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