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 $NN\to N\hat{I}”$ cross section is calculated in the framework of the one-boson exchange model by including the isovector mesons, i.e. $\hat{I}´$ and $\ddot{I}$ mesons. Due to the isospin exchange in the $NN\to N\hat{I}”$ 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 $N\hat{I}”$ pair. This effect is investigated in the calculation of the in-medium $NN\to N\hat{I}”$ cross section. With the corrected energy conservation, the cross sections of the $\hat{I}{”}^{++}$ and $\hat{I}{”}^{+}$ channels are suppressed, and the cross sections of the $\hat{I}{”}^0$ and $\hat{I}{”}^{-}$ 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, $R=\ddot{I}{ƒ}_{NN\to N\hat{I}”}^{\ast }/\ddot{I}{ƒ}_{NN\to N\hat{I}”}^{\text{free}}$, on the charge state of $NN\to N\hat{I}”$ especially around the threshold energy, but the isospin splitting of medium correction factor $R$ becomes weak at high beam energies.

8 pages, 5 figures, accepted by Phys.Rev.c