Forward asymmetry of the photoneutron angular distribution

Nuclear Physics 31 (1962) 53--64; ~ ) North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher

F O R W A R D A S Y M M E T R Y OF T H E P H O T O N E U T R O N

ANGULAR

DISTRIBUTION O. B O R E L L O t

F. F E R R E R O tt, R. M A L V A N O and A. M O L I N A R I

Istituto di Fisica dell'Universit& di Torino and

Istituto di Fisica Nucleate, Sezione di Torino Received 26 S e p t e m b e r 1961 An analysis is m a d e of the p r e s e n t e x p e r i m e n t a l d a t a on the fast p h o t o n e u t r o n a n g u l a r d i s t r i b u t i o n f r o m Bi 2°°. A sure indication of a conspicuous f o r w a r d a s y m m e t r y is found t h a t c a n n o t be explained on t h e basis of a n y available t h e o r y . Some indications are given for a possible e x p l a n a t i o n of tile a s y m m e t r i c t e r m . I n a p p e n d i x 2 some new d a t a are given of the fast p h o t o n e u t r o n a n g u l a r d i s t r i b u t i o n f r o m Bi 2°~, obtained using the AW (n, ~)Na 24 reaction as a detector.

Abstract:

1. I n t r o d u c t i o n

Present experimental knowledge on the photonucleon angular distributions lead to the following classification 1, ~.): (a) Neutrons: the low energy component of the energy spectrum shows an isotropic angular distribution. The fast neutron component is frequently anisotropic, but it preserves the symmetry around 90 ° . (b) Protons: although the experimental data are different from nucleus to nucleus, the angular distribution, besides an anisotropic behaviour, shows also an evident asymmetry around 90 ° with preference for the forward angles (the maximum of the angular distribution shifting towards 0 ~ 60 °, 70 °, where 0 is the angle between the incident photon and the emitted proton). The theoretical interpretation generally accepted of these experimental results is the following: (a) For neutrons the angular distribution of the low energy spectrum is clearly due to evaporation processes and can be understood on the statistical model of the nuclear reactions, which in fact predicts, particularly in the case of the photoreactions 3, 4), isotropic angular distribution if many final states can be reached b y the emitted particle. On the other hand the angular distribution of the fast neutron component can be understood on the basis of the direct interaction model. This model, if the t Fellow of the N a t i o n a l Council of R e s e a r c h of Brazil, on leave of absence f r o m the University of S. Paulo, Brazil. tt At p r e s e n t a t C.E.R.N., Geneva. 53

54

O. BORELLO et al.

possible transitions of the nucleon in the nucleus are of the electric dipole character, predicts an angular distribution W(O) of the type W(O) = A + B

sin e0.

(b) In the proton case the theory interprets the experimental data on the basis of the direct interaction model, also taking into account the interference between electric dipole and electric quadrupole transitions. It is interesting to observe that the good results obtained b y this theoretical approach, essentially due to the high effective quadrupole charge of the proton, are one of the most convincing arguments for the existence, in the giant resonance energy region, of other types of absorption than the electric dipole one. The aim of the present work is to point out the inconsistency of the accepted neutron angular distribution classification, b y showing the existence, at least in the case of Bi 2°9, of a clear forward asymmetry, and to prove that the theoretical interpretation of these experimental results cannot be made in the limits of a multipole interference phenomenon without the introduction of an absorption model more complicated than the direct interaction one. 2. Survey of the Experimental Results In the case of Bi 2°9, there are ten experimental investigations whose results are summarized in table 1. In this table we find, besides some indication of the experimental data of interest, like the bremsstrahlung maximum energy and the neutron detecting reaction (and thus its threshold energy), also the ratio B / A of the coefficients

of w(o). We have only taken into consideration those papers from which we could obtain complete information both about the experimental points and their errors and which could be compared with each other: in this way we have chosen ref. s) (case b) and ref. 7) (case g) with neutron threshold energy 3.5 MeV, and ref. ~) (cases e, f), ref. 9), ref. 10) (case n) and refs. 11,12) with neutron threshold energy ~ 5.5 MeV. The photoneutron angular distribution from Bi ~°9 recently measured at the neutron threshold energy of 8 MeV b y the Turin Laboratory is described in appendix 2 and included in the discussion. The number of experimental points in the quoted refs. is between three and nine. The best fit has been made using the following function: /(0) = ao+a 1 cos O+a 2 cos 20,

which is the Fourier analysis stopped at the third term t of the differential cross section. t The following simple relations exist between the coefficients of ](0) and W(O) = A + B s i n ~ 0 +

C cos O: ao+az=A,

--2a~ = B ,

al = C.

a

b c d

e f g

h i j

k

1 m n

o

p

q

5)

6)

7)

8)

9)

10)

11)

i~)

13)

P r e s e n t work

Case

Ref.

