Spectroscopic study of 31P and 32S by the (d, n) reaction at Ed = 7 MeV

Nuclear Physics A267 (1976) 217-236; (~) North.Holland Publishing Co.. Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher

SPECTROSCOPIC STUDY OF 31p AND 32S BY THE (d, n) REACTION AT E., ffi 7 MeV J. UZUREAU

lnstitut de Physique, BP 1044, 44037 Nantes, France and A. ADAM, O. BERSILLON and S. JOLY

Servieede PhysiqueNucl~aire,CEBruybres-le-Chdtel, BP 61, 92120 Montrouoe, France Received 20 April 1976 Abstract: The 3°Si(d, n)31P and 31P(d, n)32S reactions have been studied at 7 MeV deuteron bombarding energy using the time-of-flight technique with a good neutron energy resolution. Angular distributions of neutrons leading to 18 levels in 3~p and 30 levels in 32S were analyzed in the framework of the DWBA and HF theories to deduce lp values and transition strengths. New spin and parity assignments were obtained for some levels. The transitions to unbound states are described in terms of the conventional DWBA theory using complex-energy eigenstates as form factors. The experimental results are compared with the corresponding data from previous studies and with shell-model

calculations.

E

NUCLEAR REACTIONS 3°Si(d, n), 31P(d, n), E = 7 MeV; measured ~r(E,, 0). 3~p and ~2S deduced levels, lp, J, 7r, T, spectroscopic factors. Natural and enriched targets.

1. Introduction The present work is part of a general study of nuclear structure in the ld t and 2s½ shell region by means of the (d, n) reaction ~' 2). Because the information derived from the 3°Si(d, n)31P and 3~P(d, n)32S reactions a) was rather scarce a new study of these reactions was undertaken. The experiments described in this paper, performed at a deuteron bombarding energy of 7 MeV with good neutron energy resolution, have been undertaken in order to compare the spectroscopic factors deduced from (d, n) reactions with values determined from previous (~, d) reaction studies. In fact, large differences have been observed for some levels of light nuclei, especially for isobaric analogue states 4), between the spectroscopic factors deduced from these two types of one-proton transfer reactions. We also have observed significant differences for the first two T = a2 levels in 27A1 [ref. 2)] and we were interested in a further comparison for near-by nuclei. Here we present results for levels in 3~p and 32S populated by the (d, n) reaction. 217

218

J. UZUREAU

et al.

A more general discussion about these and other previously published 1,2) results will be made in a subsequent paper s).

2. Experimental procedure The pulsed deuteron beam was accelerated by the EN Tandem Van de Graaff generator at Bruy6res-le-Ch~itd. The details of the neutron time-of-flight facility have been given previously 6.7). Six NE 213 liquid scintillator detectors mounted on 58 DVP Radiotechnique photomultipliers were used for the neutron spectrometer. For the 3°Si(d, n)alP experiment the scintillators were 10.2 cm in diameter and 2.5 cm in thickness but, in order to improve the counting rate, the thickness was increased to 5.1 cm for the study of the 31p(d, n)3ZS reaction. Further details can be found in recent publications 6, 7). T h e 3°Si target, supplied by HarweU, consisted of a layer of 95 #g/cm 2 SiO 2 enriched to 95.5 % in 3°Si on a 0.5 mm gold backing 7). The 31p target was prepared at Orsay by evaporation of red phosphorus on a 0.5 mm gold backing using the method proposed by Hooton s). The target thickness was about 190 #g/cm 2 [ref. T)]. Angular distribution measurements were taken in 5° steps from 0 ° to 50° and extended to 60 °, 70 ° and 80 °. For the 31P(d, n)S2S reaction two more angles, 55 ° and 100°, were added. A constant flight path of 18.3 m was used. For such a path, the energy resolution was about 90 and 20 keV for neutrons leading to the ground state and the 7.90 MeV excited state in 31p, respectively.

3. Cross-section analysis In the analysis of the angular distributions it was assumed that the theoretical cross sections can be expressed as an incoherent superposition of direct-reaction (DI) and compound-nucleus (CN) cross sections according to dr7 da (dd--~),h -- (d-~)D + (d-~)cN,

da da with ( ~ ) ¢ N = R ( ~ ) .

v.

(1)

The direct part was calculated in the framework of the DWBA theory and the compound-nucleus contribution was evaluated in the Hauser-Feshbach (I-IF) formalism. 3.1. DWBA ANALYSIS

3.1.1. Bound levels. For the bound levels, the DWBA cross sections were calculated by means of the code DWUCK 9). For the (d, n) reaction, the cross section is given by the expression

DI

2J t + 1 2 - ~ \d--~JDWUCK (mb/sr),

(2)

alp A N D a2S

219

where Ji and Jf are the spins of the initial and final states and j is the total angular momentum for the transferred proton; Sp.iS the spectroscopic factor and C is the isobaric Clebsch-Gordan coefficient. For 3°Si(d, n)31P, C 2 = za for the T = ½ states and C 2 = 13for the T = a2 states. For 3tP(d, n)32S, we have C 2 = x2 for both T = 0 and 1 states. Woods-Saxon optical model potentials with a surface absorption term were used in these calculations. The deuteron potential parameters used were determined by Schwandt and Haeberli to) from the elastic scattering of 7 MeV deuterons on 27A1. The neutron parameters were taken from the energy-dependent parameters of Wilmore and Hodgson 11). Furthermore, a spin-orbit interaction with Vs.o. = 7 MeV was added according to Percy and Percy 12). The bound-state potential was of the usual Woods-Saxon type with a depth adjusted in order to reproduce the experimental proton separation. In the DWBA calculations, the corrections for the finite range of the n-p interaction (R = 0.62 fm) and for the non-locality of the potentials in the entrance (fld = 0.54 fm) and exit channels (fl~ = 0.85 fro) have been applied. The optical model parameters used in the DWBA analysis are given in table 1 for the 31p(d, n)32S reaction. TABLE 1 Optical model parameters used in D W B A and H F calculations for the 3tP(d, n)32S reaction Channel

V

r

a

W

r w

(MeV)

(fro) ( f l n ) ( M e V ) ( f m )

31p+da)

112.05

32S+nb )

e)

1.05 0.86 1.30 0.66

Captured proton 32p +pC) 3°Si+~d) 29Si+ctd)

s)

