JULY 1979

RADIATIVE CAPTURE OF POLARIZED NEUTRONS BY ALUMINIUM AND MANGANESE NUCLEI

BY

P.P.J. DELHEIJ

ECN dots not assume any liability with respect

to the use of, or for damages resulting from

the use of any information, apparatus, method

or process disclosed in this document.

Netherlands Energy Research Foundation ECN

P.O. Box 1

1755 ZG Petten (NHI

The Netherlands

Telephone (0)2246 - 6:62

Telex 57211

JULV1t7»

RADIATIVE CAPTURE OF POLARIZED NEUTRONS

BY ALUMINIUM AND MANGANESE NUCLEI

P.P.J. DCLHEIJ

Delheij, P.P.J. ECM-62

RADIATIVE CAPTURE OF POLARIZED NEUTRONS BY ALUMINIUM AND MANGANESE

NUCLEI.

Petten, ECN-FOM Nuclear Structure Gro-tp, Netherlands Energy Research

Foundation ECN. 1979, July.

59 pages, 18 figures, 6 tables.

The angular distribution of the intensity is calculated for primary

and secondary gamma-rays eaitted after polarized neutron capture in

a polarized target. Also the circular polarization is derived for

capture of polarized neutrons by unoriented nuclei. Interference be­

tween the reaction channels and all possible dipole/quadrupole mixing

is taken into account. Some aspects of p-wave capture and s-p inter­

ference are discussed. The results of these calculations are applied

to the experiments on aluminium and manganese. In the nuclear orien­

tation experiment with aluminium a "brute force" polarized target

was used. For five levels in 28A1 the spin *alue could be determined

uniquely. No evidence for significant M2/E1 mixing is found. A ferro­

magnetic MnSb sample was used to polarize the manganese nuclei.

Unique spin values are assigned to 13 states in 56Mn. The magnetic

hyperfine field on the Mn nuclei is determined to be negative.

Keywords:

POLARIZED TARGETS MULTIPOLE TRANSITIONS

CAPTURE ALUMINIUM 27 TARGET

GAMMA RADIATION ALUMINIUM 28

ORIENTED NUCLEI MANGANESE 55 TARGET

ANGULAR DISTRIBUTION MANGANESE 56

SPIN NEUTRON REACTIONS

- 1 -

CONTENTS

INTRODUCTION

ÏBSË.

CHAPTER I ANGULAR DISTRIBUTIONS JF GAMMA RADIATION EMITTED

AFTER CAPTURE OF PCÏ.ARIZED NEUTRONS 7

1. Introduction 7

2. The density matrix and efficiency matrix 8

3. Pure s-wave capture 10

4. Pure p-wave capture 17

5. Remarks on interference between s- and p-wave

capture 20

6. Conclusions 22

CHAPTER II A STUDY OF THE 27Xl(n,y)28Al and 2 7A1 V'',Y)28A1

REACTIONS

1. Introduction

2. Angular distributions

3. Experimental arrangements

4. Analysis

5. Discussion

6. Conclusions

23

23

24

26

31

35

40

55. >56. CHAPTER III A STUDY OF THE ^ n ( n , y ) Mn and Mn(n,Y) Mn

REACTIONS 42

1. Introduction 42

2. Experiments 42

3. Results in terms of the decay scheme and jpins 51

4. The hyperfine field on Mn nuclei in the

compound MnSb 56

5. Conclusions 56

SUMMARY 58

- 3 -

Introduction

The study of interactions between neutrons and nuclei is an extensive

subject, of which the radiative capture forms only a small part.

However, thermal neutrcns are captured alaost exclusively in s-states,

and therefore the angular momentum characteristics of this reaction are

quite simple. So, the utilization of thermal neutrons offers definite

advantages, in particular as regards the spin assignments to the nuclear

levels that are populated in the radiative decay.

A further simplification of the angular momentum analysis of the (n,y)

reaction is provided by the method of polarizing the neutrons, the

nuclei or both and by detecting the degree of gamma-ray circular

polarization. This fundamental advantage may in many cases off-set the

practical disadvantages associated with a more complicated experimental

arrangement and with lower counting statistics. But the recent development

of large-volume Ge(Li)-detectors has, besides the energy-analysis, also 3 4

improved the statistics considerably. The introduction of He- He

dilution refrigerators for sample coding and of superconducting coils

for sample magnetization (to polarize the nuclei) has removed some

of the limitations of earlier experiments. More advanced cryogenic

techniques have extended the possibilities for useful experiments, in

particular as regards the introduction of "brute-force" polarization

of atomic nuclei. It has become possible, as described in this thesis,

to combine the method of neutron polarization with the technique of

"brute-force" polarization.

A schematic view of the set-up used for these experiments is given in

fig. 1. The neutron beam, emerging from the reactor, is diffracted

horizontally over 37 by Bragg-reflection in a vertically magnetized

Heussler single crystal (Cu?MnAl). Since the nuclear and magnetic scat­

tering amplitudes interfere coherently, tht scattered mono-energetic

beam is polarized in the vertical direction.

The neutron polarization can be reversed by a radio-frequency spin

flipper. This device works according to the principle of transverse

nuclear magnetic resonance.

The beam passes through a titanium foil, which is mounted in front of

the sample.

- 5 -

In the nuclear orientation set-up angular distributions have been

measured with a "brute-force" polarized aluminium sample and a ferro­

magnetic manganese compound (MnSb).

Additional information on the angular momenta involved in the (n,y)

reaction is obtained by determining the degree of circular polarization

of the gamma-radiation that is emitted after polarized neutron capture

in unpolarized nuclei. A schematic view of the set-up is shown in

fig. 2. The neutrons, which emerge from the reactor, are totally reflected

by the magnetized Co-Fe mirror system only if their spin is parallel

to the m£_netization. The reflecting system contains two sets of focussing

mirrors which make a small angle with each other. This construction

prevents direct transmission of the neutrons.

By means of a set of twisted coils (1 m long) the neutron spins are turned

over +90 or -90° from the vertical direction into the horizontal plane,

while they remain perpendicular to the propagation direction. The polariza­

tion of the captured neutrons defines the circular polarization of the

emitted gamma-radiation.

rntcnm

MS I »c I

^

*H

*>%

MS Mirror System NS Neutron Spin

STC Spin Turning Coils T Target ^ A RHTntndur AnoJyzer M: Magnetization

BSBoam Stop Ge(Li) Garmaniun detector

PS-Photon-Spin

Fig. 2. Schematic view of the circular polarization set-up. The full and dashed arrows indicate the two directions of the neutron polarization behind the STC, to which the photon spin is related directly.

- 6 -

The transmission of polarized gamma-radiation through magnetized Materials

is determined by the compton cross-section, which contains a polarization

dependent part. The degree of circular polarization is measured with the

aid of magnetized permendur cylinders. By reversing the neutron polar­

ization and consequently the gamma-ray polarization a difference in

intensity of the gamma-rays is measured by the germanium detectors

behind the two analyzers. This difference is directly related to the

degree of circular polarization of the gamma-radiation. Also with this

set-up measurements on aluminium and manganese have been performed.

It may be noted that for the calculation of the angular distribution

coefficients in the next chapters, the choice of the z-axis in the

frame of reference is essential. It should be emphasized that this

choice differs for the two set-ups that are described here. In the

nuclear orientation experiment the z-axis is defined parallel to the

external magnetic field which polarizes the nuclei. For the determina­

tion of the circular polarization the z-axis points in the direction

of the magnetization in the permendur analyzers.

At present, these experiments yield a wealth of experimental data

compared with earlier measurements, in particular with respect to the

number of accessible nuclear states. Moreover, the spin assignments in

the earlier work have become questionable in view of the important

observation that the two reactionchannels with different spin may

interfere coherently. This effect remained unnoticed until 1973.

In the first chapter an introduction to the calculation of the angular

distribution coefficients is given. These are applied in chapter 2 to

the analysis of the experimental results on aluminium. The last chapter

contains a discussion of the experiments with manganese.

- 7 -

CHAPTER I

ANGULAR DISTRIBUTIONS OF GAMMA RADIATION EMITTED AFTER CAPTURE OF

POLARIZED NEUTRONS

1. Introduction

Spins can be assigned to nuclear levels by aeans of capture gamma ray

experiments with polarized neutrons

Directional intensity distributions of gamma radiation fro* oriented

nuclei (NO) are calculated. Also the angular dependence of the gamma-

ray circular polarization (CP) from unpolarized samples is investigated.

With respect to ref. 1 an extension is reported here in which, for

s-wave capture, multipole adaixture is included for both reaction

channels c « t + 1/2 (fig. 1), where t is the spin of the target nucleus

and r the channel spin. Mixed multipole radiation and channel spin inter­

ference is also treated for secondary gamma-rays.

For p-wave capture the influence of the orbital angular momentum on

the angular distributions is investigated. Although the latter is hardly

observed in case of thermal neutron capture, in section 5 the effects

of s-wave and p-wave interference are considered . This concerns

transitions with impure parity.

The monograph of Ferguson provides the general basis for the calculation

of the angular distributions of radiation from states with impure

spin and/or parity. For convenience some of the basic concepts are

shortly repeated in the next see*ion, in order to define the symbols

used in the present context.

c=Ub

I.

- 7=Uc

h

f=M«T

Fig. 1. Angular momenta, involved in the (n,y) reaction.