30

55

22

22

30 30 30

19

18.9 18.9 18.9

20 30 30

22 22 18

20

(MeV)

Maximum energy

A127(n, p ) N a 2~

Si~S(n, p)A128

nuclear emulsion

Si~S(n, p)A128

nuclear emulsion nuclear emulsion nuclear emulsion

nuclear emulsion

nuclear emulsion nuclear emulsion nuclear emulsion

Si~8(n, p)A12s Si28(n, p)A128 A12~(n, p)Mg ~7

Si~S(n, p)A12s A127(n, p)Mg 27 A127(n, p)Mg 27

Al~7(n, p ) M g 2.

Fast neutron detectors

TABLE 1

:>8

:>5.5

>5

_~5.5

2 < E~ < 4 < En ~ > 5

4 5

5 < E a < 11

~1.5 >4 >7

:>5.5 ~5.5 :>3.5

~5.5 :>3.5 :>3.5

:>3.5

(MeV)

Neutron energies E n

S u m m a r y of e x p e r i m e n t a l d a t a

sing0

+ 5 . 6 sinZ0 + 0 . 9 9 sin~0

+2.0

+0.4 +2.0 +2.1

sin~0 sin20 sin20

cos 0 cos 0

1

1

+1.1

+1.1

sin20+0.155cos0

sin20

symmetry 1 + 0 . 7 sin=0 0.83 4- 0.54 sin 20 + 0.12 cos 0

0 . 2 8 + 0 . 7 2 sin20 0.07 cos 0

1 1 1

1 + 0 . 9 sin20 0.504-0.50 sin~0+O.12 0.60+0.40 sin20+0.05

1 1

1

,4 + B s i n Z 0 + (C cos 0)

0.524-0.04

0.65+0.34 sin20+0.26

cos 0

a n g u l a r d i s t r i b u t i o n anisotropic a n d m a r k e d forward asymmetry

0.86+0.15

1.4 4-0.15

0.7 0.65

2.53

0.4 2.0 2.1

0.9 ± 0 . 1 1.0 4-0.1 0.674-0.1

5.6 0.994-0.1

2.0 4-0.5

B]A

e.a

56

o. BORELLO et al.

On making the best fit we have used the following criterion: in the case of more than three points the least square method has been used and in the case of only three points we have solved the system of three equations in the unknowns a0, al, a 2. The errors of the three coefficients have been calculated, in the first case, b y the least squares method ~4), in the second case using only the general error propagation formula, i.e., if .

=

then

a"2

\~Pff % +

\Spa/ %' where Pl, ib2 and P3 are the experimental values of W(O) at the angles 01, 02 and 03 and %1' %, and %, are the relative experimental errors. Table 2 shows the various/(0) deduced from the data of the different refs., together with the values of al/(ao+a2) which is a quantity directly comparable with theory. (See sect. 3). TABLE

2

Values of /(e) Refs.

Case

6) ~) ~) ~) 8) 10) 11) 18)

c g e f k n o p

Present work

N e u t r o n energy E n (MeV)

al ao + as

> 3.5 _>-- 3.5 _--> 5.5 => 5.5 5 < E n < 11 > 5 > 5.5 > 5 ~

/(0) = ao+a I cos O+a2 cos 20

0.354-0.07 0.054-0.03 0.234-0.06 0.14±0.11 1.1 4-3.00 0.354-0.18 --0.024-0.09 0.314-0.25

8

0.72+0.16 0.78+0.03 0 . 7 7 + 0.07 0.76+0.12 0.54+0.09 0.71+0.12 0.75--0.01 0.76+0.16

0.384-0.03

TABLE 3

(aa0_~)

