Study of (3He,n) reactions on nuclei in the 2s-1d shell

Nuclear flhystcs A198 (1972) 449--465, (~) North-Holland Pubhshmy Co, Amsterdam l~,tot to be reproduced by photoprmt or microfilm without written permlssaonfrom the publisher

STUDY O F (aHe, n) REACTIONS ON NUCLEI IN T H E 2s-ld S H E L L R. BASS, U. FRIEDLAND, B. HUBERT, H. N A N N and A. REITER

Institut fur Kernphyslk der Umversttat, Frankfurt am Mare, Germany Received 8 September 1972 Abstract: The (SHe, n) reaction has been studied on 28S1, 29S1, 3°Si, a2S, ssc1 and s7C1 near 14 MeV bombarding energy. Angular dlstnbutlons have been measured for all ground state transitions and for the transition to the first excited state in a°S. The neutrons were detected with an arrangement of reeoll proton telescopes, each consisting of two plastic scintillators. Pronounced L = 0 stripping patterns were observed for the ground state transitions, with cross sections of the order of 1 mb/sr at 0 ° The results are compared with DWBA calculations based on various sets of shell-model wave functions, and with (SHe, p) data for transitions to analogous final states. E

N U C L E A R REACTIONS 28Si, 29Si, a°Sl, a2S, asC1, a7Cl(aHe, n), E = 14 MeV, measured or(0). Natural and enriched targets

1. Introduction

The differential cross section of a two-nucleon transfer reaction is coherent in the quantum numbers of each of the transferred particles a), and hence depends sensitively on the shell structure of the nuclear states involved. Tins feature has been exploited prevmusly in a series of studies of the (3He, p) reaction on sd shell target nuclei 2-s). The results of such stuches can be compared quantitatively with predictions on the basis of extensive shell-model calculations due to Glaudemans et al. 6, 7) and Wlldenthal et al. 8-10). The earlier calculations of Glaudemans et aL 6) consider an inert 28Si core and valence nucleons in the 2s¢ and ld~ shells, and yield wave functions by fitting matrix elements of the residual Interaction to experimental level energies. In the more recent calculations 7 - t 0), on the other hand, a phenomenological residual interaction is Introduced expficitly and the configuration space is extended by including a limited number of holes in the 1d_~ shell The present paper describes measurements and results of the two-proton transfer reaction (aHe, n) with a number of target nuclei m the same mass region. The interest in tins type of reaction arose mainly from its expected similarity with the (3He, p) reaction and from the fact that proton rich members of isobaric multlplets, winch are not easily accessible by other means, can be reached. Moreover It was hoped to deduce mformat10n on the vahdity of a charge-independent description of the reaction mechanism and the nuclear states involved from a comparison of analogous (3He, n) and (aHe, p) transitions. 449

450

R. BASS et al

2. Experimental method 2.1. BEAM A N D TARGETS

Beam currents between 0.4 and 0.9/~A of doubly charged aHe ions were produced with the 7 MV Van de Graaff accelerator at Frankfurt University. Measurements were made at an incident energy of 14 MeV with the 28,29, 3Os1' 32S and 35C1 targets, and at 13 MeV with the 37C1 target. Some additional runs were taken at lower bombarding energies, down to 10 MeV, with results essentially similar to the higherenergy data a a). The target characteristics and reaction data are collected in table 1. All targets were TABLE 1 Target and reaction data Target nucleus

2 sSa 29S1 3°S1 a2S 35CI a7C1

Target composxtmn

St-metal St-metal Sl-metal CdS KCI KC1

Isotopic abundance (~o)

Target thickness (mg/cm z)

Q(3He, n)

En (max)

(MeV)

(MeV)

92 2 92 0 95.5 95.0 96.9 54.6

0.325 0 100 0.100 0.268 0.700 0.500

--0.565 +3.959 + 8 433 --0.759 + 2 645 +8.898

13.1 17.8 22.3 12.9 16.5 21.8

Scintillator thickness (cm) 0.2 0.5 05 02 03 05

evaporated onto tantalum backings and mounted at an angle of 45 ° with respect to the incident beam &rectlon. Thus the effective thickness of each target was 1.41 times the value given in table 1. The 2SSi and 3ZS targets were of natural isotopic composition and prepared in this laboratory, whereas enriched targets of z9, 3os1 and 35, 37C1 were obtained from A E R E Harwell, England. The target thicknesses were obtained by weighing, or taken from the specifications of the supplier. The target backings were cooled by a stream of compressed air, and the accumulated charge was measured w~th a current integrator. 2 2. N E U T R O N SPECTROMETER

Neutrons from the (SHe, n) reactions under study were detected at five angles simultaneously with recoil proton telescopes. The mechanical and electromc arrangement of such a telescope is shown schematically in fig. 1. Two plastic scintallators (Naton 136) PL1 and PL2 are mounted at a distance of about 10-12 cm on the axis of an evacuated chamber CH, and coupled via suitably shaped light grades to photomultlphers PM1 and PM2 (RCA 6342 A). After penetrating the front window of the chamber C H and the crown glass prism PR, neutrons from the target reach the first scintillator PL1, where they may scatter from hydrogen nuclei. Those recoil protons

(3He, n) R E A C T I O N S TARGET

451

PL2

PLI

3He

---JL

E

Fig. 1. Recoil p r o t o n telescope wJth associated electromcs. t

1

t

1

I

0 x

>..