- 8 -

2. The density —tri» «ad the efficiency —tri»

The angular distribution function W for nuclear reactions is generally

obtained by suaning the products of the probability density and the

detection efficiency over all substates (ref. 2, ch. 2)

W • Tr[pe]. (2.1)

Mere o and c are the density matrix and efficiency matrix and the

trace operator Tr sua» over all diagonal elements of the product

matrix. For an impure state •, characterised by the sets of quantum

numbers A and A', a density matrix element is defined by:

<A|p|A«> - C<A|*><#|A'>]average (2.2)

If the quantum numbers are the angular momenta a and a', the calculations

are simplified by a transformation to a spherical basis, in which the

irreducible tensorial sets are defined:

p,_„ (aa«) - E (-)a'"V (am .a'-m .|k.c)<amJp|a'm .> (2.3) t 4* 4» « 1 3 'kK

a a

ek|c ( a a ' ) - E ( - ) * " " a ' ( a m a , a ' - m , |kic)<aa | c | a ' a , > . (2 .4 ) m m '

a a

Here m is the projection of a on the z-axis, which is usually chosen

in either the direction of the detector, or along the propagation of

the beam or in the polarization direction. Under a rotation R of the

coordinate axes the tensors are transformed by means of the Wigner D

matrices:

pk<'<aa'>^DïK'<R",> V ( a a'>- (2-5>

The capture of neutrons with intrinsic and orbital angular momenta

s and 1 by a target with spin t and the subsequent emission of gamma

radiations with multipolarities L and M is schematically shown in fig. I.

The following vector relations are valid:

- 9 -

8 + ï » b (beam)

-• -• ->•

b • t « c (channel)

c + L « x (intermediate state)

ï + H - 1 (final state).

Then the angular distiibution function can be written as:

Z Pk „ < « ' ) P t r OH') P. „ (LL') x KfKf TTM TL

x e* (ff') e? r (MM') e* (LL'). (2.6) *f f TTM TL

The summation will be specified below. (Because of the normalization

all factors 4it finally cancel in this text and will therefore be

omitted throughout). The statistical tensors are expressed step by 2)

step in terms of the tensors of the incoming particles . These

reflect the state in which the system is prepared initially. The

efficiency tensors c.(LL') of the gamma radiation contain a factor

J {S0+S3+(-)d(SQ-S3)} with d - L + L' + ir + ir' - k. Here ir, IT' take

the values 0 or 1 depending on the electric or magnetic character of

the multipole components L and L' respectively. This factor reflects

the absolute sensitivity of the detector for an intensity or a degree

of circular polarization» and must be inferred from a calibration. This

quantity is omitted from further consideration. So the Stokes parameters

S~ and S. can be arbitrarily set equal to unity. A first simplification

of (2.6) is possible because the recoiling nuclei are not detected:

Vf (££,)-1 W 6 " " (2,7)

where f - /2f+J".

It should be noted that the angular momentum characterization of the

reaction channel c may be impure. This will giv* rise to interference

effects in the angular distribution coefficients.

- 10 -

3. Pure 3-wave capture

Capture of s-wave neutrons means 1 • 0 so p. 0>b') * p (ss'). D O s s

It is assumed that the neutrons are polarized perpendicular to the

propagation direction and that this direction is coincident with the

axis of nuclear polarization. This direction is denoted as the z-axis.

So the system is utationally symmetric and therefore only tensor

components with K * 0 occur, which can be expressed in terms of

orientation parameters (ref. 3). Regarding the gamma transitions only

dipole and quadrupole radiation are considered. If the gamma radiation

is detected in an arbitrary direction, the frame of reference must be

rotated so that the final z-axis is coincident with the direction of

the detector. The Wigner D matrices, which accomplish this rotational

transformation»can be reduced here to Legendre polynomials P. (cos 6).

3i2i_Primar2_radiation

Considered is the gamma radiation emitted directly after che capture

process. The angular distribution can then be written as:

_ . ft s c i H T p k Q(tt) pfc 0(ss) (k 0,k0|k 0 ) ( c r ( c ' r k t k U s c»[ x

t s lk k k J t s c

li-K i, C U / T „ T I „ I . i t . \ tit / . ^ ', x (-1) c ** c WdeL'c'jik) LL'(-r "'(Ll,L'-l|kc0) x

x <c | | s | t><c , | | s j t>*<i |L| | c><i|L'||c'>*Pk (cos 9) . (3.1) c

The summation is over k , k , k , c,c', L, L' with s • 1/2, L • 1,2, t D C

L' - 1,2, c « t + s, c' - t • s, |L-L'|sk SL+L', Osfc «52t, 0*kgS2s

Ik -k |sk £k +k and k +k +k even, ' t s ' c t s t s c

The orientation parameters f. are substituted ' for the statistical

tensors p, n, with f_ - J and f "f, (k • J). The summation is carried kO 0 n k s

out partially, giving the A-coefficients:

A; 10

>t»1

y,

/

»

y

C—I

/

\ /

/

\

1*2,—,

1

/ i A«4

\

\

i«r--..

* i

c -^

IC—11 — 2

/

*'* 4**

' M

- W

1 . •

S

0

- .V

(C—H— I

M

- 1 . ^ * — • — • —

I'J

. V5 ,

W

'"'

Fig. 2. The angular distribution coefficients for pure dipole radiation from a target with apin t = 5/2. The parameter A^ is related to the circular polarization experiment^ and the other parameters give the intensity distribution in the nuclear orientation experiment. The full (dashed) curves indicate constructive (destructive) interference as a function of the fraction (a) of a gamma transition that originates from the reaction channel with the highest spin value.

r-\

. i — •

•"*-"•

,-v, , t

* •

- 13c -

o * L •

5

• i ' Ir."

i

- IM -

or-*-.

Q •

O -.

I_.

rs-

IT"

!^v^3^^i

5- .. .^ ^"S-

U y

13d -

- 16 -

W(NO) - A £ ° + i j 1 f , fn • a\l f , fn • 7? f2 • A j 3 f 3 f n ) F 2 (cos8)

+ (X43 Vn + *T f4 + K5 Vn)P4 (cOS 9)* ° ' 2 )

W(CP) - AJ5° • A ° fn P^cos 6 ) . (3.3)

In practice terms containing f. may be neglected for k>2.

In the X-coefficients the following continuous parameters will be intro­

duced:

<t+s s|t> - _ <i|L-2 s|t> L <i|L»I

t-s> . _ <i|L»2|| t*s> t-s> H <i L»1 t+s>

kskt ~kskt -00 In fig. 2 soae examples of the normalized coefficients A, «A. /Afl

are given as a function of:

2 o » (t*1)n - for — s n s - and «.-«„-O.

t+(t+l)n L H

In fig. 3 the behaviour of some coefficients is shown for a • 0.5 and

Ó., 6 as free parameters. 1* H

3.2. Secondary radiation

The distribution coefficients are calculated for gamma-rays originating

from levels that are populated by only one primary transition.

2 2r - fC s c 1 M - E p 0(«)p k Q(ss)(k 0,k 0|k 0)(2)'(8

,)Vk t s c x t s *k k k '

t s c

x (-)L"C_iW(cic'i;Lkc)(i)2 (-)f"M"i W(MiM'i;fkc) x

x MM» (-)M "' (MI,M'-![k 0) x

x <c|| t | s><c' i l t |s>*<i |L|[ c><i|L|| c'>*<f|M|| i><f|M'|| i>* Pk (cos 0) c

(3.4)

- 17 -

The summation is over k , k , k , c, c', L, M, M* with s • 1/2, L * 1,2, t s c

c « t+s, c' * t+s, M - 1,2, M' - 1,2, |M-M'|sk <M+M', 0<k s2t, Osk <2s, Ik -k |<k <k +k and k + k + k even,

s ' ' t s' c t s t s c After an analogous transcription as carried out for primaries the result

is identical in terms of A-coefficients. Furthermore the numerical values ~00 11

of A. and A are the same. The other A-coefficients behave completely

different. In fig. 2 some examples are given for all mixing parameters

zero. In fig. 4 the multipole mixings of the secondary transition

°s <f|L-l u *- '".5.

-T— and one of the primary components are varied for

A. Pure p-wave capture

For p-wave capture an additional angular momentum appears in the formula,

namely the orbital angular momentum 1 of the neutrons. Firstly 1 and s

are coupled. Thus the intrinsic and orbital angular momenta are combined

in the statistical tensors of the beam. With these new tensors the

above used procedure is carried out again.

According to ref. 2 the statistical tensors for a beam of spinless

particles can be written as:

Pk 0 (11') - 11' (-)1' (10,1'Olk^). (4.1)

A beam of particles with intrinsic spin can be then described by:

Pk K (bb') - Z pk K (ss) (10,l'o|k10)(k10,kgKs|kbKb) x b b k k. s s

s 1

rl s b 1» f1 s D I x (-)1 11' bb' k.k il' s b'k (A.2.)

\ k V 1 s b

This implies a choice of the z-axis along the propagation direction of

the beam. It is assumed that the neutrons are polarized perpendicular

to the beam and this direction is chosen as x-axis (fig. 5).

Because p-wave capture through only one reaction channel (1»1') is

considered, two situations can be distinguished with respect to the

nuclear orbital in which the neutrons are captured:

p .„-capture (i.e. b-b'-l/2) and p_,„-capture (*'.e. b»b'-3/2).

18 -

Fig. 5. Frame of reference in which the system initially is defined. For the notation 9 = $ = i t we refer to section 4.2.

4.1. Capture in p . -orbitals

In this situation k. can only take the values 0 or I.