1.25

0.65

~ 50 h) 1.25 145 1.30 197.1 1.35

0.65 0.67 0.59

a) e) f) s) h)

a ~,

W o

rD

(fm)(MeV)(fm) 14,68 f)

aD Vs.o. r .... (fm)(MeV)(fro)

1.57 0.62 1.26 0.48

9 7

a .... r, (fm) (fm)

0.75 0.40 1.30 0.66

2=25 9.54 18 17

1.63 1.35

1.25

0.47

7.5

1.25

fl (fm)

1.25

0.54 0.85

1.3

0

0.65

0.48 0.59

Ref. 1o). b) Refs. 11,12). c) Ref. 13). d) Ref. t4). V = 47.01-0.267 E - 0 . 0 0 1 8 E 2 [ref. 12)]; both V a n d E a r e in MeV. W D = 9 . 5 2 - 0.053 E [ref. 12)] ; both Wv and E are in MeV. Adjusted by the computer code D W U C K . Ref. 13).

Additional DWBA calculations have been performed for some of the bound levels using the code VENUS xs). It was found that the shape/rod the magnitude of the calculated angular distributions were roughiy the same. 3.1.2. Unbound levels. Some of the levels in Sip and twelve levels in S2S observed in the present work have an excitation energy above the proton emission threshold (E x >__7.30 MeV for 31p and Ex ~ 8.86 MeV for 32S). In order to calculate in a more accurate way the angular distributions corresponding to these levels, we have used the method developed by Coker et aL 16,17).

220

J. UZUREAU et al.

According to this procedure, complex-energy eigenstates (or Gamow functions) of a single nucleon in a real Woods-Saxon potential are first computed. For a given optical potential, the GAMOW-3 program 16,17) determines the complex energy at which the single-particle wave function asymptotically approaches a purely outgoing Coulomb wave. The well depth Vp is adjusted for each resonance in order to find a resonance energy in agreement with the experiment. The geometrical parameters used in the program were r = rs.o. = 1.25 fm,

a = as.o. = 0.65 fm,

V~.o. = 6.25 MeV.

The resonance energies Ex, the well depths Vp and the single-particle widths Fs.p. are given in table 2. TABLE 2

Resonance parameters for 3Jp and 32S and spectroscopic strengths obtained with Gamow (GS) and weakly bound state (BS) form factors

E~

ER a)

(MeV)

(MeV)

31p

7,90 8.05 8.25 8.57

0.604 0,753 0.954 1.267

Pl/2 P3/2 P3/2 P3/2

32S

9.06

0.204 0.344 0.344 0.375 ~ 0.427 0.427 0.516 0.625 0.866 0.987 1.213 1.477 1.534

P3/2 st/2 daj 2 P3/2 sl/2 da/2

Residual nucleus

9.21 9.24 9,29 9.39 9.49 9.73 9.85 10.07 10.33 10.40

Ij

P3/2 P3/2 P3/2 P3j2 P3/2 Paj2 P112

J~

Vp

F~ p

(MeV)

(ke'V)

G6 s b)

GBs, )

12 (~2-) 12 ~2

64.62 60.08 59.51 58.59

0.026 0.30 4.06 25.34

0.22 0.04 0.04 0.06

0.29 0.06 0.07 0.14

11+ 1+ 11+ 1+ 2111210-

61.20 41.35 45.46 60.77 41.15 45.32 60.42 60.13 59.50 59.16 58.52 57.74 61.64

0.33 x 10 -8 0.93 x 10 -4 0.4 x 10- 5 0.34 x 10- * 0.13 x 10 -2 0,5 x 10-* 0.17 x 10 -2 0.015 0.63 2.7 14.3 32.4 37

0.10 0.013 0.04 0.04 0.01 0.06 0.23 0.06 0.075 0.02 0.31 0.08 0.07

0.07 0.015 0.05 0.04 0.01 0.06 0.27 0.08 0.11 0.04 0.60 0.21 0.20

") E a = E ~ - B p where Bp is the proton binding energy in the final nucleus. b) Spectroscopic strengths obtained using Gamow states as form factors. c) Spectroscopic strengths obtained in the approximation of a weakly bound state (by 50 keV).

In a second step, the D W B A calculations, with the Gamow states as form factors, are performed with the code V E N U S I s) using the same optical potential parameters as those used for the bound-level analysis. The spectroscopic factors corresponding to unbound states are then extracted through the relation da

31p AND 32S

221

For the unbound states, the DWBA calculations with Gamow form factors have been compared with those obtained in the approximation of a weakly bound state (by 50 keV). The shape of the angular distributions, as computed for lp = 1 in the two methods, was found to be different especially for levels unbound by more than 1 MeV. These discrepancies become larger for states with higher excitation energy as shown in figs. 3 and 6. The same conclusion applies for the computed cross sections, and the derived spectroscopic factors, as can be seen in table 2. The more realistic values are evidently obtained with Gamow form factors because the tail of the proton wave function is taken into account in the region of the interaction. 3.2. HAUSER-FESHBACH CALCULATIONS

The Hauser-Feshbach cross sections were calculated by the computer code CINDY is). The optical model parameters used in the DWBA and HF calculations for the 3iP(d, n)32S reaction are given in table 1. The calculated cross sections (da/dO)n F must be multiplied by an empirical normalization factor 0 ~ R _< 1 [ref. tg)]. This factor takes into account the channels which absorb the incident flux but which are not explicitly included in the CN calculations, i.e., all of the direct-reaction cross sections as well as transitions to unobserved levels. The reduction factor was determined by requiring optimum fit between the calculated angular distributions and the experimental ones which did not contain any discernible direct component. The experimental distributions chosen for this comparison were for well resolved transitions to levels with known spin. The following levels were used: 3.41 ( 7+ ~ ) , 4.78 (~+ 2 ) , 5.34 (2~+) and 5.89 MeV (2~+) in 3tp [refs. 3,20)] and the levels at 4.28 (2+), 4.46 (4 +) and 5.41 MeV (3 +) in 32S I'refs. 3.7)1" Good agreement between calculated and experimental cross sections was obtained for the mean values R = 0.070 and 0.075 in the 3°Si(d, n) 31p and 31P(d, n)32S reactions, respectively. These values were then used for all the studied levels and good fits to all the experimental distributions were obtained except for some of the lp = 0 transitions.

