The energy levels of 90Y

LEA: 2.G

Nuclear Physics 79 (1966) 65--76; (~) North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or m l e r o f i l m without written permission from the p u b l i s h e r

T H E E N E R G Y L E V E L S O F 90y J. L. BLACK*, W. DARCEY and M. M. ISLAIVft* Nuclear Physics Laboratory, Oxford, England Received 20 October 1965 Abstract: The energy levels of 90y have been studied from the reactions 89Y(d, p)90y at Ea = 11.95 MeV and ~2Zr(d, ~)~0y at Ed : 12.00 MeV. A total of 45 energy levels have been observed in the (d, p) reaction up to an excitation of 3.88 MeV. Angular distributions for 18 levels have been obtained and reduced widths extracted for them from DWBA analysis. Single-particle states arising from the neutron configurations 2d~, 3s½ and 2d~ have been identified at 0/0.202; 1.214/1.374 and 2.479/2.628 MeV, respectively. It is noted that some of the single-particle strengths are distributed in a number of weak levels above 1.4 MeV. An l ~ 4 distribution has been observed for the 2.938 MeV state and possibly for the levels at 1.965 and 2.245 MeV; the low-lying l = 4 transitions are expected from the 1g~ neutron configuration. The positive parity states of 90y arising from the configuration [(2p~)-e(1g~_)~]p[2d~]~ could not be observed in the (d, p) reaction, Extra states observed in the (d, ~) reaction at 0.68, 0.78 and 0.965 MeV have been interpreted as belonging to the above configuration. The results have been compared with the theoretical predictions of Kim and Auerbach and Talmi.

E

NUCLEAR REACTIONS 89Y(d, p), E = 11.95 MeV; measured cr(E~, 0p). ~oy deduced levels, ar, ze, 1.Natural target. 92Zr(d, ~), E = 12.0 MeV; measured cr(E~). 9oy deduced levels. Enriched target.

1. Introduction

Resonances observed in 8 9 y + p reactions at p r o t o n b o m b a r d i n g energies above 4.8 M e V have been interpreted as c o r r e s p o n d i n g to the analogues of the g r o u n d a n d low-lying excited states of 9 oy. Several strong resonances have been observed 1, z) i n 89y(p, p,)89my a n d 89y(p, n)89Zr which do n o t have k n o w n analogues i n 9oy. It has been suggested by Jones, Lane a n d M o r r i s o n ~) that these additional resonances c o r r e s p o n d to positive parity states of 9 0 y belonging to the excited p r o t o n configuration (p~2 g~)p(d~).. The six states of 9 o y with J~ --- 2 +, 3 + . . . 7 + belonging to this configuration are predicted from the shell m o d e l calculations of A u e r b a c h a n d T a l m i 3) a n d K i m 4) to lie at excitation energies below 1.5 MeV. The only m e m b e r of the positive parity sextet which is k n o w n with certainty is the 7 + state at 0.68 MeV. This state has been p o p u l a t e d in the 93Nb(n, 009°Y reaction 5) a n d decays via a n M 4 t r a n s i t i o n (t~ = 3.1 h) to the 3 - first excited state. B a r t h o l o m e w et al. 6) in 7-ray studies of the reaction 89y-(n, 7)9°Y have seen evidence for a y-ray t r a n s i t i o n to a n d f r o m a state at 0.78 M e V to which they have assigned Present address: Department of Physics, Stanford University, Stanford, California. ** Permanent address: Atomic Energy Centre, Dacca, East Pakistan. 65

66

J.L. BLACK.e t

al.

