Chemld Ph>slcs 74 (lQS3) 51-66

North-Holland Puhhshmg Comp.q

THE POLARIZATION DEPENDENCE OF TWO-PHOTON ABSORPTION RATES FOR RANDOMLY ORIENTED MOLECULES

Marco A C. NASCIMENTO

Reccned 17 May 19X2

1. Introduction

With the advent of powerful tunable lasers. multiphoton processes became a very important tool in the mvestlgation of atomic and molecular structure and properties_ Multiphoton processes are now being used m high-resolution studies of excited states of atoms and molecules. laser ISO- tope separation, laser-induced fusion. gas breab- down, etc.

Two-photon processes that depend quadrati- cally on the light beam Intensity have been predtc- ted as early as 1931 by Gbppert-Mayer [l] Be- cause of their small cross section, they are very dlfflcult to observe with conventlonal light sources The first observation of a two-photon absorption process was made 22 years later by Brossel et al. [2] in the radio-frequency region of the spectrum The development of lasers opened the visible re- gion for the observation of two-photon processes [3-81 The number of applications increased rapidly. following the improvements in laser tech- nology, and sufficient material was produced to justify several reviews that appeared in the last ten years [9- 181.

In practice. most of the initial studies on two-

photon absorption processes used direct absorp- tlon e\penmcnts [S. 191 and fluorescrncc detection e\psrlmsnts [4.20-27]_ More recrntl>_ t\\o-photon resonance multIphoton Ionization spsctroscopv (MPI) [X-31] has been used to detect r\cit& states of atoms and molecules. particularl! by Johnson and co-xxoorhers [26-291 and Parker et al and Berg et al. [30]. AlPI has rccentl! been re- vle\\ed by PJrher et ,tl. [31]

One of the most mterestmg features of t\\o- photon spectroscop) 1s the possibiht! of identifl- cation of the nature of the excited state from polarlzatlon studies. OLanJer [X] considered the polarization dependence m Raman scattering b? crystals. T\\o-photon absorption b> c~srals \\as considered by lnous and To>oza\\a [33] and also by Badsr and Gold [S-I] For r.mdoml\ orxntcd

molecules the pioneer \\orl; \\ds done by Monson and McClam [3J.36] \\ho dsrixsd an s\prssslon for the axeraged transltion rate and sho\\rd how to distinguish states of dlffercnt symmetries using .m appropriarc combmatlon of photons \~ith different polanzatlons. The effects of molecular rotation were considered b\ Bra> and Hochstrasser [37]. More recently. Michl and Thulstrup [38] presented 3 thsoc for the t\\o-photon absorption by par-

0301-0104/83/0000-0000/$03.00 0 1983 North-Holland

52 M A C Na.wtnmro / The polan:olron dependence of IH o -phoron absorpflou rater

t~ally onented molecules Resonance effects have been examined by Fujimura and Lm, and three- photon processes by Friedrich [39]

The present work may be consldered as a mod- Ificatton and extension of the Monson and Mc- Clam work (351 We used a different averaging procedure and a different process to obtain the tensor patterns This approach can be easily ex- tended to higher-order processes without assump- tions about the nature of the Initial state. Work in thts direction IS tn progress. Perturbation theory IS assumed to be valid since. as dlscussed by Lambropoulus [ 161. II should provide correct re- sults for photon fluxes up to IO”’ photons/cm’ s (Typical fluxes for focused dye lasers are of the order of 10” photons/cm’ s )

2. The mo-photon absorption transition rate

Wtth the advent of tunable dye lasers. most of the experiments m multlphoton spectroscopy are being performed m the single-beam regime. That is. both photons have the same energy and polari- zat1on. Consequently_ our derivation will assume identical photons.

The two-photon transition rate for excitation of a molecule from initial state 11) to fmal state If) in the dipole approximation is given by

T,, = (277)“tlcu’( h~)‘F’g(2h~)ln~,,l’. (1)

where hv is the energy of the mcldent photons, F IS

the photon flux (in photons/cm’ s). and M,, is the second-order matrix element,

M,, = C(fle’*rlk)(kle^.ril)/( EL, - h)_ (2) I.

In eq. (1). g(2lrv) represents the hne-shape func- tion normalized over the absorption band.

J g(llp) d(kY)= 1. (3)

In eq. (2). the summation mdex runs over all intermediate states and the energy E,, is relative to the initial state Ii}.

