA 74,78]

were used in the analysis of the experimental magnetic

dipole coupling cons tants . As explained in chapter I I , the

A-factors can be expressed in terms of one-electron hf-

99

parameters. With the computerprogram "Aufspa" the angular

contributions of the reduced matrix elements (2-38) were

evaluated for the configurations 4f'r'6s6p and 4f'35d6s-9.

In these calculations contributions arising from interac-

tions between different configurations were neglected.

If the configuration 4f95d-'6s is omitted the A-factor can

be expressed as a linear combination of 13 one-electron

hf-parameters. Since only 13 experimental A-factors are

available, the number of free parameters has been reduced

in the following way:

1. The three parameters of the 6p-electrons in the 4fi06s6p

configuration can be mutually related, \1sin3 (2-10) with

known relativistic correction factors [KOP 58]

a]0(6p) - -0.1380 a(6p)

aQ](6p) = 1.2898 a(6p)

a,2(6p) = 1.7601 a(6p)

Core polarizations will be neglected in this analysis.

The same procedure was applied to the 4f-parameters:

a|Q(4f) = -0.003 a(4f)

aQ1 (4f) = 1.007 a(4f)

a]2(4f) = 1.017 a(4f)

The remaining hf-parameters for the configuration

4f106s6p then are a)Q{6s), a(6p) and a(4f)

2. The three parameters of the 4f-electrons of the configu-

ration <5fq5d6s2 were expressed in a(4f in 4flf)6s6p) by

means of the ratio of the known finestructure constants

^ ( f M s 2 ) = 1987 cm"1 and f,^f(flosp) = 1713 cm"1

[GRI 72].

The three 5d-parameters were reduced to one a(5d)-para-

meter, again with the relativistic correction factors:

100

a]Q(5d) = - .0226 a(5d)

aQ((5d) = 1.0463 a(5d)

a] ,,(5d) = 1.1 163 a(5d)

In the fit of calculated to experimental A-factors of nearly

pure 4f'°6s6p-lGvels a(5d) was calculated with (2-39) and

(2-40). With the known finestructuro constant r,5d(f°ds?) -•

771 cm"1 [WYA 74] and g] =-.1902 [PER 74] a value a(5d) =

-42.62 MHz was obtained.

In this way the A-factors of nearly pure 4f'06s6p-levels

(the upper part of table VI.9., see also table VI.3.) can

be expressed in terms of only three free parameters:

A = o£ a] (6s) + Si a(6p) + -,-. a(4f) - 42.62 (6-1)

Table VI.9. Comparison of experimental A-factors of lflI)y with values

calculated with the one-electron parameters: a (6s)»-1622 MHz, a(6p)--42.5 MHz,

-154.9 MHz and a(5d)«-42.6 MHz. The coefficients of these parameters

(see (6-1)) are given in the last four columns.

• The A-factor of the level at 18021 cm"1 was measured by Clark c.s. [CLA 77].

energy

Icnflj

16693

16733

17727

18021*

20341

20766

21899

15972

17687

20554

21675

21783

21838

main

LS-component

5HV

%

7K

%

7K7S,'t,

5H7r'K71K

Aexp

[MHz]

- 64.2 (2)

- 88.6 (2)

-148.0 (2)

-110.19(1)

-200.6 (3)

-102.6 (2)

-163.6 (3)

-186.9 (2)

-113.2 (3)

- 82.3 (2)

-101.0 (2)

-107.3 (2)

-194.7 (2)

A ,calc[MHz]

- 65.1

- 89.2

-146.0

-108.4

-202.2

-102.6

-164.0

-202.2

-123.4

-101.3

- 93.6

-122.2

-188.7

a.1

-.034

-.024

.025

-.004

.048

-.021

.032

.046

.001

-.014

.002

.001

.054

-.203

.175

.081

.047

.188

.162

.081

.159

.006

-.054

-.009

.001

.094

Yi

.829

.781

.662

.724

.753

.833

.702

.776

.700

.769

.518

.712

6.

.012

.003

.001

.003

.002

.002

.316

.170

.244

.246

.631

101

Rounded values for the coefficients a., A., y. and '. as

calculated with "Aufspa" with the given assumptions are

given in table VI.9. From a least squares fit of (6-1) to

the experimental A-factors of 1(1Dy the free parameters

were determined, yielding: a. (6s) = -3622(24) MHz,

a(6p) = -42.5(6.0) MHz and a(4f) = -154.9(1.0) Mil?..

