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 δ3 besides quadrupole δ2. We are interested in the value of error for R ≥ RT (touching distance). We found that for values of |δ3|≤0.1 the error at R = RT reaches reasonable values when six terms expansion is used. For |δ3| = 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 δ3 = -0.1 produce error at orientation angle θ equal in value to that produced at angle (180°-θ) for the positive values δ3 = 0.1. We also found that the error decreases as the mass number of the projectile nucleus increases.
Possible octupole deformation of
Pb208
and the ultracentral
v2
to
v3
puzzle