3

--

Z LLI

LL hi

G=2 715 " 10 -2 =

•

-

I

t

t

I

I

5

10

15

20

25

NEUTRON

ENERGY

I'MeV'I

F~g. 2. Efficiency o f t h e n e u t r o n detector as a f u n c t i o n o f n e u t r o n energy.

452

R. BASS et al

which leave the back face of PL1 into a narrow forward cone are Intercepted and stopped by the second plastic scintillator PL2. The signals from the anodes of the two photomulhphers are amplified An preamplifiers (PRE) and double delay hne clipped linear amplifiers (DDL) and subsequently added by a summing circuit (SUM) in order to produce a signal characteristic of the energy of the primary neutron In addition, the amplifier output signals are fed vla zero-crossover discriminators (DIS) to a fast coincidence circuit (CO). The latter controls a linear gate (LG), which admits the summed linear signals after suitable delay (DEL) to a stretcher (STR) and multichannel pulse-height analyser (PHA). The thicknesses of the two plastic scintillators are chosen equal and shghtly larger than the maximum range of a forward recoil proton, as expected from the reactions under study. Thus the effective radiator thickness IS, for each neutron energy, essentially equal to the corresponding proton range in the plastic scintillator, and all protons emerging from the first scintillator are fully stopped in the second. Thicknesses much larger than the maximum recoil range are avoided, on the other hand, in order to reduce the v-ray background, which otherwise tends to obscure the lower parts of the pulse-height spectra. The scintillator thicknesses chosen for the present measurements are given In table 1. The angular acceptances of neutrons and recoil protons depend on the scintillator diameters d I, d2 and on the distances DI, D2 between the target and PL1, and PL1 and PL2, respectively. These geometrical parameters therefore determine not only the angular and pulse-height resolution of the Instrument, but also its detection efficiency As a result of extensive calculations 11), the following values were chosen for the present design: d 1 = 2.0 cm, d2 = 4.0 cm, D1 ~ D2 ~ 11-13 cm. Thus an angular resolution of about 10 ° and half-width of the geometrical resolution function of about 4 % were obtained. The latter number represents the contribution of the fimte recoil acceptance angle to the energy resolution, and must be combined with the inherent resolution w~dth of the plastic scintillator-photomultlpher combinations (typically about 5 %) to yield the overall energy resolutmn of the Instrument. In practical measurements the energy resolution varied between 6 and 9 %, corresponding to a halfwidth of about 1 MeV at E n = 14 MeV. With this resolutlon only ground-state transitions could be clearly resolved for most of the target nuclei studied The detection efficiency e(E) of the instrument, defined as the ratio of the number o f neutrons detected to the number of neutrons incident on the first scintillator, can be expressed by the following equation" 8(E) = (1-exp(-nHCXnpR))G ~ nuCrnp(E)R(E)G.

(1)

Here/'/it is the number of hydrogen atoms per unit volume, a.p the total n-p cross sectmn and R the range of a recoil proton of energy E (equal to the energy of the incident neutrons) The geometry factor G depends on dl, dz, D1 and D2 and gives the fraction of the recoil protons produced within the active region of PL1, which is intercepted by PL2 In the neutron energy region of interest ~(E) is approximately proportional

(aHe, n) REACTIONS

453

to E; actual values for the geometry used in this work (G = 2.715 x 10 -2) are shown in fig. 2. It should be noted, that a small correction must be applied to these values in practice for the finite discriminator thresholds in the coincidence circuitry, which prevent detection of recoil protons originating from or stopped in thin layers close to the sclntlUator surfaces. Another effect to be taken into account is the attenuation of the mcldent neutron flux in the prism PR. This was deternuned experimentally to be about 13 9/0 at neutron energies above 8 MeV [ref. 12)] 2 3 MEASURING PROCEDURE AND DATA REDUCTION