The non-vanishing tensor components of the intrinsic spin are:

'00 (ss) - -!- P, + 1(ss) - i - p

where P is the neutron polarization. Consequently the only non-zero x 1

components for the beam as a whole are Pnf.(bb) » -jm and

p .(bb) • -p (ss). It should be noted that the last parameters contain

two contributions from k , k, » 1,0 and k , k, » 1,2.

s i ' s i Since we are interested in intensities perpendicular to the beam, it is easiest to rotate the co-ordinate system over x around the y-axis. This

kb 2

is performed by the rotation matrices D , (e 9.C.) with 9. • 9- * 0 ir b b

'2 ~ " 2* For the present purposes (CP and NO) only tensor components in the final frame with K • 0 are important:

and 6,

V0 D

The result is:

»óo (bb) J_ /I

P'10 (bb) x (4.3)

- 19 -

For s-wave neutrons p..(1/2) * -ym would hold. So it appears in this

capture process that the polarization of the total angular momentum of

the beam is opposite to that of the intrinsic spin.

4.2. Capture in p. ..-orbitals

With the same approach as in section 4.1 for b • b' » 3/2 the following

tensor components can be formed in the original frame of reference:

P0Q (bb) - p0() (ss) p0{) (11) (...) ^4.4a)

pi+i (bb) - p i + .

( s s ) p o o ( n ) ( — >

+ P1+l (ss) p 2 Q (11) (...) (4.4b)

P2+] (bb) - p 1 + J (ss) p 2 Q (11) (...) (4.4c)

P2Q (bb) - p Q 0 (ss) p 2 Q (II) (...) (4.4d)

P3+, (bb) « pJ + J (ss) p2() (11) (...) (4.4e)

The dots (...) denote products of Clebsch-Gordan and Wigner 9-j symbols.

Because of the rotation over •=• around the y-axis the components p.

and p_ . do not contribute to the distribution. Compared with p. . -capture

p?f) (bb) is a new term which is independent of the polarization of

the intrinsic neutron spin. It reflects the intensity distribution with

respect to the beam axis for unpolarized p-vave capture. ~02

Consequently a new term B. has to be added to the formulas (3.2) and

(3.3).

W(NO) - A?0 + B?2 + X'1 f,f + ... (4.5) (J i u I n

W(CP) - A°° • B?2 • A»0 f • ... (4.6) o i in

In the direction of the neutron polarization (9 • j , $ • 0) for target

spin t • 5/2 an explicit calculation has been carried out for the

- 20 -

coefficients A and A. .

It follows that their values are a factor 1.2 larger for p. ..-capture

(spin i • 0 or 5) than for s.,--capture (spin i « 1 or 4). No channel

spin interference occurs for these extreme spin values.

5. Remarks on interference between s- and p-wave capture

The frame of reference is chosen as in section 4. Now tensor parameters

for the beam with mixed orbital angular momenta (1^1') occur:

p00 ( 1 1> , , 1

10 " ' P_

20 P,A (ID ^ (SS) * * f

where 1 - 1,2, 1' « 1,2 and s - 1/2.

A list of all possible tensor components is given in table 1 with their

constituent terms. If only the intensity and circular polarization are

considered [only p' (bb') in an arbitrary direction],the transformation

under a rotation is given by the spherical harmonics:

pk0 (bb'> " I \K (bb?) C <e*>'

The explicit rotational properties are listed in the fourth column of

table 1.

The interference between s- and p-wave neutrons shows up in the terms

numbered 2, 4 and 7 in the first column. Under the assumption that no

parity violation occurs in the gamma transitions these terms contribute

to the intensity distribution for odd k and to the circular polarization

distribution for even k. Consequently from term 2 follows an intensity

asymmetry with respect to the propagation direction of the neutrons.

For the products of reduced matrix elements in the terms 4 and 7 the real

and imaginary part must be considered separately. Since in term 4 the

factor p. (SS)(10,1K|1K)K sin 8 has opposite signs for K • 1 and K • -I,

the real part vanishes but the imaginary part gives an intensity

asymmetry for ( 9 ^ 0 , <f> + 0) if the neutron polarization is reversed.

From an analogous consideration it follows that for term 7 the imaginary

part vanishes and the real part gives a contribution to the circular

polarization for (6 + 0, 6 ^ T , $ + •*•).

Tabel 1: Statistical tensors for polarized s- and p-wave neutrons.

n

\

2

3

4

5

6

7

8

9

PkK

PQ0(bb)

P , 0 ( b b ' )

P , + 1 ( b b ' )

P 2 0 (bb ' )

P 2 l , ( b b ' )

P 3 ± 1 ( b b ' )

const i tuent

parameters

rotat ion

propert ies

= P 0 0 ( l l ) p Q 0 ( s s ) ( 0 0 , 0 0 | 0 0 ) x . . . x 1 x

» p . _ ( l l ' ) p ( s s ) ( 1 0 , 0 0 | 1 0 ) x . . . x cos e x

» P 0 0 ( l l ) P 1 + , ( S S ) ( 0 0 , 1 _ + 1 ' 1+_1) x . . . x _ + s i n 8 exp(+i<t>) x

+ p J 0 ( l l ' ) p ( s s ) (10,^+11 HI) x . . . x _+ s in 8 exp(+i<tO x

• P 2 0 ( l l ) p ( s s ) ( 2 0 , m 11+J) x . . . x _ + s in 6 exp(+i<fr) x

- P20<11) p Q 0 ( s s ) ( 2 0 , 0 0 | 2 0 ) x . . . x (3 c o s 2 6 - l ) x

- p . - d l ' ) p (ss)(IO,!_+! |2+1) x . . .x _+ s in e cos 6 exp(+i*) x

+ p „ A ( l l ) p _ , ( s s ) ( 2 0 , l + 1 |2+1) x . . . x + s i n 6 cos 6 exp(+i*) x

» P 2 0 ( l l ) P J + j ( s s ) ( 2 0 , I + l | 3 + I ) x . - . x + ^ s i n 6(5 c o s 2 6 - l ) e x p ( + i * ) x

reduced

matrix elements

<i |L|j o A < c | | t | b '>*<b ' | | l ' | s > * < i

ti

i i

ii

II

II

i t

II

II

|L| | C><C| | t | b x b | | l | s >

l\J

1

- 22 -

6. Conclusions

In the past several authors had to interpret* their experimental

circular polarization data by including multipole mixing ' , assuming

that only one reaction channel was involved. This restriction is removed.

It will be demonstrated in chapter 2 that, as a result, the previously 28

reported E2/MI mixing ratio for the ground state transition in Al should

be refuted . So far no significant M2/E1 multipole admixture has been

found in primary transitions.

The effect of s-vave and p-wave interference is treated because this

may affect the results in ref. 4 that are obtained from parity non-

conserving experiments with polarized neutrons. But this influence can

only arise from the imaginary part of the transition probability. For

thermal neutron capture the real part is usually much larger. This can

be determined by measuring, perpendicular to the neutron beam, the circular

polarization of gamma rays that are emitted after capture of neutrons

with a polarization along the beam axis.

References

1) J.J. Bosman and H. Postma, Nucl. Instr. Meth, U£ (1978) 331.

2) A.J. Ferguson, Angular Correlation Methods in Gamma-Ray Spectroscopy,

(North-Holland Publ. Co., Amsterdam, 1965).

3) H.A. Tolhoek and J.A.H. Cox, Physica J£ (I953) 101.

4) Yu.G. Abov, O.N. Ermakov and P.A. Krupchitsky, Soviet Phys. JETP

38 (1974) 870.

Yu.G. Abov, H.M. Danilov, O.N. Ermakov, I.L. Karpikhin,

V.K. Rissukhin and A.M. Skornyakov, Soviet J. Nucl. Phys. j£ (1973)

670.

5) F. Stecker-Rasmussen, K. Abrahams and J. Kopecky, Nucl. Phys.

A181 (1972) 225.

6) A.M.J. Spits and J. Kopecky, Nucl. Phys. A264 (1975) 63.

7) This thesis, chapter 2.

- 23 -

CHAPTER II

27-* -»• 28 27 -»• •*• ?R A STUDY OF THE Al(n,Y) Al AND Al(n,y) Al REACTIONS

1. Introduction

28 1 Levels of the odd-odd nuclide Al have been studied by neutron capture as well as by charged particle reactions. For a few transitions

3) the degree of gamna-ray circular polarization has been determined.

Parities and transferred orbital angular momenta have been obtained

from (d,p) and ( He,p) experiments. By means of the (3,a) reaction

the natural or unnatural character of the parity has been measured.

Lifetimes have been determined by application of the Doppler shift 7) 8)

attenuation method to the (d,p-y) reaction . Shell model calculations

have only reproduced the positive parity states below 2 MeV excitation

energy.

In the present investigation brute-force polarization was used for the

first time as a new stage in the continuous development of nuclear

orientation applied to neutron capture gamma-ray spectroscopy.

The target was natural aluminium. To perform such an experiment it

is important to use as high a magnetic field as possible. The magnet

system of the equipment at the High Flux Reactor in Petten is able to

produce fields up to 5 T. However, depolarization of the neutron beam

at the entrance and the exit of the cryogenic system so far prohibited

to use the magnet above 2.7 T. By improving the guide-field system it

is now possible to apply the maximum field strength. This has made it

useful to measure the gamma-ray anisotropics after capture of polarized 27

neutrons by polarized Al nuclei at a temperature of 35 mK.

In addition, another experiment was carried out to determine the degree

of circular polarization of gamma transitions after capture of polarized

neutrons by unoriented aluminium nuclei.

From these reported experiments angular distribution coefficients could

be determined for a large series of gamma-rays, some of them coming

directly from the capturing state, others being intermediate transitions. 28

In total characteristics of 43 transitions and 22 levels in Al could

be studied.

