The angular distributions of gamma rays following (α, n) and (p, n) reactions

Nuclear Physics A l l 3 (1968) 193--205; (~) North-Holland Publishmg Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the pubhsher

THE ANGULAR DISTRIBUTIONS OF GAMMA RAYS FOLLOWING (~, n) AND (p, n) REACTIONS L. BIRSTEIN, R. CHECHIK, Ch. DRORY, E. FRIEDMAN, A. A. J A F F E and A. WOLF

Physics Department, The Hebrew University, Jerusalem, Israel Received 4 March 1968 Abstract: The angular distribution of gamma rays excited by both (p, n) and (~, n) reactions leading to the final nuclei 59N1, 6sZn and eSGa have been investigated. The observed angular distributions are consistent with those theorehcally predicted by the compound nucleus statistical model whenever the spin sequence is previously known. The (p, n) and (~, n) reactions yield identical values of the multipole mixing ratios for all the transitions. The variation of the gamma-ray angular distributions with incident energy following the (p, n) reaction is correctly predicted by the model. The energies of the low-lying levels of eSGa have been accurately determined, and the first excited state at 175 keV excitation is found to have a spin 2 (+). The results indicate that the level at 375 keV is probably a doublet.

E [ N U C L E A R REACTIONS 6~Co,63Cu, 6sZn (p, nT'), E = 3.1 -- 5.2 MeV; " F e , e°Ni, e6Cu (~, nT'), [ E = 6.5 --9.3 MeV; measured ~(E?, O) 59Ni, 68Zn, eSGa deduced levels, J. Enriched targets.

1. Introduction

The angular distribution of the reaction products of some nuclear reactions at relatively low incident energies may be interpreted using the Hauser-FeshbachSatchler statistical model 1, 2). Several angular distributions of gamma rays following the inelastic scattering of protons and neutrons have been measured, and agreement with the theory is good a). There is little previous experimental information for the angular distributions of gamma rays from the reactions (p, nv) and (~, nv) except for the present work; part of it has been reported in preliminary accounts 4, 5) and by Iyengar et al. 6). The (p, n) and (~, n) reactions often have negative Q-values so that the energy of the incident particle may be adjusted to be just above the threshold for the excitation of any chosen level in the final nucleus. This has several advantages. Firstly, if the energy of the outgoing neutron is kept below about 1 MeV, conditions for a compound nucleus reaction mechanism are ideal. Secondly, the energy of possible excitation in the final nucleus may be controlled, so that the level decaying by the gamma transition under investigation may be fed directly by the reaction, and the excitation of higher states which could cascade to it may be avoided. Finally, the gamma-ray angular distribution has the maximum anisotropy for low outgoing neutron energies since the neutron will be mainly s-wave, and thus the de-alignment of the compound state is kept to a minimum. 193

L. BIRSTEIN et aL

194

In the present work, a study of a number of gamma-ray transitions excited by (p, n) and (~, n) reactions is described. The primary aim of this study is to examine the mechanism of these reactions. As has been pointed out by us 5) and is discussed below, the comparison of the results for the same gamma-transition excited by both the (p, n) and (~, n) reactions provides a powerful test of the mechanism. Thus, the following pairs of reactions have been investigated: 63Cu(p, n) 63Zn, 6°Ni(~, n)63Zn; 68Zn(p, n)6aGa, 65Cu(~, n)6SGa; 59C0(p, n)59Ni, 56Fe(ct, n)SgNi. 2. Theory An expression for the angular distribution of gamma rays following a nuclear reaction involving incident and outgoing particles of spin ½ based on the compound nucleus statistical model has been derived by Satchler 2) and Sheldon 7) has included the effect of spin-orbit interactions. The gamma-ray distribution following any nuclear reaction of the type (a, by) has been derived by Wolf a) using the compound nucleus statistical model and the general relation of Rose and Brink 9). The gamma-ray angular distribution for either the (p, n~) or (~, n~) reactions where particles of spins of 0, ½ are involved is given by

w 0)

= l--JIJ2

fo

(_ I)'o+'.-Y~-',- I,(djl2 ),/Jo) z 3 1,~J,k (keven)

x (j,s,A-s, lkO)W(1,J~J212; kY2)W(J~J~jljX; Iclo)Mk(a)Pk(cos 0),

(I)

where f = 2 J + l , s 1 is the spin of the incoming particle, and Jo, J1, J2, Ja,Jl,J2, Mk, 6 and z have the same meaning as in ref. 3). For the (p, ny) reaction, this relation yields the identical formula to that given by Sheldon and Van Patter 3), and for the (u, lay) reaction it is in agreement with that also derived by Sheldon 10) from relations previously available 11). The computer code MANDY 12) was modified to include the (u, n~,) reaction.