If the initial and/or the final states are degener- ate, there will be a transition matrix element con- necting each of the two elements of both mani- folds. Eq. (2) can be re\\ritten in a more general form as

where a and /3 are the degrees of degeneracy of

states If) and 11). Our mam concern m this paper IS to analyze eq.

(2) in terms of the symmetries of the states in- volved in the transition under the assumption that the sample molecules are randomly oriented

3. The averaged transition rate

To obtain an averaged transition rate that 1s apphcable to the case of randomly oriented molecules, we introduce in eq. (2) the vectors e’ and r, expressed relative to the molecular coordmate system,

r=xP+yj+ zr;, (5)

t?=li+n$+ni, (6)

where 1. m. and n are the direction cosines of the polanzation vector. Eq. (2) can be rewrttten as

A$,=~(f~xl+yn~ +znlk)(X-)xl+ynz+~,zjl)/(E,, -hv). (7) h

Defining the transition matrix elements

(7) becomes

Ml, = 1’0,. i- tnb, , + m=u,, + 2( Itno,, + Itq; + mu,,) _

It is important to bear in mmd that when degeneracy IS present there ~~1111 be one term Me (9) connectmg to any two components of If) and I[). To make the notation easier. \\e will 01 .din the aLerage for one such term and at the end of the process, we will generalize It for degenerate zases In terms of eq. (3). the averaged transltion rate can be written as

where Av, represents the average over all possible onentations of the molecule rslatne to the laboratory- fIxed axis. When 1 f > and/or 11) are degenerate. each term of the summation in (4) IS averaged separately. The quantities a,, are the components of a second-rank tensor.

In the above analysis, the polarization P is expressed in terms of the molecular coordmate system (m terms of I, tn. tz). We must now express 1. III, and tz with respect to the laboratory coordinate system. Starting with vector P expressed relative to the molecular coordmate s)<tem. we perform the followmg sequence of counterclockwtse rotations (+, 0. and I$ are the Euler angles):

(a) Rotation by an angle Q about the E axIs_ (_x_ J _ -_) + (A ,_ J~_ -_ ) (b) Rotation by an angle 6 about the s, axis. (X,-J 1_ -_) + (s2_ J,. -_-) (c) Rotation by an angle # about the zz axis such that the fmal system comcides ~lth the laborator>-flxed

axis. (X2, _V?. II) + (X’, y’. z’)_ Denoting the overall transformation above as T. then 7. the Inverse of T. ~111 represent the transformation from the laboratory coordinate system to the molecular coordmate system Wrltmg the polarization e^ as

i?= (Z’*iuj’)/(l +~)l’~.

where CI is the ellipticity, the 1. IN. II are obtained from

1 ( 1 1

nr =i(l + a2)-‘/2

i i

fia t1 0

(11)

(12)

Using the explicit form of -?- [40] leads then to

c0~~co~~-cosf?sin~sin~-~la(sin1;cos~tcos~cosocos+)

cos~sin++-cos8cos~sm~-iin(sin~smo-cos8cos~cos&) (13)

sinBsin#+iasinBcos#

Introducmg m eq. (9) the values of 1. m. and tt from (13). one obtams the transltion moment in terms of 8. 9, and J$, M,J#, 9, +)_ The fmal averaged transition rate is given by

(7,) = c j$Gj?d4jOn sin @ff,(o.4. 4) dfl I

j,'"d+j~"d#~,' sin tId0 -

Integrating (14) and taking care of possible degeneracles. one obtains

(14)

54 MA 12 N,ZXCIWVI~O / The polarmm~n dependence of IWO-phomi ahsorprro~r ram

The particular cases of linearly and circularly polarized radiation can be obtained from (15) by setting u = 0 and LJ= 1 respectively.

