The reaction 28Si(3He, α)27Si at E(3He) = 12 MeV

2.G

[ I

Nuclear Physics A130 (1969) 41 --48; ( ~ North-Holland Publishing Co., Amsterdam N o t to be reproduced by photoprint or microfilm without written permission from the publisher

T H E R E A C T I O N 2SSi(aHe, ot)27Si A T E ( a H e ) = 12 M e V K. H. BRAY t and J. NURZYI~SKI Research School of Physical Sciences, Australian National University, Canberra

Received 17 February 1969 Abstract: Angular distributions for the Si(3He, aHe)Si and the 28Si(3He,~)27Si reactions induced by 12 MeV 3He particles have been measured. The analysis in terms of the optical model and the DWBA has been carried out and the results are discussed in conjunction with other data for the neutron pick-up reactions from 2ssi. Occupation numbers for neutrons in d~_,d] and s~ orbits are obtained for the ground state wave functions of 2aSi and compared with the proton occupation numbers. E I

I

NUCLEAR REACTIONS 2aSi(31-Ie,ct) and Si(3He, aHe), E = 12 McV, measured ~r(0). 2aSi deduced neutron occupation numbers.

1. Introduction Direct nucleon transfer reactions have long been used as a powerful tool in nuclear spectroscopy. The best understood and the most c o m m o n l y studied are the single nucleon transfer reactions in which a nucleon is stripped to or picked up from the target nucleus. In addition to the spin selection rules that limit the number of the open channels in these reactions, the transitions in the pickup reactions are restrained by the available nucleon configurations in the bombarded nuclei. These reactions, therefore, have been found useful in yielding valuable information on the ground state wave functions of the target nuclei. Neutron pickup reactions induced by low-energy 3He particles have been studied at the Australian National University for a n u m b e r o f light element targets. As a part of the p r o g r a m m e 2aSi has been included and the results of the measurements and the analysis are discussed in this paper. The reaction 28Si(31--1e, ct)27Si has been studied recently at the incident 3He particle energies o f 10 MeV [ref. 1)] and 15 MeV [ref. 2)]. There is some disagreement between spectroscopic factors derived from these two experiments and it is of interest to c o m p a r e them with the present results. Also included in the discussion are two studies o f the analogous reaction 28Si(p, d)27Si induced by 27.6 MeV [ref. 3)] and 33.6 MeV [ref. 4)] protons. t Now at the University of Manitoba, Winnipeg, Canada. 41

g. H. BRAY AND J. NURZYlqSKI

42

2. Experiment The beam of 12 MeV 3He + ÷ ions, used to study the reaction reported in this paper, was provided by the Australian National University tandem accelerator. Experimental equipment and technique were similar to those described elsewhere 5, 6). The silicon targets were produced in this laboratory by vacuum evaporation of natural silicon powder using a V A R I A N e-gun. Initially, an attempt was made to produce 3000

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(x II I00) 2000 0

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(b)

Ei 8OO (x 1 / 1 6 )

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To •

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..,..'.2 --_~L,.~

--

90

";."

-"l

120

Chonnel

•

"---

"

1% . _ 150

'

"

i80

Number

Fig. 1. Spectra obtained with 12 MeV 3He particles incident on a carbon-backed, natural silicon target at (a) 30~(lab) and (b) 60"~(lab). T h e groups labelled 0, 1, 2, etc, correspond to the g r o u n d state a n d the excited states o f 27Si from the reaction 2sSi(3He, 0027A1. T h o s e labellcd " ; 6 0 " a n d "~2C" were produced by the reactions '60(31-Ie, ~o)150 a n d 12C(3He, ~ o ) " C respectively. T h e group marked " T a " is the elastic peak from Ta(3He, aHe)Ta a n d that m a r k e d " E l " is from the S i + 3 H e elastic scattering.

self-supporting targets. These, however, were found to have too short lifetime under beam bombardment to be of practical use, and a target which was backed by a thin carbon foil was used to record the data reported here. This target also contained impurities of both oxygen and tantalum. The tantalum was due to the use of a tantalum dish as a lining inside the e-gun crucible in order to facilitate the silicon evaporation. Due to these impurities and the carbon backing the angular range of the data for both the elastic scattering and the (3He, "~) measurements was restricted mainly to the for-

ZSSi(3He. a) Z'tS,

43

ward scattering hemisphere. Fig. 1 shows two spectra obtained with 3He particles incident on this target. Contaminant groups are shown by their chemical symbols. When possible, yields for the 2SSi(3He, ~)27Si and Si(3He, 3He)Si elastic scattering reactions were extracted by hand. In cases where a contaminant peak overlapped a I.O

2 8 Si(3He,~He)2aSi

•

I

hO

2 0.5

•

+

0.5

e

I

I

zBSi(3 He ,a )2 7Si ee

2 I

coO•Co

0.2

O.2

e•

e 0 . ,=

#o• 0.1

0.1

I

I

I

I

I

I

2BSi(3He,a)z 7Si

I0

5

I

10

5

Z

e•

*

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I

'F e

0.5

r..

