The in-medium $NNrightarrow NDelta$ cross section and its differential cross section in isospin asymmetric nuclear medium are investigated in the framework of the one-boson exchange model by including the isovector mesons, i.e., $delta$ and $rho$ mesons. Our results show that the in-medium $NNrightarrow NDelta$ cross sections are suppressed with density increasing, and the differential cross sections become isotropic with the density increasing at the beam energy around the $Delta$ threshold energy. The isospin splitting on the medium correction factor, $R=sigma_{ NNrightarrow NDelta}^*/sigma_{NNrightarrow NDelta}^{text{free}}$ is observed for different channels of $NNto NDelta$, especially around the threshold energy for all the effective Lagrangian parameters. By analyzing the selected effective Lagrangian parameters, our results show that the larger effective mass is, the weaker medium correction $R$ is.
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