Mutual excitation of 32S + 28Si at 90 and 97.09 MeV

Volume 149B, munber 1,2,3

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13 December 1984

MUTUAL EXCITATION OF 32S + 28Si AT 90 AND 97.09 MeV A. BAEZA, J. DIAZ, J.L. FERRERO Instituto de Fisiea Corpuscular, C$IC, Universidad de Valencia, Bur/asot, Spain

B. BILWES, R. BILWES Centre de Recherches Nucl$aires, Universitd Louis Pasteur, Strasbourg, France and

J. RAYNAL Service de Physique Thdorique, Centre d'Etudes Nucl~aires de Saclay, Gif-sur-Yvette, France

Received 5 September 1984 The mutual excitation of projectile and target was measured for 32S + 2Ssi scattering at 90 and 97.01 MeV on a large angular range. A coupled channel analysis of the angular distributions is in good agreement with the data. It is used to demonstrate the important interference of simultaneous and sequential excitation amplitudes and the sensitivity of this process to the nuclear surface shape.

The mutual excitation of projectile and target in heavy ion scattering is an interesting phenomenon to study in that it has been predicted that the multiple excitation of collective states plays an important role in the energy loss process leading to deep inelastic scattering [1]. Moreover such studies could also afford new insight into the shapes of the nuclear surface [2] and the ion-ion potential [3], as well as allow for a greater in-depth verification of the models usually used for nuclear reactions. Only a few angular distributions of mutual excitation involving ions heavier than p shell nuclei have been reported to date [ 2 - 4 ] . Their theoretical analysis has revealed the superposition of both sequential and simultaneous excitation reaction mechanisms whose relative importance depends on the nuclei involved. We report in this paper experimental data and a theoretical analysis of inelastic scattering of 32S on 28Si, at 90 and 97.09 MeV incident energy. The Coulomb interaction is here lower than in previous cases [2,3] and careful study of the nuclear and Coulomb interferences will be a sensitive method to shed more light on the surface nuclear interaction. Targets were 9/ag/crn 2 of 28Si made from enriched 0370-2693/84/$ 03.00 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

SiO 2 (99.4%) evaporated on a carbon backing of 20/2g/ cm2 and were bombarded with the 32S beam of the Tandem Van de Graaff at the CRN at Strasbourg. The outgoing particles were identified by the kinematic coincidence method using two-position sensitive detectors. Our experimental set up is described in more detail in ref. [5]. Q-value spectra of 32S ions, taken at an incident energy of 90MeV and at different angles are shown in fig. 1. At the top of this figure the level schemes of both nuclei, with single-phonon states emphasized, are given. The Q-value resolution ( ~ 2 0 0 keV) is sufficient to resolve the low lying inelastic and mutual excitation peaks. Nevertheless, it was impossible to extract with confidence the angular distribution of the peak observed at some angles at Q "" - 4 , 4 MeV. This peak, when it exists, is always weaker than the peak which corresponds to the mutual excitation. It may correspond to the sum of the 47 level excitation of both nuclei. Due to the low cross section of these excitations, we disregarded this eventually second-order effect in the analysis of the mutual excitation process. Angular distributions for elastic scattering, for inelastic scattering to the 28Si 2 + state at 1.78 MeV, to 73

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the 32S 2+state at 2.14MeV and to the mutually excited 2 + states in both nuclei are shown in figs. 2 and 3. A complete study of elastic and inelastic data (including 3 - level excitation in each nuclei) will be published elsewhere [6]. We took particular care to extend the angular distribution toward backward angles. The observed oscillations at these angles could be due to the interferences between a-transfer and scattering [7]. It is not our aim here to provide a detailed reproduction of this part of the angular distributions. But to obtain results which are not dependent on this superposition two kinds of Woods-Saxon optical potentials were derived from the elastic data analysis. The first one (T), rather surface transparent, allows for the rough reproduction 74

of the oscillations at backward angles at 97.09 MeV. The second (A), more absorptive, reproduces only the general trend in this angular range. Starting from the best-fit potentials obtained at 90MeV for the elastic data alone, we adjusted the parameters by fitting the elastic and the 2 + inelastic curves at the same time, the three levels being coupled. The theoretical curves obtained by full coupled channels calculations using the two potentials, whose parameters are given in table 1, are compared in figs. 2 and 3. The coupled channel code ECIS 79 [8] was used in all calculations and 200 partial waves were included. The integration step was 0.1 fm. The Coulomb corrections included in ECIS made the value of 14 fm used for the matching radius sdfficient.

Volume 149B, number 1,2,3

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(+ 0.42). The rotational model was assumed for both nuclei as evidence exists that their static quadrupole moments agree with those predicted by this model [9,10]. The charge quadrupole deformation parameters/32 (28Si) = -0.42 and/32 (32S) = 0.29 were derived from lifetime measurements given in refs. [9-12] using r 0 = 1.2 fm. The potential deformation parameters were calculated by the usual scaling/SR. The transition form factors were derived by assuming a deformed radius of the real, imaginary and Coulomb parts of the optical potential of the form: R i =Roi (1 + ~(2p) r20(~2p) + ~ ) Y20(~2t)),

where ~2p and 12t are the spherical angles with respect to the body coordinate system of each nucleus. The form factors for the single and sequential excitation and reorientation terms were obtained in the intrinsic system of each nucleus as is usual in the rotational model [13], neglecting the deformation of the spectator nucleus. The transition form factors for simultaneous nuclear excitation were derived in the laboratory system by expanding the potential in terms of the deformation parameters (the intrinsic system is different for each nucleus). These form factors were taken as the first term in the expansion which contributes to the mutual excitation

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tipole l = 4, as shown in ref. [14], the Coulomb form factors disappear when the two charges do not overlap. The radial form factors for l --- 0, 2, 4 were computed within the framework o f this crude model and were used for the simultaneous Coulomb interaction in the coupled channels calculations. The coupling diagram in the upper right-hand comer of fig. 4 shows all the couplings taken into account.

