Elastic scattering of 27Al+27Al at near barrier energies

PHYSICAL REVIEW C VOLUME 58, NUMBER 6 Elastic scattering of DECEMBER 1998 Al؉ 27 Al at near barrier energies A. Zerwekh, R. Liguori Neto, N. Added, J. C. Acquadro, N. Carlin, M. Frizzarini, and F. Malandrino ˜ o Paulo, C.P. 20516, Sa ˜ o Paulo, 01498-970, Brazil Instituto de Fi´sica, Universidade de Sa J. Lubian, * R. Cabezas, P. R. S. Gomes, R. M. Anjos, G. M. Santos, A. M. M. Maciel, C. Muri, and S. B. Moraes Instituto de Fi´sica, Universidade Federal Fluminense, Av. Litoranea s/n, Gragoata´, Nitero´i, R.J., 24210-340, Brazil G. Ramirez and C. Tenreiro Departmento de Fi´sica, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago, Chile Received 13 July 1998 Elastic scattering angular distributions for the symmetric 27 Alϩ 27 Al system were measured at bombarding energies from 50 to 70 MeV. The integrated inelastic cross section for the first two excited states was determined by the in-beam ␥ -ray spectroscopy method. The data were analyzed by the optical model and by coupled channel calculations. The spin-orbit couplings of the ground states of both nuclei are analyzed. S0556-28139802112-8 PACS numbers: 25.70.Bc, 27.30.ϩt I. INTRODUCTION The elastic and inelastic scattering of asymmetric sys- tems, at near barrier energies, have been investigated exten- sively in the last years. Very interesting results have come out from these studies, including the threshold anomaly of the optical potential at low energies and the coupling effects on the fusion process 1. For two identical nuclei, the Cou- lomb scattering is described by the Mott distribution, which exhibits a pronounced interference pattern in the angular dis- tribution. Near barrier scattering for such systems show fine structures and deviations from the Mott angular distributions, which are easier to be detected than those from the structure- less angular distributions of the Rutherford scattering. There- fore, the scattering of identical particles is very sensitive to details of the nuclear potential and should allow the deriva- tion, with high accuracy, of the optical model parameters. There are very few symmetric systems of identical sd-shell nuclei for which the elastic scattering have been measured 2–4. All of them are for n- ␣ nuclei. As the 27 Al is a nucleus with a ground-state spin equal to 5/2, the measure- ment of the scattering of the 27 Alϩ 27 Al system allows also the investigation of the influence of the ground-state spin of the nuclei on the scattering and reaction processes. In Sec. II of this paper the experimental methods and results are presented. In Sec. III, the elastic scattering of identical particles is described, and the optical model analy- sis of the elastic scattering data is discussed. In Sec. IV, the results of the coupled channel analysis of inelastic scattering are shown. Finally, in Sec. V, some conclusions are drawn. II. EXPERIMENTAL DETAILS AND RESULTS The experiments were performed at the 8UD Pelletron ˜o Paulo. The beam inten- accelerator of the University of Sa sity on the target was typically of the order of 10–50 nA. Experiments have been performed at seven bombarding en- * Permanent address: CEADEN, P.O. Box 6122, Havana, Cuba. PRC 58 ergies from 53 to 70 MeV the nominal Coulomb barrier is E Lab Х54 MeV). There were targets with thickness of 15 and 50 ␮ g/cm 2 . A layer of 5 ␮ g/cm 2 of 197 Au was depos- ited on the targets, for calibration and normalization pur- poses. The detection system was an array containing nine silicon surface barrier detectors. The angular separation be- tween two adjacent detectors was 5°. In front of each detec- tor there were collimators with diameters of 4 mm. The angle determination was made by reading on a goniometer with a precision of Ϯ0.5°. A monitor was placed at 20° with the beam direction. The normalization was made by two differ- ent methods. In both, the scattering was supposed to be purely of the Coulomb type: at forward angles for the 27 Al target Mott scattering and for the 197 Au target Rutherford scattering. The angular distribution range of the data was taken from very forward angles up to ␪ Lab ϭ70°. The energy resolutions of the detectors were in the range from 300 keV full width at half maximum FWHM, for forward angles and thin tar- gets, to 1000 keV FWHM for backward angles and thick targets. Due to the kinematical broadening, the resolution was not good enough to separate the elastic and first inelastic 0.844 MeV peaks of the 27 Al at backward angles. Further- more, at backward angles, the elastic scattering was super- posed with the recoil peaks of the 12 C and 16 O contamina- tion. As a consequence of that, some asymmetries were noticed in the elastic angular distributions, with respect to ␪ c.m. ϭ90°. Therefore, in order to avoid these systematic er- rors, and using the fact that target and projectile are indistin- guishable, only the data in the range up to ␪ c.m. ϭ90° were used in the analysis. Figure 1 shows a spectrum at E Lab ϭ55 MeV, ␪ Lab ϭ49°. One can see the first two inelastic peaks with very small intensities and well resolved from the elastic peak. The uncertainties in the elastic cross sections are due to the statistical errors and possible normalization errors. They were found to be smaller than 5%. A further investigation of the integrated inelastic scatter- ing cross section was performed by the in-beam ␥ -ray spec- troscopy method. Two HP germanium detectors were placed ©1998 The American Physical Society