A value of a(4f) can also be calculated with (2-39) and

(2-40) with the finestructuro constant r/)f(flnsp) and g( ,

resulting in -171 MHz. In a similar analysis Rosen c.s.

[ROS 72] extracted a value a(4f in flns'") = -155.658(9) MHz

for the ground state configuration flPs". Accounting for the

ratio of the finestructure constants r,r (f' 'V ) = 1751(28)

cm-1 [CON 71] and t;/|f(f10sp) = 1713(11) cm-1, the value

a(4f in f10sp) = -152.3(3.4) MHz is obtained, which is in

agreement with present results.

Also a value of a(6p) was calculated with (2-39) and (2-40),

substituting f;65(flnsp) = 1369(37) cm"1 [WYA 74]. The

result js a(6p) = -62.3(2.3) MHz, which differs considerably

from the experimental result.

The calculated and experimental A-factors of 161Dy are also

given in table VI.9. It can be concluded that a fit of the

7 upper levels with only three parameters is possible, the

largest deviation being 1.7 % for the level at 18021 cm"1.

The A-factors of the remaining 6 levels were also calculated

with the same parameter set. Results are given in the lower

part of table VI.9. Here the differences between experimental

and calculated values are significantly larger. This can be

ascribed to the influence of the configuration fqdsr (see

table VI.3.). The approximations, especially in regard to

a(4f) and a(5d) are not justified any more.

c. //;',•;-.;.i'->"?,.-7;/

The hfs-anomaly for the A-factors of 5 excited levels of

dysprosium has been calculated by Clark c.s. [CLA 77] from

their very accurate experimental values. The accuracy of

102

present experiments was not sufficiently high to reveal the

small anomaly, which is in the order of .1 % or less. The

mean value of the ratio A(163)/A(161) = -1.4002 (8), calcu-

lated from all levels studied in this work, is in good

agreement with the corresponding ground state ratio:

-1.40026(3).

J. Vavamcbr'tixatiai of blw ^-fa^tovu

The parametrization of the B-factors was performed only for

the nearly pure 4f'06s6p-levels of |(i|Dy. The number of free

parameters in the parametric expression of the B-facfcor was

made as small as possible by neglecting contributions of the

configuration 4fg5d26s and to a certain extent contributions

of 4f95d6s?.

For the configuration 4flo6s6p five one-electron hf-parameters

(bQ2(4f), b(3(4f), b n(4f), bO2(6p) and b( ] (6p)) are required

in the parametric analysis, whereas the configuration 4ff5d6s?

yields six more parameters: b' (4f), b! (4f), bj (4f), b' (5d),

b' (5d) and b! (5d)). The prime is used to indicate the config-

uration 4f95d6s2.

The total number of parameters was reduced in a way similar

to the reduction of parameters in the analysis of the

A-factor:

1. In the configuration 4f'°6s6p the 6p-parameters were

coupled by means of their relativistic correction factors

[KOP 58].

The same procedure was applied to the 4f-parameters,

leaving only two parameters: b 7(6p) and b (4f).

2. The hf-parameters of the configuration 4f95d6s7 were

related to the corresponding parameters of the 4flo6s6p

configuration through the ratio of their finestructure

constants.

In the analysis it turned out, that contributions of the 5d

electrons could be neglected since the coefficients of the

5d-parameters are very small.

103

For the parametrization of the B-factors only two parame-

ters are left: b (6p) and bQ2(4f). Thus:

B = «,bO2(4f) + P.b 0 2(6p) (6-2)

Rounded values for the coefficients i. and \>. of the hf-

parameters, as calculated with the help of "Aufspa" arc

given in table VI.10.

Table VI.10. Comparison of experimental B-factors of the nearly pure

4flo6s6p levels of 1610y with values calculated with the one-electron parameters

bQ2(4f) • 4286 MHz and bQ2(6p)»284l MHz. The coefficients of these parameters

(see (6-2)) are given in the last two columns.

