Comparison between different proximity potentials and the double-folding model for spherical–deformed interacting nuclei

Abstract

The Coulomb barrier parameters have been calculated for a spherical-deformed interacting pair of nuclei using fourteen different versions of the proximity approaches and a simple analytical formula for the Coulomb part of the heavy ion potential. The results of these proximity versions have been compared with more accurate results obtained from the double folding model (DFM). We have considered the interacting pair 48 Ca + 238 Pu as an example and assumed the presence of the quadrupole, octupole and hexadecapole deformation parameters for 238 Pu. The orientation angle dependence of the Coulomb barrier parameters has been computed for different sets of the deformation parameters. We found that the proximity types named; Prox77, BW Prox91, AW Prox95, Bass Prox77 and Bass Prox80 are the best ones of the available fourteen versions of the proximity approaches for calculating the nuclear part of the interaction potential for a spherical-deformed pair of nuclei.

Effects of the deformation orders β6 & β8 on the fusion parameters for spherical-deformed interacting pair

“…We use its definition as following, [3,8,7,20,23,24,25,28] , (1) where R is the distance between the centers of mass of the interacting nuclei, γ is the surface energy coefficient, b the nuclear surface thickness, R is the geometrical factor, ξ is the universal function and Smin is the minimum distance between the surfaces of the interacting pair of nuclei. The surface energy coefficient [14,15] can be calculated by, , (2) where Q is the neutron skin stiffness coefficient and ti is the neutron skin of the nucleus, [ 14,15] , (3) where J is the nuclear symmetry energy coefficient, , b1 = 0.757895 MeV and r0 = 1.14 fm [14,15]. To calculating the minimum distance, Smin, we need to minimize the surfaces separation distance, S, by making use of Fig.…”

“…To calculating the minimum distance, Smin, we need to minimize the surfaces separation distance, S, by making use of Fig. (1) where, we will find that [14].…”

“…As known that the radius of a deformed nucleus of an axially symmetric deformation can be written as [4,7,11,15,21,22,25,27], (10) R0i is the matter radius, βi, l is the deformation parameter of order l, Yl0(θ, φ) is the spherical harmonic of order l. In PROX the matter radius [14,15] is calculated as,…”

“…The Coulomb part of the interaction between spherical-deformed pair of nuclei using the relation deduced by Denisov [14,15,27].…”

“…where We will then go on to present the nuclear potential in DFM, which is given by [4,5,11,14,15,17,19,21,29]; (15) where ρ1(⟶r1) & ρ2(⟶r2) are the density functions of the projectile and the target nuclei respectively, VNN(S) is the NN interaction potential, and ⟶R is the relative position vector of the centers of mass of the interacting pair of nuclei. To simplify calculation of the six dimensional integral (eq.…”