The 16O(6Li, dγ)20Ne reaction

Nuclear Physics A313 (1979) 467-476; (~) North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher

THE M. A. ESWARAN

160(6Li,

d~)2°Ne REACTION t

tt, R. N. BOYD *tt, E. SUGARBAKER, R. COOK and H. E. GOVE

Nuclear Structure Research Laboratory, The University of Rochester, Rochester, New York 14627 Received 9 May 1978 (Revised 21 July 1978) Abstract: The discrepancy between observed reaction strengths and those predicted from'SU(3) con-

s~derations in the 160(6Li, d) reaction has been studied. The effects of both 160 ground state correlations and of inelastic couplings on the reaction strengths are included. Particle-gamma angular correlations are presented as a test of the reaction predictions, It is found that inclusion of both the ground state correlations and the inelastic couplings does help to resolve the theoreticalexperimental discrepancy, and results in generally improved representations of both cross section and angular correlation data.

E

NUCLEAR REACTIONS 160(6Li, d~,), E = 32 MeV; measured d-y angular correlation function, W(thp, 0~., ~;.). Compared DWBA and CCBA reaction predictions to data.

I. Introduction The (6Li, d) reaction has been used in recent years to provide an abundance of nuclear structure information x, 2). The application of SU(3) to the prediction of reaction strengths in such studies has resulted in a fairly complete understanding of four-particle substructures in the lower half of the sd shell 3). The t 6 0 ( 6 L i , d) reaction, however, has been a special case in that the SU(3) predicted strengths to the 2°Ne ground state band members were in poor agreement with those observed "~). Several possibilities have recently been proposed as the explanations of this difficulty, most recently, that of correlations in the t60 ground state 5). In the present paper, we show results of calculations in which the correlations and inelastic excitations between the final states in 2°Ne are included. In addition, data resulting from general particle-gamma angular correlations (PGAC) in the 160(6Li, d) reaction are presented. The comparison of these data with the results of the reaction calculations is used to test our understanding of the reaction mechanisms involved. The experimental arrangement used in the present study is discussed in sect. 2. * Work supported by the National Science Foundation. ** Present address: Nuclear Physics Division, Bhabha Atomic Research Centre, Bombay 85, India. ,tt Present address: Department of Physics, Ohio State University, Columbus, Ohio 43210, 467

468

M . A . ESWARAN et al.

The data are presented and compared to the results of several reaction calculations in sect. 3. Finally, sect. 4 presents some discussion of the results.

2. Experimental details The N S R L MP Tandem Van de G r a a f f accelerator and *Li source were used to provide the 32 MeV 6Li beam on a self-supporting T a 2 0 5 target. This target was made by anodic oxidation of an approximately 100/~g/cm 2 thick foil in the presence of water. The N S R L spin meter 6) was used to observe the PGAC. This system allows the simultaneous measurement of coincidences between each of six y-ray detectors and each of four particle detectors. In the present experiment, one of the particle detectors was used to check the run to run normalization given by the Faraday cup. Useful P G A C data were obtained at three lab particle scattering angles: 19.6 °, 39.6 ° and 59.6 °. The 7-ray detectors used were 7.6cm x 7.6 cm NaI(TI) scintillators mounted on RCA 8054 photomultiplier tubes. In all data collection runs, three of these detectors were located in the horizontal plane, at a polar angle of 0 r = 90 ° in a polar-

TIMING PICK-OFFS

DISC 5nsec.

I

I

I S~D

NONMI.JLTI::~..E PULSE DISC

DiSC 5nsec.

I COINC.

S~D

COINC.

I A~_.] DIRECT MEMORY ACCESS TO I::E)P8 COMPUTER

I

Fig. 1. Electronics diagram used for the experimental setup involving four particle detectors and six y-ray detectors.

160(6Li, dy)2°Ne

469

spherical coordinate system in which the ~ axis is the upward normal to the reaction plane. Two of the detectors were located out of the horizontal plane at 0r = 45 °, and one was set on the ~ axis pointing straight down at the target. The azimuthal angle is defined to be zero in the incident beam direction. The particle detectors were 1500 or 2000 #m surface barrier solid state detectors collimated to subtend a solid angle of 4 msr. Absorber foils were put in front of the detectors to maximize the energy deposited therein by the reaction deuterons. Coincidences between particle and 7-ray detectors were determined using the electronics scheme shown in fig. 1. In this scheme the fast signals from the photomultiplier anodes and from the timing p.ick-off units of the particle detectors are used to provide the time-to-amplitude-converter (TAC) inputs, the routing signals,

IZO0

'SO(eLi,dY)Z°Ne

PART ICL E S

(a) 800 >

.400

0I ._J U2 Z Z < -r n~ I.d a_ co I-Z

6OOO

5O

J

I00

26o

15O

'60(~Li ,dy)Z°Ne TAC

(b)

4000

2000

0

o6 6O

5o

~

15o

zoo

'60(SLi,dy)ZONe GAMMA RAYS 4÷ ,, 2 +

4020

> ~ ~"5-.~

25

~1~.