• The B-factor of the level at 18021 cm"1 was measured by Clark c.s. [CIA 77].

energy

[cm 1]

16693

16733

17727

18021*

20766

21899

20341

main

IS-component

5H73K85«95ia5K77Ie

Bcxp[MHz]

892 (4)

1405 (5)

1566 (5)

589.9(9)

1647 (5)

1297 (4)

- 183 (9)

calc[MHz]

888

1473

1542

588

1694

1227

• 140

"i

.236

.292

.241

.219

.251

.215

.277

Si

-.043

.078

.178

-.123

.217

.108

-.366

A fit of the parametric expression (6-2) to the experimental

results was possible only, when the level 20341 cm"1 was

excluded. In the analysis of the 4f'06s6p-levels the experi-

mental value of the level 18021 cm"1, determined by Clark

c.s. [CLA 77] was included. From the least squares fit the

two paremeters b (4f) and b (6p) were determined to be

bQ9(6p) = 2841 (187) MHz

bQ2(4f) = 4286(102) MHz .

104

The calculated and experimental B-f actors of '()! Dy for the

levels considered are given in table VI.10. The largest

deviation for the level 21899 cm ' is only 7 %, demonstrat-

ing the applicability of a two parameter fit. In the last

row the value of the B-factor of the level 20341 cm"1, as

calculated with the two parameters b _(6p) and b,.,,(4f) is

compared with the experimental value. Although the order of

magnitude is correct, the opposite sign was obtained. This

is unexplained until now.

From the hf-parameters b ,(4f) and b (6p) the nuclear

quadrupole moment was evaluated with equation (2-39c). The

values of <r~3(4f)>.„ and -r~3(6p)> required for this

calculation were obtained with (2-40) using the finestruc-

ture constant t, £ (4f106s6p) = 1713(11) cm"1 and i, (4flo6s6p)

1369(37) cm"1. This resulted in:

<r"3(4f)>02 = 9.55(6)a~3 and <r"3 (6p)>Q2 = 4.38 (12)a"

3.

From these values the quadrupolemoment was obtained:

161Q> (4f) = 1.91(5) * 10-^ cm2

161Q'(6p) = 2.76(20) * lO"2'4 cm7

The prime is used to indicate that the quadrupole moments

Q1 are still uncorrected for quadrupole shielding caused by

distortions of the innershells (Sternheimer effect) [STE

66,67].

The true quadrupolemoment Q can be derived from the relation:

Q = (1-Rni)"1 Q1 (nl)

where R is the atomic shielding factor. Childs [CHI 70]

quoted the value R,f = .1 ± .05 for dysprosium. This yields:

Q = (1.11 ± .0.7) Q' (nl) .

105

The true quadrupolemoment evaluated from !€1<,}'(4f) =

1.91(5) * 10~?1< cm2 becomes:

1 6 Q = 2.12(14) * 10~:Ml cm'

This value is in good agreement with the quadrupolemoment

calculated from the ground state hfs-ronstant:

KllQ = 2.35(26) * lO-?'' cnv [ ROS 72] or1G'Q = 2.37(28) * 10-'"' cm? [CHI 70].

The quadrupolemoment of Ul 3Dy was calculated with (2-43).

The averaged ratio of the experimental B-factors for the

studied levels is:

B(161)/B(163) = 1.0559(13).

This is in agreement with the ground state value 1.05614(6)

[CHI 70]. With the present value of this ratio the quadru-

polemoment of ]63Dy becomes:

1G3Q = 2.23(15) * 10~?" cm2.

From the ratio of the quadrupolemon;ents Q', the ratio of

the Sternheimer correctionfactors for the 4f and 6p elec-

trons can be obtained:

(6p)/1GIQ' (4f)(1-R,

= 1.44(11)

This value can be compared with the ratio of the correspond-

ing quadrupolemoments of Ii|7Sm, as determined by Brand

[BRA 78]: ' '* 7Q' (6p) / ' '• 7Q' (4f) = 1.43(12).

*Thauks Lo Jncqucs Uoum.i, Kr if K1 i u 1 , W i m drim i t , Kc i n dv i l j .m, l\"i v.in Li't'ii

Ben Vast, SLcvcn Verst r a t on , Hans van V 1 iol .ind iiunn it1 Wosse 1 i nj; f or l ht'i r

e n t h u s i a s t i c c o o p e r a t i o n d u r i n g I ho experitnt'iit s .

106

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110

SAMENVATTING

De spektraallijnen van veel elementen blijken bij onderzoek

met hoog oplossend vermogen te bestaan uit meerdere dicht

bij elkaar gelegen komponenten. Enerzijds wordt dit veroor-

zaakt door een interaktie tussen elektronen en atoomkern

(hyperfijnstruktuur), anderzijds door do aanwezigheid van

meerdere isotopen van eenzelfde element (isotopieverschui-

vingen).