3. Experimental techniques 3.1. GENERAL ARRANGEMENT AND TARGETS Beams of protons or alpha particles of the desired energy were obtained from a tandem Van de Graaff accelerator. The experimental techniques which were used in obtaining the levels and decay scheme of 6aGa have been described previously 13). However, the accuracy of measurement of the gamma-ray energies was improved by the use of a precision pulse generator and of a 4096-channel analyser. Thus, using appropriate calibration sources, the energies of the gamma rays from 6gGa could be determined to within an error of + 0.1 keV. The 60Ni target was a self-supporting foil ( ~ 1 mg/cm 2) prepared by electrolysis of the separated isotope onto copper foil and dissolving the copper foil in a concen-

(~, n) AND (p, n) REACTIONS

195

trated solution o f chromic acid in sulphuric acid. The 63Cu target was prepared by electrolysis of the separated isotope on to a thin nickel backing and was ~ 1 mg/cm 2 in thickness. The 6SCu0t, n) reaction was investigated using a target of natural copper foil of ,~, 1.7 mg/cm 2 in thickness. Two targets of 6aZn, one about ,~ 200/~g/cm 2 thick and the other about ~ 1 mg/cm 2 thick, were prepared by the electrolysis of the separated isotope onto thin nickel foil. The thinner target was used in the investigation of the levels of 6SGa and the thicker target in the measurement of the angular distribution. An additional target of 6aZn on a copper backing of thickness ~ 1 mg/cm 2 was also used. The 59C0 target was a self-supporting foil ~ 1 mg/cm 2 in thickness prepared by the method described by Harchol 14). The 56Fe target was prepared by electrolysis of the separated isotope onto nickel and was ~ 400 #g/cm 2 in thickness. 3.2. MEASUREMENT OF ANGULAR DISTRIBUTIONS The targets were p l a ~ d in the centre of a target chamber of 7 cm radius. The plane of the target was at an angle of 45 ° to the incident beam. A slot in the target chamber covered with a thin beryllium-copper strip allowed measurement of the intensity of the emitted gamma rays in the angular range of from - 20 ° to 110 °. Sheets of various materials (Ni, W, or T a as described below) were mounted immediately behind and parallel to the target to stop the beam. The angular distributions were measured using a Ge(Li) detector which could be rotated about the centre of the target chamber. A second detector placed at a fixed angle of - 9 0 ° to the incident beam opposite an additional window in the target chamber served as a monitor. Using low-noise preamplifiers (Ortec type 118 A) an energy resolution of ~ 3 keV was obtained for the 122 keV gamma rays of 57Co. The gamma rays entering the movable detector pass through the beam stop, and a correction for the relative absorption was made as described below. The angular distributions were obtained by integrating the number of counts in the total energy absorption peak at the various angles. In general, the height of this peak compared with the level of the continuum from Compton absorption of other gamma rays in the detector was noticeably worse when using a beam stop directly behind the target than in experiments in which the beam was allowed to proceed to a Faraday cup as described in ref. 13). For this reason, angular distributions were measured only for the more intense gamma-ray transitions. Corrections due to the finite size of the detector were found to be negligible. 3.3. CORRECTION OF ANGULAR DISTRIBUTIONS FOR ABSORPTION IN BEAM STOPPER The absorption of the observed gamma rays is dependent on angle, since they pass through the beam stopper before entering the detector. This may be taken into account by correcting each point of the measured angular distribution before determining the coefficients/12 and A 4 as defined below. Alternatively it may be shown that, for

196

L. BIRSTEIN et al.

values of #x occurring in this work (~< 0.1), the values of the coefficients of the expansion of differential cross section as a series of Legendre polynomials (ao, a2, a4) may be obtained to a very good approximation by fitting the experimental distribution to the expression W'(0) = a~ + a~ P2 (cos 0)+ a~P4(cos 0) and using the relation (ao) [(10 0 i ) / 1.19-0.06 O.09~']/a~\ a2 = 1 +/~x|-0.16 1.37 a4 0 0 \ 0.37 0.09 1.26/d\a'J

0.06l//a l,

(2)

where # is the absorption coefficient of the observed gamma ray in a beam stopper of thickness x. The fit to the experimental angular distribution was made using the method of least-squares, and after correction for absorption, .42 = a2/ao and .44 = aJao were found. In all cases, the effect of absorption on 1.421 was less than 0.03 even for absorption of 11 ~ in the beam stopper at 0 = 45 °.