(16)

(17)

At this point it is convenient to introduce the polarlzarron rat:0 fi?_ defmed as the ratlo of the averaged transitIon rate for crrcularly polarized light over that for linearly polarized lrght.

fi = (T,,IJ(T,,,>r- (18)

As has been shown by Monson and McClain [35] and as will be dlscussed in the sectlon 4. the measurement of Q allows one to determine whether the transition mvolves a change in symmetry_ Using eqs. (16) and (17) we obtam

52 = (2r + 6s + 2r)/(31- + 4s + 2r), (19)

where

These quantities r, s, and 1. are related to the SF. S,, and sir of Monson and McClain [35] for two identical photons by the relations

6,=ri-21. &,=li,=r+Zs

4. The determination of the tensor patterns

Given the wavefunctlons for the system. one could compute the transition matrix elements a,, and thereby obtam the transltion rate 7 and the polarlzauon ratio 0. However. the quest& here is what conditions are placed on D solely by the symmetnes of the mltial and fmal states, mdepen- dent of the specifics of the individual state? That IL we wish to exploit the use of group theory m evaluatmg 52. This 1s valuable because it can be turned around so as to use an experimental de- termination of I2 to help assign the symmetry of the transitlon Early work m this directlon was done by Monson and McClain [35] assuming a totally symmetric imtial state.

The quantities a,, are the components of a second-rank tensor and they determme a property of the system. namely. 7,. Because of that. the tensor has two kmds of symmetry properties The first one is due to an mtrmsic symmetry deriving from the nature of the property itself. For exam- ple, the tensor u defines the probability of absorp- tion of two identical photons. Since two photons of the same energy and polarization are indls- tmguishable. the tensor CI has to be symmetric. The second kind of symmetry is due to the geometric symmetry of the system, and that will determine which of the tensor components have to be zero.

Our procedure is based on the following three observations-

(a) The quantities a,, are the components of a

symmetric second-rank tensor. Therefore they transform exactly like the product of any two coordinates s. J’. z (or as combinations of prod- ucts). This lmphes that from now on one can indlstinguishably use u,, or x’, 0,: or ~2, etc.

(b) The tensor pattern is a property of the states involved in the transition and IS solely de- termined by the symmetry of states II> and If). the intermediate virtual states jk) playing no role at all.

(c) The transition rate, T,,. is a property of the molecule and should be invariant to any symmetry operation of the molecular point group. This ml- plies that the tensor pattern is such that it will only contain products of any two coordinates (s. J. z) or combinations of these. that form a basis for the totally symmetric representation of the group

With these facts m mmd. the construction of the tensor patterns can be easily performed in three steps:

(a) Take the direct product (or symmetric prod- uct If 11) and If) belong to the same degenerate representation) of the representations to which states 11) and If) belong, r, X r,= r’.

(b) From the character table obtain the prod- ucts of any two coordinates (x. ) _ z) or combina- tlons of these products that form a basis for r,_

(c) See how these products can be recombmed with the operators x2. _x_v. etc.. so as to generate the combination that forms a basis for the totally symmetric representation of the group.

What may appear to be a very awkward proce- dure 1s. in realtty. a very simple one. a mere exercise of consultmg character tables. And a quick look at a character table ~111 reveal that there are not many different combmatlons of two-coordl- nate products that form the bases for the Irreduci- ble representations of the point groups. This means that many of the tensors will be equal and that we only have to work out a few of them.

To demonstrate how simple this procedure cdn be. we will determine the tensor patterns associ- ated with four different transitions. The examples were chosen to point out different situations that can occur in the process. As a first example we take a transition between two states that transform like the totally symmetric representation of the Czh point group. The direct product r, contams only

A+ and a looh at the character table shows that .X ‘. .,-_ 2 and _\_I are the bases for the A, representa- tion_ Therefore these are the only non-vanishing components of the tensor for this transition. Ths tensor pattern is sho\\n in table l(b)_ but. of course. for an> other non-degenerate and equal- symmetry states \\e ha\e r, = A,. which nnplirs the same tensor pattern This example sho\\s that for any point group the tensor pattern for a transi- tion involvmg two states that belong to the same non-degenerate representation are equal. As d scc- ond example \\e examine the transitions betlxeern states that belong to the A and B, representations = of the &, point group.

