(3He, α) reaction on 64Zn and 70Ge

Nuclear Physics A97 (1967) 458--468; ( ~ North-Holland Publishing Co,, Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher

(3He, ~) REACTION ON 64Zn AND 7°Ge C. M. FOU, R. W. ZURM~HLE and J. M. JOYCE University of Pennsylvania, Philadelphia, pennsylvania t Received 27 December 1966

Abstract: The low-lying levels in 63Zn and 69Ge have been studied by the ~4Zn(aHe, ~)63Zn and 7°Ge(3He, 0069Ge reactions at 18 MeV. Angular distributions of s-particles leading to strong states in 63Zn and 69Ge up to 7 MeV excitation energy were measured using solid-state detectors. Optical-model potential parameters determined from the analysis of the 64Zn(3He, 3He)64Zn angular distribution were used in the DWBA analysis. The following spin and parity assignments are made for 63Zn: ground state, 3-; 0.19 MeV state, ~-; 0.64 MeV state, (~-, ½-); 1.64 MeV state, (~-); 2.60 MeV state, (5-); 3.28 MeV state, (5-); 5.42 MeV state, (~-); 6.80 MeV state, (~-) - for 6~Ge: ground state, ~-; 0.09 MeV state, (~-); 0.23 MeV state, (~-, ½ ); 0.38 MeV state, ~-; 1.00 MeV state, (~-, ½-); 7.00 MeV state, ~-. The 5.42 and 6.80 MeV states in 63Zn are probably analogue states of the ground state and 1.42 MeV state in 63Cu. The 7.00 MeV state in 6~Ge is identified as the analogue state of the ground state in 69Ga. Spectroscopic factors were extracted. The result shows that the neutron occupation numbers of the P~t, f~r and p~_ levels in s4Zn and ~°Ge are approximately 2, 3, 1 and 4, 4, 1, respectively. E

NUCLEAR REACTIONS ~4Zn(3He, 3He), E = 18 MeV; measured 6(0). 64Zn(3He, ~), 70Ge(3He, cQ, E = 18 MeV; measured cr(E~, 0). e3Zn, SaGelevels deduced l, J, spectroscopic factors. Enriched targets.

1. Introduction The (3He, ~) reaction, like the (p, d) a n d (d, t) reactions, is very useful in s t u d y i n g n e u t r o n deficient nuclei 1,2). I n general, it has very large positive r e a c t i o n Q-value allowing the investigation o f higher excited states in the residual nuclei with the 3He b e a m energies available f r o m the t a n d e m V a n de G r a a f f accelerator. As a c o n t i n u a t i o n o f the study o f n e u t r o n deficient nuclei in the 28 =< N -< 50 region, the targets 64Zn a n d 70Ge were chosen. O u r interests were first, the low-lying states in 63Zn a n d 69Ge; second, the excitation o f a n a l o g u e states o f 63Cu a n d 69Ga; third, the n e u t r o n c o n f i g u r a t i o n o f the g r o u n d states o f 64Zn a n d 7°Ge. D i s t o r t e d wave B o r n a p p r o x i m a t i o n ( D W B A ) p r e d i c t i o n s were c o m p a r e d with the e x p e r i m e n t a l a n g u l a r distrib u t i o n s in o r d e r to g a i n spectroscopic i n f o r m a t i o n p e r t a i n i n g to the low-lying states in 63Zn a n d 69Ge. Previously, the low-lying states in 63Zn u p to an excitation o f 1.5 M e V have been r e p o r t e d in (d, t) w o r k 3). S o m e i n f o r m a t i o n a b o u t the level structure o f 63Zn has also been o b t a i n e d f r o m the 63Cu(p, n)63Zn r e a c t i o n 4). A level at 0.23 M e V in 69Ge has been o b s e r v e d in y-decay o f 69Ge excited states following t h e / / ÷ - d e c a y 5) o f 69As" * Research supported by the U.S. National Science Foundation. 458

