A FINITE RANGE DWBA PROGRAM FOR MULTI-NUCLEON TRANSFER REACTIONS AND A COMPARISON WITH (6Li, t) AND (6Li, d) REACTIONS

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A FINITE RANGE DWBA PROGRAM FOR

MULTI-NUCLEON TRANSFER REACTIONS AND A COMPARISON WITH (6Li, t) AND (6Li, d)

REACTIONS

R. Devries, G. Bassani

To cite this version:

R. Devries, G. Bassani. A FINITE RANGE DWBA PROGRAM FOR MULTI-NUCLEON TRANS- FER REACTIONS AND A COMPARISON WITH (6Li, t) AND (6Li, d) REACTIONS. Journal de Physique Colloques, 1971, 32 (C6), pp.C6-175-C6-177. �10.1051/jphyscol:1971633�. �jpa-00214851�

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JOURNAL D E PHYSIQUE Co[foque C6, supplkment au no 11-12, Tome 32, Novembre-Dkcernbre 1971, page C6-175

A FINITE RANGE DWBA PROGRAM

FOR MULTI-NUCLEON TRANSFER REACTIONS

AND A COMPARISON WITH (6Li, t) AND (6Li, d) REACTIONS

R. M. DEVRIES and G. BASSANI

DCpartement de Physique NuclCaire, C . E. N. Saclay, France

ResumC. - Les predictions d'un programme de DWBA avec portee finie sont comparees aux resultats exph-imentaux relatifs a l'excitation de quelques etats de ^{1 6 0}observes i I'aide des rkc- tions (6Li, t) et (6Li, d). L'accord est bien meilleur que dans le cas des programmes avec portke nulle ou portee fixe.

Abstract. - The predictions of an exact finite-range DWBA program are compared with the experimental data for the excitation of a few states in ^{1 6 0}produced via (6Li, t) and (6Li, d) reactions. Calculations using the zero-range and fixed-range approximations suggest that only exact finite range calculations are capable of producing quantitative spectroscopic information.

This paper represents a progress report on an attempt to relate multinucleon transfer reaction data to quantitative spectroscopic information using the DWBA. An exact finite range DWBA program [l]

has been written t o analyse such reactions and is used in this paper in conjunction with a program due t o Yoshida [2] for calculating the spectroscopic factors for such reactions.

Since the clusters making up the 6Li are in a relative 2 S state one might hope that less complicated calcu- lations using the zero-range or fixed-range [3] approximations might be satisfactory. Figures I and 2

- - Z k r o range (unnormabzrd)

- E x a c t flnltc range

FIG. 1. - DWBA calculations for 12C(6Li, d)160 g . ~ . ^FIC;.^2.^-^DWBAcalculations for 13C(6Li, t ) 1 6 0 g.s.

E ~ t i = 28 MeV. E6~1 = 28 MeV.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1971633

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C6- 1 76 R. M. DEVRIES A N D G. BASSANI

compare the results of zero-range (ZR), fixed-range (FR), and exact finite-range (EFR) calculations for production of the 160 g. s. All calculations use the same parameter values, however, the ZR and F R

calculations are unnormalized. If the L), calculated in the EFR program is used in the ZR program the correct order of magnitude is produced, but not the shape. The F R calculations come closer to the EFR and in fact this approximation can be used to obtain qualitative spectroscopic information 141. The use of the EFR is encouraged by the fact that the compu- tational time required is not great (less than one minute on the Saclay IBM 360191).

The poor performance of the ZR and F R approximations can be understood by looking at the EFR kernels (which are the two-dimensional equivalent to the ZR form factor) in figure 3. The scale is loga- rithmic, but negative levels indicate negative kernels, not small values. The ZR locus is represented by a 450 diagonal from the origin. Clearly the largest contribut- ing region is not limited to near the diagonal as it is the case of a single nucleon transfer [I].

The EFR calculations are found to be similar to ZR calculations in their sensitivity to the distorted wave potentials used, but somewhat less sensitive to changes in the bound-state wave functions. We find that increasing the radius of the 160 bound state wave function increases the magnitude of the predictions but changes the shape very little. The (6Li, d) calculations were performed using a 2s state for the cc

+

d system.

Using the same radii parameters, the cross sections for the 6.137 MeV 3- and 10.353 4' states were calculated and the unnormalized results shown in figures 4 and 5. The 3- statc consists of a mixture of Ip-lh and 3p-3h states [5] which are not expected

200 4.00 6.00 8.00 10.00 12.00 R ~ i 6

3b)

FIG. 3. - EFR kernels - see text for details. 3a : 12C(6Li, d)160

g.s. K = 0 kernels ; 36 : I3C(6Li, t)160* [10.4 MeV 4+].

K = 0 kernels.

FIG. 4. - EFR DWBA calculations for 12C(6Li, d)160*.

E61,i = 28 MeV.

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A FINITE RANGE DWBA PROGRAM FOR MULTI-NUCLEOK C6-177

to be strongly excited in the (6Li, d) reaction and indeed the experimental magnitude can be reproduced only if a large compound nucleus contribution is included. The 4' state is primarily a 4p-4h state with some 2p-2h admixture. The EFR calculations indicate that the observed cross-section is almost entirely due to the 4p-4h configuration. The (6Li. t) production of the 3- state appears to be dominated by compound nucleus effects, however the EFR is able to reproduce the magnitude of the forward angle data quite well. The (6Li, t) reaction can populate the 4+

state only through its 2p-2h component, thus a large compound nucleus contribution is necessary to reproduce the observed magnitude.

In conclusion it appears that EFR DWBA calculations using spectroscopic factors calculated from shell model wave functions are capable of producing quantitative agreement with the 3 and 4 nucleon transfer data studied here. This result along with other recent calculations [2], [6] suggests that such reactions can further our quantitative knowledge of nuclear wave functions.

Frc;. 5. - E F R DWBA calculations for 13C(hLi, t ) 1 6 0 * . E61.i ²28 MeV.

Acknowledgement. - W e would like to thank Dr. H. Yoshida for letting us use his program to calculate spectroscopic factors and for stimulating advice and discussions.

References

[ I ] PEKRENOUD (J. L.) and DEVRIES (R. M.), Phys. Letters, [4] D E . ~ R A Z ( C . ) et al., Nucl. Phys., 1971, A 167, 337.

1971, 36B, 18. [5] ZUKEK (A. P.), BUCK (B.) and MCGKORY, BNL-14085 [2] GUTBROD (H. H.), YOSHIDA (H.) and ROCK (R.), (unpublished).

Nucl. Phys., 1971, A 165, 240.

[3] PUHLIIOFFER (F.) et al., Nucl. Phys., 1970, A 147,258. L6] B ~ T H G E (K.), this