The influence of $delta$ meson on the isospin splitting of in-medium $NNto NDelta$ cross sections

The isospin splitting of the in-medium $NNrightarrow NDelta$ cross sections in asymmetric nuclear medium are investigated in the framework of the one-boson exchange model by including $delta$ and $rho$ mesons. Our results show that the that the correction factors $R=sigma_{ NNrightarrow NDelta}^*/sigma_{NNrightarrow NDelta}^{text{free}}$ have $R_{pp to nDelta ^{++}} < R_{nn to pDelta ^{-}}$ and $R_{NN to NDelta ^{+}} <R_{NN to NDelta ^{0}}$ by using the without-$delta$ sets. By including the $delta$ meson, it appears the totally opposite results in the $R$ for different channels, i.e., $R_{pp to nDelta ^{++}} > R_{nn to pDelta ^{-}}$ and $R_{NN to NDelta ^{+}} >R_{NN to NDelta ^{0}}$.