(3He, ct) REACTION

459

2. Experimental procedure A detailed description of the experimental procedure and set-up has appeared in previous publications on (3He, ~) reactions 1, z). The targets were prepared by vacuum evaporation of isotopically enriched metal and were mounted as self-supporting foils. Their approximate thickness was 100 to 150 pg/cm 2. The 18 MeV aHe beam from the University of Pennsylvania Tandem Accelerator was used to bombard the targets in a 60 cm scattering chamber. Surface-barrier silicon detectors with 500 pm depletion depth were used to detect the particles from the reaction. The maximum energy loss of protons in these detectors was about 9 MeV. The a-particle spectra above the elastic scattered 3He peak from eight detectors were recorded simultaneously in a TMC-4096 multi-channel pulse-height analyser t. The detectors were placed 10 ° apart to measure the differential cross sections. Normalization of different runs was made by using a monitor detector at a fixed angle. Absolute cross sections were obtained by comparison with the elastic scattering of 3He at angles smaller than 30 ° which is assumed to be pure Rutherford scattering. They are accurate to within 20 ~ . For the determination of the excitation energies, two 1024-channel spectra were taken at different angles. The linearity and calibration of the pulse-height analyser were checked with a precision pulse generator. The peak locations of a-particles leading to the ground states of 11C and 150 from the (3He, ~) reactions on carbon and oxygen contaminants in the target served as energy reference points. The uncertainties of the excitation energies and ground state Q-values were due to channel resolution and detector resolution. They are less than 50 keV. The Q-values measured were in agreement with the value given by Mattauch et al. 6) within these uncertainties.

3. DWBA analysis The DWBA analysis was carried out at the Oak Ridge National Laboratory. First the H U N T E R 7) computer program was used to search for the optical-potential parameters by fitting the measured elastic scattering angular distribution of aHe by 64Zn. The optical potential is the Saxon-Woods type gopt(r) = U c ( r ) -

V

1 + exp Zv

iW

1 + exp Zw'

where Uc(r) is the Coulomb potential of a uniformly charged sphere of radius rc A + and Iv = ( r - r v A ~ ) / a v , Z w = ( r - rw A~)/a w.

The geometric parameters, that is, the radius parameters rc, rv, rw and diffuseness parameters av, aw, were kept constant in the search. They were the same as those obtained previously from 58Ni(3He, aHe)SSNi angular distributions. Optical potential parameters for the e-particles were taken from refs. s, 9). t Technical Measurement Corporation.

460

c.M. EOU e t al.

The J U L I E computer code was used for the zero-range DWBA analysis i o, 11). Spins and parities of the ground state and the first excited state of 6 3 Z n a r e known to be 3 - and 3 - , respectively. Therefore, the orbital angular momentum transfers TABLE 1

Parameters of the optical model potentials used in the DWBA calculations V(MeV) aHe

14Z(MeV)

43.16 79.0

15.33 12.0

rv(fm)

rc(fm)

1.67 1.52

1.4 1.4

av(fm)

rw(fm)

0.58 0.60

1.67 1.52

aw(fm) 0.58 0.60

The comparison of the predicted elastic scattering angular distribution with the experimental data is shown in fig. 1 for the 8He channel and in ref. 9) for the ~-channel.

l

I

7

I

I

I

Zn 64 ( He 3,He 3 ) Zn 64

,ff

i.

~'~'~

-

v

A

1.0--

I . C )o

I

:500

I

60 °

I

90 °

I

120 °

I

150 °

180 o

~C.M.