4. Spectroscopic information from the 3°Si(d, n)31P reaction 4.1. PREVIOUS EXPERIMENTS

The 3°Si(d, n)3tP reaction has been previously studied by Cujec et al. 21) and by Davies et aT~ 2) especially to locate the first T = ~2 levels in 3xp. The reaction was studied at deuteron bombarding energies between 3 and 5 MeV and no spectroscopic factors have been determined. On the other hand, spectroscopic information has been obtained for thirty levels with excitation energies below 7 MeV in the 3°Si(~, d) reaction 23- 2s).

222

J. UZUREAU et al.

4.2. EXCITATION ENERGIES AND ANGULAR DISTRIBUTIONS

A typical time-of-flight spectrum from the 3°Si(d, n)atP reaction at E d = 7 MeV is shown in fig. 1. The neutrons were detected at 0 = 10° with a flight path of 18.3 m.

NEUTRON ENERGY |MeV) EO

~0

z..O

7.0

I

o 7

-i1

=

;

8.0

9.0

10.0

I

I

I

11.0

12.0

3°'Si(d, n ) 31p

J

Ed = 7 MeV Blab. = 10=

g

200

Flight path =18.3 m

p~

g I00

"4

8~o

9~10

1000

,,k

O~

UnW

~J

#~

,2ha CHANNEL NUMBER

Fig. 1. Neutron time-of-flight spectrum from the 3°Si(d, n)31P reaction; taN, l~F and 29p states are excited through the (d, n) reaction on the contaminants of 12C and 160 and on the 4.5 % 28Si present in the target.

About thirty levels in 31p can be identified up to an excitation energy of 8.5 MeV. Prominent peaks arise from the contaminants 12C and 160 in the target and inhibit the analysis of near-by states. A rather precise determination of the excitation energy of the strongest populated levels in 31p was possible by a least-squares fitting procedure. Transitions to the ground state and the first excited state of the residual nucleus along with the peaks from ~aN and ~7F were used as calibration peaks. The excitation energies given in table 3 were extracted from eight different spectra. The adopted errors represent two standard deviations with respect to the mean values. It can be seen that our values are in fair agreement with the energies quoted by l~ndt and Van der Leun 3). The angular distributions of tansitions to eighteen levels are plotted in figs. 2 and 3 in increasing order of excitation energies. The absolute differential cross sections were corrected by about 15 % for neutron absorption in the wall of the scattering chamber and in the air along the flight path. The total uncertainty in our absolute cross sections lies between 15 % and 25 % and is due primarily to statistical considerations 7).

223

31p AND 32S '

' I ' I ' I ' I

~.

t0.O

I

'

3.0'

200

'

I

'

I

Ex= G.50t,4eV Ip= 1 "

Ex= 0 MeV Ip=0

5.0

I

asl121I2..........~---.~.~

aS

Ex =6,59÷6.6tIdeV tp=l*3

0.~

1.O~ . ~ +

Ex =1.27MeV Ip= 2

2.( I.O

*

b

,

0.1 .....................................................

~+

0.5 q

.

Ex=S.91.6.92MeV ~ ~

2.0 "

0.1~

1.0 (15

Ex=2.23'MeV

T

0.1

'

$ 5.0 N.

0.5 t , ~

lp=0 •

0

20

Ex= "/'1/'MeV

1.0 ~

_1

Ip=O

t~L~

t,0

G0 80

0

20

t.0

60

80

L

I . I , I

20

,

z0 60 80

Oc.m. 30 Si(d, n) 31 P reaction. The dotted lines represent the c o m p o u n d - n u c l e u s c o n t r i b u t i o n calculated with the H F f o r m a l i s m . T h e solid lines are the i n c o h e r e n t s u m s o f the D W B A a n d H F predictions. T h e vertical bars represent statistical errors.

Fig. 2. A n g u l a r distributions o f n e u t r o n s f r o m the

4.3. THE lp VALUES AND J" ASSIGNMENTS

4.3.1. Positive parity states. Four lp = 0 transitions were observed in the 3oSi(d ' n)3 ip reaction; the first one excites the ground state and the others the levels at 3.13, 5.25 and 7.14 MeV. The only possible spin and parity values restricted by selection rules (J" = ½÷) agree with previous determinations 3, 25). It has been shown also that the level at 7.14 MeV is the analogue of the first excited state in 31Si [refs. 3,25)]. The experimental angular distributions associated to these four levels are well fitted by theoretical curves with lp = 0 especially at forward angles (fig. 2). However,

J. UZUREAU

224 •

e t al.

'

' I ' I ' I ' I

i

,

' I ' I ' I Ex= 8.DSMeV

E x = 721 MeV lp = 1

1.0

g ! I: .............. "-.~.-

0.1

0051 ~

0.05

2.0:]

~'~

Ex: 825 MeV tp=l

1.01 ~

nsl Ex-_7.90 MeV

Ill l 0~051 ............................

|.0

3.0"]

0.5

Ex= &56 MoV

t01 ~

I.......

OJ

"t

0.O2

Ill I. aosl

0

20

z,O

60

tp=l

,

,

20

80

,

,

/,0

:-7-~.--~,

60

90

9c.r~

Fig. 3. Angular distributions of neutrons from the a°Si(d, n)31P reaction. The dot-dashed curves represent the incoherent sums of D W B A cross sections calcuiated using G a m o w states form factors and HF cross sections. See also caption of fig. 2. the agreement between experiment and the calculations is not so good for angles greater than 30.o A similar effectwas observed in the previously studied 26 Mg(d, n) 27 A1 reaction 2). Then we can assume the same effect applies to the target nucleus 3°Si for which the deformation was found to be/3 ~ 0.30 [ref. 26)]. The angular distributions associated to the levels at 1.27 (2+ 2 ) , 2.23 (2~+) and 6.38 MeV (2~+) are well reproduced by an lp = 2 DWBA curve. The level at 6.38 MeV is also the first T = a2 state in 31p. 4.3.2. Negative parity states. Angular distributions with lp = 1 are also presented in figs. 2 and 3. In general the agreement between the experimental and theoretical distributions is very good except for the 8.05 MeV level. The deduced J" = 12- or { - values for the levels at 5.01 (2~-), 6.50 (½-, 2~-), 6.91 (2~-), 7.21 (½-, 2a-), 7.90 (½-), 8.05 (2~),8.25 (2~) and 8.56 MeV ({-) are in agreement with previous results 3). We can assign negative parity to the levels at 8.05 and 8.25 MeV. The level at 4.43 MeV ({-) is the first negative parity state in 31p and the corresponding angular distribution is well reproduced by an lv = 3 calculation. The transitions to the levels at 6.59 (2~-) and 6.61 MeV ({-) have not been resolved experimentally. However, it was possible to reproduce the angular distribution of the sum of these transitions by a mature of lp = 1 + 3 in agreement with spins and parities 3).

