Effect of energy conservation on in-medium $\mbox{NN}\to \mbox{N}Δ$ cross section in isospin-asymmetric nuclear matter

Abstract

In this paper, the in-medium $NN\rightarrow NΔ$ cross section is calculated in the framework of the one-boson exchange model by including the isovector mesons, i.e. $δ$ and $ρ$ mesons. Due to the isospin exchange in the $NN\rightarrow NΔ$ process, the vector self-energies of the outgoing particles are modified relative to the incoming particles in isospin asymmetric nuclear matter, and it leads to the effective energies of the incoming $NN$ pair being different from the outgoing $NΔ$ pair. This effect is investigated in the calculation of the in-medium $NN\rightarrow NΔ$ cross section. With the corrected energy conservation, the cross sections of the $Δ^{++}$ and $Δ^+$ channels are suppressed, and the cross sections of the $Δ^0$ and $Δ^-$ channels are enhanced relative to the results obtained without properly considering the potential energy changes. Our results further confirm the dependence of medium correction factor, $R=σ_{ NN\rightarrow NΔ}^*/σ_{NN\rightarrow NΔ}^{\text{free}}$, on the charge state of $NN\rightarrow NΔ$ especially around the threshold energy, but the isospin splitting of medium correction factor $R$ becomes weak at high beam energies.