E I

b

÷

+

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0ol

0.1

0.5

0.5

0 .2

0.2

..Q

E

g ¢.)

It++

0.1

0.1

"1o 2 e e

0.2

0.5

o.gs

0.2

b "1o

0 o

c;

0.5

+t

2.65

I

0.5

O.

0.5

0.2

0.2

0.2

0.2

0.1

0.1

0.1

0.1

• ~, 0

O

O.;'B

0.05

0.05

I

I

I

30

60

90

I 120

0

50

I 60

90

120

ec.m. (deg)

ec.m. (deg) Fig. 2. Angular distributions for the reactions Si-~ 3He elastic scattering and 2nSi(3He, a)27Si at 12 McV incident particle energy. Each (3He, ~.) angular distribution is labelled by the excitation energy of the residual state.

peak o f interest a computer code S K E W E D 7) for unfolding Gaussian distributions was used. Results o f measurements are prescntcd in fig. 2. Relative errors greater than the experimental points are indicated. The absolute normalization o f the differential cross sections was estimated to be accurate to within + 6 ~/o.

44

K. H. BRAY AND J. NURZYNSKI

3. Analysis

The elastic scattering angular distribution was analysed using a six-parameter Woods-Saxon optical model potential with volume absorption t. Geometrical parameters were fixed and the search was made on V and W only. The best fits are presented in fig. 3 and the corresponding potentials are compiled in table I.

0.8 0.6 0.4

"~ 0.2

0.1 0.08 0.06 0

I

I

I

I

25

50

75

iO0

125

Oc.m. (deg) Fig. 3. The optical model calculations for Si ~ 3He clastic scattering at 12 M c V . Thc full curve and thc dash-dot curve correspond to the set I and sct 2 paramctcrs of table I. Thc dashcd curve corresponds to set 3. TABLE I Final optical-model parameters for the Si(~He, aHe)Si elastic scattering. The geometrical parameters were fixed at the indicated values

Parameter

V

W

set no

(MeV)

(MeV)

1 2 3

108.0 145.3 155.9

16.3 23.3 18.3

ro (fro)

1.07 1.07 1.08

a (fro)

ro' (fro)

a" (fm)

%2

0.854 0.854 0.800

1.81 1.81 1.78

0.650 0.650 0.600

l 0. I 9.4 10.2

The potentials of table 1 were used in the subsequent DWBA analysis of the 28Si(3He, ~)2Vsi distributions. The parameters for the exit channel were the same as in the analysis of the 27AI(3He, ~)27Si reaction 6) and were based on the elastic scat* The authors are indebted to F. G. Perey for supplying his c o m p u t e r code for the optical model calculation.

28Si(3He ' ~t)27Si

45

tering analysis of McFadden and Satchler a). The neutron bound state wave functions were calculated for a real Woods-Saxon potential of radius 1.2 A + fm and diffuseness of 0.65 fm. The depth was adjusted to give the separation energy for the transferred neutron. I

:

I

[ .......

0.96 MeV ( 3 1 2 + )

O.OOMeV ( 5 / 2 + )

IO.C

g:

,g=2

2

5,C

2.0

1.0 0.5 0.2 0.1

E

I

I

I O.78MeV ( I/2 + )

d

5.0

"~

2.0

2.65 MeV ( 5 / 2 + ) g=2

.e=O SET

i ~',I,

1.0

.......

SET

....

SET B

,'h

0.5 4

0.2

t-,

OJ 0.05 -

0

~0

I

I

60

90

I

120 0 Oc.m. ( deg )

30

60 l

9G

Fig. 4. D W B A fits to the 2sSi(3He, ~)27Si a n g u l a r distributions. T h e y are labelled by the excitation energies o f the relcvant residual states. Curves for three 3He potentials (sets 1, 2 a n d 3 o f table 1) are s h o w n for the 0.78 MeV a n g u l a r distribution. For the others, only the set 1 calculations are shown. All calculations are for a zero cut-off radius.

The calculations were performed using the D R C programme written by Gibbs e t al. 9).