Measurements were made with five telescopes simultaneously. These were mounted at fixed angular intervals of 60 ° on a turntable, which could be rotated around a vertical axis through the target. A sixth telescope could be positioned above the counter plane at an angle between 30 ° and 50 ° with respect to the beam direction, in order to monitor the neutron yield from the target. Prior to each series of measurements the complete detector arrangement was tested and calibrated with monoenergetic neutrons of appropriate energy from either the ZH(d, n)3He or the 3H(d, n)4He reaction. The higher counting rates and clean spectra obtainable with these sources greatly facihtated the necessary electronic adjustments, especially a careful matching of gains in associated channels. With the neutron energy cahbratlon thus established, a precision pulse generator was used to determine the exact positions of the discriminator thresholds and to test the linearlty of the signal channels A pulse-height spectrum obtained vc~th 22.3 MeV neutrons from the reaction 3H(d, n)4He is shown in fig. 3. Angular distributions were usually measured from 0 ° to 150 ° in 5 ° steps. Ttus reqmred seven different settings of the turntable, each telescope covering an angular range of 30 °. Overlap between adjoining ranges occurred at 30 °, 60 °, 90 ° and 120 ° and was used to check the consistency of data obtained with different telescopes The running time for each setting was typically between 5 and 10 h. Fig. 4 shows pulse-height spectra for the reaction zssi(3He, n)3°S at a bombarchng energy of 13.95 MeV and lab angles of 0 °, 25 ° and 120°. Contaminant peaks from the reactions 12C(3He, n)140 (Q = - 1 . 1 5 MeV) and 160(3He, n)18Ne (Q = - 3 . 2 0 MeV) are clearly in evidence and shown as shaded areas in the spectra. The same problem existed for the reaction 3ZS(3He, n)34Ar, which also has a slightly negative Q-value, but not for the other investigated reactions with their positwe Q-values (see table 1). In order to remove these background contributions quantltatwely from the spectra, the following procedure was applied: Immediately after each angular &strlbutlon measurement for either 28Si or 32S, background runs were made under identical conditions, except that the target under investigation was m turn replaced by a C and a PbO 2 target. The background spectra thus obtained were normalized at statable angles to the contaminated spectra and then subtracted from the data. All the ground-state transitions studied exhibited strong forward peaking. Consequently well-defined peaks were observedln the pulse-height spectra for angles near 0 °,

454

(sI-Ie, n) R E A C T I O N S

which could easdy be evaluated. Sample spectra for 29Si and 3°S~ are shown ]n fig. 5. At larger angles, however, especially near the cross-section minima, the peaks under study were not always clearly resolved from small but slgmficant background contributions due to lower-energy neutrons and 7-rays (see fig. 4). Under such circumI ._J ILl Z Z ,,~ "ICJ

I

I

1

3H(d,n)~He

600

500 Z -3 0 (--} 400

300 E n =22 3 MeV

--

,AE/E= ?°/*

200

..

I

I

100

0 50

100

150

200

1:50

CHANNEL Fzg. 3. Pulse-height s p e c t r u m for 22.3 M e V neutrons from the reactzon 3H(d, n)4I-Ie.

28Si(3He,n)3°S, I

I

i

MeV i

i

~=o0

2: 2:
E3He =13.95 •~, = 25 °

i .0,=120 °

U') I-Z O 20C ¢,..)

2( n3 nz

IOC

n1

RESIDUAL SPEC'/RUM ~tk

100

/

..

~"

5o

n~ n z n 1

io

~

12c

I, C H A N N E L

Fig. 4. Pulse-hezght spectra f r o m the reaction 2aSz(3He, n ) a ° S t a k e n at 0 °, 25 ° and 120 °.

(3He, n) REACTIONS i

I

~_1 19o :z z .<: -.i(..) Z 0o

i

16o

i

1

E3Ho=14MeV

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100

100 [ 12G

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150

200

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.',

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is01

2~Si (3He, n)315

nI

455

it /k

-

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I00

,%..-.~,'--J150..'

,

200

CHANNEL

Fig 5. Pulse-heJght spectra from the reactions 2981(zI-[e, n)31S and 3°Sz(aHe, n)a2S taken at 0 °

stances the areas under the peaks were estimated using thelr known positions and hne shapes, and assuming a smooth variation of the background with pulse height and angle. 2 4. ERRORS

Estimates of the point-to-point error due to counting statistics and uncertainties m the background subtraction range typically from ± 5 70 at angles near 0 ° up to about ± 30 7o near the cross-section minima. An adchtional error of about ± 15 70 arises for the absolute cross-section scale from uncertainties in the thickness, composition and homogeneity of the targets (typically ± 10 ~o) and in the efficiency of the neutron detector (± 10 70), whereas errors m the charge integration are comparatively mslgmficant. The overall uncertainty in the normalization of calculated to measured angular distributions is estimated as ±20 70. 3. Analysis 3.1. D W B A CALCULATIONS

Following the zero-range formalism of Glendenning 1) the DWBA cross section for the two-nucleon transfer reaction A(a, b)B may be written as do" - D 2 2 J B + l ~ C 2 r ~ I ~ G n L s j T B ~ L I dr2 2JA+ 1 r~ssr U z¢

