Fusion reaction cross-sections using the Wong model within Skyrme energy density based semiclassical extended Thomas Fermi approach

First, the nuclear proximity potential, obtained by using the semiclassical extended Thomas Fermi (ETF) approach in Skyrme energy density formalism (SEDF), is shown to give more realistic barriers in frozen density approximation, as compared to the sudden approximation. Then, taking advantage of the fact that, in ETF method, different Skyrme forces give different barriers (height, position and curvature), we use the l-summed extended-Wong model of Gupta and collaborators (2009) [1] under frozen densities approximation for calculating the cross-sections, where the Skyrme force is chosen with proper barrier characteristics, not requiring additional barrier modification effects (lowering or narrowing, etc.), for a best fit to data at sub-barrier energies. The method is applied to capture cross-section data from Ca-48 + U-238, Pu-244, and Cm-248 reactions and to fusion evaporation cross-sections from Ni-58 + Ni-58, Ni-64 + Ni-64, and Ni-64 + Mo-100 reactions, with effects of deformations and orientations of nuclei included, wherever required. Interestingly, whereas the capture cross-sections in Ca-induced reactions could be fitted to any force, such as SIII, SV and GSkI, by allowing a small change of couple of units in deduced l(max)-values at below-barrier energies, the near-barrier data point of Ca-48 + Cm-248 reaction could not be fitted to l(max)-values deduced for below-barrier energies, calling for a check of data. On the other hand, the fusion-evaporation cross-sections in Ni-induced reactions at sub-barrier energies required different Skyrme forces, representing modifications of the barrier, for the best fit to data at all incident center-of-mass energies E-c.m.'s, displaying a kind of fusion hindrance at sub-barrier energies. This barrier modification effect is taken into care here by using different Skyrme forces for reactions belonging to different regions of the periodic table. Note that more than one Skyrme force (with identical barrier characteristics) could equally well fit the same data. (C) 2011 Elsevier B.V. All rights reserved.