Experimental nuclear charge density and theoretical description of the above-barrier light heavy-ion fusion process*

Abstract

Theoretical modeling of nucleus-nucleus collision often is based on the nucleus-nucleus potential. One of the advanced methods for constructing this potential is the semi-microscopical double-folding model with the M3Y-Paris NN-forces. Proton and neutron densities are significant ingredient of this model. Correct nucleon density (ND) must reproduce experimental nuclear charge density (NCD). However, those who deal with modeling the fusion process, typically, disregard this circumstance. We aim to achieve good description of both the charge nucleon density and the above-barrier fusion cross sections of even-even light nuclei with Z=N. We consider several versions of NDs available in the literature and construct our own approximation for the ND of even-even spherical nuclei 12C, 16O, 40Ca which is abbreviated as FE-density (Fermi+exponential). We carefully compare the NCDs resulting from different versions of NDs with the experimental NCSs. After finding the nucleus-nucleus potential using the double-folding model with the density dependent M3Y-Paris NN-forces and FE densities we evaluate the above-barrier fusion cross sections for five reactions, 12C+12C, 12C+16O, 16O+16O, 16O+40Ca, and 40Ca+40Ca, where the experimental data are available. The cross sections are calculated using two approaches: a) the barrier penetration model and b) the Trajectory Model with surface friction (TM). To find the transmission coefficients for TM, the Langevin equations are employed. For all considered reactions, our TM typically reproduces the above-barrier experimental cross sections within 10-15%. The only adjustable parameter of the model, the optimal friction strength K_Rm, was found to be about 90 zs∙GeV^(-1) for light reactions 12C+12C, 12C+16O, 16O+16O and about 15 zs∙GeV^(-1) for heavier reactions 16O+40Ca and 40Ca+40Ca. The latter findings are in reasonable agreement with the systematics found earlier. Thus, the FE-recipe allows reproducing simultaneously with good accuracy both the charge nucleon density and the above-barrier fusion cross sections for five reactions involving 12C, 16O, 40Ca nuclei.