31p AND 32S

225

4.4. SPECTROSCOPIC STRENGTHS T h e spectroscopic strengths deduced f r o m the analysis o f the 3°Si(d, n)3~P reaction are s u m m a r i z e d in table 3 along with the results o f previous (~, d) studies 23-2s). TABLE 3 Spectroscopic information from proton stripping to s~p states G = (2Jf+ I)C2Sp Ex a) (keY)

Ex b) (keY)

J'~; T ¢)

lp a)

0 1268+_10 2226+_ 10 3125+ 8 4421_ 4 5006+ 4 5248+_ 4 6376+_ 4 6494+ 4

0 1266.13+0A2_ 2233.8 _+0,3 3134.3 +0.4 4431.2 +0,4 5014.9 +1.0 5253 +2_ 6381 _+3 6495 +3 6594 +2 6610 +2 6908 _+3 7139 _+2 7211 _+4 7898 +__2 8050 -I-2 8249 _+2 8556 _+2

1+2 3+2 ~-+2 ½+ 27-51+2 ~-+-2,2z

0 2 2 0 3 1

6600+ 4 6905_+ 4 7139+_ 4 7213+_ 5 7901 + 4 8050+ 4 8251 _+ 4 8564+ 7

0 2

(½, 5)-

1

~2-a-2 ±+2,2'3 (!2,2~)x~_

3 1 1 0 1 1 1 1 1

L : ~-

nO'

DWBA 2sl/2 lds/2

lds/2 2Sl/2 lfT/2

2p3/2 2sl/2 ld3/2 2p3/2 lfsj 2 2p3/2 2p3/2

2Sl/2 2p3/2 2pt/2

2P3/2 2P3/2 2ps/2

(d, n) ~) 7 MeV 1.05 2.24 0.22 0.02 2.09 0.61 0.04 0.49 0.12 0.21 0.03 0.08 0.07 0.03 0.22 h) 0.04 0.04 0.06

(r, d) d) 12 MeV 0.93 1.93 0.27 0.04 2.07 0.74 0.06 0.70 0.19 0.15 0.06 0.09 0.16 0.04

(r, d) ") (r, d) f) 15 MeV 17.85 MeV 0.88 3.20 0.48 0.06 2.29 0.83 0.13 1.07 g)

0.97 2.6 0.49 0.06 2.9 0.96 0.10 1.0 0.29

0.05

0.15 0.68

a) Present work. b) Ref. 3). ~) Ref. 3) or present work. d) Ref. 25). e) Ref. 23). f) Ref. 24). s) Corrected according to ref. 3a). h) For the unbound levels (Ex > 7.30 MeV), G is determined with Gamow form factors (see subsect. 3.1.2.).

Generally, o u r results are in agreement with the results o f W o l f f a n d L e i g h t o n 25) but some i m p o r t a n t discrepancies exist for the first two T = ~2 states in 31p. The spectroscopic strengths determined by M o r r i s o n 23) or Lutz et al. 24) are often different f r o m the present results a n d f r o m those o f W o l f f a n d L e i g h t o n 25) perf o r m e d with an excellent energy resolution. This is the case for the levels at 1.27 M e V ['ref. 2a)], 2.23 M e V [refs. 23,24)'], 4.43 M e V [ref. 24)], 6.38 M e V [refs. 23,24)] a n d 7.14 M e V [ref. 24)]. T h e spectroscopic factors deduced f r o m the present w o r k are Sp = 0.37 and 0.11 for the first two T = ~2 states I-6.38 M e V (2~+) a n d 7.14 M e V (2x+)] a n d are smaller t h a n the values S . --- 0.87 a n d 0.27 deduced f r o m the 3°Si(d, p)31Si reaction for the p a r e n t states by Wildenthal a n d G l a u d e m a n s 27). O n the other hand, the results o f

226

J. U Z U R E A U

et al.

Wolffand Leighton 2s) (S v = 0.53 and 0.24) are in better agreement with these latter values especially for the 7.14 MeV state. 5. Spectroscopic information from the 5.1. P R E V I O U S

3~p(d, n)32S reaction

EXPERIMENTS

The aZP(d, n)a2S reaction has been studied by Ferguson et al. 2s) at a deuteron bombarding energy of 4.9 MeV and angular transfer momenta and relative spectro3 scopic factors were obtained for eight levels in 32S (including two T = 1 states). The same reaction was studied recently by Hussein et al. 29) at E a = 4.0 and 5.45 MeV and the angular distributions leading to the first excited states have been analyzed in the framework of the DWBA theory. The a~P(z, d)32S reaction has also been studied 2~, 3o, al). In these experiments, spins and parities were assigned to about twenty levels in 32S and abolute spectroscopic factors were determined. 5.2.

EXCITATION ENERGIES AND ANGULAR DISTRIBUTIONS

A time-of-flight spectrum of neutrons from the alp(d, n)32S reaction is shown in fig. 4. About fifty levels can be identified in the final nucleus up to an excitation

7.0

6.0 .

400 ~_~

NEUTRON ENERGY (MeV) 80 9O

I

I

I

lO.O

11.o

12.o

13.0

I

I

I

I

I

Po

31pld'n132S

¢~c,a

,,~ .,,~ LDO0

-,,4.-..4 ~

Ed = 7 MeV

Blab, = 15"

P

Flight path = 18.3m O

cn

200

760

66o Z

~

600

9~

aN

3.0

4.0

3.5

[zz-

p

p~i

b

5.0

4.5 I

I ~D ~

o,

400

r

g

2J

200

200

300

400 CHANNEL NUMBER

Fig. 4.