2,

(2)

where spin-orbit coupling terms in the optical potentials of the entrance and exit channels are neglected. The c.m. motion of the transferred pmr about the target is described by the radial and orbital quantum numbers N, L and M, and the transferred spin, isospin and total angular momentum are coupled to S, T and or. The coefficients GNLSJT contmn nuclear smacture information_re_the form_of overlap integrals, whde

456

R BASS et aL

the B~L contain kinematic effects calculated by DWBA. The quantity Do2 is the normahzatlon factor which arises in making the zero-range approximation. The coefficients Csr are defined as

CsT ----- (TA NA TN[T~ NB) D( S, T) bsr ,

(3)

where the Clebsch-Gordan coefficient couples the isospin of the target nucleus TA TABLE 2

Two-nucleon transfer spectroscopic amphtudes Reactmn zsS1 ~ 30

29S1 ~ 31 3%1 -+ 32 a2S -+ 34 35C1 -+ 37

zvC1 -+ 39

(J, T) (0, 1) a) b) (2, 1) a) b) (0, 1) a) b) (0, 1) a) b) (0, 1) a) b) (0, 1) a) b) (2, 1)a) b) (0, 1) a) b) (2, 1) a) b)

(ld~_) 2

(2s{.) 2

(ld_~) 2

+0.4386

- - 0 8521 + 0 6175

--0.5235 +0.3091 + 0 2387 +0.1101 +0.5365 +0.5389 +0.7024 - - 0 7288 +0.9189 + 0 8571 --0.5400 - - 0 3560 +1.6688 + 1.3990 - - 0 9634 --0 9598 + 2 1541 +2.1462

+0.0174 +0.4319 --0 4312 + 0 2159 --0.1907

+ 1 0057 + 0 7789 + 1 3666 --1 2685 + 0 3687 + 0 3140 - - 0 1857 --0.1736

+ 0 0569 - - 0 2418

- - 0 2000 - - 0 1626

+ 0 1060

(ld~, 2s{)

(ld§, ld3_ ) (2s4. , I d ~ )

--0.0870

- - 0 0146

- - 0 9711 + 0 5769

+ 0 1518

+0.0502

+0.1026 + 0 0328

+0.•428

+0.0940

- - 0 2280 +0.1080

a) Wave functions taken from ref. 6). The signs o f certain wave-function components are changed owing to the Incorrect phase asmgnment o f the matrix element (ss[ V[dd)ol m r e f . 6). b) Wave functions taken from ref 1o) for A = 28 and 29, from ref. s) for A = 30-34 and from r e f 9) for A = 35-39. TABLE 3 Optical-model parameters used in the D W B A calculations

A +aHe a°S + n 31S + n 32S + n a*Ar+n 37K + n agK + n 3op + p 34C1 + p 37Ar+p

V

W

W"

ro

a

r¢

r'o

a"

(MeV)

(MeV)

(MeV)

(fm)

(fm)

(fm)

(fm)

(fm)