Consider first the A, c, A= transition. For this case I-, = A, and from the character table one sees that -1’ +_r’ and z’ are bases for this representa- non. implying that only diagonal terms ~111 be present. But. since -1’ goes into-1 ’ for some of the symmetry operations_ the only wa) of hsepmg the tensor imariant 1s to take the _I’ component equal to the J ’ compcnent. u, , = (J,, _ The tensor pattern for this transitlon 1s sho\\n m table 2 (II&. For the A, c-, Br transition. rs = B,_ and in this case _x’ - _I ’ and _XJ form the basis for r Following the same = argument as abole. the tensor mLVariance forces us to niahe u,, = - u,,. The _~_t component is also present because (_4,1\) IB.J_x_~ )) transforms l&e A, ( X’J’ IS also a basis for _40) The tensor pattern for this trdnsltlon 1s sho\\n m table 2 (Mb). As a third example. consider the transltlon be- tween t\\o states that transform hhe the A,, and El, representations of the Dhh group Fo; this tra&tlon rs = E,. and the character table shows that (sz. _I=) form d basis for this representation_ From eq. (4) one hno\\s that the transition mo- ment has two parts. and each one has associated with it d tensor pattern. In this case \\e do not need to invohe the mvarlance of each tensor ssp- arately but only of the sum of the tensors. In other words. it is the sum of the t\\o parts of the transition moment that has to be imariant and not each part itself. As the prelious cases. it is eas) to see that the first part has. for mstance. the sz component and the second part the J z component_ and that

56 M A C h’asrrrneoro / The polarrzmon drpendence oj mo-phorort absorprron mfcs

1 .lblc 1

Twwphoron tensor I;.nlrrns for nhehm groups

Pomt gmup\

(h) I 0.. -.t 0

0 I. 08, 0

0 0 a,, I

(C)

i 0 (I,, 0 0-n 0 0 0 0 0 i

(0 ( 0 0 *=‘-. 0 0 0 0.: 0 0 i

Cl C, A-A A,-4 <I

Au- Au

C. C, A'-A A-A A” n A” B-B

A’- A’

D2 4-A BI - BI B2 - B2

B, - B,

A-B

c,, Al-A, AZ-A,

BI - BI B2 - B2

c 2h

As-A& Bb - Bg Au-A, Bu - B,

<I

hnBe 3/2

Au-B,

A -B, A,- A, A, - B,, %-B3 B,-B2 B ls - Bx,

Au - B,, B zu - bu

A - BZ AI-B, A, - %g 4 - B3 AZ-B2 B ,g - B,g

Au - Bzu B I” - B,,

<I

3/2

312

A - B, A,-% A, - J%s 312 B, - Bz AZ- B2 B 16 - kg

Au - B>u B lu - BL,

transforms hke A,,. The tensor pattern for this transmon is shown in table 2 (Wb). As a final

case rg = A, + A, + Ba + Bg. and one could think of this as the four parts of the transition moment

example, we exanune the transitton between two states that belong to the same doubly degenerate representation E, of the C,, point group. In this

[eq. (4)]_ But this is not correct. If one looks in terms of the basis (xz. yz), one sees that from the possrble combinattons generated by (xz, yz) x

(sz. vr). only three are hnearly independent. which mlplies that thts product can only generate a basis for a three-dimensional representanon The stan- dard way of removing this kind of degeneracy IS to take the symmetric product [Es X EJ instead of the direct product of the representattons [41] When this is done, we obtain that [ZYs] = A, + Bs + Bs_ The antisymmetric product {Es X Es}. will contain the other As component. The transrtron moment has now three parts. which can be viewed as three different transttions A, - A, and A - Bg twrce. But the tensor pattern for these tr&sttions has already been obtained in the second example above. The fmal tensor pattern for the E, - E, transition is shown in table 2 (IId).

Tables 1 and 2 show the results of thts andlqsts for all transrtrons mvolvmg any two states of the 32 symmetry point groups

Once the tensor patterns have been determmed. we return to the more interesting problem of de- termining 52 and what kind of mformatton can be obtamed from It.

5. The polarization ratio (52)

The last columns of tables 1 and 2 show the result of applymg the defmitions of D and r. s. I to the tensor patterns obtained in the last section. Most of the results are straightforward. but here again, some examples can be used to tllustrate drfferent situattons that occur in the process. The first point to be nottced is that the tensors ob- tained in the last sectton can always be put in a diagonal form. The components ~111. of course. change values, but neither (I-,,) nor D cdn change. Their values cannot depend on the imtral chotce of orientanon of the molecule_

As a first example, tf we apply the definition of 52 for transitions between any two states of the same symmetry. for point groups C,, C,. C,. CZ_ and C,,, we obtain 0 <O-G 2, usmg the tensor patterns m table 1. But, if we transform the tensor to a diagonal form, we see that the range of Q IS. tn fact, much smaller, 1-e. 52 < 1. The question that may now be raised is why not diagonalize them all? In fact, this could be used to check the correct- ness of the results. The reader can easily check

that. for example. for the A, c+ B, transttion m C2,, of A, * Bg in D,, or any other transition rep- resented by a non-diagonal tensor. that the valur of Q IS invarrant. On the other hand. whenever the result of stratghtforward application of the tensor pattern furnishes a range of values for 52. the diagonaltzation wtll consistantly reduce the range of values for I;?.