Neutron time-of-flight spectrum from the a~P(d, n)32S reaction.

500

31p AND 32S '

5.0

~

|

'

~

I

'

E

I

'

I

'

i

I

x= 0 MeV

I

'

I

'

0.5 -

1.0

0.5

0.05

005

Ex = 2.23 MeV Lp=2

'

I

tO=2

"~t

*t

Ex= 5.80 MeV tp = 1

0.5

1.0

I

.-4-.......

2D ~ , L0

0.1

'

Ex = 5.55 MeV lp=2

Ip=O 0.1

;

227

3.1 2.........................................................

,'',

Ex = 7.19 MeV lp=O

5,0 tOI

0.1 ~:..............

O05

0.5

3.0 " t / ~ 1.0 •

0.1

Ex = 6.22 MeV Ip=l ~

+

0.t .................

t

L05

Ex= 3.78 MeV Ip=0

~.o

4¢

Ex = "/43 MeV

3.0

0.s

1.0 / O ~ ,

[p=l

\¢¢~

0.5

0.t

*

0.05

0.1

0.or Ex= 470 MeV [p = 2

to 0.5

0.3 -

Ex =6.67 MeV ' !.p= 2 "

~

0.! 0.05 I_ w

t

1.0

Ex= ?.00MeV

o.I 6OS

t(

1.0"

0

............................................................. :

Ex = 7.54 MeV lp=0

\ ~

0.5

Ip=2

--

¢¢¢

Ex=5,01MeV lp= 3

2O 40 60 8O I00

1~35

0.1

0

,

1

,

1

,

I

,

I

~

I

2O 4O 60 80 100

I

I

20

,

I

4O

,

I

60

J

1

80

,

I

100

6~m.

Fig. 5. Angular distributions of neutrons from the 3SP(d, n)32S reaction. See caption of fig. 2.

energy of 11 MeV. All levels with an excitation energy below 8.13 MeV can be resolved experimentaUy. The higher lying levels were observed for the first time throagh the a ZP(d, n)32S reaction in this experiment. fhe procedure described in subsect. 4.2 was used again to determine the excitation

228

J. U Z U R E A U

et al.

1.01

'

I

~

I

'

I

'

~

'

I-,]

o.51

Oll 1o51 5.0 I N

Ex: 8.13MeV

1.0 ~

lp:O

1.07 0 . 5 ~

)o21

Ex= 9.29MeV #p:O*2

1o.oI .

**+,

0.5

lp= 1

......................................2

ao5 w-

1.0

0.1 . 0.05

]'~ 5 . 0 ~

Ex = 9.39MeV ~p:l

Ex =8.50MeV

r ~

m

Ex = 10.07 MeV-

5O ~ .

0.1

Ip:I

1.0

I05

*

5.0

b "o

E x =10.33 MeV Ip = I

031 1.0

0,1

zO~os

0.05 !.................................................. , ~

"~

tp=1MeV

E x : 9.06

0.5

1.0 "P~'~'

Ex: 9"491MeV

I \,,:

0.5

0.1 n06

0.1 ~ ' ~ 0,05 = .........................................

O,I-

2.0 ~0

O.05

3,O Ex=

1,0

9.21MeV lp:O*2

Ex :9-73 MeV .lp:l

1.0 X 05

,.

E~<_-W-0 MeV

-'p= I

05

N

{'

*

0,1 O~

0.05 ........... ........~.~ ,

0

I

20

,

l

40

t

I

60

,

I

80

I

i I t .I I

J

100

0

20

40

•

i~'~'r"T--r60 80 I(I(}

001

i 0

"~- ........

[ i [ I i , I , l 20 40 60 80 100

8~m. Fig. 6. Angular distributions of neutrons from the a l P ( d , n ) 3 2 S reaction• See caption o f fig. 3.

energies quoted in table 4: they are in good agreement with the recent compilation of Endt and Van der /_~un 3). The experimental angular distributions with any structure are shown in figs. 5-7 along with the calculated DWBA and HF curves.

alp A N D 3 2 S I

I

I

229 I

I

E x = 1,0.22 -10.23 Me~/ 1.0

--/p= 3 _._#p = 2

(15

t O.O5

-j

3.0:

E x = 10.26 MeV --~p=3

*"v.~

__lp = 2

0-5 ---.~..

t 0.1 005 ~ E x : 10.29 MeV

1.0

.

--tp.=(1.3l

0.5

t

0.1 0.05 '

~

'

~0

'

I

60

'

I

80

'

'

100

9c.m.

Fig. 7. Angular distributions of neutrons from the 31p(d, n)32S reaction. The dotted curves are H F cross sections. Although these levels are unbound, the DWBA cross sections have been calculated using the conventional theory with a weakly bound state form factor. Here, the solid or dot-dashed curves represent the incoherent sums of DWBA and HF cross sections depending on the/p momentum. 5.3. T H E lp V A L U E S A N D j r A S S I G N M E N T S

5.3.1. Positive parity states. The ground state and the levels at 3.78, 7.19, 7.54 and 8.13 MeV are unambiguously populated by an lp = 0 transfer momentum. The same results have been obtained through the (d, n) reaction by Ferguson et al. 28) and via the (x, (t) reaction by Graue et al. 30). Up to now, no definitive lp values have been proposed for the transitions to the levels at 9.21 and 9.29 MeV. These levels can be populated by mixed Iv = 0 + 2 transitions (fig. 6) and the only possible assignment is J" = 1 + in agreement with previous results [J" = 1 + ; T = 1 for the 9.21 MeV level and J = 1 for the level at 9.29 MeV 3)-I. We therefore assign a positive parity to the 9.29 MeV state. The transitions with lp = 2 have been previously observed by means of the (~, d) reaction. The spin and parity values are in agreement with known determinations for

230

J. U Z U R E A U et al. TABLE 4

Excitation energies of states in 32S E x (keV)

presentwork 0 2226_+8 3775 -+ 7 4280 -+ 7 4459 -+6 4695 -+ 5 5007 _+6 5414_+ 7 5551 _+6 5801 _+4 6228 -+4 6414_+7 6624_+4 6672-+8 6764+6 6861+6 7005 + 4 7118-+4 7195_+4

