Medium effects on binary collisions with the Delta resonance.

Abstract

To facilitate the relativistic heavy-ion calculations based on transport equations, the binary collisions involving a \ensuremath{\Delta} resonance in either the entrance channel or the exit channel are investigated within a Hamiltonian formulation of \ensuremath{\pi}NN interactions. An averaging procedure is developed to define a quasiparticle \ensuremath{\Delta}* and to express the experimentally measured NN\ensuremath{\rightarrow}\ensuremath{\pi}NN cross section in terms of an effective NN\ensuremath{\rightarrow}N\ensuremath{\Delta}* cross section. In contrast to previous works, the main feature of the present approach is that the mass and the momentum of the produced \ensuremath{\Delta}*'s are calculated dynamically from the bare \ensuremath{\Delta}\ensuremath{\leftrightarrows}\ensuremath{\pi}N vertex interaction of the model Hamiltonian and are constrained by the unitarity condition. The procedure is then extended to define the effective cross sections for the experimentally inaccessible N\ensuremath{\Delta}*\ensuremath{\rightarrow}NN and N\ensuremath{\Delta}*\ensuremath{\rightarrow}N\ensuremath{\Delta}* reactions. The predicted cross sections are significantly different from what are commonly assumed in relativistic heavy-ion calculations. The \ensuremath{\Delta} potential in nuclear matter has been calculated by using a Bruckner-Hartree-Fock approximation. By including the mean-field effects on the \ensuremath{\Delta} propagation, the effective cross sections of the NN\ensuremath{\rightarrow}N\ensuremath{\Delta}*, N\ensuremath{\Delta}*\ensuremath{\rightarrow}NN and N\ensuremath{\Delta}*\ensuremath{\rightarrow}N\ensuremath{\Delta}* reactions in nuclear matter are predicted. It is demonstrated that the density dependence is most dramatic in the energy region close to the pion production threshold. \textcopyright{} 1996 The American Physical Society.