The isospin dependent nucleon-nucleon inelastic cross section in the nuclear medium

The calculation of the energy-, density-, and isospin-dependent Δ production cross sections in nucleon-nucleon (NN) scattering σ_NN^→ NΔ * has been performed within the framework of the relativistic BUU approach. The NΔ cross sections are calculated in Born approximation taking into account the effective mass splitting of the nucleons and Δs in asymmetric matter. Due to the different mass splitting for neutron, proton and differently charged Δs, it is shown that, similar to the NN elastic ones, the reductions of NΔ inelastic cross sections in isospin-asymmetric nuclear medium are different from each other for all the individual channels and the effect is largest and of opposite sign for the Δ⁺⁺ and Δ^- states. This approach is also compared to calculations without effective mass splitting and with splitting derived from Dirac-Brueckerner (DB) calculations. The isospin dependence of the NΔ cross sections is expected to influence the production of π⁺ and π^- mesons as well as their yield ratio, and thus affect the use of the latter quantity as a probe of the stiffness of the symmetry energy at supranormal densities.