Temperature dependence of the nucleon–nucleon inelastic cross section in an isospin-asymmetric nuclear medium

Abstract The nucleon-nucleon ($NN$) inelastic cross section plays an important role in constraining the nuclear equation of state at high baryon densities and in transport descriptions of heavy-ion collisions. In this work, the temperature dependence of $\Delta^{++}$ and $\Delta^{-}$ production cross sections in isospin-symmetric and asymmetric nuclear matter is investigated within the relativistic Boltzmann-Uehling-Uhlenbeck (RBUU) framework. Two relativistic mean-field parameterizations are employed: the density-dependent parameterization (called DD-ME$\delta$) and the nonlinear-dependent parameterization (called OMEG). The cross sections generally decrease with increasing density, whereas their thermal enhancement becomes more pronounced. The two parameterizations predict comparable temperature effects at densities up to approximately $1.5\rho_0$, while OMEG exhibits a stronger temperature dependence at higher densities. In isospin-asymmetric nuclear matter, the cross section splitting results from the interplay between the effective mass splitting and vector self-energies and therefore depends on the mean-field parameterization. The temperature dependence of the splitting is relatively weak for $nn\rightarrow p\Delta^{-}$ but more pronounced for $pp\rightarrow n\Delta^{++}$. These findings provide quantitative information on the temperature dependence of the in-medium $NN\rightarrow N\Delta$ process and may be useful for future transport-model implementations.