173 0 49 0 48 0 47 0 48 0 49.0 48 0 51.0 50.0 51.0

18 6

1 07 1.25 1 25 1.25 1.25 1 25 1 25 1.25 1.25 1.25

0.82 0.65 0.65 0 65 0.65 0.65 0 65 0 65 0.65 0.65

1 40

14 0 14 0 14 0 12 0 10 5 10 5 14.0 12 0 10.5

1 72 1 25 1.25 1.25 1.25 1 25 1 25 1.25 1 25 1 25

0 76 0.47 0 47 0.47 0.47 0.47 0.47 0 47 0.47 0 47

1 25 1.25 1.25

(3He, n) REACTIONS

457

to that of the transferred pair T to give the lsospln of the residual nucleus TB. The factor bsr describes the overlap between a and the transferred pair plus b m spin and isospin space, and has the values bit = ½ for (3He, p) and unity for (3He, n) reactions. The quantity D(S, T) allows for the possibility that the interaction potential may have different strength in slnglet and triplet states of the transferred nucleons; in the present calculations the values ID(0, 1)1z = 0.83 and ID(1, 0)l z = 0.35 have been used. Details of the present method of analysis have been described previously 2). The spectroscopic amphtudes, as defined an ref. aa), obtained by a c.f.p, expansion of wave functions from various sets of shell-model calculations, are hsted in table 2. The radial form factors were calculated with a modified version of the code F O C A L [ref. I4)] and inserted for the final DWBA calculations into the code D W U C K is). Optical-model parameters for the Incident 3He particles were taken from Morrlson 16) as m previous analyses of (3He, p) data. For the outgoing neutrons, equivalent parameters were deduced from the proton parameters, winch had resulted in good fits to the (3He, p) angular distributions z - 5). This was done using the same well geometry and subtracting appropriate Coulomb and symmetry terms i7) from the real nuclear well depths. The resulting optical-model parameters are collected In table 3 3 2 VARIATION OF THE CROSS SECTION WITH CONFIGURATION MIXING The sensmvlty of the two-nucleon transfer cross section to the magmtudes and signs of the spectroscopic amphtudes involved is illustrated in fig. 6 for the ground-state transmon of the 2SSl(3He, n)3°S reaction. For simplicity, the ld~ shell is assumed to be closed in the target nucleus, and the final state is taken as a pure two-particle configuration in the 2s~ and ld~ shells. The zero-degree cross section IS plotted In the left-hand side of fig. 6 in relative units as a function of the fractional spectroscopic intensity of either (2s~) z or (ld~) z transfer. It can be seen that the (2s~) 2 component is much more effective than the (ld~) z component, and that the relative sign of the two amphtudes has a strong Influence on the cross section. In the right-hand side of fig 6 the angular distributions obt~uned with different mLxtures of (2s~) 2 and (ld~) z transfer are shown. The shape of the angular distribution IS practically independent of the mixing ratio except for a small region of destructive interference, where the two amphtudes almost completely cancel. Results similar to those shown in fig. 6 have been obtained for the more general situation, where (ld~) 2 transfer amphtudes are present in a 0 + ~ 0 + transition, in addition to the (2s~) z and (ld~) 2 amphtudes. The conclusions to be drawn from these exploratory calculations can be summarized as follows: The shape of the angular distribution is normally insensitive to the shell-model orbits involved and determined only by the angular momentum transfer L. Therefore all nuclear structure Information is contained In the transition strength (cross sectmn), if only one L-value contributes as in 0 + -o 0 + transitions (L = 0). Problems arise, however, in the analysis of absolute cross sections both from experimental errors and

458

R. BASS e t al

50

g

40

"6 ,,.., 30 t)

\®

20

10

0 O0

02

04 '

06 •

08 C1- ~2)

10 o"

6if"

120~

180°

bOCM

F]g 6 D e p e n d e n c e o f t h e dlfferentml cross section for t h e 2 sS](3He ' n o ) 3 ° S reaction o n the (2s~)2 a n d ( l d ~ ) 2 transfer amplitudes T h e 0 ° cross s e c t m n s are s h o w n o n the left, the a n g u l a r d ] s t n b u t m n s o n the right.

from the present uncertainties m overall normahzation of zero-range D W B A calculations. F r o m this point of view, comparative studaes of several transations with ]dentical experimental and analytical techniques appear more promising than studies of asolated trans~tlons. In general at is not feasible to deduce spectroscopac ]ntensmes associated wath spec~fled orb]ts from measured angular distrabutions, even in the comparatively sn~ple s]tuataons considered here. This as partly due to the dlfficultaes mentioned above, which arise an the absolute comparison of measured and calculated cross secuons, and partly due to the amblguities introduced by the different possible choices of relative signs. Qualitative conclusions concerning the presence of (2s~) 2 transfer an strong L = 0 transitions may be possible, however, due to the enhanced effect of (2s~) 2 as compared to (ld~) z or (ld_~)z amphtudes on the cross section.

4. Results and discussion 4.1 G E N E R A L

REMARKS

The results of the present measurements and D W B A calculations are shown m figs. 7-9. Each calculated angular distribution is independently normalized for a best

(aHe, n) REACTIONS

459

TABLE 4 Comparison of experimental and theoretxcal trausmon strengths Reaction

zsS1 (SHe, n)a°S 29S1 (3He, n)31S a°S1 (SHe, n)a2S a2S (SHe, n)S*Ar aSCl(aHe, n)a7K aTCl(aHe, n)agK

Ex (MeV) 0 00 2 20 0 00 0 00 0.00 0.00 0 00

trexpltrm

0.96 0 68 0.28 0.72 1.84 0 84 1.30

1.12 2.20 0 28 0 56 1 68 1 20 0 88

For ") and b) see footnotes to table 2.

fit to the experimental points The corresponding ratios of experimental to calculated cross sections, based on a c o m m o n normalmation factor Do2 = 25 x 104 MeV 2- flu 3 for the D W B A cross sections, are collected in table 4. This value of D 2 has previously been found to give an adequate description of (SHe, p) data for the same mass region [refs. 4, 5)]. Details of the results are discussed in the following subsections 4 2. T H E REACTIONS 28, 29, aoSl(aHe, n)aO, al, 32S(g.s.)