E x (keV)

ref. 3)

presentwork

0 2230.2+0.2 3778.7 + 1.0 4281.6 -+0.8 4458.8 -+0.6 4695.3 -+0.4 5006.8 _+0.9 5412.6_+ 1.0 5548.7_+ 1.1 5797.6_+ 1.0 6224.3 _+0.9 6410 _+2 6621.0_+1.0 6665.7+0.8 6761.7_+1.0 6852 + 2 7003.3 + 1.1 7115.8_+0.9 7189.9_+ 1.4

a) For E~ = 10--10.4 MeV

7358 + 6 7431 -+5 7488 _+9 7539 _ 4 7707 _ 5 7887__+4 7962 _+4 8128_+3 8294_+4 8501 _+3 8695 _+7 9024_+4 9060+3 9210___4 9241 _+4 9288+4 9389 + 3 9483_+4 9648_+4

Ex (keV)

ref. 3) 7348 + 2. 7434 + 2 7484.8 _+ 1.0 7535.5 _+1.0 7701.7 -+ 1.4 7877 _+9 7950.8 _+1.0 8126.2_+ 1.0 8294 + 3 8502 + 5 8694 + 5 9022 + 4 9061 -+5 9207 _+1 9238 + 4 9290 _1 9389 -+ 1 9486 _+1 9650 _+ i

presentwork 9728 _ 4 9817-+4 9846 + 4 9884 _ 6 9945 -4-5 9975 __+4 10073 + 3 10220_+4 10253 _+4 10286+4 10327_+4 10394+4 10763-+4 10819 + 6

refs.

3.33)

9730_ 1 9817___1 9850 9887 _ 1 9949 -+ 1 9978 -+ 1 ! 0072 _+2 ") i" 10219_+2 ~ 10222_+2 10230+2 10256_+ 2 ~10287_+2 ~ 10289+2 10331 _+2 10399_+2 10756+ 1 10827 -+ 1

[ref. 33(].

the levels at 2.23 (2+), 4.70 (1+), 5.55 (2+), 6.67 (1 +, 2+), 7.00 (1 +) and 7.12 MeV (2 +) [ref. 3)], these last two levels are the first two T = 1 states in 32S. Determination of the transition intensity for the 6.67 MeV level was difficulty due to the nearby 6.62 MeV level. However the shape of the corresponding angular distribution allows us to remove the previous ambiguity for the transfer momentum (lp = 2 or 3) quoted by Graue et al. ao) and to confirm the assignments J" = (1 +, 2 +) proposed by Detraz et al. 32). 5.3.2. Negative parity states. Fourteen angular distributions are fitted by an lp = 1 DWBA curve. They correspond to states at 5.80(1 -), 6.22(2-), 7.43(0- - 2 - ) , 7.88 ( 0 - - 2 - ) , 8.50 ( 0 - - 2 - ) , 9.06 ( 0 - - 2 - ) , 9.24 (1-), 9.39 (2-), 9.49 (1-), 9.73 (1-, 2+), 9.85 (1-), 10.07 (2-), 10.33 (1-) and 10.40 MeV (d = 0) [ref. 3)]. The limitation J~ = 0- - 2 - given by the selection rules is in good agreement with previous assignments. The agreement between the experimental angular distributions corresponding to these levels and the theoretical DWBA + HF curves is good, except for the levels at 5.80, 6.22, 7.43 MeV and especially for the level at 9.24 MeV. The poor fit to the 9.24 MeV can be attributed to difficulties arising from nearby peaks. Other sets of optical model parameters were used without success in attempts to improve the fit for the levels at 5.80, 6.22 and 7.43 MeV.

31p A N D 32S

231

TABLE 5 Spectroscopic strengths for proton stripping to 32S states G = 2 J f + l C2Sp 2J i + 1

Ex a) (MeV)

J~; T b)

0 2.23 3.78 4.70 5.01 5.55 5.80 6.22 6.62 6.67 7.00 7.12 7.19 7.43 7.54 7.88 8.13 g.50 9.06

0+ 2+ 0+ I+ 32+ 124( I , 2)* 1+; ! 2*; 1 1+ (0-2) 0+ ; I (0-2)1+ ; 1 (0-2)(0-2)-

9.21

1+; l

9.24

I-

9.29

1 +*

9.39 9.49 9.73 9.85 10.07 10.33 10.40

2l1 -* 12- ; 1 I0-*

Ip

n(/

(d, n)

DWBA

(~,d)

7MeV present work

4MeV a)

5.45MeV ~)

12MeV ~)

15MeV ~)

0.66 0.11

0.60 1.49 0.10

0.11 0.15

0.21 0.08 0.14

0.60 1.50 0.10 0.37 0.56 0.16 0.14 0.15 0.65

0.55 ! .63 0.17 0.68 0.88 0.25 0.20 0.24

0 2 0 2 3 2 ! 1 3 2 2 2 0 1 0 1

2st/2 Id3/2 2Sl/2 Id3/2 lf~/2 ld3/z 2P3/2 2P312 lfT/2 1d3/2 ld3/2 Ida/2 2stl 2 2Pa/2 281/2 2p~t2

0.75 1.51 0.15 0.67 0.92 0.13 0.15 0.15 0.54 (0.10) 0.58 0.70 0.02 0.09 0.05 0.035

0

281/2

0.08

1 I 0 + 2 (1) 0 + 2 1 1 1 i 1 I I

2P3/2 2P3/2 2St/2

0.12 0.10 c) 0.01

lds/2 2P3/2 2st/z

0.04 0.04 0.01

ld3/2

0.06

2P3/2 2P3/2 2P3/2 2P3/2 2P3/2 2p3/z 2Pi/2

0.23 0.06 0.08 0.02 0.31 0.08 0.07

8MeV 8) 0.53 1.41 0.16 0.59 1.02 0.17 0.165 0.165

0.44 0.88 0.08 0.10 0.08 0.04 0.14 0.13 (0.07)

(0.36)

It) Refs. 3.33). b) Ref. 3). New spin and parity assignments are indicated by an asterisk. c) For the u n b o u n d levels (E x > 8.86 MeV), G is determined wRh Gamow form factors (see subsect. 3. i .2). d) R e [ zo). *) Ref. 30). t) Ref. 23). ') Ref. 31).