- 24 -

2. Angular distributions

In the past «any authors have treated the intensity and polarization

angular distribution of gamma-rvys emitted by ensembles of oriented

nuclei . The case of gamma radiation following directly after

neutron capture has also been studied in detail, including interference

effects between reaction channels with different spins . Very little

experimental work has been performed on secondary transitions and then

only for situations with one spin value for capture ' . This work

is now extended by including intermediate gamma-rays with interference

effects between the reaction amplitudes.

Ic=2.3

27 28 Fig. 1. Spins involved in the Al'nty) At reaction.

For the experiments with aluminium only s-wave capture will be considered.

In fig. I the usual sequence of primary and secondary transitions with

the spin notations of the various levels are given. Consequently the

angular distribution function can be written as:

W(9) -AJJ° • AJ' fj(S) f,(It) + [A" f,(S) £,(1^ • A°* f2(It)

• AJ3 fj(s) f 3 u t ) ] , *2 ( c o s e ) » (2.1)

where 8 denotes the angle with respect to the orientation axis,

and f.(S), fv(If.) a r c the orientation parameters of the neutron

beam and the target respectively. It should be noted at this point that H I

the A. term in eq. (2.1) is identical for primary as well as for

secondary or any other intermittant transition if the initial level

is populated by only a single cascade.

C — !

"--

~ ~ ^ l - - 2

^ n

t—i

>ü y

E . II<«V)

D °

Q-DS9

!

e

4 1

«! IC—II —?

P

^ I.*-

IC—U—3

V - - ^ -

4 1

• r

A\

.H

:J4J

f}

!•?

I C - 1 1 - 1

'•tfl

L)

I C - I I — 1

t ' i l l

I-J

Flflr. 2, Some experimental values of the angular distribution coefficient from the Al(n,y) At reaction are compared with the theoretical surves as a function of the relative contribution (a) of the reaction channels. The errors in a are obtained from a X"• analysis. The full (dashed) lines indicate con­structive ^destructive) interference. Here C •*• I refers to primary, and (C+)I •> If to secondary transitions.

- 26 -

The tern betveen brackets is strongly dependent on the position of the

transition; it includes effects due to undetected gamma-rays preceding

tbe one under consideration. If brute-force polarization is applied,

it is not necessary to take tens into account depending on f^CI^i

which is extremely small compared to f.(I ). Only in some cases fod»)

may be of interest.

The angular dependence of the circular polarization P of gamma radiation

emitted by unoriented nuclei after capture of polarized neutrons is

given by:

P (8) - AJ° + A ] ° fj(S) cos 9. (2.2)

Again the preceding unobserved gamma transitions may influence the ~J0

coefficient A strongly.

The A parameters depend on the capture cross section and the partial ~00

radiation widths of the transitions. Dividing them by AQ gives the

normalized coefficients:

k k k k A ' 2 _ r I 2.-00 (2 3 )

\ " \ /A0 * ( }

To elucidate the interference effects in primary and secondary transitions,

the relevant parameters are shown in fig» 2 for target spin 5/2 as a function

of a, the fraction of a transition originating from the reaction channel

with spin 3. Explicit formulae of the A-coefficients are derived in

chapter 1. It is obvious that the interference effects become smaller

for secondary gamma-rays compared to the preceding primary transitions.

3. Experimental arrangements

A detailed description of the equipment used for the nuclear orientation

experiment can be found in ref. 17. A sample with dimensions 3

22 x 22 x 30 mm was cut from a single crystal of aluminium. A single

crystal was chosen because of its high purity. In order to reduce

possible eddy current heating in the target, five cuts perpendicular to

the neutron beam were made with a fine saw. In the top of the sample

a threaded hole was drilled to facilitate a direct and stiff connection

- 27 -

with the mixing chamber of the He- Me dilution refrigerator which was

basically the same as described in ref. 20.

The target was irradiated by a Bragg reflected neutron beam. During

the time of the reported experiment the neutron diffraction set-up 29)

contained a set of Heussler crystals of the composition Cu MnAl with 3

dimensions 20 x 20 x 7 mm . With the existing fixed diffraction angle

of 37 the first order diffracted neutrons had an energy of 17.5 meV.

However, a considerabl' amount of second order neutrons of 70 meV reduced

the neutron beam polarization from close to 100Z to about 65%. A r.f.

spin-flip device wee used to reverse the polarization of the first

order neutrons; the s>ins of the second order neutrons rotate over

only 90 and hence for our purpose, may be considered as fully depolarized.

The guide-field system, which keeps the neutrons polarized between the

diffraction set-up and the low temperature equipment , has been

extended. Especially the region close to the magnet is crucial since

the fringing field tends to depolarize the neutrons.

In addition to the system, described in ref. 21, another set of weak-

iron rings (14 cm long, 8 cm and 10 cm inner and outer diameter) was

installed, adjacent to the former ones, to remove the field reversal

region away from the neutron beam.

Even with the central field of the magnet at its maximum value (5 T),

it was possible to run the magnet without a noticeable reduction of

neutron polarization.

3 Gamma-ray spectra were recorded with two 50 cm Ge(Li) detectors, one

located in the direction 9 - 0 and the other at 8 « 90 with respect

to the orientation axis.

The temperature of the sample was about 35 mK and the heat-load

prevented to reach a lower temperature. The degree of polarization of 27 Al was of the order of 10% at this temperature. In addition spectra

were accumulated at A K, thus with essentially unoriented nuclei.

3i2i_Circular_£olarization_feX£eriment

A description of the experimental arrangement can be found in ref. 3.

Larger gamma-ray polarimeters were installed, consisting of cylinders

of permendur, 8 cm long and 6 cm in diameter. They were magnetized

with the aid of simple coils wound from thin copper tape. The direction

of neutron polarization was switched every 100 a with the aid of twisted

00 CM

ftxW?

- S

4x10*

ï IXIO3-

O

- 1 •

- 2<

- 3 -

- 4 -

amo*-

TÜ(n. >flu 8-0 t f - t l

wW**VfW^fv^

•trl

* * . - * « W ""in**"*'

' *T *'.£* •"*!•» J ' «6»' ^ ^ , • ^ » * S "

«••»»»*

25 ao 38 4 0 4 5 5.0

^#wVMy^ > »wV^%ir*Ki|#-*'*v-t*. ~ * » ~ w W ^ jrft»*.*K. *

'KW 11-11

Mil M

*?b *<*»

i OA e.o • 8 7.0

— 1 — »

E>«W«

Fig*. 3. Gamma-ray spectrum from a polarized aluminium target, measured parallel to the orientation axis (0=0), The upper parts show the difference in intensity at 35 mK between the situations with parallel (+*) and antiparallel (+*) spins of the nuclei and the neutrons respectively. The lower parts are the single spect*>a measured at 4 K with essentially no nuclear polarization.

5X10*

' , I , , " A K n . ^ , e = 9 0 | f . , ,

- 9-

-10

3*»*-

2

1 -

UW*-

1 -

2

3

4

3X10*

J

W*1. S fe^l^fe " ^ =5 . v - - ^ _ „ v . •o?"1 ?Sli'

,*& • — » —

29 — i —

ao - 1 — as - i —

4.0 — I — 45

- 1 — 90

° - * < > ^ ^ ^ ^ *** II

,*W.VlM<»*vlv>»<*J>**-A' •

IxS

J.

M i l

»« »* f « > T r t , • * „ ^ ? « i S5 . « .» .' % * ?£* .?•*

?Sr«> — i — 99

— I — «0

— I —

u — I — 7.0

~ i — 7.9

Ek(NtaV)

Fig. 4. Nuclear orientation spectra from a •polarized aluminium target, measured perpendicular to the orientation axis (Q=90).

ISJ

I 1 I

4

3

0

• a-

«mo*

10

• <

• <

4 .

2 •

4 .

0

WxlO*

^ i V ! . ^ ^

OtftafwiM fljMctrain •>»(«. y*i

>4-

x

Sum spectrum

X •"f"]*»1 « i t

i t

,'•?• ÜT 1Ï - •^5" 4J6

— I - -

80

>*vt

Diffofortoo •p#etfufn

,••. J"j 'i^Vv-'-'-TV.^ U . V * Y * H V . A V ^ f c ^ ' v

M i l

Sum apactrum

•"•.a • » * ' • » * > ? ~°e

&a «o i

as - 1 — 7.0

~ i — 7.S EjSMtf)

Fly. £. Circular polarization spectrum from an aluminium targett irradiated by polarised neutrons. The sign of the effect corresponds with the eign of the circular polarization.

- 31 -

guide field coils. Spectra were accumulated on magnetic disk for the two

directions of polarization.

4. Analysis

4.l^_Nuclgar_orientation

The spectra, measured parallel and perpendicular to the orientation

axis, are shown in fig. 3 and fig. 4; these spectiu were obtained by

summing 25 runs, each of one day length. The unnormalized intensities

1(6) were obtained by fitting a skewed gaussian curve to the gamma-ray

peaks.

Using eq. (2.1) and eq. (2.3) the relative intensity difference e(8)

of the spectra obtained with a polarized neutron beam and an oriented

target, with respect to the unpolarized situation, is given by:

W . (6) - W (8) .,

•»» - p « (.7—*'£,<sw unp

CAJ1 f1(S)f,(It) + A°2 i2Ut>3 ?2 (cos 8). (4.1)

The intensities of the unpolarized spectra I (6) must be carefully

normalized to the intensities I , (8). This was performed with the aid pol

of the strong Ti-lines at 6.76, 6.42, 1.59 and 1.38 MeV from a thin

titanium foil, placed in front of the aluminium target. Then the relative

difference e(9) is related to the measured intensities by:

W . (6) I , (8)

unp N unp

where C„ is the normalization constant.