When dealing with degenerate states. tt :s ml- portant to consider that one cnn elctte to any one of Its components or to a state formed by d superposition of the two components. but that the final value for Q has to be the same. Suppose. for instance_ the A c-f E transitron for .I molcculc that belongs to the C, point group_ One cdn hale a transrtton to the state that transforms hke (_\’ - _I ‘_ _YJ) or to the state (s-_._t=) or to a lmear combma- tion of these. The reader can east& check using the appropriate tensors m table 2 (lb) that (a) for ths A ++ E(x’ -_L ‘. _\_I ) trdnsltton one gets r = la:,. s=cz . and I= -a,‘,. and (b) for the A f--t E(_c~~Lz) transition one gets r = 0. s = u,‘, + u%t_ and r = 0. Applying eq. (19). one obtams $2 = 3/Z for both cases.

6. Discussion and applications

If one examines the results III tables 1 and 2. one clrarlj sees that the measurement of !? allo\vs us. tn some cdscs. to determine the ndturc of the excited state tf the irutlal state 1s bnovvn If the molecule belongs to a lo\v-s>mmetq pomt group (such as C,. C,. C,,. C:. S,. C;,. Dj_ D,,). the measurement of -r? determines unrquil ocall> the symmetry of the excited state. XS the s~nnnetr> increases. $2 still can pro\tde some informatton but_ depending on tts value. the state assignment is not unique. This IS the case of the trdnsltron

A?? -If) m ths D 2h group. for instance_ A value of 2 less than 1 ~111 assrgn If) as -4%. but If Q = 3/2_ we have three different posstbiltties for If). namely. B,,. B2s. and B,,. In this case 2 IS useful in eliminatmg Ar AS a possible assrgnmsnt for If). but more information is needed to char- acterize If).

AS one mo\es up to highl_v symmetrrc groups. such as T. T,. TJ. 0. and 0,. the two-photon

58 &I A C. Nascmenro / The polarrzafron dependence of IH o - photon absorprron rates

x V V

- V

t-4 l-4

,\ ,\

d

o- 0 0 :

000 --

00 e-

00 0

-I- -

d 0 0

0 00

‘f 000

0; 0 0

0 6 3

i-

000

: 0 00

I

: 000

+

0 o- 0

00 d

00 0

+

d 0 0

0 00

0 0 6 - +

0 0 6:

0 6 0

_

0 0 o-

0 00

000 + -

V

w I w

303

E 3 0

V

M A C Nascmenro / The polarr:nrron dependence of hl o -phoron absorpnon rares

V I x x

V

% =

z > 3 = >

+ - 000

M A C Nascmenro / The polanzarron dependence of 18% o - phoron absorprron raws 61

% E 54

7 5

P a g n

8 s

3 = f > 3

62 MA C Nammenro / The polar~arron dependence of fwo-phorot~ absorprlott rules

x V

r-4

2 I 3

W

t w

l- t

l-

- 555

000

I

0 PO :

000

+

0 6 0

00 d:

E +

+ T,

E +

. T

2

forh

idd

al

(IX

h)

s3fr

K

35 (

lk)

(IX

C)

sam

e as

( V

h)

\”

SJ

\‘-

WJ

-f-l,

+, T

I, T

zp -

Tzg

T

mu +

, I-

1,

T 2u

a+

T

2u

E,

+,

TI,

E,

+,

T2g

Eu

- T

,,

Eu

- T

2,

Cl 31

2

absorption process becomes more selecltve For any molecule belonging to one of these groups. transItIons between two states that transform hke

the torally synmelric representation of the group wll only occur with hnearly polarized hght. One w.~y of interpretmg this result is to assume that these states have almost spherlcal symmetry. In that way one could look at this transltion as being equivalent to an s ---) s transition tn a central fteld. where total angular momentum IS a good quantum number. Then, because of conservation of angular momentum, s + s transItIons can only occur with hnearly polarized light.

