Effect of energy conservation on the in-medium NN→NΔ cross section in isospin-asymmetric nuclear matter

Abstract

In this paper, the in-medium $NN\ensuremath{\rightarrow}N\mathrm{\ensuremath{\Delta}}$ cross section is calculated in the framework of the one-boson exchange model by including the isovector mesons, i.e., $\ensuremath{\delta}$ and $\ensuremath{\rho}$ mesons. Due to the isospin exchange in the $NN\ensuremath{\rightarrow}N\mathrm{\ensuremath{\Delta}}$ 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 ingoing $NN$ pair being different from the outgoing $N\mathrm{\ensuremath{\Delta}}$ pair. This effect is investigated in the calculation of the in-medium $NN\ensuremath{\rightarrow}N\mathrm{\ensuremath{\Delta}}$ cross section. With the corrected energy conservation, the cross sections of the ${\mathrm{\ensuremath{\Delta}}}^{++}$ and ${\mathrm{\ensuremath{\Delta}}}^{+}$ channels are suppressed, and the cross sections of the ${\mathrm{\ensuremath{\Delta}}}^{0}$ and ${\mathrm{\ensuremath{\Delta}}}^{\ensuremath{-}}$ 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 $R={\ensuremath{\sigma}}_{NN\ensuremath{\rightarrow}N\mathrm{\ensuremath{\Delta}}}^{*}/{\ensuremath{\sigma}}_{NN\ensuremath{\rightarrow}N\mathrm{\ensuremath{\Delta}}}^{\mathrm{free}}$ on the charge state of $NN\ensuremath{\rightarrow}N\mathrm{\ensuremath{\Delta}}$ especially around the threshold energy, but the isospin splitting of medium correction factor $R$ becomes weak at high beam energies.