J~ = 2 + from angular correlation measurements. No evidence for this state has been observed in other reactions but there is a (analogue) resonance in 89y(p, p,)89my at Ep = 5.62 MeV which corresponds closely in energy to a state in 9Oy at 0.78 MeV. None of the positive parity states have been observed in the 89y(d, p)9Oy reaction 7, 8). Hamburger and Hamburger 7) have placed an upper limit on the excitation of the 0.78 MeV 2 + state in the (d, p) reaction of ~-~- that of the ground state 2-, 3- doublet belonging to the configuration (p4)p(d~_)n ; Watson, Moore and Sheline 8) have extended this upper limit to x~o~-- This very small upper limit is surprising since it bears directly on the reaction mechanism and the purity of shell model states in the mass 90 region. In particular it places a very high limit on the purity of the (p~l)p configuration for the 89y ground state. In view of the current interest in the positive parity states a study of the 89y(d, p)90y and 92Zr(d, c~)9°Y reactions has been made using magnetic analysis. The (d, p) work is a repeat of the work of Hamburger and Hamburger 7) and of Watson, Moore and Sheline 8) but with betterresolution and increased intensity. The (d, ~) reaction was chosen for study since the 92Zr ground state is predicted 3) to have the configuration [70 ~(2p~) z +30 ~(lg~)2]p[(2d~)Z]n so that the positive parity states of 9Oy with the configuration (g_~)p(d~)n may be expected to be formed through direct deuteron pick up. The (d, p) reaction is useful to test the purity of the single-neutron shell model states and to determine the distribution of 3s and 2d single particle strength among the low-lying states of 9oy. 18 angular distributions for groups leading to excited states of 90y below 3.2 MeV have been obtained and a DWBA analysis has been carried out to deduce reduced widths. 2. Experimental Procedure 2.1. THE sgY(ci,p)~oy EXPOSURES Two exposures were taken with 11.95 MeV deuterons accelerated in the AWRE Aldermaston Tandem accelerator and the charged reaction products were analysed with the multichannel magnetic spectrograph 9) using 50 /~m Ilford K2 emulsion plates as detector. For the first exposure a thin, carbon-backed ( ~ 10/zg/cm 1) yttrium target of thickness g 45/zg/cm 2 was used and the exposure taken for 500 #C. For the second, a 200 #g/cm z self-supporting yttrium foil was used and the exposure taken for 5500 #C. The ground state Q for the (d, p) reaction is 4.64 MeV so that the high proton energy allowed the use of an absorber of 0,02 cm polythene in front of the emulsions to stop heavy particles. 2.2. THE 9~Zr(d,c~)°°YEXPOSURE The Q-value for this reaction is 8.71 MeV. An exposure for an integrated current of 2500 #C was taken at E a = 12.00 MeV. The c~-particles were analysed with the multichannel magnetic spectrograph and were detected with Ilford K-l, 25/~m emulsion plates. The target was isotopically enriched to 95.3 ~ in 92Zr and was evaporated

ENERGY

PROTON 13

°o"

500

67

L E V E L S OF 9Oy

MeV

ENERGY ,

14.

15

16

I

I

I

Co13

ysg(d,p ) ygO

l

Ee =11"95 NeV 0,.=35 °

4 t..- 400 z

x~ E E 300 3

I.U G.. u)

1

200

100

36

14.

10 9

Fig. 1. Proton spectrum f r o m t h e reaction 8°Y(d, p)0oy; 0 L = 3 5 o. Target t h i c k n e s s ~ 4 5 ~g/cmZ; exposure: 500 #C.

PROTON 13

15 T

14. I

' = = " - ' ~ 1'~ Oo

28 13 29 Co

21

ENERGY, MeV 16

~,

17

ysa(d,p)yg° Ee =11.95 NeV G,. =50 °

0

3

~_

OOO B

~L:°~r~o If] ii ii it,o, t

iii!l!iij! 21ili

" ¢i?t~iJ"t::!,~

,"!

t

" !i

so

~°°i i-

,j:..::Ut_.:..:,J!.., ...... ::.i,-o

~i

Fig. 2. Proton spectrum from the reaction sgY(d, p)~oy; OL = 50 o. Target thickness ~ 200/zg/cm2; exposure: 5500 pC.

Energy levels o f ° Y o b t a i n e d

Group 0 1 2 3 4 5 6 7

Excitation energy (MeV) 0 0.203 1.045 b) 1.214 1.374 1.425 b) 1.572 a) 1.645 a)

8 9 10 11 12 13 14 15 16 17 18 19 20 21

1.763 1.819 1.965 2.030 2.094 2.185 2.245 2.325 2.369 2.479 2.504 2.563 2.585 2.628