Fig. 1. Comparison of experimental elastic scattering angular distribution with the optical model prediction using the optical-model potential parameters listed in table 1.

are l = 1 for the ground state and l = 3 for the first excited state. Various combinations of aHe and 0c-particle optical potentials were tried to fit the angular distributions assuming these/-values. One combination was found to yield best overall agreement

(81-Ie, Or) R E A C T I O N

461

with the measured angular distributions of the ~-particles leading to the ground and first excited state in 63Zn. The parameters of this combination are listed in table 1. They were used in the calculations for 64Zn(3He, ~)63Zn and also for 7°Ge(3He, 0t) 69Ge" Spectroscopic factors were extracted using the customary separation energy prescription ~,2). The relationship between the experimental differential cross sections and the predictions of the DWBA calculation is given by ~r~xp(l, J ) =

NS(I,

J)trDWBA(I, J )

for the (3He, c~) reaction. The factor N depends, in part, on the overlap of the 3I-[e and alpha particle wave functions and the strength of the interaction responsible for the transition. If one assumes that the wave function of the neutron relative to the aHe ion is given by an exponential with wave number related to the neutron separation energy, one finds N = 1.63. In the previous DWBA analysis of (3He, ~) reactions 1,2) with similar sets of parameters the predicted cross section was too small by a factor of 25__+5. We assume that the same factor applies to the present work. Consequently, the uncertainties of the absolute values of the extracted spectroscopic factors are roughly 20 %. 4. Results

An ~-particle spectrum from the 64Zn(3I-{e,c063Zn reaction is shown in fig. 2. DWBA analysis yielded the following/-value assignments: ground state, l = 1; 0.19 MeV state, 1 = 3; 0.64 MeV state, l = I; 1.64 MeV state, possibly l = 3; 2.60 and I 80

J

I

I

I

Zn64( He~ a ) Z n e3 18 M e V

55"

60 < o

A 4O

,,

..

~

..?.

~

~,

,

-

_

z g 20 -

,'+

600

650

m

"700 CHANNEL

to

750

4

/: 800

NUMBER

Fig. 2. The or-particlespectrum from the e4Zn(SHe,~)6~Zn reaction. The numbers above the peaks are excitation energies in MeV. 3.28 MeV states, both possibly l = 3; 5.42, 6.80 states, both possibly l = 1 (figs. 3-7). Also identified were levels at excitation energies 1.02, 1.22, 2.96 and 4.25 MeV. No angular distributions were obtained for these levels. The ground state, whose spin and parity is known from the fl-decay of 63Zn, results from pick-up of a p~ neutron. The

462

c.M.

FOU

et al.

8 >

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o

(aHe, ~x) REACTION

463

0.19 M e V state is a {- state probably resulting from pick-up o f a f~ neutron in 64Zn. The 0.64 M e V state is either a -}- or ~ - state resulting from pick-up o f a p~ or p~ neutron. Because o f its l o w excitation energy, the 1.64 M e V state is believed to be another ~2 - state rather than a -~- state. The 2.60 and 3.28 M e V states are probably -~- states resulting from the pick-up o f an f~ neutron. I°k;'

I

'

I

IO

'

'

I

,1-

~ ~/~; 1.64MeV State

'

I

'

I

3.28 MeV State .U'=5

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%

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>

,.o

"k~2 60 MeV Slate 2=5 ki. k

o.I

~l

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Zr164(He3 cl) Zn63 "~ 18 MeV

t .

Zn64(He3a) Zn 63

18MeV 001,

i

[

50 o

,

1

60 o

I"

90 °

Oc.m, Fig. 6. D W B A fits for the 1.64 a n d 2.60 M e V states in naZn. See caption to fig. 3.

0o

I 30 o

,

I 60 °

,

[ 90 °

~c.rn.

Fig. 7. D W B A fits for the 3.28, 5.42 a n d 6.80 M e V states in e3Zn. See caption to fig. 3.

The extracted spectroscopic factors are listed in table 2. The sum o f the spectroscopic factors o f the ground state, 0.19, 0.64 and 1.64 M e V states is 5.6. This value is quite reasonable since there are six neutrons in 64Zn outside the closed f~ shell populating the p~, f{ and p½ shell m o d e l levels. Previously, l = 1 assignments have been given to the ground state, 0.64 and 1.04 M e V states in (d, t) work. This agrees with our result for the ground state and the 0.64 M e V state. However, four levels around

c.M. FOU et al.

