Medium Effects on Binary Collisions with the Delta Resonance
Abstract
Description
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.
20 pages, RevTex
20 pages, RevTex