The experimental results and D W B A curves are shown in fig. 7. All three angular distributions exhibit a pronounced L = 0 pattern as required by the selection rules for 0 + ~ 0 + or ½+ ~ ½+ transitions. Therefore the shape of the angular distribution does not depend on details of nuclear structure, as discussed in subsect. 3.2. In the simplest possible shell model, all three transitions are pictured as the transfer of two protons into the previously empty 2s~ shell, and should thus have the same cross section apart from Q-value effects. The latter alone produce a ratio 0"(2851) ." 0"(2951) a(3°Si) = 1 : 0.50 : 0.16, as can be shown by D W B A calculations assurmng transfer into the same final orbits in all three cases. Experimentally one finds a ratio 1 : 0.18 0 24 m marked disagreement with the simple expectation. This presumably reflects changes m the proton configuration as a consequence of the adchtlon of neutrons to the 2aS1 core. D W B A calculations based on configuration-mixed wave functions due to Glaudemans et al. 6) and Wlldenthal et aL s, lo) yield the ratios O'exp/0"thgwen in table 4. Both sets of shell-model calculations reproduce the strength of the 28S1 reaction quite well. For the wave functions of ref. 6) _ wlth sign changes as suggested in ref 18) _ this agreement must be considered somewhat fortmtous m view of the obviously unreahstic assumption of a dosed-shell target nucleus 2SSi. On the other hand, the cross section for 29S1, and to a lesser extent for 3°$1, are overestimated by both calculations. 4 3 THE REACTIONS 3s.aTCl(aHe ' n)37, a9K(g s.)

In contrast to the S~ reactions here both L -- 0 and L = 2 transfers are allowed by the selection rules, since the target and final nuclei have spin and parity ~3 + . Both

460

R. BASS et aL Sm ( 3 H e . n o )

S.

ELo b

14.0 MeV

=

10

~

l

° s l (ZHe'n°)3°S O =-0.57

MeV

(3He, no)32S

2951 (3He, no)315

3°Si

O = + 3 9 6 MeV

Q = + 8 43 MeV

ffl

+++++

o "0

t/-

01

t

0 01

0001

.

.

.

.

30°

.

.

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.

60°

90 °

3¢

120'

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30°

60°

90°

120°

0c H Fig 7 Angular dastnbutlons and D W B A fits for the 28'29,3°Sl(3Hic, n)a°,31,a2S ground state transitions

10

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35C[ (3He.no)37K

37C[ (3 H e . n o ) ~ K

ELa b = 14 0 MeV

ELa b = 1 3 . 0 M e V

Q = 265MeV

Q

=

8.90 MeV

1

o

01

1

001 \

0001

, . . . . . ~ i t m , r , 30° 60° 90° 120°

~'

'3'0o' '6'o °' Oc H

Fig. 8 Angular ¢hstnbutlons and D W B A fits for the 35, 37C1(3He ' n)37,

,.~o.... 39

12o°

K ground state transitions

t00

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'~ 2SSi(3He,n)3°S(2 20 MeV) ELab = 140MeV

~, 2SSt(3He,n)3°5(0 00 MeV) ELab = 14.0MeV

2BSi (3He, p)3° P(2 84MeV)

(?

2SSi (3He, p) 30 P(O 67 MeV) ELab = 15.0 MeV

10

i

EL(~b = 160 MeV

m

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I-..--4

01 13 "O

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3SC[ (3He.n)37K(O 0 MeV) 3SC| (3He.p)37Ar(O 0 MeV)

~, ~2S(3He,n)3~Ar(0 0 MeV ) 32S (3He,p)34C[ (0.0 MeV) ELab = 140 MeV

ELa

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1/-*.0

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T=O÷I • T = 1 only

1

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i

i

30 ° v

I

i

I

60 °

t

w

!

i

90 °

ec M

Fig 9 Comparison of analogous (3He, n) and (3He, p) reactions.

i,,i

r

120°

462

R. BASS et aL

experimental angular distributions, as shown in fig. 8, are dominated by L = 0 contrabutions, with somewhat more L = 2 admixture in the 3~C1 case. Calculated angular chstrlbutions based on the wave functions ofref. 9) are shown as solid curves, those based on the wave functions of ref. 6) as dash-dotted curves. Both sets ofca/culations predict mainly (ld~) 2 transfer for both transitions and reproduce fairly well the observed transation strengths (see table 4). The wave functions of ref. 9) yield a larger L -- 2 contribution to each angular distribution, resulting in a somewhat improved fit to the 35C1 data as compared to the wave functions of ref. 6). The opposite is true, however, for 37C1, where the almost pure L -- 0 pattern, predicted with the wave functions of ref. 6) (as a result of destructive interference between (ld@)2 and (2s@1d~) amplitudes in the L = 2 component), gives a superior fit to the data. 44 COMPARISON OF ANALOGOUS (aHe,n) AND (3He, p) REACTIONS ON 2sS1, a2S AND asCI In general the (aHe, p) reaction may proceed by either' singlet (S, T = 0, 1) or triplet (S, T = 1, 0) transfer of the two nucleons, whereas only slnglet transfer is allowed for the (3He, n) reaction. These selection rules follow from the assumption of a spatially symmetric wave function for the transferred pair. If the imtla/and final states considered differ in total lsospin by one, both types of reaction revolve only slnglet transfer. In this case the differentia/cross sections of analogous (aHe, n) and (3He, p) transitions are simply related by isospm coupling coefficients, apart from kinematic effects and assuming charge-independent wave functions. If, on the other hand, the imtia/and final states have the same total isospin, then both smglet and triplet components can contribute to the (3He, p) cross section. In ttus case a quantitative comparison with the analogous (3He, n) cross section should, in principle, a/low one to determine the two components separately. The experimental and calculated differentia/ cross sections of some analogous (3He, n) and (3He, p) transitions for the target nuclei 28S1, 32S and 35C1 are shown in fig 9. The experlmentM data on the reaction 2aSI(3He,p)aOp are due to Betts et aL 19) for the transition to the 0.67 MeV 0 + state (incident energy 15 MeV) and due to Hafnet 20) for the transition to the 2.84 MeV 2 + state (incident energy 16 MeV). The (3He, p) ground state transitions for 32S and a5C1 have been measured at this laboratory [see ref. a) for the asC1 work]. For purposes of quantitative comparison, the distortion and kinematic effects have been removed by calculating the double ratio R - a°*P(3He' n) ath(aHe, p)