In dit proefschrift wordt een onderzoek beschreven aan de

hyperfijnstruktuur en isotopieverschuivingen in de spektra

van de zeldzame aarden europium I en dysprosium I. De expe-

rimenten zijn uitgevoerd met behulp van afstembare lasers

en atoombundels.

De belangrijkste bijdragen tot de hyperfijnstruktuur in een

spektraallijn worden geleverd door de wisselwerking van het

magnetisch dipoolmoment van de kern en het elektrisch

kwadrupoolmoment van de kern met de elektronen. Uit metingen

van hyperfijnstruktuuropsplitsingen kan zowel atoomfysische

als kernfysische informatie verkregen worden.

De isotopieverschuivingen in spektra van een element met

meerdere isotopen wordt veroorzaakt door enerzijds een ver-

schil in massa, anderzijds een verschil in ladingsverdeling

in de kernen van de betreffende isotopen. Metingen van iso-

topieverschuivingen leveren informatie op over veranderingen

in de ladingsverdeling bij toename of afname van het aantal

neutronen in de kern.

In de experimenten werd absorptie van laserlicht door de

vrije atomen in een atoombundel gedetekteerd door het

fluorescentielicht waar te nemen, dat afkomstig is van het

verval van de aangeslagen atomen. Met de experimentele

111

opstelling, waarin laserbundel en atoombundel elkaar lood-

recht snijden, konden absorptiespektra nagenoeg vrij van

Doppler-verbreding gemeten worden. Uit de spektra werden

zowel hyperfijnstruktuur als isotopievcrschuivingen bepaald

in de onderzochte overgangen in europium I en dysprosiuM I.

In hoofdstuk II wordt de theorie van de isotopieverschuiving

samengevat. Er wordt ingegaan op de berekening van verschil-

len in kernladingsstraal en kerndcformatie uit experimenteel

bepaalde isotopieverschuivingen. Eveneens wordt het cffek-

tieve operatorformalisme voor de analyse van de hyperfijn-

struktuur beknopt behandeld. In dit formalisme v/orden hyper-

fijnstruktuuropsplitsingen van vele niveaus geïnterpreteerd

m.ó.v. een beperkt aantal atomaire parameters.

De experimentele opstelling, bestaande uit afstembare kleur-

stoflasers, atoombundelapparatuur, kalibratie-interferome-

ters en een golflengtemeter, wordt besproken in hoofdstuk

III.

De experimentele opstelling is getest in experimenten aan

natrium en indium (hoofdstuk IV). Deze experimenten zijn

uitgevoerd om de kalibratie-interferometers in de verschil-

lende golflengtegebieden van de kleurstoflaser te ijken op

de goed bekende hyperfijnstruktuur van de grondtoestand van

natrium en indium. De gevoeligheid van de opstelling is

bepaald d.m.v. experimenten aan een van de natrium D-lijnen.

Tevens is de hyperfijnstruktuuropsplitsing van de 2S^-geëxci-

teerde toestand van indium bepaald. Uit de isotopieverschui-

ving tussen ']3In en l T5In in de overgang bij 451.1 nm is

het verschil in kernladingsstraal berekend.

In hoofdstuk V wordt het onderzoek van 8 spektraallijnen in

het spektrum van europium I besproken. In de 8 (4f76s2 -

4f76s'6p)-overgangen zijn de isotopieverschuiving tussen en

de hyperfijnstruktuur van de beide isotopen 151Eu en ls3Eu

bepaald. De hyperfijnstruktuur van de aangeslagen toestanden

112

is geanalyseerd n.b.v. het effektieve operatorformalisme.

Het verschil in kernladingsstraal tussen beide isotopen is

bepaald uit de isotopieverschuiving.

In het laatste hoofdstuk worden resultaten gepresenteerci

van metingen van 15 dysprosiumlijnen. Uit de isotopiever-

schuivingen zijn de veranderingen in kernladingsstraal en

in kerndeformatie tussen de zeven isotopen van dysprosium

bepaald.

De hyperfijnstruktuur in de geëxciteerdo toestanden liet

zich op bevredigende wijze beschrijven m.b.v. het effoktieve

operatorformalisme. Hierdoor was het mogelijk de kern

kwadrupoolmomenten van de isotopen IfIDy en ' '•• 3Dy te bepalen.

113