Medium effects on the double-Δproduction and absorption cross section

Abstract

The explicit expressions for calculating the in-medium $N+N\ensuremath{\rightarrow}\ensuremath{\Delta}+\ensuremath{\Delta}$ and $\ensuremath{\Delta}+\ensuremath{\Delta}\ensuremath{\rightarrow}N+N$ cross section have been derived within the framework of the self-consistent relativistic Boltzmann-Uehling-Uhlenbeck approach in which the deltas and nucleons are treated on an equal footing. The obtained cross sections are consistent with the other integrands of the transport model. The theoretical prediction of the free double-$\ensuremath{\Delta}$ production cross section is in good agreement with the experimental data. All the medium effects on the double-$\ensuremath{\Delta}$ production and absorption cross section are studied systematically, and strong medium corrections are found. Our numerical results show that it would be important to take the $N+N\ensuremath{\rightarrow}\ensuremath{\Delta}+\ensuremath{\Delta}$ and $\ensuremath{\Delta}+\ensuremath{\Delta}\ensuremath{\rightarrow}N+N$ channel into account in the study of relativistic heavy-ion collisions at intermediate and high energies.