The distribution con'esponding to the 2.17 MeV, J~ = 7 + state was not analysed as it does not exhibit characteristics of a direct pickup transition.

46

K. H. BRAY

AND

1. NURZY?hSKI

The results of the calculation are compared with the experimental data in fig. 4. The three I = 2 angular distributions did not evince a preference for any of the three sets of the The I = 0 fig. 4 were off radius

3He parameters and only the set 1 predictions for 1 = 2 are shown in fig. 4. first excited state transition is fitted best by set 2 potential. All the curves in calculated with zero cut-off radius. DWBA calculations with a lower cutof 3.5 fm were also tried but did not produce any significant difference in

the calculated

distributions. 4. Discussion

The observed direct pickup transitions to the low-lying states of “Si and the relatively large absolute cross sections indicate a significant admixture of d,, s+ and d, orbits in the ground state wave function of “Si. Further, since the third excited state has J” = 3+, its excitation by direct pickup would require a gz admixture. The character of the angular distribution corresponding to this state does not indicate the presence of an admixture of this type. TABLE

Spectroscopic

factors

for neutron

2 pickup

reactions

PHe, a) 7 PHc, a) ‘9 PHe, Co7 I 27Si . _0 0.714 0.952 2.647 2.90 ‘) 4.215 6.343

“) Ref. I). doublet.

10 MeV

from

12 McV

15 MeV

0, d) ‘) 21.6 MeV

3.00 0.33 0.67 0.72

2.99 0.42 0.38 0.16 (1.43)

2.14 0.65 0.37 0.23 (0.82)

**Si (P,

s

d) ‘)

33.6 MeV

1”

neutron pickup

-.2 0 2

2.043 0.70 0.50

1.30 (:I 2 2

b, Present

work.

‘) Ref. 2).

d, Ref. a).

‘) Ref. 4).

3.45 0.64 0.34 0.47 (0.81) 0.34 0.45

2.12 0.55 0.45 0.70 1.02 0.34 0.45

‘) Unresolved

The contributions of d,, s_; and d, orbits in the ground state wave function of “Si can be estimated by calculating neutron occupation numbers (nu) = ciS,lj), where 5’:;’ is the experimental spectroscopic factor of the ith state corresponding to the0 configuration. Spectroscopic factors found in the present experiment as well as those from some other studies of neutron and proton pickup reactions from 28Si are compiled in tables 2 and 3. The present results were calculated using an average normalization factor R = 31 as determined for the ‘60(3He, a)r50 reaction lo). Comparing them with other (3He, cz) measurements taken at two adjacent energies it may be seen that the 12 MeV results agree better with the 15 MeV data than with those obtained at 10 MeV.

28Si(3He, 0t)27Si

47

TABLE 3 Spectroscopic factors for proton pickup reactions from 28Si E~ (MeV) 27A1

J,~

l

0 0.843 1.013 2.760 2.988 ~) 4.410

z~+ ~÷ ~÷ ~÷ ~+ (~)+

2 0 2 2 (2) 2

~) Ref. it).

a) Ref. ~2).

(d, aHe) a) 34.4 MeV

(d, aHe) b) 16.1 MeV

3.76 0.49 0.56 0.61 ~0.40 0.35

Sa~ proton pickup

3.12 0.79 0.75 0.75 :< 0.24

3.44 0.64 0.66 0.68 ~ 0.32 0.35

¢) Unresolved doublet.

TABLE 4

Scaled spectroscopic factors for the neutron pickup from 2aSi E~ (MeV)

jr

l

(aHe, ~) ") 10 MeV

0 0.774 0.952 2.647 2.90 r) 4.275 6.324

~÷ ½+ ._a,+. ~÷ (~)÷ (za, .~)+ (.~, ~)+

2 0 2 2 (2) 2 2

1.84 0.65 0.46 1.20

") Ref. 1). doublet.

b) Present work.

(3He, ct) b) 12 MeV 2.64 0.29 0.59 0.63

c) Ref. 2).

(aHe, ~) ¢) (p, d) d) 15 MeV 27.6 MeV 2.71 0.38 0.34 0.72 (1.30)

a) Ref. a).

