On the accuracy of multipole expansion of deformed density distribution

Abstract

The interaction potential for a deformed-spherical pair of nuclei is calculated using the folding model derived from different range nucleon–nucleon (NN) interactions. Five spherical projectiles of different mass numbers scattered on the 238U deformed target are considered. The error in the heavy ion (HI) potential by using the truncated multipole density expansion is evaluated for each case. We find systematic trends of the percentage error in the HI potential depending on the number of multipoles considered; this percentage decreases if the mass number of the projectile or the range of the NN force increases, and it becomes smaller for small values of the separation distance between two nuclei or when higher deformation parameters vanish. The maximum error in using the truncated density expansion is estimated in the case of two deformed interacting nuclei.