50

(C)

?5

CHANNEL NUMBER

Fig. 2. Typical spectra for (a) particles gated with all y-rays, (b) the TAC (the FWHM is about 3 ns), and (c) the ~,-rays gated with the 4.25 MeV particle group.

470

M . A . ESWARAN et al.

and the pile-up rejection signals. The slow signals provide the energy information from the detectors. The slow particle signals are generated both in an ungated and a gated mode. Thus, cross sections and PGAC can be measured simultaneously. The signals from the y-ray detectors, however, are always gated by a particle-gamma coincidence requirement to provide an acceptable count rate for the computer. The coincident events were put into the NSRL PDP8-PDP6 on-line computer system, partially analyzed on line, and recorded event by'event on magnetic tape. Then the final data analysis was done off-line using the same computer system. Typical spectra of coincidence particle, coincidence y-ray, and TAC are shown in fig. 2. In the gated particle spectra, only the deuteron peaks corresponding to the first and second excited states of 2°Ne were observed to have energies above those of the other reaction products. The PGAC data, then, were determined by summing just the photopeaks in the coincidence y-ray spectra. All PGAC data for each particle detector angle were then normalized to an average value of unity.

3. Experimental results and comparison to reaction calculations 3.1. PRESENTATION OF THE DATA

The differential cross sections 4) for 160(6Li, d) to the 0 +, ground state, 2 +, 1.63 MeV state and 4 ÷, 4.25 MeV state at an incident 6Li energy of 32 MeV have been measured previously; those results, shown in fig. 3, were used in the present study. The curves shown in conjunction with the data are discussed in subsect. 3.2. The PGAC data for the 2°Ne(2 +, 1.63 MeV) ~ 2°Ne(0 ÷, g.s.) decay are shown in fig. 4 for the three particle detector angles examined, and for the 2°Ne(4 ÷, 4.25 MeV) -~ 2°Ne(1.63 MeV) decay in fig. 5. As can be seen in fig. 4 sharp oscillations are seen in the in-plane correlation pattern for the 2 + ---, 0 f decay at the forward most detector angle, while these oscillations are attenuated at the more backward scattering angles. The 4 ÷ ~ 2 ÷ PGAC show less dramatic oscillations. 3.2. REACTION CALCULATIONS

Following the work of Rybicki, Tamura and Satchler 7), the PGAC are defined as

W(O~, c~) = 1 + Z

PKQ RK(y)CKQ(O~,~ ) , Poo where PKQ are the usual statistical tensors and R K and CKQ are as defined in ref. 7). Thus the average value over all angles of W(Or, ckr) is 1.0. it, Q > 0

Reaction calculations for the present study were performed using the CCBA code C H U C K s). This code was modified 9) to calculate the PGAC according to the formalism ofref. 7).

160(6Li ' d~)2ONe 1.0

i

,

,

,

471

~

~

'

160(6Li.d) Z°Ne E%i: 52 MeV

.~.,,

..Q

°%,

oV oOOO o

I

o

2b

I

4b

'

6b

i

ao

Bern Fig. 3. Differential cross sections for 160(6Li, d) to the 0 ÷, g.s. ; 2 ÷, 1.63 MeV; and 4 ÷ , 4.25 MeV levels in 2°Ne. The solid (dashed) curves are results of CCBA (DWBA) calculations, and are explained further in the text.