N

The values of the orientation parameters i\(It) and f o ( 0 can be

calculated from the temperature of the target. This temperature was

monitored with th« aid of a carbon Speer resistor attached to the

mixing chamber, and with the nuclear orientation thermometers CoCo 54

and MnPe mounted to the bottom side of the sample. These temperature

measurements are mutually consistent within the experimental errors.

The neutron polarization of the initial beam was measured to be 0.65.

From the experimental differences e(9), measured for the polarization

- 32 -

of the neutron beam and target parallel and antiparallel respectively,

at the two angles 9 = 0 and 9 • 90 , it is possible to arrive at

values for A , A and A , which are given in table 1. As an illustration

the data for some levels are shown in fig. 2.

4i2i_Circular_golarization

In fig. 5 the sum and differer •: of the circular polarization spectra,

recorded for 6 = 0 and 6 = 180 , are displayed for one detector. To

determine the peak contents the following procedure was used.

For each peak a skewed gattssian curve was fitted to the sum of the

spectra. Then a fit was performed to the difference of those spectra

while the tailing, the f.w.h.m. and the position of the peaks were taken

over from the sum spectrum. This approach is allowed if the peak para­

meters in both spectra are equal within the errors, as was checked to be

the case. In this way the errors in the asymmetries originating from the

fitting procedure, are suppressed appreciably.

32 The 5.42 MeV (1/2^3/2) transition of the S(n,y) reaction was employed

in a separate run for calibration purposes. This determines the only

free parameter in the formula which gives the energy dependence of the 22)

sensitivity for circular polarization of the polanmeter . The 23)

usefulness of this technique has been proved in earlier experiments

The resulting A values are listed in table 1.

2 4i3i_Method_of_^_-anal^sis

2 . . . The spin assignments are based on a X -analysis in which the measured

values (table 1) were compared with the theoretical coefficients as a

function of the free parameter a. If the feeding of a level occurs via

one gamma transition only, which is the case for all negative parity 28

states in Al above 3 MeV, also the available data from the deexciting 2

gamma-rays are included in the same x -calculation. This is permitted

since the feeding is within the errors equal to, or exceeds the de-

exciting intensity. Because also intensities do*., to 0.02% have been

claimed it is very improbable that important side feedings of those

levels are missed.

The errors in a are obtained from the relation ' :

- 33 -

Table 1: Angular distribution coefficients for gamna transitions in Al

E X (keV)

0

31

972

1014

1623 C )

2139

2273

3296

3465

3591

3876

3936

4691

4765

E Y (keV)

7725

7695

941

2131 b )

1014

983

1623

1592

6102

2139

2108

5586

2273 b )

4428

3465

4260

3591

2577

4133

3876

2256

3850

3790

4691

4660

3034

4765

4734

2626

2960

A11 n u

-0.89 +

0.43

-0.39

1.07

-0.08

-0.06

-0.10

0.05

-0.05

-0.66

-0.64

0.47

0.18

0.02

0.58

0.67

-0.05

0.16

-0.05

-0.96

-0.16

-0.54

1.42

0.31

0.56

C.32

-0.27

-0.87

-0.21

-1.21

0.11

0.21

0.64

0.76

0.17

0.22

0.20

0.51

0.31

0.22

0.19

0.62

0.31

0.49

0.12

0.13

O.II

0.21

0.10

0.34

0.90

0.31

0.74

0.13

0.23

0.13

0.47

0.16

0.29

0.19

"z i.

-0.31 +

0.44

-0.76

0.15

0.27

0.02

0.24

-0.26

-0.42

-0.73

-0.02

1.31

-0.02

0.66

0.20

0.16

-0.22

-0.53

0.04

-0.11

0.46

-0.57

-0.78

-0.69

0.41

0.04

0.22

0.02

-0.14

0.17

0.11

0.29

0.61

0.99

0.20

0.25

0.22

0.76

0.41

0.27

0.18

0.84

0.36

0.68

0.14

0.14

0.13

0.29

0.12

0.34

0.88

0.38

0.86

0.17

0.29

0.16

0.55

0.17

0.39

0.20

A 0 2 A2

0.0 +

-0.5

2.8

-0.2

-0.7

-0.4

0.6

-0.6

0.5

-0.4

0.0

-0.5

-0.3

a)

0.5

0.9

0.9

1.0

0.8

0.6

0.7

0.6

0.6

0.7

0.8

0.8

0.8

*!° 1

0.85 +

0.78

-0.31

0.64

0.61

-0.48

0.15

-0.56

-0.07

-0.32

0.19

0.56

-0.30

0.39

-0.10

-0.15

0.03

0.07

0.10

0.23

0.07

0.05

0.09

0.05

0.17

0.12

0.07

0.11

0.06

0.34

0.06

0.06

- 34 -

Table 1: Continued

E X (keV)

4903

5134

5443

5742

5798

5861

6200

6316

E Y (keV)

4903

2822

5134

2591

5411

3302

2283

1982

1927

1864

1525

6316

1409

A11 Ao

0.27 + 0.38

0.63 0.14

0.59 0.24

0.79 0.16

-0.24 0.76

-0.73 0.33

-1.16 0.20

-0.23 0.34

-0.14 0.28

1.32 0.65

0.22 0.30

0.64 0.19

0.91 0.21

A11 A2

0.18 + 0.53

0.21 0.16

-0.46 0.28

-0.74 0.21

0.46 1.11

-0.05 0.36

0.24 0.21

-0.03 0.44

0.62 0.35

0.31 0.83

-0.66 0.31

-0.29 0.22

0.22 0.19

02 a) A2

-1.0 + 0.7

-0.4 1.0

-1.6 1.0

-1.3 1.0

-0.4 1.0

1.8 0.7

A10 Al

0.31 + 0.12

0.33 0.09

0.02 0.16

0.00 0.37

0.87 0.13

a) Only values with errors ^ 1.0 are considered.

b) Doubts exist where this transition should be placed in the level

scheme (see ref. 19).

c) Unresolved doublet at E - 1.62 MeV.

- 35 -

2 2

Here XL1v determines the error interval, X^TM *S t n e «minimum value of

the x -distribution, F is called the statistical F- or Fisher function,

and n is the number of degrees of freedom.

5. Discussion of the results

Spin values have been excluded if their probability in the present

analysis is less than 0.1Z. For a probability less than 5Z the values

are placed between brackets. The final conclusions about the spin 25)

values, obtained from a combination of the known data and the

present work, are listed in table 2 and shown in fig. 6.

The intensity weighted contribution of the reaction channel with spin 3

to the capture process is EI a /EI « 0.47. The summation EI over the Y Y Y Y

primary transitions adds up to 83% of the total capture strength.

The ground state

From the reported experiments spin 3 is concluded. This is in agreement

with (d,p) and (d,ot) reaction experiments ; spin 3 is also strongly

suggested by a (6,Y) circular polarization correlation measurement

The deviation of the circular polarization parameter A. by more than 3) 5 standard deviations from the earlier obtained value 0.68 + 0.02 is

not fully understood. An underestimation of the error or a contribution

of the unpolarized aluminium background gamma radiation may be the cause.

A comparison for other transitions is not possible because of the lack

of accuracy in the earlier experiment.

Since the statistics is very good for this transition, a search for

uiultipole mixing is carried out. If quadrupole radiation is only

allowed to occur in the reaction channel with spin 2, which gives the 2

strongest contribution, the multi-dimensional x 'analysis yields

o - 0.15 + O.n* and 6_ - 0.00 • 0.14. Taking mixing in both channels

into account, the result is ct • 0.15 + 0.08, 6, • 0.0 +0.3 and

6, - 0.0 + 0.6.

- 36 -

no Table 2: Channel spin mixing ratios and spins in * Al

E X keV

0

31

1014

1623

2139

3296

3465

3591

3876

3S36

4691

4765

4903

5134

5443

5742

5798

5861

6200

6316

a) a

c 0.15+0.02

c 0.99+0.03

0.54+0.08 c )

0.53+0.11 c )

0.21+0.08 d )

1.00+0.13 e )

1.00

d 0.56+0.05

d 0.20+0.15

1.0 +0.5

d 0.82+0.05

0.00+0.01

d 0.12+0.03

d 0.85+0.12

1.0

1.00+0.05

0.50+0.17

J* b)

literature

3+

2+

3+

2+(3+)

+ 2

3*

4~

3~

2"

2+

(2,3)"

1

2"

3"

(1,2)"

(0-2)"

J

present work

3

2 (3)

2,3(1,4) e )

2(3) e )

2,3,4(1)

4

3

2,3

2,3,4

3

2

3

(3)

(4)

3

2,3,(1)

2,3(1,4)

2,(3)

2,3,4

3(2,4)

(4)

final conclusion

+ 3

2+

3+

2+(3+)

2+

+ 3

4~

3"

2~

2+

3"

2~

2",4"

3"

2"d")

2,30,4)

2~

2,3,4

3(2,4)

(4) 1

- 37 -

Table 2: Continued

a) Constructive and destructive interference are indicated by c and d

respectively.

The value a - c 0.99 + 0.03 denotes the regions c 0.96 -»• c 1.00 and

d 1.00 -»• d 0.98 since the values at « = c 1.00 and a * d 1.00 are

b) See ref. 25.

c) This a value is an average for all feeding cascades obtained from

100% of the de-excitation.

d) This a value is an average for all feeding cascades obtained from

93% of the de-excitation.

e) Obtained from the primary transition to this level.

