In-medium effects of nucleon-nucleon cross sections in heavy-ion collisions

TL;DR

The paper addresses how in-medium nucleon-nucleon cross sections influence heavy-ion collision observables and the high-density equation of state. It integrates microscopic Brueckner–Hartree–Fock cross sections into an isospin-dependent BUU transport framework, explicitly incorporating medium effects on the scattering amplitude via the $G$-matrix, density of states via the effective mass, and the total pair momentum $K$, and compares several cross-section variants. The results show that density-of-states corrections and $K$-dependence substantially affect stopping and pion production, while the $n/p$ ratio and neutron–proton transverse-flow difference are largely robust; the neutron–proton differential flow is notably sensitive to in-medium modifications. The findings underscore the necessity of including full microscopic in-medium cross sections in transport simulations to reliably extract symmetry-energy information and other high-density nuclear-matter properties from HIC data.

Abstract

Based on the isospin-dependent Boltzmann-Uehling-Uhlenbeck transport model, we systematically investigate the in-medium effects of nucleon-nucleon ($NN$) cross sections on nucleonic and pionic observables in heavy-ion collisions, employing microscopic cross sections derived from the Brueckner-Hartree-Fock approach. Key observables include nuclear stopping, the neutron-to-proton ($n/p$) ratio, neutron-proton transverse flow differences, differential collective flow, pion multiplicities, and the resulting $(π^-/π^+)_{\text{like}}$ ratio. The analysis disentangles the respective contributions from the scattering amplitude, the density of states, and the total momentum ($K$) of the colliding pairs. We find that larger in-medium $NN$ cross sections generally enhance free nucleon emission and nuclear stopping, with the nucleon effective mass playing a dominant suppressive role. However, it is insufficient to account only for the medium corrections from effective mass: both the medium effect from the scattering amplitude and the $K$-dependence exert noticeable influences on the observables. In particular, nuclear stopping is found to be highly sensitive to these in-medium modifications of cross sections. While the $n/p$ ratio and transverse flow difference remain largely insensitive, the differential collective flow and pion yields are strongly affected. These results indicate that the interplay between scattering amplitude, density-of-states and $K$-dependence is essential to accurately describe medium effects in heavy-ion collisions.

Figures (7)

• Figure 1: The calculated in-medium $NN$ cross section within BHF approach as a function of the incident laboratory energy $E_{\rm Lab}$. The left, middle and right panels correspond to the in-medium $pp$, $np$ and $nn$ cross sections, respectively. While the upper and lower panels show the results with the microscopic effective $NN$ cross section $\sigma_{\rm BHF}^*$ and microscopic $NN$ cross section $\sigma_{\rm BHF}$, respectively. The black, red, blue and orange lines correspond to the total momenta 0.9, 2.25, 3.6 and 4.95 $\text{fm}^{-1}$, respectively. The green dashed line denotes the free-space $NN$ cross section.
• Figure 2: Rapidity distributions of neutrons (a) and protons (b) in $^{132}\text{Sn}+^{124}\text{Sn}$ reaction at 270 MeV/nucleon, which are simulated with the free-space cross section $\sigma_{\text{free}}$, effective cross section $\sigma_{\text{eff}}$, microscopic cross section $\sigma_{\text{BHF}}$ and microscopically effective cross section $\sigma^*_{\text{BHF}}$ and $\sigma^K_{\text{BHF}}$.
• Figure 3: The proton $vartl$ for central $^{132}\text{Sn}+^{124}\text{Sn}$ at 270 MeV/nucleon for the impact parameter $b=0.0\ \text{fm}$ as a function of the cross section.
• Figure 4: The $n/p$ ratio (left panel) and the difference of the neutron-proton transverse flow (right panel) in semi-central reaction of $^{132}$Sn+$^{124}$Sn at 270 MeV/nucleon. Left panel: The $n/p$ ratio as a function of the transverse momentum. Right panel: The difference of the neutron-proton transverse flow as a function of rapidity.
• Figure 5: Same reaction as Fig. \ref{['np-px']}, but for the results of the neutron-proton differential transverse (left panel) and elliptic (right panel) flow.