464

0.64 M e V excitation have been observed. See ref. 12). The 1.04 M e V state was weakly excited in the (3He, ~) reaction; therefore, no a n g u l a r d i s t r i b u t i o n o f the a-particles l e a d i n g to this state was m e a s u r e d . Recently, the g a m m a decay o f the 0.19 M e V state in 63Zn has been studied ~2). T h e spin a n d p a r i t y 3 - o f this state was confirmed. TABLE 2 Spectroscopic factors extracted from the e4Zn(SHe, ~)eaZn reaction assuming N to be 25 × 1.63 Excitation energy (MeV)

1

J

0.00 0.19 0.64 e) 1.64

1 3 1 3

~~](]-, ½-) (~-)

2.60 3.28

3 3

(~-) (]~-)

5.42 6.80

(1) (1)

(9-) (:~-)

Spectroscopic factor

Analogue of

1.5 2.3 1.0 0.8 5.6 a) 1.2 0.9

0.4 0.1 0.5 b)

63Cu g.s. 63Cu 1.42 MeV state

a) Subtotal of the spectroscopic factors of the first four states, which are probably the result of the pick-up of one of the six valence neutrons in 64Zn. , b) Subtotal of the ] - states analogue to G3Cuground state and 1.42 MeV state. The sum rule predicts that the sum of the spectroscopic factors of all T> (9-) states be equal to 0.40 assuming that both valence protons in ~4Zn are in the P~r shell. e) Unresolved levels at 0.627, 0.636, 0.649 and 0.694 MeV excitation. 5. The analogue states of 63Cu T h e shape o f the a n g u l a r d i s t r i b u t i o n o f the 5.42 M e V state in 63Zn is in fair agreem e n t with the l = 1 D W B A p r e d i c t i o n (fig. 7). This state could be the a n a l o g u e o f the g r o u n d state o f 6 3 C u ( 3 - ) . I f this is correct, the C o u l o m b d i s p l a c e m e n t energy is c a l c u l a t e d to be 9.57 + 0.05 MeV. This value is in a g r e e m e n t with the value 9.55 + 0.15 M e V o b t a i n e d b y A n d e r s o n et al. f r o m the (p, n) r e a c t i o n 13). T h e a n g u l a r distrib u t i o n o f the 6.80 M e V state was also in fair agreement with the l = 1 D W B A prediction. Hence, this state could be the a n a l o g u e state o f the 1.42 M e V ( 3 - ) state in 6aCu (ref. 14)). N o states a n a l o g u e to the 0.668 M e V ( ½ - ) a n d the 0.961 M e V ( 3 - ) states o f 63Cu were identified. F o l l o w i n g the s u m rule o f F r e n c h a n d M a c F a r l a n e this p r o b a b l y implies t h a t the two valence p r o t o n s in the 64Zn g r o u n d state are p r e d o m i n a n t l y occupying the p~ level. F o r (3He, ~) reactions on d o u b l y even nuclei the sum rule can be written

~Sj(T> ) - (proton j), N-Z+I E S j ( T > ) + •Sj(T<)

= (neutron j),

T> = Ttar~ot+½;

T< = T, arget-½,

(3He, ~) REACTION

465

where ( p r o t o n j ) and (neutron j ) are the occupation numbers of protons and neutrons in the j subshell, respectively. N is the number of neutrons and Z the number of protons in the target nucleus. Consequently, the sum of the spectroscopic factors of all T>(-~-) states is expected to be less than or equal to 0.40. The present analysis yielded 0.5 for the sum of the spectroscopic factors of 5.42 and 6.80 MeV states. This is about 25 % higher than the predicted value. The failure of the customary separation energy prescription in extracting spectroscopic factors of the analogue states was known for some time 16). A more accurate method has been proposed recently by Stock and T a m u r a 17).