22 23 24 25 26 27 28 29 30 31 32

2.675 b) 2.705 ~) 2.754 2.786 a) 2.853 2.873 a) 2.938 3.092 3.053 3,142 3.164

33 34 35 36 37 38 39 40 41 42 43 44 45

3.210 3.275 3.315 3.351 3.495 3.522 3.584 3.642 3.690 3.760 3.800 3.861 3.878

TABLE 1 in the present experiment sY(d,

p)90y

1

Configuration

Jn

S

2 2

(2pk)p(2d})n (2p~)p (2d_~_)n

23-

1.03 0.88

0 0

(2p~_)p(3s})n (2p~_)p(3s~_)n

O1-

0.63 0.63

( 2 J + 1)S

2 2 0 2 2 4

0.09 0.05 0.08 0.18 0.39 1.08

4

1.49

a) a) b) b) 2

(2p~)p(2d~)n

2-

0.60

2 0

(2p~)p(2dff)n

1-

0.49 0.04

u)

4 2 2

2.54 0.73 0.21

2 0

0.46 6.12

b) b) b) b)

b) b) b)

a) Bracketed by Watson et al. 8) and confirmed in this experiment. b) N o t previously observed. T h e spectroscopic factor S has been obtained f r o m D W B A analysis. Where the spins are n o t k n o w n with certainty, the (2]-t-1)S value is indicated.

ENERGY LEVELS OF 99V

~9

on to a thin carbon backing. The 9ZZr target thickness was ~ 200 /.tg/cm2 which represents an energy loss of 30 keV for 20 MeV ~-particles. 3. Results

3A. THE 89Y(d, p)9oy REACTION Figs. 1 and 2 show typical proton spectra obtained from the (d, p) reactions. Fig. 1 shows the spectrum obtained at 0~b = 35 ° from the short exposure and fig. 2 the spectrum at 0j~b = 50 ° from the long exposure. The groups labelled numerically (e)

60

i

Group

0

it/

Group

6.0

0.202 NoV

÷

.o

Group

1

~:2

12o oup3 I

1.214

\

,

NoV

I:0

|ly.0

z~

Group

1

6

Group

7

i "~.~'\

,,/~,=2

10.0

0os

0os

,/

x.. 0

20

,~0

60

\, 80

100

0

20

40

~0

80

100

0

20

\\\,

,

... ~ 40

60

[ 80

100

0C.N. (DE@.)

Fig. 3. Angular distributions of protons from the reaction 89Y(d, p)~0y. The indicated curves are predictions from DWBA analysis. are those identified from kinematics as arising from the s9y(d, p ) 9 0 y reaction. The groups arising from target contaminations are labelled alphabetically, as follows: A: 24Na(E~ = 0.000 MeV); B: 41Ca(1.947); C: 24Na(0.473); D: 24Na(0.564); E: 41Ca(2.469); F: 2°F(0.652). At angles forward of 80 ° the intense groups could not be scanned in the long exposure. A normalization between the two exposures was obtained by counting

'

(b)

0.3

i\

,.,53,ov

I

•

I

,.8,,Mev

~

0.2

0.1

~,,, E

%

0.2

1.0

/

0,1

I 20

I~

\

\'-t~ I

6.0[

Group

16

2,369

MeV

1=4

~t"~

Group

/~

1?

2.479

MeV

I=0

0E

\

2.0

I 40

I 60

I 80

I 100

20

40

60

80

100

o e..~...~Q

I

I

I

I

I

20

40

60

80

100

eC.M. (DEG.)

Fig. 3b. (c)

3.0[F

{'"

Group

21

Group

0.4

,/I',

24

2.754 MeV

0.2

~'~./'

tP~

',/

t'.¢~---- I : 0 + 2 ÷ 4

~%..

y-i=2 ;...,~

/,..-~ o ..'~-...~_.~= \ -- ..," . . 4" .. ~,..~ b.,

...... ~x~;'~ ~ ~ ~.\ ~ ...L......... ~

E Group 1.0

Group

30

3.053 MeV

2.(

32

3.164 HeY

,:2

0,4 ~?.-~ i = 2 O[ o +8012

,\

1.C

0.5 0.2

0

I

20

I

4.0

I

60

!

80

I

100

I 20

I 40

I 60

I 80

8C.N. ( D E G.)

F i g . 3c.