4. Results 4.1. P R E L I M I N A R Y E X P E R I M E N T S

The most direct test of the mechanism of either the (p, nT) or (~, nT) reactions would be to observe gamma transitions to a state of zero spin, so that multipole mixing would be absent and the gamma-ray angular distribution would be uniquely determined. To reach a doubly even residual nucleus via the (p, n) reaction, it would be necessary to have a doubly odd target. The (~, n) reaction to a doubly even final nucleus

63Cu (p,n)63Zn

60Ni ( =(,n)63Zn

10

o9

E =5.2 MeV

/

Ep=4.8 MeV

~: b

II

024

018

If

i

I '

i 0

i

j

/

~

,iL-h J-

~-l

7o

'

"

E =4.65MeV Pi i i i L i i 30

60

E =190keY J 90

GAMMA

i

i

i COUNTER

i 0

ANGLE

i

i

i 30

i

i

i 60

i

i

i 90

i

i

(DEGREES)

Fig. 1. Observed angular d,stnbutions for the 190 keV g a m m a ray in 6aZn. The solid lines are computed from the series of Legendre polynomials fitted by the method of least-squares.

TAnLE 1

591qi 343 keV

6SGa 201 keV

esZn(p, n)SSGa

6SGa 375 keV

5~Co(p, n)59Nl ~eFe(ct, n)S~Ni

esCu(oqn)eSGa

6sZn(p, n)~SGa

esCu(~t,n)OSGa

6sZn(p, n)6SGa

esCu(~, n)6SGa

6sZn(p, n)6SGa

8°Nl(~, n)83Zn

e3Cu(p, n)6aZn

Reaction

eSGa 321 keV

SaGa 175 keV

ezZn 190 keV

Gamma-ray transition

3.1 6.57

4.25 4.47 8.33

4.25 4.47 8.33

4.25

4.05 4.25 8.33

4.65 4.80 5.20 9.25

Incident energy (MeV)

0.0324-0.029 --0.20 4-0.06

--0.73 4-0.02 --0.54 4-0.05 --0.59 4-0.10

--0.20 4-0.04 --0.23 4-0.02 0.02 ±0.06

0.03 4-0.02

--0.37 4-0.02 --0.29 4-0.02 --0.19 4-0.04

--0.1054-0.019 --0.0764-0.020 --0.0764-0.020 --0.21 4-0.04

A~exp

0.0344-0.037 0.0424-0.073

0.I0 4-0.04 --0.09 4-0.07 0.0124-0.050

--0.06 4-0.04 0.0034-0.027 --0.04 4-0.08

0.0154-0.030

0.0074-0.025 0.0244-0.029 0.0194-0.050

--0.014-t-0.025 0.0114-0.024 0.0104-0.026 --0.0344-0.051

A~exp

~- -+ ] -

3 + -+ 1+

2 + ~ 1+

2 + ~ 1+ 1+ ~ 1+

2 + ~ 1+

[- ~ ]-

Assumed spins and parities

0.054-0.05

--0.254-0.05 --0.2 4-0.1 --0.4 4-0.1

0.104-0.05 0.034-0.05 0.2 4-0.1

0.204-0.03 --0.054-0.05

--0.014-0.02 --0.024-0.03 --0.034-0.06

0.044-0.04 0.074-0.04 0.07±0.04 0.074-0.03

E2/M~

Ni(120)

Ta(15)4-W(45)

W(100)

Ta(15)+W(45)

W(100)

W(100)

N1(120) W(100) Ta(15)+W(45)

Ta(15)+W(45)

Ni(120)