- 38

Vi

tl?

6316 6200

5742

5442

5134

4903 4765 4691

3936 3976

3591 3465

3296

2139

1014 972

31

'AUn

- r

!

_!!_

5£

8 8!

m

"Al Fig. 6. Partial decay scheme of *'°Al.

(4) 3(24

hm nu

r r r-

?

rirj

£

- 39 -

The level at 31 keV

The data indicate spin 2 for this level though spin 3 cannor be completely

excluded. However, the very strong de-excitation from the 972 keV J = 0 25)

state to this level makes spin 3 very unlikely . Spin 2 is confirmed

by (d,p) and (d,a) experiments * . Hence we accept spin 2 as the

only possible assignment.

The spin values of the ground- and first excited state have been used

in the analysis for all other levels.

The levels at 3465 keV* 3591 keV and 5134 keV

The unique spin values from the present experiments confirm the results

.P) 28)

from the combination of (d,p) and (d,ct) data ' ' with the recommended

upper limits for the decay

The level at 4691 keV

From the present data the spin value 3 can be assigned uniquely to this

level. For this spin value a search for quadrupole admixtures in the

feeding [6_(3034) and 6.(3034)] and de-exciting transitions (6(4691) and

6(4660)) is carried out, yielding two solutions:

a - 0.78 + 0.07 and a - 0.78 + 0.07

|62(3034)l - 0.2 + 0.7 |fi2(3034)| > 4

|63(3034)| - 0.0 + 0.2 |«3(3034)| - 3.1^

|6(469I)| - 0 . 0 + 0 . 1 |6(469I)| -0.0 +0.1

|5(4660)| -0.0 + 0.2 |<5(4660)| - 3.14;

The first solution gives no evidence for quadrupole admixture and the

second solution can be rejected because the M2-strength of the 4660 keV 28)

transition exceeds the recommended upper limit by an order of magnitude.

The level at 4903 keV

The analysis yields 3 and 4 as possible values for the spin of this

level but the probabilities are lower than 51. From (d,p) and (d,a) 4 6) -

reactions ' it follows that this state has spin 2 or 4 . With the 3 . . . ( He,p) reaction a L * 1 transfer is measured which restricts the spin value to 2 . But in the last work the resolution allows no distinction

- 40 -

between the levels at 4903 keV and 4928 keV. Therefore doubts about the

spin of the 4903 keV level seem justified.

The level at 6316 keV

The only possible spin value is 4 but the probability is again lower

than 5%. According to ref. I and ref. 2 an appreciable part of the feeding

is missed. This may strongly influence the distribution of the 6316 keV

transition.

6. Conclusion

In a completely model-independent way and without any a priori assumptions 28

it is possible to assign five spin values uniquely to levels in Al.

Furthermore several restrictions on the spin values are obtained. In

addition» the fractions of the gamma-ray transitions are determined which

originate from the reaction channels with spin 2 and 3.

Both channels contribute about equally to the total capture cross section.

No significant quadrupole admixture has been found in the present

investigation.

References

1) A.F.H. Ishaq, A.H. Colebrander and T.J. Kennett, Can. J. Phys.

50 (1972) 2845.

2) R. Hardell, S.O. Idetjarn and H. Ahlgren, Nucl. Phys. A126 (1969)

392.

3) F. Stecher-Rasmussen, K. Abrahams and J. Kopecky, Nucl. Phys.

A181 (1972) 225.

4) T.P.G. Carola and J.G. v.d. Baan, Nucl. Phys. A173 (1971) 414.

5) R.R. Betts, H.T. Fortune and D.J. Pullen, Phys. Rev. C £ (1974) 589.

6) D.O. Boerma, W. Griiebler, V. König, P.A. Schmelzbach and R. Risler,

Nucl. Phys. A270 (1976) 15.

7) F.A. El-Akad, S, Backe, T. Holtbekk, F. Ingebretsen and J. Rek»tad,

Nucl. Phys. A283 (1977) 12.

8) F. Meurders, P.W.M. Glaudemans, J.F.A. van Hienen and G.A. Timmer,

Z. Physik A276 (1976) 113.

F.E.H. van Eijkern, thesis (1976) State University Utrecht.

- 41 -

9) H.A. Tolhoek and J.A.M. Cox, Physica ^8 (1952) 357.

10) K. Alder, Helv. Phys. Acta 25 (1952) 235.

11) H.A. Tolhoek and J.A.M. Cox, Physica _19. (1953) 101.

12) J.A.M. Cox and S.R. de Groot, Physica \± (1953) 683.

13) Chr.D. Hartogh, H.A. Tolhoek and S.R. de Groot, Physica 20 (1954)

1310.

14) S.R. de Groot, H.A. Tolhoek and W.J. Huiskamp, in Alpha-, Beta-

and Ganma Ray Spectroscopy, ed. K. Siegbahn, vol. 2 (Morth-Holland

Publ. Comp., Amsterdam, 1974) p. 1199.

15) A.J. Ferguson, Angular Correlation Methods in Gamma Ray spectroscopy

(North-Holland Publ. Comp., Amsterdam 1965).

16) R.D. Gill, Gamma Ray Angular Correlations (Academic Press,

New York 1975).

17) J.J. Bosman and H. Postma, Nucl. Instr. Meth. _U8 (1978) 331.

18) H. Postma and E.R. Reddingius, Physica 34 (1967) 541.

19) H. Postma and J.F.M. Potters, Physica 45 (1969) 559.

20) J. Mellema and H. Postma, Nucl. Phys. A154 (1970) 385.

21) J.J. Bosman, thesis (1976) State University Leiden.

22) H. Schopper, Nucl. Instr. _3 (1958) 158.

23) J. Kopecky, private communication.

24) A.N. James, P.J. Twin and P.A. Butter, Nucl. Instr. Meth. 115

(1974) 105.

25) P.M. Endt and C. v.d. Leun, Nucl. Phys A310 (1978) 1.

26) L.G. Mann and S.D. Bloom, Phys. Rev. J^9 (1965) B540.

27) P.G. Ikossi, A.M. McDonald and J.A. Kuehner, Nucl. Phys. A297

(1978) 1.

28) P.M. Endt and C. v.d. Leun, Nucl. Phys A235 (1974) 27.

29) A. Delapalme, J. Schweizer, G. Couderchon and R. Perrier de la Bathie,

Nucl. Instr. Meth. 95 (1971) 589.

- 42 -

CHAPTER III

A STUDY OF THE 55Mn(n,y)56Mn AND 55Mn(n,7)56«n REACTIONS

I. Introduction

56. About two hundred levels in Mn have been established by means of neutron 1,2)

capture gamma-ray spectroscopy . Gamma-ray anisotropics from

neutron capture in an aligned target yielded several restrictions on 3) the spin values . Such restrictions also followed from experiments on

the degree of circular polarization of gamma-rays, emitted after polarized 4) neutron capture . Parities have been obtained from the orbital angular

3 momentum transfer in the (d,p), ( He.p) and (d,a) reactions.

In the present investigation 65 gamma-ray transitions were studied by

polarized neutron capture in polarized nuclei and by measuring the degree

of circular polarization after capture of polarized neutrons in an

unpolarized target. In order to define the symbols, various possibilities

for the spins that are involved in s-wave neutron capture are shown in

fig. 1.

Ic=2.3

c c eg

Fig. 1. Spins involved in the Mn(n,y) Mn reaction.

2. Experiments

The experimental procedure and the analysis are in general described in

chapter 2. Therefore only details, specific for the present work on

manganese,will be given here.

- 43 -

2.I. Nuclear orientation

As a target material MnSb was chosen for two reasons: firstly it is

ferromagnetic and secondly the radiative capture of neutrons in anti­

mony does not contaminate the gamma-ray spectra. A polycristalline

cylindrical sample of MnSb (22 mm in diameter and 13 mm thick) was cooled

to about 40 mK. Thermal contact was achieved with a copper ring (13 mm

wide, 1 mm wall thickness) clamped around the target with Apiezon-N grease

between the sample and the copper.

The NiAs structure of the sample was verified by x-ray diffraction.

The derived lattice parameters a • 4.127(1)A and c - 5.785(2)A are in

good agreement with ref. 5 and ref. 6.

It has been found previously that at 77 R the magnetization of a small

MnSb single crystal is saturated in magnetic fields larger than 0.3 T.

Hence, it may be assumed that at 40 mK and for fields of a few tesla the

electron spin polarization is almost complete. However, it was found that

with the maximum field of 5 T still some depolarization of the neutrons

occured. It should be noted that the polarization of the transmitted beam

is very sensitive co small deviations from perfect magnetization, as

follows from the theoretical considerations in ref. 12.

As a result the polarization of the neutron beam was reduced from 0.65

to about 0.50. The temperature was monitored with a crlibrated carbon

Speer resistor attached to the mixing chamber and with the nuclear

orientation thermometers CoCo and MnFe attached to the bottom side

of the sample. These measurements indicated internally consistently a

temperature of 40 mK.

The magnetic hyperfine field is measured to be 24.5 T on the Mn nuclei 8)

in MnSb . As will be shown below, the sign of this field is negative.

After subtracting the external field of 5 T a nuclear polarization of

0.27 at 40 mK is calculated in good agreement with the capture gamma-ray

results reported furtheron in this chapter.

With the neutron counter, positioned "down-stream" behind the target* a

transmission effect

T N +N

was measured to change from -0.013 to +0.002 if the sample was cooled

We thank dr. B. Knook of the Kamerlingh Onnes Laboratory in Leiden for the preparation of the MnSb sample.

