Aspects of the momentum dependence of the equation of state and of the residual $NN$ cross section, and their effects on nuclear stopping

Abstract

With the semiclassical Landau-Vlasov transport model we studied the stopping observable $R_E$, the energy-based isotropy ratio, for the $^{129}$Xe\,+\,$^{120}$Sn reaction at beam energies spanning 12$A$ to 100$A$ MeV. We investigated the impacts of the nonlocality of the nuclear mean field, of the in-medium modified nucleon-nucleon ($NN$) cross section and of the reaction centrality. A fixed set of model parameters yields $R_E$ values that favorably compare with the experimental ones, but only for energies below the Fermi energy $E_F$. Above $E_F$ agreement is readily possible, but by a smooth evolution with energy of the parameter that controls the in-medium modification of $NN$ cross section. By comparing the simulation correction factor ${\cal F}$ applied to the free $NN$ cross section with the one deduced from experimental data [Phys.\ Rev.\ C\,{\bf 90}, 064602 (2014)], we infer that the zero-range mean field almost entirely reproduces it. Also, in accordance with what has been deduced from experimental data, around $E_F$ a strong reduction of the free $NN$ cross section is found. In order to test the impact of sampling central collisions by multiplicity an event generator (HIPSE) was used. We obtain that high multiplicity events are spread over a broad impact parameter range, but it turns out that this has a small effect on the observable $R_E$ and, thus, on ${\cal F}$ as well.