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

TL;DR

This paper calculates isospin-dependent nucleon-nucleon inelastic cross sections in nuclear matter, revealing how effective mass splitting affects pion production and the interpretation of symmetry energy in nuclear physics.

Contribution

It introduces a relativistic BUU approach to compute energy-, density-, and isospin-dependent NΔ cross sections considering effective mass splitting in asymmetric matter, highlighting differences among channels.

Findings

Different reductions of NΔ inelastic cross sections for various isospin channels.

Largest and opposite effects on Δ++ and Δ− states.

Comparison with other models shows the significance of effective mass splitting.

Abstract

The calculation of the energy-, density-, and isospin-dependent $\Delta$ production cross sections in nucleon-nucleon (NN) scattering $\sigma^*_{NN\rightarrow N\Delta}$ has been performed within the framework of the relativistic BUU approach. The N$\Delta$ cross sections are calculated in Born approximation taking into account the effective mass splitting of the nucleons and $\Delta$s in asymmetric matter. Due to the different mass splitting for neutron, proton and differently charged $\Delta$s, it is shown that, similar to the NN elastic ones, the reductions of N$\Delta$ 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 $\Delta^{++}$ and $\Delta^{-}$ 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 N$\Delta$ cross sections is expected to influence the production of $\pi^+$ and $\pi^-$ 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.