6. The 69Ge nucleus The states which were excited strongly enough to be identified were the ground state, the 0.23, 0.38, 1.00, 1.45, 3.60, 3.80 and 7.00 MeV states. A weakly excited state was also identified around 90 keV excitation (fig. 8). The D W B A analysis yields the folI GeTO(He3,a) Ge69 150

-

18MeV 50 °

.-4. 100

3

°

o;5. "l

50

}

{~51

I..:.;.: ," " . . ' . , :.-..l ~ . , . . . . ", ~ J ,.,,;;.-q.,.:."

ol.

-__''';"

900

950

,; !~ .-,:......

"":."t "

iO00

1050

i I 150

1200

1250

CHANNEL NUMBER

Fig. 8. The e-particle spectrum for the 7°Ge(3He, e)ngGe reaction. The numbers above the peaks are excitation energies in MeV.

lowing/-value assignments: ground state l = 3; 0.38 MeV state, l = 1; 1.00 MeV state, possibly l = 1; 7.00 MeV state, l = 1 (figs. 9-11). The 1.45, 3.60 and 3.80 MeV states were not resolved from neighbouring states at many angles and, consequently, no angular distributions could be obtained. F r o m the shell model, the low-lying states of 69Ge are expected to be ~ - , z - or 1 - states. Hence, their orbital angular m o m e n t a should be either I = 1 or I = 3. The angular distribution of the c~-particles leading to

i

I

"~kGeT°( He3,ct ) Ge69 Ground State ~=3

_~

J

1.0

O.09MeVState

k

~'{'-~,~ \

1.0

- -

{\

_

to

b~

%\ , 0.58MeV State

\

-\

18 MeV

I

~oo

v;;

~\7k$ c " . ~

GeT°(He3,Q~) Ge 69

o.O,o~_

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<..

--'~,~;~ ~oo

,~oo

~'~

i.OOM= I

I

0o

~c.m.

30 o

60 °

~C.M. Fig. 10. D W B A fits for the 0.09, 0.23 a n d 1.00 M e V states in "gGe. See caption to fig. 9.

Fig. 9. D W B A fits for t h e g r o u n d a n d 0.38 M e V states in egGe. A s s u m e d / - v a l u e s for the D W B A calculation are given u n d e r the excitation energies. T h e error bars indicate statistical uncertainties o f the d a t a points only. I

I

7.00 MeV State

°°L-Ge 'I 0°

'87'v , 30 °

60*

90*

Oc.m. Fig. 11. D W B A fit for the 7.00 M e ¥ state in 6~Ge. See caption to fig. 9.

(aHe, ~) REACTION

467

the 0.23 MeV state had poor statistics. It is, however, in better agreement with an l = 1 D W B A prediction than with an l = 3 D W B A prediction (fig. 10). The angular distribution of the a-particles leading to the 0.09 MeV state was obtained by subtracting the peak of the strongly excited l = 3 ground state from the spectra. This introduces a sizeable experimental error. The result is in fair agreement with an l = 3 D W B A prediction (fig. 10). According to the shell model, spin and parity of the ground state with l = 3, as assigned in the present analysis, can only be 5 - . The 0.38 MeV state is likely a 3 state resulting from the pick-up of a Pk neutron, since its spectroscopic factor exceeds two - the m a x i m u m number of p~ neutron available in 70Ge _ by almost a factor of two. The 0.23 and 1.00 MeV states are either 3 - or ½- states. The extracted spectroscopic factors are listed in table 3. The sum of the spectroscopic factors of the ground state, the 0.09, 0.23, 0.38 and 1.00 MeV states is 8.8. This value is very reasonable since there are ten valence neutrons in 70Ge" TABLE 3 Spectroscopic factors extracted from r°Ge(3He, c~)6aGe reaction assuming N = 25 × 1.63 Excitation energy (MeV)

l

Jn

spectroscopic factor

0.00 0.09

3 (3)

~(~-)

3.4 0.6

0.23

(1)

(~-, ½-)

0.2

0.38 1.00

1 1

~(~3--, ~1 - - )

3.9 0.7

7.00

1

~-

8.8 a) 0.2 b)

analogue of

69Ga g.s.

a) Subtotal of the spectroscopic factors of the first five states, which are probably the result of the pick-up of one of the ten valence neutrons in ~°Ge. b) Sum rule predicts the sum of the spectroscopic factors of all T> (~-) states should be 0.57 if the four valence protons in 7°Ge are all in the p~ shell.

