Simple interpretation of nuclear orientation for Coulomb barrier distributions derived from a realistic effective interaction

Abstract

A simple straightforward method has been presented to predict the dependence of barrier distributions at arbitrary orientations on different deformations. The proposed interpretation is developed independently of the complicated numerical calculations. It is related to the change of half-density radius of the deformed nucleus, in the direction of the separation vector. The microscopic calculations of Coulomb barrier are carried out by using a realistic density dependent nucleon-nucleon ($\mathit{NN}$) interaction, BDM3Y, for the interaction between spherical, $^{48}\mathrm{Ca}$, and deformed, $^{244}\mathrm{Pu}$, nuclei, as an example. To do so, the double-folding model for the interaction of spherical-deformed nuclei is put in a suitable computational form for the calculation of the potential at several separation distances and orientation angles using the density dependent $\mathit{NN}$ force without consuming computational time. We found that the orientation distributions of the Coulomb barrier parameters show similar patterns to those of the interacting deformed nucleus radius. It is found that the orientation distribution of the Coulomb barrier radius follows the same variation of the deformed nucleus radius while the barrier height distribution follows it inversely. This correlation (anticorrelation) allows a simple evaluation of the orientation barrier distribution which would be very helpful to estimate when the barrier parameters will increase or decrease and at which orientations they will be independent of the deformation. This also allows us to estimate the compact and elongated configurations of the interacting nuclei which lead to hot and cold fusion, respectively.