232

J. U Z U R E A U et al.

The transfer momentum lp = 1 deduced for the level at 9.73 MeV can be used to reject the assignment J" = 2 + leaving the only possible value J" = 1-. The negative parity we assign to the level at 10.40 MeV has also been recently deduced by Vernotte et al. 33) by means of the reactions alp(p, ~) and alp(p, p). Only two levels, at 5.01 MeV (3-) and 6.62 MeV (4-), are unambiguously populated by an l v = 3 transition. The angular distributions associated to the levels at 10.22+ 10.23, 10.26 and 10.29 MeV show some structure but it was not possible to make a definitive choice between different transfer momenta (fig. 7). 5.4. SPECTROSCOPIC S T R E N G T H S

The experimental transition strengths deduced from the present work are given in table 5 and compared with the values deduced from previous (d, n) [ref. 29)] and (~, d) [refs. 23, 3o-31)] reactions studies. There is general agreement concerning the first eight levels. However for the two states at 4.70 and 5.01 MeV, our results are in agreement with the results of both Morrison 23) and Kalifa et al. 3~) but in disagreement with the values obtained by Graue et al. 3o). Besides our results, the only available spectroscopic strengths for levels above 6.5 MeV have been obtained by Graue et al. T h e main discrepancies concern lp = 0 transitions populating the levels at 7.19, 7.54 and 8.13 MeV, the last two being T> states. Because many levels were observed in the present study of the 31p(d, n)32S reaction, the total transition strengths have been calculated and reported in table 6. It appears that all of the s, and d~ strengths were observed according to the sum rules given by French and MacFarlane 34) but a large part of the total strength for the p~ and fl states remains unobserved. 'TABLE 6

Summed spectroscopic strengths from 3 t p(d, n)32 S and comparison with sum rule predictions 3,)

n O"

T

Ida/2 2sl/2 2sl/2 ld3/2 ld3/2 Total 2s-I d 11"7/2 2P~/2 2p3/2

0 0 1 0 ! 0 0 1

2Jr + 1 C2Sp ~ 2Ji + 1 (d, n) at 7 MeV 0 0.93 0.14 2.37 a) 1.32 4,76 1.46 1.16 0.31

") Uncertain spectroscopic factor for the 6.67 MeV state is not included.

Sum rule limit

0 1 0 2 2 5 4 2 2

31p A N D a2S

233

5.5. ISOBARIC A N A L O G U E STATES IN 32S

The T = 1 states in 32S observed in the present work can be compared with the recently studied levels in 32p through the alp(d, p)32p reaction by Van Gasteren et al. as). T h e excitation energies of these T = 1 states in 32S and of parent states in 32p are reported in table 7 along with the spectroscopic factors determined in TABLE 7 Comparison of some T -- 1 levels in 32p and 32S

32p a) E~ (MeV)

j~

0 0.08 0.51 1.15

1÷ 2+ 0÷ 1+

2.23

1+

3.26

2-

32S b) l.

2 2 0 0

1

S.

1.0 0.94 0.32 0.18

004

0.13 0.22

E~ (MeV)

j~

7.00 7.12 7.54 8.13

I÷ 2+ 0÷ 1÷

9.21

1÷

10.07

2-

lp

Sp (d, n)

Sp (z, d)

2 2 0 0

0.77 0.56 0.20 0.11

0.59 0.70 0.32 0.19

+ 2 1

0.05 0.25

{0

002

") Ref. 3s). b) Present work or ref. 3o).

the (d, n), (z, d) and (d, p) reactions. Generally, the spectroscopic factors Sp obtained in the (d, n) reaction appear to be smaller than the S, values determined by means of the (d, p) reaction. This discrepancy was also observed for the two first T = states in 3ip (see subsect. 4.4). These differences are discussed in detail in the following paper 5). It can be noted that the spectroscopic factors Sp obtained in the present work for a2S are in very good agreement with the theoretical values predicted by Wildenthal et al. a6) in shell-model calculations.

6. Comparison with sheH..modei calculations The spectroscopic factors of positive parity states in 31p and 32S have been obtained in shell-model calculations 36, 37). Glaudemans et al. 37) assumed an inert core with configuration space restricted to the 2s½ and ld~ orbits. Wildenthal et al. 36) enlarged the configuration space by including two holes in the d t subshell and used two types of residual interactions (MSDI and FPSDI). These calculated spectroscopic factors are presented in tables 8 and 9 and compared with our results. The agreement is satisfactory for the T = xz states in 3~p except for the level at 3.51 MeV. However, our values are nearly a factor of two smaller than the predicted ones for the two first T = ~ states. In 32S, the agreement between

J. U Z U R E A U et al.

234

TABLE 8 Comparison o f spectroscopic factors from 3°Si(d, n)31P with predictions o f the shell model S 0 (th) E, (MeV)

j,

0 1.27 2.23 3.13 3.30 3.51 4.19 4.26 4.59 4.78 5.25 6.38 7.14

T

l+ 2 3+ 2 ~+ 2 x+ 2 ~-+ 2 a+ 2 ~-+ 2 3+ 2 ~+ 2 l+ 2 l+ 2 a+ 2 .t+ 2

Is

12 12 x2 X 2 t 2 l2 12 12 12 l2 12 z2 ~2

S o (exp) (d, n) at 7 MeV

0 2 2 0 (2) (2) (2) (2) (2) (2) 0 2 0

Glaudemans et al. c)

0.79 0.84 0.06 0.02 weak ") weak a) weak b) weak ") weak b) weak ") 0.03 0.37 0.11

Wildenthal et al. d) FPSDI

MSDI

1.09 0.76 0.04 0.04 0.00 0.18 0.00 0.00 0.01 0.00 0.01 0.72 0.14

0.97 0.78 0.06 0.08 0.00 0.12 0.01 0.00 0.06 0.00 0.01 0.71 0.19

1.30 0.81 0.00 0.05

0.83 0.27

") S 0 < 0.01 from the (~, d) reaction 2s). b) S0 __ 0.03 from the (¢, d) reaction 2s). ~) Ref. 37). d) Ref. ~6). TABLE 9 Comparison of spectroscopic factors from 3t P(d, n)32S with predictions o f the shell model Sp (exp) E. (MoV)

J"