(4)

n) e, (3He, p)' where o-th is the DWBA cross section including all spin and lsospm-dependent factors [see eq. (2)]. Values of R for the cases considered are listed in table 5. A direct comparison between (3He, n) and (aHe, p) is possible for the target nuclei 2ssI and 32S, where the reactions proceed from mltIa/states with T = 0 to final states

463

(SHe, n) REACTIONS TABLE5 The (aHe, n)/(SHe, p) cross-sectmn ratios to analogue states Reactmn a°S 28S1 ~ aop a°S 28S1 -~ sop a4Ar 32S --~ a4C1 37K asC1 --~ aTAr

Excitation (MeV)

EI~ (MeV)

j~r

0.00 0 67 2.20 2.84 0.00 0 00 0 00 0.00

14 0 15 0 14 0 16 0 14.0 14.0 14 0 14 0

0+ 0+ 2+ 2+ 0+ 0+ 3+ 3+

R a)

0.95 1.10 0.91 1 15 (0 94)

a) For definition see text. The experimental uncertainty is about i 3 0 oYowith T = 1. In these cases R was found to be independent of assumptions on nuclear structure, provided the same wave functions were used in the calculation oftrth(aHe, n) and atb(aHe, p). The results, as gwen m table 5, are close to unity and therefore strongly support a charge-independent description of the states involved. For the (3He, n) and (aHe, p) reactions on aSCl the situation is different, because the mirror final states have the same lsospin (½) as the target nucleus. Here the (3He, p) cross section contains a triplet contribution, which is not present m the (aHe, n) cross section. Fig. 9 shows the experimental angular distributions and D W B A fits based on the wave functions of ref. 9). The slnglet contribution to the calculated (3He, p) angular distribution is shown separately by the broken curve. The combined (3He, p) angular distribution clearly has too much L = 2 admixture, resulting in an inferior fit to the data as compared to the (aHe, n) results. It follows, that this chfficulty arises mostly from the m p l e t contribution, and that an improved fit could be obtained by arbitrarmly omitting the triplet contrlbutlon and renormallzing the singlet contribution to the experimental data. The latter procedure yields a normalization factor 6exp/ath = 1.28 (as compared to a~,p/ath = 1.04 for the D W B A calculation including the m p l e t contribution) and the corresponding double ratm R is given m brackets m table 5. It may be concluded, that the triplet contribution to this (3He, p) transition is comparatively small, in qualitative agreement with the D W B A calculation based on the wave functions of ref. 9) The calculation fails, however, to reproduce the triplet contribution quantltatwely, and especially predicts too much L = 2 component. 4 5. SUMMARY AND CONCLUSIONS The (He, n) reactmn has been studied for five target nuclei in the upper half of the 2s-ld shell at bombarding energies near 14 MeV. In most cases only the groundstate transitions could be resolved, and these were found to exhibit pronounced stripping patterns of pure or predominant L = 0 character, with differential cross sections of the order of 1 mbfsr at 0 °.