Beam stopper thickness in mg/cm ~ in parenthesis

Summary of the experimental results and the derived values of the multipole mixing ratio obtained for the various gamma-ray transitions excited by (p, n) and (et, n) reactions

c

198

L. BIRSTEINeta[.

has in general a Q-value, which is not sufficiently negative to give reasonable penetration through the Coulomb barrier near threshold. In preliminary experiments, some (p, n) and (ct, n) reactions leading to residual doubly odd nuclei known to have ground state spin 0 were investigated. These were ¢2Ca(p, n7)¢2Sc, ¢GTi(p, ny)46V, 66Zn(p, nT)66Ga, 39K(tx, n7)¢2Sc and a 1P(ct, ny)agc1. In none of these cases could g a m m a rays corresponding to transitions to the ground state be identified with certainty, presumably since the (p, n) reaction is too weak compared with competing reactions. 4.2. ANGULAR DISTRIBUTION OF THE GAMMA RAYS OF 63Zn

The angular distributions of the gamma transitions 1a) of 190 keV and 246 keV were measured for both the reactions 6aCu(p, nT)6aZn (Q = - 4 . 1 4 7 MeV) and 6°Ni(~, nT)6aZn (Q = - 7 . 9 0 5 MeV) at incident energies of E v = 4.65, 4.80 and O

oso

GBZn( p, n) SSGa

O45 o °~°

t

a~0.35

I

o32~ 1

I

I

o~G~

i~',*'

0 30

I

I

I 40

I

I

1 45

I

I

I

I

I 5~

PROTON ENERGY(MeV)

Fig. 2. The neutron counter ratio as a function of incident proton energy at 90° with a lithium scatterer. The arrows indicate the positions of the levels found in the investigation of the gamma rays of "Ga assuming a ground state Q-value of -3.700 MeV for the reaction "Zn(p, n)"Ga.

5.2 MeV and E~ = 9.25 MeV. Beam stoppers of nickel and tungsten were used, respectively. The results are presented in fig. 1 and after correction for absorption by the beam stoppers in table 1. 4.3. THE GAMMA RAYS OF "Ga The levels of 6aGa have been investigated previously by Rester et al. is). Before measuring the angular distributions, the levels of 6aGa were re-investigated through the reaction 6SZn(p, n)GaGa by two methods. The first method was based on the resonance scattering of neutrons from lithium (fig. 2) and the second on the successive excitation of g a m m a rays using a Ge-Li detector (fig. 3); both these techniques have been described previously 1 a). The results obtained are summarised in fig. 4. The agreement with Rester et al. is in general good, though in our work the energy

199

(~, n ) AND (p, n ) REACTIONS

resolution is better by a large factor allowing improved accuracy in the measurement of gamma-ray energies. Instead of a single level at 573 keV, there is apparently a triplet of levels at 555, 565 and 585 keV. It is interesting that we also observe a gamma ray of ~ 118 keV for Ep > 4.45 MeV, that is Ep of ~ 700 keV above the threshold 175 t

lO

68Zrl+p

%

)t J zTs

¥ RAY ENERGIES IN keY

n

2

~< lo (n

I

8_J sl ~2 uJ 1(3 I-Z

L~

~JL1

"

"~'~" ~'~'~'%'-~,"

Ep=4 25MeV

-~*

Ep=405MeV

5

U

lO

%

"~'¢~

',,,

Ep=370 MeV

" ~ " i

100

i

i

200 300 CHANNEL NUMBER

i

400

Fig. 3. G a m m a - r a y spectra taken at 90 ° to the incident p r o t o n b e a m o n a asZn target using a Ge(Li) crystal 2.5 m m in thickness.

for the excitation of the ground state of 6SGa. Rester et aL were unable to fit this gamma ray in the level scheme of 6SGa; it possibly originates from a level at about 680 keV, which decays only by cascades. It is natural to assume that the 201 keV gamma ray arises from branching of the 375 keV level. However, careful measurements at 90 ° to the incident beam (and without a beam stop) indicate energies of 200.7, 174.9 and 374.7 keV ( _ 0. I keV) for the three

200

L. BIRSTEINet

al.

relevant g a m m a rays. As will be seen below, the discrepancy between the sum of the energies of the first two g a m m a rays and that of the third, and other evidence, introduces serious doubt about the above assumption. 4.4. ANGULAR DISTRIBUTIONS OF GAMMA RAYS FROM 6SGa The angular distributions of the 175, 201 and 375 keV g a m m a rays were measured for both the 6SZn(p, n)6SGa and 65Cu(a, n)6SGa reactions which have Q-values of - 3 . 7 0 and - 5 . 8 4 MeV, respectively. The angular distribution of the 321 keV g a m m a

Ep(MeV)

E (MeV)

LAB.