T

lp

(d, n) at 7 MeV sl/2

0 2.23 3.78 4.28 4.70 5.55 7.00 7.12 7.54 8.13 9.21

0+ 2+ 0+ 2+ 1+ 2+ 1+ 2+ 0+ 1+ 1+

0 0 0 0 0 0 1 1 1 1 1

0 2 0 (2) 2 2 2 2 0 0 0+ 2

d3/2

3.00

Sp (th) ref. 37) s1/2 2.82

1.21 0.60

0.07

sl/2

0.36 0.15 0.02

st/2

0.85 0.68

0.00 0.78 0.15 0.68 0.66

0.59 0.75 0.21 0.10 0.01

d3/2

2.26

0.44

0.24 0.03

MSDI ")

0.83

0.07

0.02

d3/2

2.57 1.05

0.48 weak 0.89 0.10 0.77 0.56

0.20 0.11 0.02

d3/2

FPSDI ~)

0.09

0.00 0.78 0.15 0.65 0.67 0.26 0.14 0.02

0.03 0.09

") Ref. 36).

experimental and theoretical spectroscopic factors is good for both T = 0 and 1 states.

alp A N D 328

235

7. Summary Excited states in 3tp and 32S have been studied by means of the 3°Si(d, n)31P and 31p(d, n)a2S reactions at a bombarding energy of 7 MeV with a good neutron energy resolution. The angular distributions extracted for 18 levels in 3~p (E x = 0-8.6 MeV) and for thirty levels in 32S(E~ = 0-10.5 MeV) have been analyzed in the framework of the DWBA theory. In order to obtain correct spectroscopic factors for unbound levels, the form factor was calculated using Gamow state functions. New spectroscopic information has been obtained for some levels. The assignment J~ = 3- was given to the levels at 8.05 and 8.25 MeV in 31p and J~ = 1 ÷, 1 - and 0 to the levels at 9.23, 9.73 and 10.40 MeV, respectively, in 32S. The other results of the present study are generally in agreement with previous results from the (z, d) reaction. However differences appear for some spectroscopic factors deduced from these two types of one proton transfer reactions. Shell-model calculations correctly reproduce the spectroscopic factors obtained in the present work for 31p and 32S. We are indebted to Dr. A. Michaudon for continuous support of this work. We thank Dr. D. M. Drake for a critical reading of the manuscript. One of the authors (J.U.) is grateful to Dr. P. Avignon for many helpful discussions and to Dr. S. Gales for allowing him to use the computer codes GAMOW-3 and VENUS.

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

J. Uzureau et al., Nucl. Phys. A230 (1974) 253 J. Uzureau, A. Adam and S. Joly, Nucl. Phys. A250 (1975) 163 P. M. Endt and C. van der Leun, Nucl. Phys. A214 (1973) 1 R. H. Siemssen, G. C. Morrison, B. Zeidman and H. Fuchs, Phys. Rev. Lett. 16 (1966) 1050 J. Uzureau et al., Nuct. Phys. A267 (1976) 237 A. Adam and J. Cab~,lNucl. Instr. 121 (1974) 339 J. Uzureau, thesis, Univ. of Nantes (1975) B. W. Hooton, Nucl. Instr. 27 (1964) 338 P. D. Kunz, Univ. of Colorado, report COO-535-613 (1967) P. Schwandt and W. Haeberli, Nucl. Phys. A l l 0 (1968) 585 D. Wilmore and P. E. Hodgson, Nucl. Phys. 55 (1964) 673 C. M. Perey and F. G. Perey, Nucl. Data Tables 10 (1972) 539 F. G. Percy, Phys. Rev. 131 (1963) 745 J. E. McQueen, J. M. Joyce and E. J. Ludwig, Nucl. Phys. A147 (1970) 81 T. Tamura, W. R. Coker and F. J. Rybicki, Comp. Phys. Comm. 2 (1971) 94 W. R. Coker and G. W. Hoffmann, Z. Phys. 263 (1973) 179 W. R. Coker, Phys. Rev. C7 (1973) 2426 E. Sheldon and V. C. Rogers, Comp. Phys. Comm. 6 (1973) 99 P. E. Hodgson, Nuclear reactions and nuclear structure (Clarendon Press, Oxford, 1971) p. 292 P. J. Twin e t al., J. of Phys. A7 (1974) 1410 B. Cujec et al., Phys. Lett. 15 (1965) 266 W. G. Davies, W. K. Dawson and G. C. Neilson, Phys. Lett. 19 (1965) 576 R. A. Morrison, Nucl. Phys. AI40 (1970) 97

236

J. UZUREAU et al.

24) 25) 26) 27) 28) 29) 30) 31) 32) 33) 34) 35) 36) 37) 38)

H. F. Lutz, D. W. Heikkinen, W. Bartolini and T. H. Curtis, Phys. Rev. C2 (1970) 981 A. C. Wolff and H. G. Leighton, Nucl. Phys. A140 (1970) 319 G. W. Hoffmann et aL, Phys. Lett. 5lIB (1974) 249 B. H. Wildenthal and P. W. M. Glaudemans, Nucl. Phys. AI08 (1968) 49 A. T. G. Ferguson, L. Nilsson and N. Starfelt, Nucl. Phys. A I I I (1968) 423 A. H. Hussein, G. C. Neilson, W. J. McDonald and W. K. Dawson, Can. J. Phys. 52 (1974) 128 A. Graue, L. Herland, J. R. Lien and E. R. Cosman, Nucl. Phys. AI20 (1968) 513 J. Kalifa, G. Rotbard, M. Vergnes and G. Ronsin, J. de Phys. 34 0973) 139 C. Detraz et al., Nucl. Phys. A203 (1973) 414 J. Vernotte, S. Gales, M. Langevin and J. M. Maison, Nucl. "Phys. A212 (1973) 493 J. B. French and M. H. MacFarlane, Nucl. Phys. 26 (1961) 168 J. J. M. van Gasteren, A. J. L. Verhage and J. F. van der Veen, Nucl. Phys. A210 (1973) 29 B. H. Wildenthal, J. B. McGrory, E. C. Halbert and H. D. Graber, Phys. Rev. C4 0971)1708 P. W. M. Glaudemans, G. Wiechers and P. J. Brussaard, Nucl. Phys. 56 (1964) 529, 548 P. M. Endt, Atomic Data and Nucl. Data Tables, submitted