The dashed curves in figs. 3, 4 and 5 represent the results of DWBA calculations, assuming the four nucleons transferred in the (6Li, d) reaction go into (sd) 4 configurations. Thus the four nucleons go into bound states having n nodes and l units of angular momentum: 2n + 1 = 8. These calculatio,s used the optical potential parameters of Chua et al. ~o) for 6Li, and of Perrin et al. ~ ~) for the deuterons. The bound state well parameters were chosen to be (r o, a) = (1.33, 0.65) and the depth was adjusted to give the correct binding energy. These parameters are summarized in table 1. While a similar prescription (although not with those optical potential parameters) has proved successful for (6Li, d) studies over a wide range of nuclei 1- a), it is this DWBA reaction interpretation which motivated the present study. The shapes of the present cross section predictions are in reasonable agreement with the data, but the resulting relative spectroscopic strengths for the 0 ÷, 2 +, 4 + levels are 1:0.77:0.57 respectively. This is in qualitative agreement with previous results 5), and is in contrast with the SU(3) predicted strengths of 1 : 1 : 1 for the three levels. The in-plane PGAC data at the forward most particle detector setting are seen to be reasonably well represented by this calculation (dashed curves), but the agreement is much less good for the other data sets. A recent study 5) has suggested that proper accounting of the ground state correlations in the ~60 target improves the agreement between the SU(3) predicted

M. A. ESWARAN et al.

472

160(6Li, dY)Z°Ne ANGULAR CORRELATIONS

d-Yz+-.o +

~d =22.5°

8 r = 90"

8r = 45*

2.4

i 1.6 I

I

0.8

Z 0 --I W n"

i

o~

60

120

180

o

\v, do

,~o

,80

~d=4Z5 °

1.6 ,

',

0

/

#

#

(18 n,
~s

0;

,~

Z

,80

o

6'0

I~O

#80

~

,~o

,80

~Pd= 70*

2.4

L6

oE

~

,~o

~7.(deg)

,80

o

~),(deg)

Fig. 4. Particle-gamma angular correlation data for the 2°Ne(2 +, 1.63 MeV) --, 2°Ne(0 +, g.s.) decay. The solid (dashed) curves are the results of CCBA (DWBA) calculations.

spectroscopic factors and those observed in this reaction. Thus, the DWBA reaction calculations were also performed assuming a 22 ~ two-particle two-hole component in the t60 ground state. The DWBA calculations produced shapes essentially identical with the dashed curves shown in figs. 3, 4 and 5. However the spectroscopic strengths achieved in those calculations are now 1 : 0.78 : 0.78, in better agreement with the SU(3) predictions. Since the three Z°Ne levels in question are thought to be members of a rotational band having a large deformation ~2), the effects of inelastic couplings between

160(6Li, dy)Z°Ne

473

'60(6Li, dy)ZONe d-Y4,-..,z ÷ ANGULAR CORRELATIONS 8), =90"

8), =45" ~d • 22.5*

0.81Z 0

!!

o~ ~" ~

,:~o ,~

o

~

,~o

,8o

~o

,~o

,~

~

,~

,~

,tbd =4Z5 ° / ILl n-Ir 0 (.D

0.8

n.-

o~,

do

,~

Z

,8o

o

~d = 70"

ae

o~ ~

,~o

,~7(deg)

,8o

o

,~7.(deg)

Fig. 5. Particle-gamma angular correlation data for the Z°Ne(4 +, 4.25 MeV) ~ 2°Ne(2 +, 1.63 MeV) decay. The solid (dashed) curves are the results of CCBA (DWBA) calculations.

members of this band might be important to a proper description of the t 60(6Li, d) reaction to these states. Thus calculations were run in which these inelastic couplings, as well as the 160 ground state correlations discussed above, were accounted for. The formalism for such couplings is described by Tamura 13); in the present CCBA calculations the inelastic excitations between the 0 ÷ and 2 +, the 2 ÷ and 4 ÷, and the 4 ÷ and the 6 ÷ (at 8.78 MeV) final states were included. The form factors used for the inelastic excitations are from a Legendre expansion of a Woods-Saxon potential, i.e., V2(r) = S[VR(r, O) + iVl(r, 0)-IY~2(0)df2, where VR(r, 0) and Vl(r, 0) are the real and imaginary potential terms (see table 1). C o u l o m b excitation was also included in the excitations. If the 0 + ~ 2 + and 2 + ~ 4 + inelastic scattering strengths are extracted 14) from ~-ray decay data 15), they are f o u n d to be essentially the same. Thus a typical value of/~2 = 0.45 was

474

M. A. E S W A R A N et al. TABLE 1 Optical potential parameters

Channel

Vo

roR

aR

Wv

6Li+160 d+2°Ne c~+ 160

210 87 a)

1.30 1.13 1.33

0.70 0.80 0.65

25.0

.