464

R BASS et aL

In performing DWBA calculations for the transmons studied, extensive use was made of procedures and parameters previously estabhshed in a series of anvestigataons of the (3He, p) reaction in the same mass region. This was found essentml for a meanmgful analysis of absolute transataon strengths. Wath one exception (29Si) the latter could be reproduced mthan about a factor of 2 using wave functmns from various sets of shell-modeI calculatmns. It as anterestmg to note, that the different shell-model calculations consadered in this work produce remarkably sxmflar predlctmns with respect to (3He, n) ground-state cross sectaons, an spate of the different configuration spaces and resadual anteractmns employed. Thas result as consistent with the prevaous observatmn 2), that two-nucleon transfer data are not very sensitive to the presence of ld_~ hole excitation m the upper half of the sd shell. It moreover raises the question, to what extent some common feature of the calculations - for example low-lying energy levels used an fitting the mteractmn parameters - might be the dormnating factor an determining (3He, n) ground state strengths, rather than details of the shell-model ansatz and resulting wave functions. To clarify this point, a systematic study of the dependence of predicted two-nucleon strengths on mdavldual shell-model parameters would be of great interest The present comparison of (3He, n) and (3He, p) cross sections for analogous transitions lends support to the assumptaon of a &rect transfer mechamsm and to a chargeindependent description of the states revolved. For anatial and final states of the same asospm, information on the triplet contribution to the (aHe, p) cross sectmn can be deduced, as shown here for the 35C1(3He, p)37Ar ground state transatIon. The authors are indebted to W. Patscher for has contributions to the development and cahbratlon of the neutron spectrometer, to W. Kessel and has assocmtes for the design and constructaon of the electromc equipment, to K. Meinel and has assocmtes for thear efforts m producing and maintaining statable beam condmons, to Drs. P W. M. Glaudemans and B. H. Wlldenthal for the commumcatlon of their shellmodel wave fanctaons and to Drs. R R Betts and H. Hafner for the communacatlon of and perm~sslon to quote their 28Sa(3He, p)3Op data praor to pubhcation. One of the authors (R B.) would take to express has gratitude to Drs. H. W. Newson and E. G. Bflpuch for the hospltahty extended to ham at Duke Umverslty and T U N L during 1971/72. The work was supported by the Bundesminastermm ffir Blldung und Wissenschaff of the Federal Republic of Germany. Note added m p r o o f After submlsslon of this paper the enriched targets used in the present work (29, aosi and 35, 37C1) were tested by comparing 7-ray yields from (p, p'y) and (l9, nT) reactions at smtably chosen bombarding energies with those obtained with natural targets of known thackness. It was found that the thacknesses and enrichments differed considerably from the values quoted by the suppher (AERE Harwell) and given in table 1. Consequently the experimental (3He, n) cross sections

(3He, n) REACTIONS

465

s h o w n m figs. 7-9 a n d the c o r r e s p o n d i n g ratios gwen in tables 4 a n d 5 should be m u l t l p h e d by the following factors: 2.13 (29S0, 3.45 (a°si), 1.63 (35C1)and 1.40 (37C1). These changes result in a s o m e w h a t i m p r o v e d overall agreement for the $1 isotopes with shell-model predictions (compare subsect. 4.2 a n d table 4) b u t affect ad,¢ersely the q u a n t i t y R for the 3sC1 isotope (see table 5). The a p p a r e n t deviation of the latter from u m t y is, however, considered to be within the uncertainties of the present a n a lys~s. All m a j o r conclusions r e m a i n u n c h a n g e d .

References

1) 2) 3) 4) 5) 6) 7)

N K. Glendermmg, Phys Rev 137 (1965) B102 IcI Naun, B. Hubert and R Bass, Nucl. Phys A176 (1971) 553 B. I-[ubert, H. Nann, W Schafer and R Bass, Nucl Phys A181 (1972) 1 H Nann, T. Mozgovoy, R. Bass and B I-I Wlldenthal, Nucl Phys A192 (1972) 417 H Nann, L Armbruster and B. H Wlldeuthal, Nucl Phys. A198 (1972) 11 P W M Glaudemaus, G Wlechers and P. J. Brussaard, Nucl Plays 56 (1964) 529, 548 B. H. Wddenthal, J. B. McGrory, E C. Halbert and P. W. M. Glaudemans, Phys Lett 27B (1968) 611, P W. M Glaudemaus and B H Wfidenthal, private communication 8) B I-I Wlldenthal, J. B. McGrory, E C I-Ialbert and H. D Graber, Phys Rev. C4 (1971) 1708 9) B FI Wildenthal, E. C. Halbert, J. B McGrory and T T. S. Kno, Phys Rev C4 (1971) 1266 10) B H Wlldenthal and J. B McGrory, to be published 11) U. Friedland, thesis, Frankfurt, 1972 12) W. Patscher, Dlplomarbelt Frankfurt, 1969 13) i. S Towner and J C Hardy, Oxford Nucl. Phys Lab report 19/68; Adv. in Phys 18 (1969) 401 14) F Puhlhofer, Nucl. Phys All6 (1968) 516, and private communication 15) P. D Kunz, University of Colorado report, 1967, unpubhshed 16) R A Niorrison, Nucl. Phys A140 (1970) 97 17) L Rosen, J C. Beery, A S Goldhaber and E Auerbach, Ann of Phys 34 (1965) 96 18) J C Hardy and I. S. Towner, Plays Lett. 25B (1967) 577 19) R. R. Betts, University of Pennsylvania, Philadelphia, private commumcatlon 20) t-I Hafner, Max-Planck-Iustitutfur Kernphyslk, Heidelberg, private communication