.,__ 835L A B . ) 25

-82=~ t, 5Z

tO0

• (5B~

:(55--~ ',56~ /, 25

• 514

8,'/5

'-~ ~2(43(4; ":"~"~"-'~"=--'-;:" : i (37q '37!

'321

550

/, 01 .175 .0

37~

68Ga Fig. 4. The observed levels and decay scheme of 6SGa. The differences between these results and those of Rester et al. 15) are discussed in subsect. 4.3. ray was measured for the (p, nT) reaction only, since it was too weak in the (~, ny) reaction. The incident proton energies used in the (p, n?) measurements were 4.05, 4.25 and 4.47 MeV. The incident alpha-particle energy was 8.33 MeV. The results are shown in fig. 5 and in table 1. Beam stoppers of tungsten and of nickel were used. 4.5. ANGULAR DISTRIBUTION OF THE 343 keV GAMMA RAY OF 59Ni The levels and decay scheme of 59Ni are well known t6). The angular distribution of the 343 keV g a m m a ray which is strongly excited by the reactions 59Co(p, n)S9Ni and 56Fe(~, n)59Ni (Q = - 1.858 and - 5.099 MeV, respectively) was measured at incident energies of Ep = 3.1 MeV and E= = 6.57 MeV. The results are shown in fig. 6 and table 1.

(=, n) AND (it3,n) REACTIONS

68

68

65

Zn(p,n) Ga

"

g 08 E

E =833MeV O7

E~ = 375

Ep=425MeV

08 ~o6

68

Cu(,~,n) Ga

03 E =447HEY ~ 02 03 Ep=4 25 M.eV/~,...~F_}_{_t_~o 02

~-~A ~

201

I keV

E~=321 keY

~

06

30 2

~ o4 ~ 02

~

o5 04 E =425MeV

~

O3 O2

E~= 201 keV

100t E==833MeV 05 E =425MeV, L_~t 03 ~ m ~ " ~ } ' 6080f ~ 1 ~ 09 E = 405 MeV ..~ft 07 05 ' I J i ~ i J i E i k 0 30 60 90 30 60 GAMMA COUNTER ANGLE(DEGREES)

'

E~=175 keY '6 ........ 9'0'

Fig. 5. Observed a n g u l a r distributions o f s o m e o f the g a m m a rays f r o m 6aGa. T h e s o h d lines are the best fits c o m p u t e d f r o m t h e series o f Legendre polynomials.

59Co(p,n)59Ni

I E.~=6.57MeVI l

~o4 ~o3~,_~°5 ~ [ Ep=3.1MeV

b

&

I

0

I

r

I

30

I

i

56Fe (,<,n)59Ni 14 13 12 11 10

E.,.34a,eV I

I

I

I

I

I

I

60 90 0 30 GAMMA COUNTERANGLE(DEGREES)

I

I

60

I

I

I

90

I

Fig. 6. Observed a n g u l a r distributions for the 343 keV g a m m a ray f r o m baNi.

202

L. BTRSTEIN et al.

A4 6 8 . . . 6 8 ^ I ,'ntp,n) ~a o4~Ep= 4.05MeV /E =1752÷-~÷ keV / ~ [=-50

~'=tO-

A4r

E=zo 3+~_~+/~ W/ ~'.= [=50 ,%s0//

0

1+L1 +

[=-0~)d ~'-~0

/ I

~

I

-10

-05

0

A41

6Szn (p,n)SSGa 3+-7,-2+

[

=

0

-04

"

5

-08

-04

0

;

(a) i

I

04

0.8

t2

Z = - 0 " 5 ~ + - - 2 +

oL)41 0.8 'A2

04

0

-0.8

-04

0

0.4

'A 2

08

A4

68Zn (p,n)68Ga E =4.25MeV p E~= 375 keY

2+.-m1+ ~:-~o

,' ~.=

~,_zo~° - /, 3÷~.I/ "//L,',=

E=_~~i~ ~,=5.0 //

006 0304

[=-20

~ _ ~ ,~3+~L

002

~:~o//~:0"

0

02

~

o

/

/

-02

.%o.5~J//

l+--'u

-0.02

//

-0.8

,

-04

,

0

-0.06

E== 8.33 MeV E~ = 375 keY i

,

08

-01

6eZn( p,n)68Go

=1.0

C

-0~. _1~0

i -05

I

0

I 0.5

(d; i0 1

t

-05

i

0

0.5

'

tO

A 2

Fzg. 7. A comparison with theory of some of the results for gamma rays of 6SGa excited by the (p, n) and (~, n) reactions. The experimental results are indicated by the shaded rectangles. In Co) the double ellipses represent the extrema obtained using a large number of different sets of transmisszon coefficients. Even for the (~, n) reaction, the absolute effect of the variation of the transmission coefficients is small; the scale of .4, is greatly expanded.