E n

3.5 5.5 => 8

--0.26 --0.19 --0.23 --0.23 --0.46 --0.37 --0.22 --0.24

cos cos cos cos cos cos cos cos

20 20 20 20 20 20 20 20

0.82+0.26 cos 0 --0.17 cos 20

Values of the weighted m e a n for the ratio al/(ao+a,) N e u t r o n energy (Me V)

cos 0 cos 0 cos 0 cos 0 cos 0 cosO cos 0 cosO

mean

0.10±0.09 0.18±0.04 0.384-0.03

See *cote added iv proo] at the end of this p a p e r

F O R W A R D ASYMMETRY

57

Finally for each of the three groups of neutron energies the weighted means for the ratio al/(ao+a2) have been calculated, as shown in table 3 and plotted in fig. 1. O0~ O |

|

I

I

0.5

0,4

0.3

0,2

0. t

3.5

[ 5.5 Neutron

I 8 Energy

MeV Threshold

Fig. I. The weighted m e a n s of the ratio

al/(ao+a=).

3. D i s c u s s i o n The experimental evidence of the rather high forward asymmetry in the photoneutron angular distribution from Bi ~°9 enables us to exclude the possibility that the photon absorption would be only electric dipole in character. In fact the only asymmetry which we could have in this case is that resulting from the measurements being expressed in the laboratory system. But a short calculation shows that this is far too small to explain the experimental data *. It must be noted besides that the azimuthal angular distribution also provides an argument to exclude that the photon absorption would be only El. In fact one would have, if the photon beam is plane polarized 15), an anisotropic azimuthal distribution, while the experimental work of Goldemberg, Dyal and O'Connel for Bi 209 indicates a nearly isotropic behaviour 16). We shall try to interpret the experiments b y assuming, in the framework of the direct interaction model, that other multipoles than the electric dipole contribute to the photon absorption. t F r o m the relation tg 0 = sin O*](p+cos 0"), where 0 is the scattering angle in the l a b o r a t o r y s y s t e m , and 0* is t h a t in the b a r y c e n t r i c s y s t e m , we have, b y p u t t i n g 0* = ½~z, tg 0 = 1/p. I n o u r case we have

Then the m a x i m u m shift forward of the a n g u l a r distribution is 3'.

58

O. BORELLO et al.

Actually the differential cross section for (El/E2) absorption, when the interaction Hamiltonian between the electromagnetic field and the nucleus is .O)

- * - e"l gc

r-

0) 2

e2(¢ • r)(K

• r),

(I)

is given b y the following relation 18):

a(O) = a+b sin 2 0 + A cos O+B sin 2 0 cos 0.

(1')

Here, e1 and e2 are the neutron effective charge for the electric dipole and electric quadrupole absorption, o~ is the polarization vector of the photon and Kv is the incident photon wave number. The coefficients a, b, A and B are functions of the radial integrals and the phase shifts and their explicit expression can be found in ref. 17). Relation (1') is, however, quite different quantitatively for neutrons and protons; in fact the effective charge for electric quadrupole absorption is 2) een=

( 1 - - ~2+ ~ z) e

eet: = (Z /A 2)e

for protons, for neutrons.

For instance, in the case of Bi 2°9, the ratio between the effective charge for electric quadrupole absorption of neutrons and protons is approximately 2-10 -3. Because the neutron quadrupole effective charge is so small, also the coefficients A and B in relation (1') will be much smaller than a and b and the interference effect is consequently negligible. An effective calculation of the expression (A + ¼B)/a which is directly comparable with the experiment *, gives

A+¼B)

e~ (/+2)(9l+3)K,+~.

a(zZ+3)

K,+I'

(2)

where K,+ 1 and K,+ 2 are the radial overlap integrals for E1 and E2 transitions, respectively. The expression (2) is an upper limit deduced b y taking into account both the Pauli exclusion principle, forbidding the transitions 1l-+ 1 (l--l), and the destructive interference in the radial overlap integrals between shells with different principal quantum numbers, for which the transitions ll -+ 2 (l--1) are quite small. One should calculate the expression (2) for different shell model excitations and then sum the results. But, for the purpose of illustration, we limit ourselves to an evaluation of the quantity (2) assuming that the incident photon interacts * I t is enough to s h o w t h a t expanding eq. (1') in F o u r i e r series, s t o p p i n g at the third term, we get ai/(ao+a2) = ( A + J ; B ) / a .