I 100

0

20

40

60

80

100

ENERGY LEVELS OF-9Oy

71

the t r a c k s in the g r o u n d state d o u b l e t at 0j, b = 80 ° a n d i n d i c a t e d t h a t for the l o n g exposure there were 70 000 t r a c k s at the p e a k o f the g r o u n d state a n g u l a r distribution. T a b l e 1 lists the energy levels o f 9 0 y o b t a i n e d f r o m the p r e s e n t (d, p) work. T h e TABLE 2 Optical m o d e l p a r a m e t e r s for d e u t e r o n a n d p r o t o n

Parameter

U (MeV)

deuteron proton

65 51.4

W (MeV)

ro (fro)

a (fm)

16

1.35

0.60

10

1.27

0.55

150

92Zr ( d,a) 90 ¥

< >

E d = 12 N e V

LU I-Z

Eloo

E II ._1

<

IZ} "4"

f~ UJ

m50

o

o

0

o

I--

7

<

! i ,..

"

.:i i,,.:.".A.

2000

oi

...

1000

Ex

"

i

......~...... J'.... k: l 0

(keY)

Fig. 4. The summed spectrum of c~-particles from the reaction 9~Zr(d, c090y for nine angles between 20 ° and 80°. The energy levels of 90y are indicated with their excitation energies. excitation energies o f the m o r e p r o m i n e n t g r o u p s are those o b t a i n e d b y W a t s o n et al. 8); o t h e r energies have been o b t a i n e d b y i n t e r p o l a t i o n between these values.

72

J.L. BLACKet al.

A total of 45 states were observed up to an excitation of 3.88 MeV. The existence of several states listed by Hamburger and Hamburger 7) and Watson et ale 8) as possibilities have now been verified and in addition 14 previously unreported levels have been identified. Of these, only one (group 2 in the insert of fig. 2) was observed in the expected energy region of the positive parity states. Angular distributions for 18 groups have been obtained at angles forward of 90 ° . They are shown in fig. 3(a-c). The curves shown are the results of DWBA analyses performed using the computer programme of Yates 1o) for the Aldermaston I.B.M. 7030 computer. The radial dependence of both the real and the imaginary part of the optical model potential was taken to be Saxon-Woods in form. No cut-off radius was used and spin-orbit coupling was neglected. The distorting parameters used were those obtained by Macefield et al. 11) for the 7ZSe(d, p)77Se reaction. They are listed in table 2. The spectroscopic factor S was extracted by normalization at the peak of the angular distributions. The results are shown in table 1. Where the spins are not definitely known the ( 2 J + 1)S values are shown in table 1. Because of the uncertainty in target thicknesses the absolute cross sections and reduced widths are probably only accurate to within +_25 ~ . 3.2. THE 9eZr(d;'~)9°YREACTION The cross section for the ground state group in the (d, e) reaction was found to be less than 20 #b/sr. Because of the very low yield the spectra at nine forward angles from 20 ° to 80 ° have been summed taking kinematic variations into account. The resulting spectrmn is shown in fig. 4. In addition to those states observed previously in the (d, p) experiment new states were observed at 0.68, 0.78 and 0.965 MeV.

4. Discussion The low-lying states of 9Oy are expected 4) to have the following shell model configurations and spins. (2p~)p(2d}) n, (2p~ 2 lg~)p(2d~).,

2-, 3-, 2 +, 3 + . . . . 7 +

(Zp~)p(3%),,

0-, 1-,

(2p~)p(2d~) n,

1-, 2-,

(2p~)p(lg~),, (2p~ 2 lg~)p(3S~)~,

3-, 4 - , 4 +, 5 +,

(2p~)p(lh~).,

5 +, 6 +.

From considerations of reduced widths it has been possible to identify some of the states belonging to the above configurations as shown in table 1. The ( 2 J + 1) rule has been employed to assign spins for states belonging to the same configuration. Spins and parities are also included in table 1.