A i W t "**tn(n, jl^Mn e*o

* \^^/,AA^V^VW^N\VA

• IA

I J

4-

»

2 —

lilO*

a-

^ ' M , . , V W Is.W*' A55^=«^^-f^fe^.'

M

0- i-v**» jtff^Mr^fi^*^/^»^

11-11

x w

A#T \ , ...X

44 so

1 1-1 1

"-y^ "rt»»Li ' •** Il J» I ' J I H T " S'

t *J V tam

X

A ?VlT SA • 0 &S 7.0 E t OMA

spectra measured at 4 K with essentially no nuclear polarization

-1.1P-

4x«F

"On (n, |/*Mn e=9o

, ^ 4 ^ ^

w\u " ^ v u VA UW J^JögÖL ^L^Srid^J^ fi X

E)(MtoV)

Fig-, 3. Nuclear orientation spectra from a polarized manganese target, measured perpendicular to the orientation axis (8=90J.

2x10*

1 "j different* apactrum

"MndS.^rMn

"| dlffaranca apactrum ( f i

2x10'- ,•

1-5 J u rn «pactrum

* -5! a. fi 1.5x10*-

/ i . _ _ , ' P°°*A«io«" MM 5«3 s l l r

-/ V

4.0 45 5.0

.5

0-

- . 5 -

- 1

15x10*

1.

.5

0

'W*>'V /^rv^wv^^^^ # ^ ^ W V W l^p*^\^^A , ^ - A M "

diffstonc* spectrum \ ;"V v * J y'

tan A

• •04

>' ' A.

uu' I Tim- ' raw' , I i fl ; ' M M

' i I • ; / ' " • • » • f , «t04,J , J <J \ - v__ 71 I WO'

L „ A « W

mm apactnan

55 ao — i —

&5 — T 7.0

Fin. 4. Circular polarization spectrum from a manganese target, irradiated by polarizeu neutrons. The sign of the effects corresponds with the sign of the circular polarization.

EiWWfl

Table 1: Angular distribution coefficients for gamma transitions in Mn

E

(keV)

0

26

110

212

341

486

716

1166

1240

1509

E

(keV)

7270

7244

7160

7058

212

6929

314

6783

459

354

274

271

231

6429

6104

6031

5761

A

-0.83

-0.87

-1.03

0.71

-0.10

0.33

-0.55

-0.93

-0.32

-0.9

-0.92

-0.99

0.4

11 lo

+ 0.16

0.09

0.10

0.10

0.07

0.11

0.08

0.16

0.17

0.9

0.15

0.15

0.6

A

-0.16

0.33

-0.34

0.10

0.11

-0.83

-0.03

-0.25

-0.23

-0.1

0.82

-0.48

0.5

11 2

± 0.29

0.07

0.08

0.11

0.08

0.18

0.09

0.28

0.19

0.6

0.12

0.21

0.9

A

-0.6

-0.7

0.8

0.5

0.5

0.1

1.2

-0.5

-0.5

-3.3

-0.3

02 L2

+ 0.7

0.3

0.3

0.3

0.3

0.5

0.4

0.6

0.7

1.0

0.6

A02 A2 ref. 3

-0.06 + 0.14

-0.93 0.09

0.93 0.11

0.16 0.07

0.51 0.05

-0.21 0.13

0.04 0.08

0.82 0.11

0.8 0.5

0.38 0.05

0.6 0.5

0.93 0.21

-0.21 0.23

A10

0.29 +

0.051

-0.50

-0.44

0.80

-0.01

-0.5

-0.55

1.4

0.8

0.04

0.011

0.03

0.03

0.07

0.05

0.3

0.06

0.4

0.4

A10 Al ref. 4

0.40 + 0.05

0.04 0.02

-0.46 0.04

-0.45 0.04

0.56 0.08

0.04 0.08

-0.23 0.19

-0.55 0.11

-0.2 0.3

0.67 0.11

Table 1: Continued

(keV)

1743

1833

-

1866

2016

2071

2089

2202

2235

2255

2300

E Y (keV)

5527

5437

5433

5404

5254

5199

2045

5182

2063

5068

2177

5036

5015

4970

A11 A0

-0.09

-1.0

0.6

-0.1

-0.8

-0.70

-0.70

-1.14

-1.01

-0.98

-0.3

-0.54

+ 0.10

0.6

0.5

0.5

0.3

0.13

0.10

0.17

0.12

0.29

0.3

0.09

A11 A2

0.72

0.0

0.5

0.03

0.08

0.10

-0.39

0.2

0.9

-0.45

+ 0.15

0.8

0.5

0.16

0.10

0.23

0.16

0.3

0.4

0.08

A02 A2

-0.6 + 0.5

-0.5 0.6

-0.5 0.4

0.3 0.7

0.1 0.4

-0.4 0.9

0.05 0.29

A02 A2 ref. 3

-0.78 + 0.10

>0.1 0.4

-1.3 0.4

-0.03 0.10

0.93 0.18

0.04 0.07

A

0.70

-1.2

-0.40

-0.8

-0.63

-0.08

-0.19

-0.59

1.00

1.02

-0.3

10 1

+ 0.05

0.3

0.21

0.3

0.20

0.13

0.03

0.06

0.23

0.08

0.6

A10 Al ref. 4

0.56 + 0.04

f-0.02 0.17

-0.57 0.20

-0.3 0.2

-0.1 0.07

-0.32 0.07

1.0 0.2

0.81 0.06

Table 1: Continued

E X (k«V)

2321

2362

2395

2441

2545

2626

2704

2720

2824

3002

3047

3291

E Y (keV)

4949

2321

2295

2211

4908

4875

4829

2331

4725

4644

4567

4551

4446

4269

4223

3979

A11 A0

0.8 + 0.4

-0.3 0.6

-1.17 0.23

-0.93 0.22

0.3 0.5

-1.07 0.24

-1.18 0.17

-0.57 0.23

-1.1 0.4

-1.01 0.19

0.04 0.27

-0.9 0.5

-0.6 0.3

A11 A2

0.6 • 0.8

0.2 1.0

0.44 0.23

0.20 0.27

1.6 0.9

0.4 0.5

-0.01 0.27

0.1 -0.4

-0.4 0.9

-0.10 0.26

0.4 0.5

0.1 0.9

-0.9 0.6

A02

2

0.2 + 0.7

-1.5 0.7

-0.2 1.0

-0.2 0.9

-0.2 0.7

-1.3 0.6

A02 A2 ref. 3

-1.5 + 0.4

0.26 0.23

0.44 0.22

A ; ° I

-0.25 + 0.09

0.68 0.21

0.96 0.30

0.46 0.13

-0.13 0.07

0.17 0.24

-0.33 0.09

0.15 0.20

0.04 0.27

0.4 0.4

0.4 0.4

1.2 0.5

A!° i

ref. 4

-0.06 • 0.19

-0.15 0.09

-0.63 0.19

0.04 0.13

Table 1: Continued

E X (keV)

3455

3628

3689

3771

3861

4841

-

E > (keV)

3815

3642

3627

3581

3499

3409

4841

2090

A " Ao

-0.5 + 0.4

-0.51 0.26

-0.2 0.5

-0.5 0.5

0.2 0.3

-0.89 0.12

-0.6 0.4

A H

A2

0.1 + 0.7

-0.6 0.4

1.2 1.0

-0.7 0.8

0.4 0.?

0.36 0.14

0.1 0.7

A02 A2

-0.7 0.5

A02 A2 ref. 3

10 A«

0.8 + 0.8

-0.6 0.4

-0.03 0.07

-0.41 0.24

A10 Al ref. 4

- 51 -

from 4 K to 40 mK. Here N..(N ) is the count rate obtained for (anti) TT tt

parallel spins of the neutrons and nuclei.

As a consequence it follows that the neutron flux, integrated over the

sample, is different for these two situations. It is shown in chapter 2

that the gamma-ray anisotropics e(6) are related to the measured intensities

by: W .(9) - W (9) I ,(e)

e(9) = _E°1 H22 PQl , K ' W (9) CHI (9) '•

unp N unp

Here the normalization constant CN is determined with the aid of the

strong Ti-lines at 6.76, 6.42, 1.59 and 1.38 MeV from a titanium foil

placed in front of the MnSb sample. But to this constant C„ a different N

correction must be applied for parallel and antiparallel spins because

of the transmission effect: i n(e) if+(e)

S t ( 6 ) = C UI (6) ' ' and eT* ( 9 ) " C,XI (9) - '• TT unp ++ unp

in which C, » C„ and C,,» (1+6)C„. It was measured that 60 percent of TT N T+ N

the neutrons is removed from the beam by the sample. Herewith the value

of 6 can be calculated from the transmission effect.

The spectra measure parallel (9-0°) and perpendicular (9"90 ; to the

orientation axis are shown in fig. 2 and fig. 3. Taking all these

considerations into account it is possible to derive the values for

A , A and A_ , listed in table 1, from the experimental data.

2i2i_Circular_golarization

With a sample of 20 g manganese flakes contained in a thin walled

aluminium cylinder the same experimental procedure was followed as has

been described in chapter 2. In fig. 4 the sum and difference of the

circular polarization spectra, recorded for 9-0 and 9-180 are dis­

played. The resulting values for A. are given in table 1.

3. Results in terms of the decay scheme and spins

3iili_Gamma;rax_s£ectrosco£y_

In general fair agreement is observed between the previously found 1 2 3) gamma-ray energies and intensies ' ' and the present work.

