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 $Δ$ resonance in either the entrance channel or the exit channel are investigated within a Hamiltonian formulation of $πNN$ interactions. An averaging procedure is developed to define a quasi-particle $Δ^*$ and to express the experimentally measured $NN\rightarrow πNN$ cross section in terms of an effective $NN\rightarrow NΔ^\ast$ cross section. In contrast to previous works, the main feature of the present approach is that the mass and the momentum of the produced $Δ^*$'s are calculated dynamically from the bare $Δ\leftrightarrow πN$ 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 $NΔ^\ast \rightarrow NN$ and $NΔ^\ast \rightarrow NΔ^\ast$ reactions. The predicted cross sections are significantly different from what are commonly assumed in relativistic heavy-ion calculations. The $Δ$ potential in nuclear matter has been calculated by using a Bruckner-Hartree-Fock approximation. By including the mean-field effects on the $Δ$ propagation, the effective cross sections of the $NN\rightarrow NΔ^\ast$, $NΔ^\ast \rightarrow NN$ and $NΔ^\ast \rightarrow NΔ^\ast$ 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.