ENERGY LEVELS OF O0y

73

4.1. T H E N E G A T I V E P A R I T Y S T A T E S

Since the low-lying negative parity states of 90y have a proton configuration the same as that of the ground state of S9y, it is to be expected that they will be strongly excited in the (d, p) reaction, corresponding to neutron capture into single-particle orbits. The reduced width for the states of the low-lying doublets can be expected to be a large fraction of unity if the shell model is a reasonable approximation in the mass 90 region. The measured reduced widths indicate that this is so. The l = 2, l = 0 and l = 2 assignments for the doublets at 0/0.202; 1.214/1.374; and 2.479/2.627 MeV, corresponding to the single-particle configurations (2p~)p(2d~)n, (2p~_)o(3s~), and (2p~.)p(2d~)n, respectively, agree with the assignments made by Hamburger and Hamburger 7) and the tentative assignments of Watson et al. s). The measured angular distributions for the states at 1.645, 2.628 and 3.164 MeV could not be fitted by pure l = 0 or l = 2 curves, but a combination of the two I values in the percentages indicated in fig. 3 would account for the observed distributions. Either the states have J~ = 1 - and a mixed neutron configuration containing 3s~ and 2d~ or else they are unresolved doublets. The states at 2.03, 2.095 and 2.853 MeV although excited strongly in the (d, p) reaction, could not be analysed because of overlapping contaminant groups at several angles. Hamburger and Hamburger have assigned I = 0 and possibly 1 = 2 for the 2.369 and 2.754 MeV levels, respectively. Our present experiment confirms l = 0 for the former but disagrees with a pure l = 2 for the latter. A combination of I = 0, 2 and 4 could fit the observed distribution to the 2.754 MeV state but it is doubtful whether such a fit is meaningful. From the measured reduced widths and the/-assignments for several of the weakly excited states in the excitation region above the 3s~ doublet it seems that rather more than 50 ~ of the 3s~ and 2dI_ single-particle strength is taken up by the levels at 1.214, 1.374 and 2.479 and 2.628 MeV. The rest is distributed over a very large number of states in the excitation region above 1.4 MeV. The angular distributions for the proton groups to states at 1.965, 2.245 and 2.938 MeV (see fig. 3) all have their main peak at about 45 ° and l = 4 predictions from the DWBA programme are shown on fig. 3. The prediction fits the data reasonably well for the 2.938 MeV state but is not as satisfactory for the 1.965 and 2.245 MeV states. Two states formed through l = 4 are expected in this excitation region: Kim has predicted that the 3-, 4 - doublet of states arising from the single-particle configuration (2p~)p(lg~_)n will lie at 2.57 and 2.44 MeV, respectively. Watson, Moore and Sheline 8) suggested the states at 3.002 and 3.164 MeV as the expected doublet. This experiment has shown that the angular distribution for the proton group to the 3.002 MeV state is fitted quite well with l = 2 with possibly some admixture from a higher/-value. The angular distribution for the 3.164 MeV state is fitted well by an admixture of about 80 ~ 1 = 2 and 20 ~ I = 0. Hamburger and Hamburger suggested tentative assignments of I --- 3 and 1 = l for the 3.002 MeV and 3.164 MeV states, respectively. Our improved data do not support these assignments.

74

J.L. BLACKet al.

Despite improved statistics for the distributions leading to states with possible l = 4 assignments, it is not considered that the (2p~)p(lg~)~ doublet has been adequately identified. A similar situation still exists for the l = 5 doublet expected from the (2p~)p(lhq) n configuration; the states may well exist above 3.2 MeV but the high density of states and interference from strong contaminant groups have prevented the extraction of adequate distributions to these high-lying states. 4.2. THE POSITIVE PARITY STATES The non-appearance of the positive parity states belonging to the (2p2 2 lg~)p (2d~)~ configuration in the intense (d, p) exposure is surprising. The upper limit placed by earlier workers on the cross section for excitation of the J~ = 2 + state (formed through angular momentum transfer l = 1) has been extended downward considerably in this experiment. The cross section has been found to be less than 1.5 #b/sr, corresponding to less than ~ of the cross section for the excitation of the ground state group. Although configuration selection rules forbid the formation of an excited proton state in a (d, p) stripping reaction the state may be formed through either compound nucleus formation or a scattering process such as 89y(d, d')89*y(d, p)9Oy where the 89y target is elevated to a new virtual ground state (the first excited state with the configuration (2p2 2 lg~)p), then stripping proceeds. This is presumably very weak in this instance because the inelastic scattering cross section depends on matrix 9+ ½- is elements rather similar to radiation matrix elements and the transition ~M4. It is not unreasonable that the compound nucleus cross section is low since for a heavy nucleus at high excitation energy the number of decay channels is extremely large. It is noted that it would be possible in principle to extract the ratio of compound to direct reaction cross sections at bombarding energies near 12 MeV by measuring an excitation function in fine energy resolution and carrying out a fluctuation analysis. The quite heavy forward peaking of the (d, a) angular distributions shows that the direct pickup mechanism is also playing an important part in determining the (d, e) cross section. 4.3. COMPARISON WITH THEORETICAL CALCULATIONS In 1963 Kim 4) predicted the energies of the low-lying states of 9Oy. He used the odd group model w i t h j - j coupling in which the nuclear properties are assumed to be entirely determined by the odd particles outside the "closed" Z = 38 shell and the N = 50 shell. The residual interaction between proton and neutron is assumed to be sufficiently weak so that it may be considered as a perturbation on the central field of the nuclear core. The residual force was taken to have a central plus tensor part. The predictions of Kim are included in fig. 5 along with the experimental energy levels obtained from the present (d, p) and (d, e) reactions. The agreement with experiment is poor. The splittings for the d~ and s~ doublets are predicted to be some five times smaller than those observed experimentally and the 1-, 2- d~ doublet is predicted to have its centre of gravity about 300 keV lower than observed.