V = V ~ - VoJ(roR, art, r, O ) - i W v f ( r o l ,

Vc =

l

Ze~ 2rcA l,,3

3_~,3

Ze2,

f o r r > reAl"3;

d

Wo

rol

aj

rc

f12

12

1.70 1.426

0.90 0.721

1.4 1.3 1.4

0.0 0.45 0.0

.

a l, r, O ) + 4 t a l W o ~rrJ(rol , al, r, 0);

f o r r < rcA 1/3 ,

=

r

I(r~, a j, r, O) =

+ exp aj

_1

") Vo for the bound state was adjusted to give the correct binding energy.

used for all of these couplings. The results of this calculation, shown as the solid curves in figs. 3, 4 and 5, do slightly better than those of the DWBA in representing the cross section data to the 0 ÷ and 2 + levels, and about as well as the DWBA for the 4 ÷ level. Furthermore, the spectroscopic strengths which produce these CCBA results are in the ratio of 1 : 1 : 0.90, in good agreement with the SU(3) predictions. The PGAC predicted by the CCBA calculation are seen to be similar to those of the DWBA, although the CCBA representations are somewhat better than those achieved by the DWBA calculations, particularly for the in-plane (0r = 90 °) correlations at 4~p = 22.5° and 47.5 °. Because neither the DWBA nor the CCBA provides a good representation of the differential cross section data for angles larger than 50°, it is not surprising that the PGAC data at the backward particle scattering angle are not well represented either. For the two forward angle particle detector settings those representations are fairly good, with only the point at (~bp, 0~, ~b~) = (22.5 ° , 45 ° , 105°) being badly represented. Tests of the sensitivity of the results to the optical parameters showed the deuteron real-central to be the most critical term. Reduction of that well depth by 10 % produced significant changes in the shapes of the (6Li, d) differential cross sections, but the relative spectroscopic strengths were only about 5 % changed. Some changes were also produced in the calculated PGAC. However, in general the sensitivity of the PGAC to parameter changes is less than that of the differential cross sections. Calculations were also run with the optical parameters used 1,2) in previous (6Li, d) studies. The representations of the cross sections were considerably worse than those shown in fig. 3. However, the relative spectroscopic strengths obtained were consistent with those listed above: inclusion of both the 160 ground state correlations and

160(6Li, d),)2°Ne

475

the inelastic excitations were necessary to achieve good agreement with the SU(3) predictions. Both DWBA and CCBA calculations described above were run assuming the 6Li and d to have zero spin in order to accommodate size and time limitations associated with the coupled channels calculations. Test calculations in which the spins were taken to be 1, and for which a standard deuteron spin orbit term t l) was added, revealed that this approximation could affect the relative spectroscopic factors by no more than a few percent. Inclusion of the spin did produce a general smoothing effect on the PGAC, but did not affect the qualitative shapes or phases of the oscillations. The maximum change from the spin zero case for the q~p = 22.5 ° and 47.5 ° PGAC was less than 0.20. Calculations with and without the 4 + ~ 6 + inelastic coupling showed that its inclusion produced a considerably larger effect than that of proper spin inclusion. Thus the 6 + channel was included in the calculations which gave the CCBA results shown in figs. 3, 4 and 5. Calculations with values of/32 varying by + 20 ~ from the value quoted above showed the ratio of transition strengths to have a sensitivity to that parameter of less than + 10 ~ . Several studies ~2) have suggested the existence of a non-zero/34 in the inelastic scattering couplings. The CCBA calculations with typical values for this parameter less than 0.1 produced results which were changed very little from those with/34 taken to be zero. More complicated reaction effects might also be involved, e.g., sequential transfer and finite range effects. The former is an unlikely possibility, since the "0t-transfer" mechanism has proved so uniformly successful in previous (6Li, d) reaction studies ~' 2). Meaningful calculations of that type would be difficult to perform in any event, since the number of intermediate states is large in any such calculation. Finite range effects are a definite possibility. However, inclusion of the standard finite range and nonlocality corrections included in the zero range code a) was found to produce a negligible correction to the relative spectroscopic strengths. The various effects described above give some indication of the uncertainty on the relative spectroscopic strengths: it is apparently around +0.15 for the data for the 0 ÷ and 2 + levels, which are fit reasonably well. Since both DWBA and CCBA calculations did less well in reproducing the 4 + angular distribution, the uncertainty in its relative spectroscopic strength is due mainly to ambiguities in the fitting procedure. Normalization to the 4 + data around 30° was adopted so as to be consistent with the procedure used in ref. 5), but normalization to the 23 ° point would shange the ratio of spectroscopic factors to 1 : 1:0.62. Thus the relative strength of the 4 + level must be assumed to be uncertain to about 0.30. Cobern et al. ~6) have performed a study of 2°Ne levels by the 160(7 Li, t) reaction, and have also included coupled channels effects between 2°Ne states. Their ratios of spectroscopic factors was 1 : 1 : 0.75, with uncertainties, presumably, of roughly the same magnitude as in the present work. Ground state correlations, however, were not included in that analysis. A similar analysis of the present (6Li, d) data would have resulted in a smaller spectroscopic factor for the 4 + state, i.e., the

