Isospin-dependent in-medium nucleon-Delta elastic cross section

In heavy-ion collisions at intermediate energies, the production and propagation of $\Delta$ particles are crucial to understanding the nuclear equation of state and inferring the properties of nuclear matter at high densities. Based on the self-consistent relativistic Boltzmann-Uehling-Uhlenbeck (RBUU) transport theory, by introducing the isovector $\rho$ meson exchange into the effective Lagrangian and adopting the density-dependent coupling constants, the detailed expressions for isospin-dependent in-medium $N\Delta\rightarrow N\Delta$ elastic cross sections $\sigma_{N\Delta}^{*}$ have been calculated. The energy and density dependence of the isospin-related $\sigma_{N\Delta}^{*}$ as well as the total contributions of $\sigma$, $\omega$ and $\rho$ meson fields are analyzed. It is found that the total $\sigma_{N\Delta}^{*}$ has a sensitive center-of-mass energy dependence at lower energies while exhibiting a slight increase as the center-of-mass energy increases. The isospin effect between different isospin-separated channels weakens as the energy and/or density increases. The isospin effect on the density- and energy-dependent in-medium $N\Delta$ elastic cross sections is dominantly caused by the delicate balance of the isovector $\rho$ meson exchange.