Accuracy of The Multipole Expansion of Density Distribution for Deformed Nucleus

Abstract

The present thesis deals ith the density distribution of defonned nuclei and the heavy ion (HI) nuclear interactions for spherical-defonned nuclear pair. In the first chapter, the accuracy of multipole expansion of density distribution for defonned riuclei is tested. We extend our study to different values of surface diffuseness parameter a of uranium nucleus U 238 and assume the presence of quadrupole8 ,

hexadecapole 84 in addition to octupole 83 defonnations. The dependence of the percentage error in multipole density expansion, on the number of tenns, order and sign of defonnation parameters, values of diffuseness parameter and orientations angle of symmetry axis of the defonned nucleus is considered. We have found that the percentage error decreases when the value of the surface diffuseness parameter increases at all values of radial distance r in the surface region, for all orientation angles. Results of four tenns are better than the three tenns expansion for th.e three cases of positive 82 inside the internal region and the surface region but in case of negative 82 , the error in multipole expansion is reasonable in the surface region and reaches large values outside this region (in the extreme tail region) and the addition of •fourth tenn does not improve it. The existence of hexadecapole defonnation increases . the value of error. When octupole defonnation besides quadrupole and hexadecapole defonnations are present in the defonned nucleus we found that more tenns should be ' <:.. ia:ad'.eBjn the multipole series to get reasonable accuracy of density in the physically important surface region of the nucleus. In the second chapter, the interaction potential for a defonned-spherical pair of nuclei is calculated using the folding model derived from zero-range nucleon-nucleon (NN) interaction. We considered two spherical projectiles Ca 40 and Pb 208 scattered on