E p= 4.25 MeV 2+T.1+ Eli = 321 keY ~=-~o ~.= / J':so E=~I~

~ =-2o ~'t .~:4.o (c:

.o

04

/I[.o,

-004

H//=° ,

0.2

I

65Cu(~.,n)68Ga E =8.33 MeV

oo21 Ol oo2i

A4

O4

i

0061 oo41

~

-0.8

l

E~ =201 keY

/

0.2

-

~1÷

. ~

g=-40 =0

tO A2

O~

A4;

2. ~

-0.06

0'5

~ = 201 keY

0.5

H

-0.04

(I

Ep=4.25MeV

~=-~o~

00~ nt

J'='L0

m.

E = 175 k.V

02 [=-

A4

65Cu(,<,n)6SGa

0"06, E~.= 8.33 MeV

A2

(=, n) AND (p, n) I~ACTIONS

203

5. Analysis of results The theoretical values of A 2 and ,44 for the angular distributions were computed as a function of the multlpole mixing ratio 6, and the comparison with experiment is shown in figs. 7-8. The transmission coefficients were calculated using various sets of optical-model parameters. For protons, they were calculated from the optical potential of Percy 17); for neutrons they were calculated from the potentials of Mani et al. is), Wilmore and Hodgson 19), Percy and Buck 20), and values given by EraA4

56 59 Fe(ot,n) Ni

0,4 -E

=6.56

h'leV

5/2-~

712-~3123/2-

E~=343keY ,=-s.o '-~ ,I=~o //I=o 0.2 0

-0`2

~,~/ ~,~ ~ o,L.+--o,,~, - 10

A4[ 63 63 I Cu(p,n) Zn 0`oos~-Ep=4.65 MeV 0/ _0.004I

7/2-

/,oo, ] ~=005.

'=-10~

=

~=(

/

,

,

/i~;o

- 0.5

0

0`5

(°)

A~ tO

A4

]--7---]

ooo, E,="°k'v

/ ~=~/ 312-/~3/2-// //

S°Ni (at, n) 63Zn 7/2-,--3/2- ~=1c 5/2- ~--~3/2- ~'=2 o// 04 E~=9 25HEY E,= 19o k,v , : - ~ o

,,=\~ \//

--//

02 ~

j

- ~--~//

~o-o~ ~=o~ ,~\~,~//~_.

-,'o

-;~

3/2-~3/2-//~:0, ; "'//~5

(b),oA~

Fig. 8. A comparison with theory of some of the results for gamma rays of bgNi and 6aZn. In (a) it may be seen that the theoretical prediction is only slightly affected by the assumed parity of the initial level.

merich 21) were also used. For alpha particles, we used optical-model parameters extrapolated from those of Bock et al. 22). AS may be seen in fig. 7b, the theoretical ellipses are not very sensitive to the exact values of the transmission coefficients, therefore the results are essentially independent of the optical-model parameters [see ref. 4)]. Also, as may be seen in fig. 8a, they are not very sensitive to the parity of the initial state. The results of this analysis are summarised in column 7 of table 1.

