Accuracy of the Multipole Expansion of Density Distribution in the Presence of Octupole Deformation

Abstract

The accuracy of multipole expansion of density distribution for deformed nuclei is tested. The interaction potential for a deformed-spherical pair of nuclei was 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 U 238 deformed target nucleus. The error in the heavy ion (HI) potential resulting from using a truncated multipole density expansion is evaluated for each case in the presence of octupole deformation δ 3 besides quadrupole δ 2 . We are interested in the value of error for R ≥ R T (touching distance). We found that for values of |δ 3 | ≤ 0.1 the error at R = R T reaches reasonable values when six terms expansion is used. For |δ 3 | = 0.2, we calculated the Coulomb barrier parameters using realistic NN force and found that the large error present in six terms for zero range force decreases strongly to less than 1% when the zero range is added to finite range forces and Coulomb interaction to form the Coulomb barrier. It is noted that the negative value of octupole deformation parameters δ 3 = −0.1 produce error at orientation angle θ equal in value to that produced at angle (180 • − θ) for the positive values δ 3 = 0.1. We also found that the error decreases as the mass number of the projectile nucleus increases.