ENERGY

L E V E L S O F gOy

75

A more recent calculation has been made by Auerbach and Talmi 3) but they have confined themselves to the 2d~ neutron shell. Predictions are made for the positions of the lg~_ 2d~ positive parity states and these are also included in fig. 5. The lg~_ proton, 2d~ neutron interaction was obtained from the known splitting of the 2 + - 7 + states of 9°Y and from the known separation of the states with J = 2, 3, 4, 5, 6, 7 in 92Nb which arise from the coupling of the 9+ ground state of 9tNb and a 2d_~ 2938

(3.4-)

2628 2479

2-

2245

2570.

3-

2443

4-

2332

!-

2166

2-

(#,44

2030 1965

(3.4-)

1819 T'76~

1820 1760

1645 1572

1645 1570

1425

1430

1374

1-

1214

o-

1-

1067

5,'-

893

2+

873

7+

3 2(d,p)

1280

29

K IM

32-

6+

.:.~,-o_ 121o 44-

1045

202

1250

"3+

4~

1370

1-

121o

o-

1090

3+

1_.000

5+

790

2+

780

2+_.

580

7+__

680

7÷

200

3-

200

,3..=.

1_045

2AUERBAC

&

H

2(d,c<)

TALMI 1-. Fig. 5. Energy level diagrams of s0y obtained in the present experiments. The t,teoretical calculations of Kim and Auerbach and Talmi are also shown.

neutron. The calculation is complicated by the fact that the 9~Nb ground state has o~(lg~). 3 The situation is unsaa mixed proton configuration: 71 °/(2-2 /or p~ lg~)+29 ~ tisfactory since five parameters must be determined from six pieces of experimental information (the splittings above). There appears to be some degree of agreement between the theory and the levels found here from the °ZZr(d, e ) 9 o y reaction. Unfortunately spins could not assigned from the (d, c0 experiment so it is difficult to make a meaningful comparison. The agreement in energy between the positive

76

J . L . BLACK e t al.

parity states of 9 0 y f o u n d from this (d, e) experiment a n d the energy of a n a l o g u e resonances i n 8 9 y + p reactions is good. This will be discussed in detail in a later paper 2). The authors are grateful to Professor D. H. W i l k i n s o n , Professor K. W. A l l e n a n d Dr. N. W. T a n n e r for their interest i n the present w o r k a n d to Dr. S. H i n d s for the facilities of the m u l t i - c h a n n e l magnetic spectrograph.

Referea~es 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11)

G. A. Jones, A. M. Lane and G. C. Morrison, Phys. Lett. 11 (1964) 329 J. L. Black et al., to be published N. Auerbach and I. Talmi, Nuclear Physics 64 (1965) 458 Y. E. Kim, Phys. Rev. 131 (1963) 1712 W. L. Alford, D. R. Kohler and C. E. Mandeville, Phys. Rev. 123 (1961) 1365 G. A. Bartholomew, P. S. Campion, J. W. Knowles and G. Manning, Nuclear Physics 10 (1959), 590 A. L Hamburger and E. W. Hamburger, Nuclear Playsics 68 (1965) 209 C. Watson, C. F. Moore and R. K. Sheline, Nuclear Physics 54 (1964) 519 S. Hinds and R. Middleton, Nuclear Physics 34 (1962) 404 M. J. L. Yates, private communication B. E. F. Macefield, R. Middleton and D. J. Pullen, Nuclear Physics 44 (1963) 309