204

L. BIRSTEIN e t al.

It may be seen that for the transition in 6 aZn ' the analysis yields uniquely the correct value ~ for the spin of the level at an excitation of 190 keV. This level is known to have negative parity. The results for the 175 keV level in 68Ga indicate a spin of 2 and those for the 321 keV level a spin of 1 or 2. From the shell model and from consideration of other nuclei in this region, it is assumed that low-lying levels of 68Ga would have positive parity, since excitation into the g~ configuration is required before negative parity appears. The 375 keV gamma-ray distribution is consistent only with a spin assignment of 2 for the 375 keV state. On the other hand, the 201 keV transition, which is extremely anisotropic, appears to originate from a level of spin 3 and cannot, on any account, be fitted assuming an initial state spin of 2 of either positive or negative parity. While it was initially assumed that this gamma ray originated solely from the branching from the 375 keV level, there is the following additional evidence against this conclusion; (i) The ratio of the intensities of gamma rays of energies 375 and 201 keV was observed to be 0.48 for the (p, n) reaction (Ep = 4.25 MeV) and 0.28 for the (~, n) reaction, thus indicating that they do not originate from a single level. The ratio of these values is in agreement with the theoretical calculation assuming that they originate from levels of spin 2 + and 3 +, respectively. (ii) There is a discrepancy between the sum of the energies of the 200.7 and 174.9 keV gamma rays and the 374.7 keV gamma ray of almost 1 keV. The possibility that 201 keV gamma ray is badly contaminated with some spurious line seems to be ruled out by the consistency of the results of both the (p, n) and (~, n) reactions, which require different targets and by testing the effect of interchanging the beam stop material and target backing. The evidence available from this work, therefore, points to the existence of a 3 + state in 68Ga at 375.6 keV as well as a 2 + state at 374.7 keV. The 201 keV gamma ray should then arise almost purely from the decay of the 3 + state since a 3 + --, 2 + transition is greatly favoured compared with a transition to the ground state, whereas 90 9/0 of the decays of the 2 + state are expected to be transitions to the ground state (on a single-particle model). The 201 keV transition is thus found to have a multipole mixing ratio of 6 ~ 0.3. This value of 6 is such that the angular distribution of the 175 keV gamma ray is not significantly affected by the feeding of the 175 keV level by the 201 keV gamma ray which occurs for Ep = 4.25 MeV and E~ = 8.33 MeV. Such feeding is in any case relatively weak. The angular distribution of the 343 keV gamma ray in 59Ni is almost isotropic in the (p, nv) reaction and agrees with theory which predicts IA2I < 0.02 and IA4I < 0.004 for a { ---, { transition. The comparison with theory is not shown in fig. 6, because the theoretical ellipse is so small, and the agreement with experiment holds within the limits of error for any value of 6. The approximate isotropy results from the high spin of the target nucleus S 9 C o ( I = 5 ) . The corresponding (~, n),) reaction on the target nucleus 56Fe(I = 0) is seen to be anisotropic.

(a, n) AND (p, n) REACTIONS

205

6. Conclusions I n all cases s t u d i e d in this work, the o b s e r v e d a n g u l a r d i s t r i b u t i o n s are consistent with those theoretically p r e d i c t e d b y the c o m p o u n d nucleus statistical m o d e l wherever the spin sequence was p r e v i o u s l y k n o w n , a n d in the case o f the 190 keV level in 6aZn the p r e v i o u s l y k n o w n value o f the spin is uniquely determined. The value o f the m u l t i p o l e mixing r a t i o s o b t a i n e d f r o m a n analysis o f (p, n~) r e a c t i o n s are identical with those f o u n d f r o m an analysis o f the (~, n~) reactions for all the transitions investigated. The v a r i a t i o n o f the a n g u l a r d i s t r i b u t i o n s o f the g a m m a rays with inc i d e n t energy for a given t r a n s i t i o n following the (p, n) r e a c t i o n is correctly p r e d i c t e d b y the model. This m a y best be seen for the 175 k e V a n d 201 k e V transitions in 6SGa where significantly different values o f -42 f o u n d at the different i n c i d e n t p r o t o n energies yield values o f 6 which are c o n s t a n t within the e x p e r i m e n t a l error. O n the basis o f indirect evidence, it is a s s u m e d t h a t the 201 k e V a n d 375 k e V g a m m a rays f r o m 6SGa d o n o t arise f r o m b r a n c h i n g f r o m a single level. I f this is n o t the case, it is i m p o s s i b l e to reconcile the o b s e r v e d a n g u l a r d i s t r i b u t i o n s o f these g a m m a rays with the t h e o r y , since this requires different initial spins for the two transitions. W i t h the a b o v e qualification, the p r e s e n t w o r k d e m o n s t r a t e s t h a t the c o m p o u n d nucleus m o d e l correctly predicts the g a m m a - r a y a n g u l a r d i s t r i b u t i o n s following (p, n) a n d (~, n) r e a c t i o n s in m e d i u m - w e i g h t nuclei for incident energies r e a s o n a b l y close to the n e u t r o n thresholds. W e gratefully a c k n o w l e d g e the extensive a n d generous assistance which we have received f r o m P r o f e s s o r E. Sheldon. W e also wish to t h a n k Dr. Y. T i k o t c h i n s k y w h o s u p p l i e d us with his c o m p u t o r code which was used for some o f the o p t i c a l - m o d e l calculations.

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