Theoretical modeling of the above-barrier fusion process for nuclei with Z = N based on the experimental nuclear charge densities

Most of theoretical models of nucleus-nucleus collision are based on the nucleus-nucleus potential. Semi-microscopical double-folding model with the M3Y-Paris NN-forces represents one of the advanced methods for evaluating this potential. Nucleon densities (NDs), being crucial ingredient of this model, must reproduce the experimental nuclear charge densities (NCDs). In theoretical approaches for modeling the fusion process, it is not always so. In the present work, we aim to reach satisfactory description of both the charge nucleon density and the above-barrier fusion cross sections of even-even nuclei with Z = N. We construct an approximation for the ND which is abbreviated as FEV-density (Fermi + Exponential tail with Variable diffuseness). The proton and neutron densities are considered to be identical and having a coordinate-dependent diffuseness. Parameters of the nucleon density are varied to obtain the best fit of the experimental NCD. Then the resulting FEV nucleon densities are used to calculate the nucleus-nucleus potential applying the double-folding model with the density-dependent M3Y-Paris NN-forces. This potential is employed for evaluating the above-barrier fusion cross sections for ten reactions: S-32+C-12, Mg-24, Ca-40; Si-28+C-12, O-16, Mg-24, Si-28; and Mg-24+C-12, O-16, Mg-24 where the experimental data are available. The cross sections are calculated using either the barrier penetration model or the trajectory model with surface friction. To find the transmission coefficients for the trajectory model, the Langevin-type equations are solved numerically. For all considered reactions, our trajectory model typically reproduces the above-barrier experimental cross sections within 10-15 % with typical chi(2) < 2. The adjustable parameter of the model, the optimal friction strength KRm, was found to be between 20 and 40 zs & sdot; GeV-1 which is in reasonable agreement with two systematics found earlier. We also make predictions for the fusion excitation functions for reactions S-32+O-16, S-32+Si-28, Si-24+Ca-40 where we did not manage finding experimental data.