Examples of the failure of proximity approach when the nuclear surface is irregular or has concave regions

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.…”

“…where C0 = − 0.1886, C1 = − 0.2628, C2 = − 0.15216, C3 = − 0.04562, C4 = 0.069136 & C5 = − 0.011454 [6,11,15,21,25,27]. The geometrical factor is given by the following relation,…”

“…where R11, R12, R21 & R22 are the principal radii of curvature of the gap between the two interacting nuclei [6,11,15,21,25,27] and are calculated using the relations below [4,7,11,15,21,22,25,27], …”

“…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].…”