Table 1 Optical potential parameters. (The depths are in MeV, the radfi and diffuseness in fm). Potential

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76

Volume 149B, number 1,2,3

PHYSICS LETTERS i

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Fig. 4. Upper part: calculated mutual excitation obtained by including either only two single-step successive routes or only simultaneous excitation. Lower part: calculated mutual excitation obtained by including either only Coulomb interaction or only nuclear interaction. The coherent sum of these components is indicated by solid lines. The full coupling scheme for these calculations and those of figs. 2 and 3 is shown in the upper fight-hand comer.

The form factor for the coupling between both 2 + levels was the same as the one for the simultaneous mutual excitation. As the contribution of this term came out to be rather small, it is expected that other higher order processes like the coupling to 4 + states will be negligible. The agreement between the theoretical calculations and the experimental data is very good for both potentials even at 97.09 MeV where the potential parameters were kept the same as at 90MeV. The curves reproduce the opposite phase pattern between the 2 + inelastic curves and the mutual one. The potential T provides a better description of the general shape at 97.09 MeV but overestimates the broad maximum observed around

90 °. In contrast, the potential A underestimates it. The integrated cross section predicted is 6 mb and 3 mb at 90 MeV, 9 mb and 4 mb at 97.09 MeV with potentials T and A respectively. These values are of the same order of magnitude as the 3 - single-phonon excitation levels at 5.01MeV in the 32S and 6.88 MeV in the 28Si [61. To test the importance of the sign of the deformation, a calculation was made using a prolate deformation for 28Si. The corresponding curves, added to fig. 2, do not fit the experimental data. In order to gain more insight into the reaction mechanimas we calculated the different mutual excitation components. The upper part of fig. 4 compares the 77

Volume 149B, number 1,2,3

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simultaneous and sequential components and the lower part compares the Coulomb and nuclear parts obtained at 90 MeV using the potential T. Both simultaneous and sequential excitations are important and their destructive interference gives rise to the characteristic minimum in the mutual excitation cross section. All the multipoles 1 = 0, 2, 4 are of similar importance for the nuclear simultaneous excitation, but the Coulomb simultaneous excitation was found to be negligible. Although the Coulomb component of the sequential excitation is necessary to reproduce the forward part of the experimental curve, the nuclear component by itself is sufficient to give almost the total shape. A similar behaviour is observed at 97.09 MeV. In conclusion we give in this paper very precise experimental data of mutual excitation of two deformed s - d nuclei. The data cover a large angular range (110 °) at two incident energies. They are well reproduced m the framework of the optical model and using a rotational collective model for the excited states. The deformation parameters extracted from life time measurements and the optical parameters obtained in the coupled channel analysis of the first 2+ excitations in both nuclei were used without modifications. This essentially parameter free description of the mutual excitation data substantiates the reliability of the models. The magnitude of the mutual cross section is estimated to be of the same order of magnitude as the cross section of the 3 - single-phonon excitations of both nuclei. The simultaneous component is found to be essential in order to reproduce the data while in refs. [2,4] two-step processes alone give a quite good description

78

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of the data. No conclusion can be drawn from ref. [3] as the agreement between theory and experiment is poor. The mutual excitation takes place mainly through the nuclear part of the interaction. It shows a remarkable sensitivity to the sign of the deformation. Mutual excitation studies may be a useful tool for the study of the nuclear shape. The authors wish to thank P. Bond for helpful discusslons and express their gratitude to the J.E.N. (Madrid) and U.P. (Valencia) for computing facilites. We would also like to thank the "Comision Asesora Cientifica y Tecnica", the "Cooperacion Cientifica Hispano-Francesa", and the C.N.R.S. for their financial support.

References [1] H. Esbensen et al., Phys. Rev. Lett. 41 (1978) 296; R.A. Brogliaet al., Phys. Lett. 89B (1979) 22 [2] P.D. Bond et al., Phys. Lett. l14B (1982) 423. [3] T.P. Cleary et al., Phys. Lett. 83B (1979) 51 [4] J. Cook et al., Nucl. Phys. A386 (1982) 346. [5] B. Bilwes et al., Nucl. Phys. A408 (1983) 173. [6] A. Baeza et al., to be published. [7] M. Mermaz et al., Phys. Rev. C27 (1983) 2408. [8] J. Raynal, Phys. Rev. C23 (1981) 2571 [9] P.M. Endt and C. Van der Leun, Nucl. Phys. A310 (1978) 1. [10] G.C. Ball et al., Nucl. Phys. A349 (1980) 271. [11] D. Sehwalm et al., Nucl. Phys. A293 (1977) 425 [12] R.H. Spear, Phys. Rep. 73 (1981) 369. [13] T. Tamura, Rev. Mod. Phys. 37 (1965) 679. [14] K. Alder and A. Winther, Nu¢l. Phys. A132 (1969) 1.