The maln results of this work can be sum- marized in terms of three rules for determmmg Sz.

(a) For any transItIon involvmg two states that transform like the same Irreducible representation of a point group, 52 < 1.

(b) Exceptions to rule (a) are found in T. Td. T,, 0. and 0,, groups for which A L-, A gives G! = 0 and E c, E gives D = 24/3 i.

(c) For any transItIons mvolvmg two states that transform hke two different lrreduclble representa- tions of the point group. $2 = 3/2

Tables 1 and 2 also show the forbidden transi- tions for all the symmetry point groups. How do these results compare with the experimental data available? Two-photon spectroscopy 1s a relattvely new field. but some apphcatlons have been re- ported m the literature, making use of the polari- zation ratlo L? to investtgate the nature of the excited state. It is interesting to notice that in the

pioneer works of Monson and McClam [35] and McClam [36]. the authors did not make use of 52 Because the experiments were conducted with pho- tons from different beams, a parttcular choice of

two dtfferent polarizations could be used to dts- tmguish between states of different symmetry In a smgle-beam regime, only L? gtves thts kind of information. Table 3 shows experimental values of D compared with the ones predicted by theory. The results are tn agreement with the above rules

Among the several Interesting problems that can be analyzed with two-photon spectroscopy, the relative ordermg of the low-lymg excited states of lmear polyenes is a very attractive one. Some work on these compounds has already been re- ported in the hterature [29-31,42-441, but some further analysis would be helpful to support the results of some recent calculations that put the X’A,o2’A, transltlons m trans-butadlene and trans-hexatriene at 7.06 and 5.87 eV respectively

WI Before concluding this section, It is important

to emphasize that all the results were obtamed neglecting molecular rotation. In the case of the multlphoton expenments, this IS equivalent to as- suming that the ionization from the two-photon state is lower than the orientation relaxation of the excited molecules. When rotation is Included, it can be shown that the same results apply for the whole rotational envelope and for rig- Q branch

alone [37]

Table 3

TKlnSlI1oI-l D (observed)

A, - E,, (3s) In benzene 13-17 A, -. A, m I-aza-blcyclo [2 2.21 octane 0 030-O 038 A, - B, (3s) m trans-butadlene 14-16 A, + A,(3p,) m trans-hexalnene 0 25-O 4 A,(na,)- A, (3s) in p>ndme 07-09

A, - Ag(3s) in p,razme 06-07 A, + E m methyl-iodme 15

Q (predIcted)

I5 Cl

15-1 c 1 h’ cl

Cl I5

Rcf

[28.31]

[311 [311 [30 461 t31.471

I311 I481

A’ -. A’ (n)-3s m acetaldehjde 0 02-O 77 <I 0 08-O 8 Cl

a1 Calculated to be 1.50 from exphclt evaluation of the o,, usmg the wavefunctIons of ref [5 I] ” Calculated to be 0 47. see ref. 1521

I501 1491

A method was presented for the analysis of a two-photon absorption experiment In d single- beam regime that can be easily extended IO

higher-order processes wlthout any .Issumptlons regardmg the nature of the Initial state Some known results were recovered [36] and some new ones presented The rdtto of the averaged trrmsi- tion rate for wcularly polarized hght to the one for linearly polarlred hght. s2. can be obtained from the followmg rules.

(a) For states of the same symmetry. Q c 1 (b) Exceptions to rule (a) are found m T, T,,.

T,,, 0, and 0, groups, where A ++ A glkes ti = 0 and E~EglvesQ=24/31.

(c) For states of different symmetry, Q = 3/2.

Acknowledgement

The author acknowledges Professor William A Goddard III for his interest in this work and for his hospitahty at Caltech, where this worb was completed. He also acknowledges Umversldnde Federal do Rio de Janeiro (UFRJ) for a leave of absence and Conselho National de Desenvolvl- mento Cientifico e TecnolQjco (CNPq) for fman- cial support.

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I31

(41

151 I61

I71

WI

[91

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(1963) 207. J J Hopfield. J M Warlock and K Parh. Ph>b Rr\ Letters 11 (1963) 414 J M Worloch. m Laser handbooh Vol Z eds ET Arecchl and E 0. Schulz-Dubols (North-Holland. Amsterdam, 1972) p 1323

[I] M Giipperi-Maler. Natutxtssenschaften 17 (1929) 932.

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