FORWARD ASYMMETRY

59

only with the neutrons belonging to the 2f½ and 2f[ shells. In fact, as we can see from table 4 t the greatest number of fast neutrons, at least for E1 transitions, are those from the 2f shells. TABLE 4 Calculations for Bi2°9(Z = 83) transition

li

l~

e

S

T:n

F

N

l i ¥ -+ l j ¥

6

7

3.73

0.58

0.04

0.02

4.3

3p½ -+ 3d~

1

2

0.66

0.25

0.87

0.30

4.9

3 p | -> 3d t

1

2

1.2

0.25

0.87

0.30

90

2f t -> 2g~

3

4

1.7

0.37

0.55

0.22

13

2f| -+ 2g t

3

4

1.7

0.37

0.55

0.22

17.9

l h t -+ litt

5

6

3.2

0.56

0.14

0.07

12.5

The headings of the various c o l u m n s represent the initial (ll) and final (lt) a n g u l a r m o m e n t u m , t h e e n h a n c e m e n t factor e, the s t r e n g t h of the t r a n s i t i o n S, the t r a n s m i s s i o n of the centrifugal b a r r i e r Tzn, the fraction of escaping n e u t r o n s F and the n u m b e r of fast n e u t r o n s N.

The result, obtained by calculating the radial integrals for a square well potential of infinite depth, is

Z=3

about 10-3 smaller than the experimental one. It must be noted that the minus sign in (3), due to the opposite signs of the neutron electric dipole and electric quadrupole effective charges would shift the maximum of the neutron differential cross section in the opposite direction to the proton one, i.e. in the backward direction. This result, however, has been obtained by putting arbitrarily all phase shifts zero: therefore we cannot make any statement on this point, without a sufficient knowledge of the phase shifts for the nucleon elastic scattering by the final nucleus. Another kind of mechanism for the E2 interaction has been proposed by Sawicki 18). He assumes that the excited nucleon interacts with the surface oscillations of the nucleus and these in turn interact with the electromagnetic incident field through the nuclear quadrupole moment. However, this mechanism cannot explain the neutron forward asymmetry because the Bi 2°9 nuclear quadrupole moment is very small (40 • 10-24 cm2); on the other hand Sawicki's mechanism could probably be efficient in strongly deformed nuclei, like Tantalum. The table reported here, based on the "Wilkinson model, corrects some mistakes contained in ref. 7).

60

o. BORI~LLO et 0~.

Leaving out the (El/E2) interference as a possible explanation of the neutron forward asymmetry, in the direct interaction model, we consider now the interference between electric dipole and magnetic dipole transitions. Actually the magnetic dipole absorption for neutrons might be as large as for protons. However, we must introduce a spin orbit coupling term in the nuclear Hamiltonian: in fact, without it, the magnetic dipole transitions in a spherically symmetric potential are impossible, because the matrix elements between the initial and final states vanish, unless both states are degenerate. The differential cross section for (E 1/M 1) absorption is given by the following relation: ~(0) = ~ + $ cos 0 + ~ cos 20. (4) Here the interaction Hamiltonian between the electromagnetic field and the nucleus is - - *.col - e l g ' r + / ~ , x T~vl ; -e?~ - nc , (6~×K~.a) ] , c

(4')

where a is the neutron spin operator. The coefficients 0¢, 3 and ? are given in appendix 1. The expression fl/(o~+?), assuming again a square well potential of infinite depth and considering the transition li~---> l i ¥ , is given by 3 *¢+? - -

~

8(2/+1) A ?~cu,, R~ -= (9/~+11/+4i Z M c ~ Kz+ 1

0.05.

The radial overlap integral for M1 transitions R~ is calculated with the aid of the time-independent perturbation theory. We should evaluate the preceding expression for different possible shellmodel excitations, but the strengths of other magnetic dipole transitions are quite small in comparison with the predominant l i ¥ -+ li~ transition. A theoretical result has been obtained, therefore, by the introduction of (El/M1) interference which is not too far from the experimental data: but it must be observed that the energy separation between the l i ~ and li~t shells is of the order of 3-4 MeV within the limits of the independent particle model, while we detect fast neutrons with energy greater than 8 MeV and consequently the energy separation between the shells should be at least 16 MeV. 4.

Concluding

Remarks.

Recently Kul'chitskii and Presperin 19) investigated in some elements the angular distribution of neutrons of energy => 10 MeV produced by high energy bremsstrahlung (90 MeV). The angular distribution was found highly asymmetric, the photoneutrons peaking sharply iorward.