(p, d) ¢) 33.6 MeV

Say

2.93 0.54 0.29 0.40 (0.69) 0.29 0.38

2.55 0.53 0.43 0.65 (1.00) 0.29 0.38

2.62 0.80 0.45 0.28 (1.00)

¢) Ref. '~).

t) Unresolved

TABLE 5 Occupation numbers and filling probabilities for 2sSi ground state Orbit

Neutrons a)

(nil),

d.(l,j)

(nll)o b)

en(l,j) b) (%)

(n,l)p

d'p(/,j) (%)

3.49 0.81-1.81 0.53

58 20-45 27

4.47 0.66-0.98 0.64

75 17-25 32

(%) d{ d~ s¢

3.76 0.90-1.92 0.55

63 23-48 28

Protons

a) In analogy to the proton pickup the numbers for neutrons were calculated assuming that the d~_ strength was shared by three states only in 27Si. b) The numbers were calculated from the spectroscopic factors normalized to the results for the (p, d) reaction. T h e first f o u r s t a t e s i n 27Si c o n t a i n a b o u t 70 ~ o f t h e t o t a l s t r e n g t h f o r l -- 0 a n d l = 2 t r a n s i t i o n s f r o m 285i. T h e m e a s u r e m e n t s a t 33.6 M e V [ref. 4)] s u g g e s t t h a t t h e

48

K.H. BRAY AND J. NURZYNSKI

remaining 30 ~o or so of the total strength is shared by three othcr transitions to states below 6.4 MeV. As, however, no l = 0 transition was observed 4) to states above the 2.647 MeV level it may be concluded that tile spectroscopic factor for the 0.774 MeV state represents the total l = 0 strength. Using the average spectroscopic factors of column 9, table 2 and assuming that, analogously to the proton pickup, the total d~ neutron strength is shared by the three states only, i.e. the ground state, the 2.647 MeV and the 4.275 McV excited states, the following estimates of the occupation numbers for neutrons in the 28Si ground state can be made: (n2~) = 3.76, 0.90 < (rt2k) <; 1.92 and n(o~_) = 0.55. In calculating the occupation numbers, absolute values of the spectroscopic factors have to be known. For the (3He, ~) reactions these values depend on the normalization factor R which contains the overlap factor for the formation of the ~-particles from 3He + n as well as the interaction strength. The normalization factor which has to be found experimentally, is not well determined, particularly at low aHe energies. It is believed that the (p, d) reaction is free from this type of ambiguity and, consequently, in order to check the effect of using different normalization factors on the calculated occupation numbers all the results from table 2 for the neutron pickup were renormalized to give, at each energy, a sum for the first four states in 27Si equal to 4.15, which is the avcrage sum for the (p, d) measurements taken at 27.6 MeV and 33.6 MeV. The renormalized spectroscopic factors are presented in table 4. They do not differ significantly from the relevant values in table 2 and consequently they would produce occupation numbers similar to those already calculated. All the calculations are summarized in table 5 which includes the occupation numbers for neutrons and protons as well as the probabilities ~(l,j) for filling the particular orbit. The probabilities are defined as d~(l,j) = (n~i)/ntj, where nti is 6, 2 and 4 for d÷, sl and d~ orbits respectively. If the assumption that the d~ strength is shared by three states only is correct, then the results indicate that neutron orbits Ida, 2s~ and ld a in the ground state of 28Si are filled to approximately 60 ~ , 30 ~,, and 30 respectivcly. Comparable results are obtained for the proton pickup as may be seen from tables 3 and 5. Both neutron and proton shells in the ground state of 2Ssi are, therefore, tilled in similar proportions. References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12)

B. H. Wildenthal and P. W. M. Glaudemans, Nucl. Phys. A92 (1967) 353 L. W. Swenson, R. W. Zurmtihlc and C. M. Fou, Nucl. Phys. A90 (1967) 232 G. D. Jones, g . R. Johnson and R. J. G r i ~ t h s , Nucl. Phys. A107 (1968) 659 R. L. Kozub, Phys. Rev. 172 (1968) 1078 K. H. Bray, J. Nurzyfiski and G. R. Satchlcr, Nucl. Phys. 67 (1965) 417 J. Nurzyfiski, K. H. Bray and B. A. Robson, Nucl. Phys. A107 (1968) 581 P. McWilliams, W. Hall and H. Wegner, Rev. Sci. Instr. 33 (1962) 70 L. McFadden and G. R. Satchler, Nucl. Phys. 84 (1966) 177 W. R. Gibbs et al., N A S A T N D-2170 (1964) K. H. Bray and J. Nurzyfiski, Nucl. Phys. A127 (1969) 622 B. H. Wildenthal and E. Newman, Phys. Rev. 167 (1968) 1027 H. E. Gove, K. H. Purser, J. J. Schwartz, W, P. Alford and D. Cline, Nucl. Phys. A l l 6 (1968) 369