However, a remarkable feature in the low energy spectra is the weakness

of the gamma-rays transitions of 2017 keV and 2024 keV.

- 52 -

20O.7

Fig. 5. The strongest gamut-ray transitions near 2 MeV from neutron

capture by manganese.

In cable 2 the intensit ies , claimed in ref. 1, are compared with the

present work after a calibration on the 2045 keV transition.

Table 2: Some gamma-ray intensities of transitions near 2 MeV

E Y

(keV)

1988

2017

2024

2045

2063

2090

I I Y Y ref. 1 and ref. 2 this work photons per 100 captures

2.74

3.36

1.11

2.10

1.41

0.94

1.11

0.20

0.09

(2.10 calibration)

1.34

0.87

If the gamma lines at 2017 keV and 2024 keV belong to Mn, they are at

least a factor 10 weaker than claimed previously.

02 In table I the A- values of

listed together with their present values and the values for A''and A''

In table I the A, values of ref. 3 and the A. values of ref. 4 are ' 11 . JI

53 -

7

If possible» the weighted average was used in the present x -analysis

unless otherwise stated below. Spin values are excluded in this

analysis if their probability is less than 0.1Z. The results are given

in table 3.

For probabilities less than 5Z the values are placed between brackets.

The intensity-weighted contribution of the reaction channel with siin 3

to the capture cross-section is EI a 111 • 0.29. The summation £1 over y y y y

the nrimary transitions adds up to 67Z of the total capture strength.

If the assigned spins froa ref.3 and ref. 4 are compared with the present

ones, it should be kept in mind that before 1973 the possibility of co­

herent interference between the reaction amplitudes with different channel

spin has been disregarded. Moreover the early assignments are partly based 9)

on resonance (n,y) experiments , from which the relative contribution

of those amplitudes (a-values) has been derived.

These predictions of the spin admixtures are reasonably good, as shown

in table 3, but have led to one erroneous conclusion.

The levels at E = 0, 26, 110, 341, 486, 1166 and 1743 keV

From the data of the primary transitions the following unique spin

values are assigned respectively: 3, 2, 1, 3, 3, 1, 2.

The level at E„ = 212 keV x

The analysis of the data for the primary transition yields spin 4 if 10 2

the A values are not averaged. Otherwise the x value does not reach

the 5Z limit. This may be caused by a small admixture of a transition

to the 215 keV level which cannot be resolved from the main transition.

The level at E = 2255 keV x 2

Taking all available data into account, no solution in the x -analysis

could be obtained for this level. Omitting the previously determination

A value results in a unique spin value 3. The a value, derived by

Auchampaugh and the A value that was measured by Stecher-Rasmussen

et.al. have formerly led to an assignment of spin 2 for this level.

However, this conclusion is untenable in view of our new and more

extended data on the A-coefficients.

- 54 -

Table 3: Channel spin mixing ratios and spins in " Mn

E X

0

26

110

212

341

486

1166

1509

1743

2016

2071

2089

2203

2232

2255

2321

2362

2395

2441

2545

2626

2704

2720

2824

3002

a

0.000+0.003

c 0.025+0.003

0

1

c 0.74 +0.08

d 0.050+0.012

0

c 0.40 +0.06

d 0.117+0.015

0

c 0.52 +0.13

c 0.34 +0.05

d 0.001+0.007

c 0.10 +0.07

d 0.12 +0.03

d 0.80 +0.17

a calc. ref. 9

0.025

0.17

0

> 0.80

0.43

0.45

< 0.24

0.38

0

0.58

J

present work

3

2

1

4

3

3

1

2,3

2

2,3

2,3

3

1

2(3)

3

2

2,3

2,3

2

2(3)

2,3(1)

2,3

2(3)

2,3

2,3(1)

•n J

ref. 2

3+

2+

1 +

4+

2+,3+

2+,3+

1 +

2+,3+

2+

2+

-

2~,3~

1

2+,3+

2+

2~,3"

-

-

1+,2+,3*

(D+or(2)

2~,3~

2+,4+

-

2+,3+

2",3"

J

final conclusion

+ 3

2+

1 +

4+

3+

3+

1 +

2+,3+

2+

2+

2,3

3~

1

2+(3+)

3+

2~

2,3

2,3

2+

2+(3+)

2",3"

2+,3*

2(3)

2+,3+

2", 3"

- 55 -

Table 3: Continued

E X

3455

3628

3689

3771

3861

a a

calc. ref. S

J

present work

1,2,3(4)

2,3(1)

1,2,3

2,3,4

2,3

J*

ref. 2

-

-

-

-

(2~,3~)

TT J

final conclusion

1,2,3(4)

2,3(1)

1,2,3

2,3,4

2", 3"

- 56 -

The levels at Ex = 2089, 2203, 2321 and 2441 keV

The spin values 3, I, 2 and 2 respectively were obtained by conbining

the data of the primary and secondary transitions.

The level at £. = 2704 keV x

With the previous A and A values ' the x -analysis yielded no

spin with a probability higher than 5Z. Disregarding those data results

in an assignment 2,3,

4. The hyperfine field on Mn nuclei in the compound MnSb

From 0-decay of Cr the spin value of the 110 keV level was established

as 1 and therefore a primary dipole transition to this level pro­

ceeds only through the reaction channel with spin I„ « 2. In such a case

the capture cross-section is larger for antiparallel than for parallel

polarized nuclei and neutrons. Since the direction of the external

magnetic field and the neutron polarization are known, the negative sign

of the hyperfine field on the Mn nuclei in MnSb can be extracted directly

from the gamma-ray intensities. This agrees with the negative sign in

MnBi, which has also a NiAs structure n ) . The result is understood in

view of the predominating contribution of the polarized core electrons

to the hyperfine field in these manganese compounds.

5. Conclusions

56 Spin values could uniquely be assigned to 13 levels in Mn. Several

restrictions were obtained for other states. For 16 primary transitions

the relative contribution of the reaction channel with spin 3 could

be determined. Finally the sign of the magnetic hyperfine field at the

Mn nuclei was established as being negative in MnSb.

References

1) A.H. Colenbrander and T.J. Kennett, Can. J. Fhys. 5J3 (1975) 236.

2) Nuclear Data Sheets, 20 (1977).

3) J. Mellema and H. Postma, Nucl. Phys. AI54 (1970) 385.

4) F, Stecher-Rasmussen, J. Kopecky, K. Abrahams and W. Ratynski,

Nucl. Phys. A181 (1972) 250.

5) I. Teramoto and A.M.J.G. van Run, J. Phys. Chem. Solids 29_ (1968)

347.

6) W.J. Takei, D.E. Cox and G. Shirane, Fhys. Rev. J29 (1963) 2008.

- 57 -

7) H. Ido, J. Phys. Soc. Japan 25 (1968) 625.

8) J. Bouwma and C. Haas, Phys. Stat. Sol. B56 (1973) 299.

9) G.F. Auchaapaugh, UCRL-50504 (1968) Lawrence Livermore Laboratory.

10) B.J. Dropesky, A.W. Schardt and T.T. Schuil, Nucl. Phys. J^ (I960)

357.

11) T. Hihara and Y. Koi, J. Phys. Cos. Japan 29 (1970) 343.

12) 0. Halpern and T. Holstein, Phys. Rev. 59 (1941) 960.

- 58 -

This investigation treats the angular dependence of the intensity and

of the circular polarization of gamma-radiation, that is emitted after

capture of polarized neutrons by polarized and unpolarized targets•

In chapter I we have discussed the interference effects between the

(n,y)-reaction amplitudes with different channel spin, in particular now

this effect propagates into the secondary gamma-ray transitions. Also, the

angular distribution coefficients are calculated in case mixing of di-

pole and quadrupole radiation occurs. Further, we have indicated how

the influence of p-wave capture stay be taken into account.

In the next chapter the first successful (n,y) experiment with brute-force

polarized nuclei is described.

The nuclear orientation experiments on aluminium yield the values of

the angular distribution coefficients of primary and secondary gamma-ray

transitions. By a measurement of the degree of circular polarization an

additional coefficient is obtained. The values of these coefficients

depend on the spin of the excited level in the final nucleus and on the

parameter a which denotes Cue fraction of a gamma-ray transition that

originates from the reaction channel with the highest possible spin. 2

By a x -analysis five spin values are assigned uniquely and several

ct-values are determined.

Many experiments have been carried out on nuclides in the s-d shell

region. But only very recently some spin values are assigned to negative 28

parity states in Al between 3 and 5 MeV excitation energy by combining

the results from (d,p) and (a,a) work with lifetime measurements. No

discrepancies occur with the present investigation.

In our analysis we have taken into account that the angular distribution

coefficients depend on the tnultipolarity of the gamma-ray transitions. So the

previously determined E2/M1 mixing ratio of the ground state transition

can be rejected. To give an impression of the attainable accuracy, upper

limits are set on the quadrupole admixture in the feeding and depopulating

transitions of the 469) keV level.

In chapter 3 the results of chapter I are applied to the experiments on

manganese. The degree of circular polarization of the gamma Tddiation

was determined with the (n,y) reaction and unpolarized nuclei. For the

nuclear orientation experiment a ferromagnetic MnSb sample was used to

- 59 -

polarize the manganese nuclei. The values for the A-coefficients re­

sulting from these measurements lead to a-values and unique spin

assignments for thirteen nuclear states in Mn.

For the spin assignments to four of these states information from

secondary transitions has been used. The previously assigned spin value

2 for the 5015 keV level is to be discarded in view of the present

experimental results which lead to the value 3.