476

M.A. ESWARAN

et al.

present 1 : 1 : 0.9 ratio would have been quite close to the (TLi, t) result. The results of the two studies certainly agree to within uncertainties. 4. Conclusions The present study helps to resolve the long-standing question of the disagreement between the SU(3) predicted (6Li, d) strengths and those observed. Inclusions of the inelastic excitations results in an improved representation of the shapes of the angular distributions. And, accounting for both those excitations and the 160 ground state correlations is found to result in considerable improvement of the agreement between theoretical and experimental spectroscopic factors. The ratios of these factors are sufficiently insensitive to uncertainties in the optical potentials that it seems unlikely that they could be affected appreciably by subsequent improvements, e.g., inclusions of finite range effects. The PGAC data presented exhibit some interesting oscillations, the most dramatic of which (in-plane, ~bp = 22.5 %) are fairly well represented by either the DWBA or CCBA calculations, although not as well as those from a (d, py) study ~7). Where discrepancies in data representation do exist, the inclusion of the inelastic excitations seems to lessen those discrepancies. The authors wish to thank N. Anantaraman for making the cross section data available to us prior to publication, and J. P. Draayer for several enlightening discussions. References 1) N. Anantaraman, H. E. Gove, J. Toke and J. P. Draayer, Nucl. Phys. A279 (1977) 474; N. Anantaraman, H. E. Gove, J. P. Trentelman, J. P. Draayer and F. C. Jundt, Nucl. Phys. A276 (1977) 119 2) H. W. Fulbright, C. L. Bennett, R. A. Lindgren, R. G. Markham, S. C. McGuire, G. C. Morrison, U. Strohbusch and J. Toke, Nucl. Phys. A284 (1977) 329 3) N. Anantaraman, H. E. Gove, J. Toke and J. P. Draayer, Phys. Lett. 6OB (1976) 149 4) N. Anantaraman, J. P. Draayer and H. E. Gove, Annual Report of the University of Rochester, Nuclear Structure Research Laboratory (1974) p. 10 5) N. Anantaraman, C. L. Bennett, H. E. Gove, R. A. Lindgren, J. Toke, J. P. Trentelman, J. P. Draayer, F. C. Jundt and G. Guillaume, private communication 6) P. M. S. Lesser, Ph.D. Thesis, University of Rochester, 1971 (unpublished) 7) R. Fybicki, T. Tamura and G. R. Satchler, Nucl. Phys. A146 (1970) 659 8) P. D. Kunz, University of Colorado, 1975, unpublished 9) H. Clement and R. N. Boyd, private communication 10) L. T. Chua, F. D. Becchetti, J. J~inecke and F. L. Milder, Nucl. Phys. A273 (1976) 243 11) G. Perrin, Nguyen Van Sen, J. Arvieux, R. Darves-Blanc, J. L. Durand, A. Fiore, J. C. Gondrand, F. Merchez and C. Perrin, Nucl. Phys. A282 (1977) 221 12) H. Rebel, G. W. Schweimer, J. Specht, G. Schatz, R. L6hken, D. Habs, G. Hauser and H. KleweNebenius, Phys. Rev. Lett. 2.6 (1971) 1190 13) T. Tamura, Rev. Mod. Phys. 37 (1965) 679 14) K. E. G. L6bner, M. Vetter and V. Honig, Nucl. Data Tables A7 (1970) 495 15) F. Ajzenberg-Selove, Nucl. Phys. AIg0 (1972) 125 16) M. E. Cobern, D. J. Pisano and P. D. Parker, Phys. Rev. C14 (1976) 491 17) R. N. Boyd, H. Clement and G. D. Gunn, Nucl. Phys. A283 (1977) 434