7. Analogue state of

69Ga

ground state

The 7.00 MeV state in 69Ge is very strongly excited in the present experiment. Its /-value assignment is in agreement with a spin and parity assignment 3 - which is identical with that of the 6 9 G a ground state 14). Thus, this state may be the analogue state. The calculated Coulomb displacement energy 10.0-4-0.05 MeV is in agreement with the value 10.1+0.15 MeV obtained from the (p, n) reaction 13). Using the separation energy prescription, the extracted spectroscopic factor of the 7.00 MeV state is 0.20. I f one assumes that the four valence protons in 7°Ge just fill up the p~ level, the sum rule predicts 0.57 for the sum of the spectroscopic factors of all T> (~--) states in 6aGe. It is known that the separation energy prescription tends to supply too

468

c.M. FOU et al.

large a spectroscopic factor for analogue states. However, it is not certain from the present experiment whether or not all the T>(2~ - ) states have been observed since only states up to an excitation of 8 MeV have been identified. Therefore, it is not clear whether the fact that the extracted spectroscopic factor is only half of the predicted sum indicates that there are more T> (~-) states or that our assumption about the configuration of the valence protons in 7°Ge is inaccurate.

8. Summary From the spectroscopic information of these two reactions 6 4 Z n ( a H e , ~ ) 6 3 Z n and 7°Ge(aHe, ~)69Ge the ground state neutron configurations of 64Zn and 7°Ge are determined. In 64Zn ground state the occupation numbers of the p~, f~ and p~ levels are approximately 2, 3 and 1, respectively. In 70Ge ground state the occupation numbers of the p~, f~, p~ levels are approximately 4, 4, 1, respectively. It is interesting to notice the gradual disappearance of strong f~ hole states in the nuclei 57Ni, 63Zn and 69Ge. In other words, the f~ hole strength is spread over many more states in 69Ge than it is in 57Ni. This is probably due to the increased number of valence particles in the p~, f~ and p~ levels which increases the number of ways of coupling these particles with an f~ hole to form ~- states. The authors are indebted to Dr. R. H. Bassel for his advise in the DWBA analysis. The use of the computer facilities of Oak Ridge National Laboratory is also gratefully acknowledged.

References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17)

C. M. Fou and R. W. Zurmiihle, Phys. Rev. 140 (1965) B1283 C. M. Fou, R. W. ZurmiJhle and J. M. Joyce, Phys. Rev., to be published B. Zeidman, P. L. Yntema and B. J. Raz, Phys. Rev. 120 (1960) 1723 R. M. Brugger, T. W. Bonner and J. B. Marion, Phys. Rev. 100 (1955) 84 F. D. S. Butement and E. G. Prout, Phil. Mag. 46 (1955) 357 J. H. E. Mattauch et al., Nuclear Physics 67 0965) 1 R. M. Drisko, unpublished A. G. Blair and H. E. Wegner, Phys. Rev. 127 (1962) 1233 L. MacFadden and G. R. Satchler, Nuclear Physics 84 (1966) 177 R. H. Bassel, R. M. Drisko and G. R. Satchler, ORNL-3240 R. H. Bassel, R. M. Drisko and G. R. Satchler, private communication L. Birstein et al., Nuclear Physics 84 (1966) 81 J. D. Anderson, C. Wong and J. W. McClure, Phys. Rev. 138 (1965) B615 Nuclear Data Sheets J. B. French and M. H. MacFarlane, Nuclear Physics 26 (1961) 168 R. Sherr et aL, Phys. Rev. 139 (1965) B1272 R. Stock and T. Tamura, Phys. Lett. 22 0966) 304