FORWARD ASYMMETRY"

61

The present critical work on the other hand states, in the case of Bi 2°9, the existence of a non-negligible forward asymmetry in the photoneutron angular distribution for low energy photons. Thus, the two results together allow the conclusion that the forward asymmetry is not peculiar to a particular photon energy region, even though there is some evidence that the magnitude of the forward asymmetry increases with neutron energy (and perhaps with bremsstrahlung energy). But, while the quasi-deuteron model provides a possible explanation of this effect in the high energy region, this is certainly not the case below 30 MeV. In view of the lack of any reliable experimental data on this point for other nuclei than Bi 2°9, it is not worthwhile to build up some more complicated interaction model for the explanation of the asymmetric term before making a systematic investigation on this point. However, the explanation is possible if the electric quadrupole effective charge of the neutron can be increased or if the energy differences between the shells in the nuclear structure are greater than those predicted by the shell model. Actually it seems difficult to allow for a greater energy separation between the shells due to a repulsive potential in the nuclear Hamiltonian. For instance, the particle-hole interaction mechanism proposed by Brown and Bolsterli 2o), which provides a conspicuous energy splitting in the case of electric dipole transitions, seems not to be useful in the magnetic dipole case, because of the lack of degeneracy in the transitions. On the contrary we believe that the increase of E2 neutron effective charge could be supported by the introduction of some correlations between the nucleons. We wish to thank Dr. R. Catolla Cavalcanti who kindly made the irradiations and Dr. S. Menardi for counting work. One of us (O. B) wishes to express her gratitude to Prof. G. Wataghin for his kind hospitality in the University of Turin.

Appendix 1 The coefficients ~, f l a n d ? in formula (4) are given by

o~ -- MKnc° I e~ [KL1(l-+-l)(31+2)+I~ ~ 1l(3l--1) ~c (4(2l+1) 2 --2l(l + l )Kz+lKz_l cos (51+1--(~l_1) fl --

M K n co eh l ~"-c ~ pnel 2 ~

1 MKn°~

- Y = - - ~ h" c

-{- \2Mc]

'

R*[K*-I cos (6,_1--6,)+K,+ 1 cos (~,+1--6~)~,

el 2

(2/+ 1) 2 {K~+I(l+ 1) (/+2) --K~_ll(l+ 1)--6/(l+ I)K,+IK,_ 1 cos (~/+1--(~/_1)},

o. BORELLO et al.

62

where M, Kn, /~n are the nucleon mass, wave number and magnetic moment. Further, Kz_l and Kz+1 are the radial overlap integrals for the electric dipole transitions and R~ is the radial overlap integral for magnetic dipole transitions. Finally, 6z-1 and 6~+1 are the phase shifts for the nucleon elastic scattering by the final nucleus. The foregoing relations are obtained using the well-known expression for differential cross sections 2~

-~-I(flH,ntli)12p(E) (photon flux) where H~nt is given by formula (4). The initial and final nucleons wave functions are those of the independent particle model with spin-orbit coupling.

Appendix 2 In the Turin laboratory, the neutron angular distribution from Bi 2°9 was studied 7) m a n y times, irradiating the Bi samples with ? rays of different maxim u m energies and using as fast neutron detectors the reactions SiZS(n, p)A12s and A127(n, p)Mg 27. After the irradiations, we measured the residual activities from A12s, which is a fl- emitter with half life of 2.30 min and from Mg27, which is a fl- emitter with half life of 9.5 min. In the case of the Si reaction, however, it was necessary to apply a correction of about 9 % to the results obtained at small angles ( < 30°), because the scattered photons from the Bi target are responsible for the reaction Si29(y, p)A1 *s. Therefore, it was interesting to obtain the neutron angular distribution without that correction 21), which is possible by using as neutron detector the reaction A127(n, ~)Na 2.. In fact, the scattered y cannot give any contribution because the threshold of the reaction A127(~, n2p)Na 24 is greater than 29 MeV, which was the maximum bremsstrahlung energy. The threshold of the neutron energy is about 8 MeV. In fig. 2 we have represented the Bi target, made of a cylinder of 1 cm radius and 10 cm height, which was conveniently cut to bring the centre of the fast neutron source into coincidence with the centre of the A1 detector circular distribution. The A1 samples were cylinders of 0.75 cm radius and 4 cm height and were distributed in a 5 cm radius circle at the angles 30 °, 60 °, 90 °, 120 ° and 150° . The ~, collimated beam was produced by a 31 MeV Betatron, and the Bi sample was at lm from the target. The system was conveniently screened with Pb and Fe.

