Experimental nuclear charge density and theoretical description of the above-barrier light heavy-ion fusion process* *Supported by the Foundation for the Advancement of Theoretical Physics and Mathematics “BASIS.”

Abstract

Theoretical modeling of nucleus-nucleus collisions is often based on the nucleus-nucleus potential. One of the advanced methods for constructing this potential is the semi-microscopical double-folding model with M3Y-Paris NN-forces. Proton and neutron densities are significant components of this model. The correct nucleon density (ND) must reproduce the experimental nuclear charge density (NCD). However, those who deal with modeling the fusion process typically disregard this circumstance. We aim to achieve a good description of both the nuclear charge density and above-barrier fusion cross sections of even-even light nuclei with . We consider several versions of NDs available in literature and construct our own approximation for the ND of the even-even spherical nuclei 12C, 16O, and 40Ca, abbreviated as FE-density (Fermi+exponential). We carefully compare the NCDs resulting from different versions of NDs with the experimental NCDs. 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, for which 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 the 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 , is found to be approximately 90 for the light reactions 12C+12C, 12C+16O, and 16O+16O and approximately 15 for the heavy reactions 16O+40Ca and 40Ca+40Ca. The latter findings are in reasonable agreement with the systematics found previously. Thus, the FE-recipe allows highly accurate and simultaneous reproduction of both the nuclear charge density and above-barrier fusion cross sections of five reactions involving 12C, 16O, and 40Ca nuclei.