6~

FORWARD ASYMMETRY

The F maximum energy was fixed at 29 MeV and the beam mean intensity was held at about 60 R/min during 10 h. I

(3 /

o o-•

j . ~ "

Fig. 2. D i a g r a m m a t i c representation of t h e Bi target.

'} AI (n,=) Si (n,p)

i

"',,

0.76+0.12 cos0-0.23 cos 20

f(e) "~.82+0.26cose

0.5

I

30

I

I

I

t

"0A7co$ 2(9

I

60 90 120 150 180 0 Fig. 3. The n e u t r o n angular distribution normalized a t 90 °.

As dose monitors, we used Cu disks detecting the reaction Cu65(~, n)Cu e~, the product Cu e4 being a fl+ emitter with 12.8 h half life. After the irradiations,

64

o. BORELLO e~ a~.

the A1 samples were introduced in the well of a NaI (T1) crystal, mounted in a 6292 P.M. and followed by conventional electronics. In order to reduce the background, the discriminator threshold was maintained at 0.8 MeV. The measurements were repeated without Bi to observe the neutron background, which, however, was only of few counts/min. The neutron angular distribution obtained and normalized at 90 ° is plotted in fig. 3. The same figure presents the values obtained in a previous work ~) (case f) with Si detectors.

Note added in proo[: After this paper was completed two extensive studies of the angular distribution of the fast photoneutrons have appeared, one by Baker and McNeil 22) and the other by Reinhardt and Whitehead*3). The average forward asymmetries worked out from these data are respectively: al/(ao+a~)----0.0824-0.008 (E n > 5.5, 22 MeV bremsstrahlung) and al/(ao+a~)= 0.114 4- 0.010 (En > 5.5, 55 MeV bremsstrahlung). References

1 2 3 4 5 6 7 8 9 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23)

V. de Sabbata, Nuovo Cim, 11 (1959) 225 S. Fujii and O. Sugimoto, Nuovo Cim. 12 (1959) 513 T. Ericson and V. Strutinsky, Nuclear Physics 8 (1958) 284 A. Molinari, Nuovo Cim. 18 (1960) 1298 H. L. Poss, Phys. Rev. 79 (1950) 539 G. A. Price, Phys. Rev. 93 (1954) 1279 F. Ferrero, O. A. Hanson, R. Malvano and C. Tribuno, Nuovo Cim. 4 (1956) G. N. Zatsepina, L. E. Lazareva and A. N. Pospelby, J E T P (Soviet Physics )5 (1957) 21 G.N. Zatsepina, V. V. Igonin, L. E. Lazareva and A. I. Lepestkin, Compt. Rend. du Congr~s International de Physique Nucldaire 1958 (Dunod, Paris) p. 156 V. E m m a and C. Milone, Nuovo Cim. 17 (1960) 365 F. Tabliabue and J. Goldemberg, Nuclear Physics 23 (1961) 144 A. Wataghin, R. B. Costa and J. C-oldemberg, Nuovo Cim. 19 (1961) 864 G. C. Reinherdt and W. D. \Vhitehead, Bull. Amer. Phys. Soc. 6 (1961) 251 Whittaker and Robinson, The Calculus of Observations (Blackie and Son Ltd, London, 1958) A. G. de Pinho Filho, Nuclear Physics 18 (1960) 271 J. Goldemberg, P. Dyal and J. O'Connel, private communication (1960) J. Eichler and I-I. A. Wcidenmuller, Z. ffir Phys. 152 (1958) 261 J. Sawicki, Nuclear Physics 6 (1958) 525 L. A. Kul'chitskii and V. Presperin, J E T P (Soviet Physics} 12 (1961) 696 G. E. 13rowu and hi. Bolsterly, Phys. Rev. Lett. 3 (1959} 472 H. \V. Schmitt and J. Halperin, Phys. Rev. 121 (1961) 827 Bakcr and McNcill, Can. J. of Phys. 39 (1961) 1158 Reinhardt and Whitehead, private communication