Spin-Isospin Modes in Heavy-Ion Collisions

Abstract

Abstract:With a view towards implementation in microscopic transport simulations of heavyion collisions, the properties of spin-isospin modes are studied in nuclear matter consisting of nucleons and ∆ isobars that interact by the exchange of π and ρ mesons. For a standard p-wave interaction and an effective g ′ short-range interaction, the dispersion relations for the spin-isospin modes, and the associated amplitudes, are calculated at various nuclear densities and temperatures, within the random-phase approximation. Quantities of physical interest are then extracted, including the total and partial ∆ decay widths and the ∆ cross sections in the nuclear medium. The self-consistent inclusion of the ∆ width has a strong effect on the ∆ cross sections at twice normal nuclear density, as compared with the result of ignoring the width. Generally, the obtained quantities exhibit a strong density dependence, but are fairly insensitive to the temperature, at least up to T = 25 MeV. Finally, it is described how these in-medium effects may be consistently included into microscopic transport simulations of nuclear collisions, and the improvements over previous approaches are discussed.

Transport simulations with π and Δ in-medium properties

“…A set of RPA equations for spin-isospin modes, corresponding to an infinite iteration of non-interacting pion (ρ-meson), nucleon-hole, and ∆-hole states, were derived in Ref. [12]. From these equations eigenvectors and eigenenergies are obtained for the different spin-isospin modes.…”

“…We also calculate total and partial ∆ widths, Nπ → ∆ cross sections, NN ↔ ∆N cross sections and ∆ spectral functions within the RPA approximation (explicit expressions are given in Ref. [12]).…”

“…In Ref. [12] was chosen a particular set that could reproduce vacuum pp → ∆ ++ n cross sections and the imaginary part of the empirical ∆-nucleus spreading potential of Ref. [22].…”

“…Unfortunately, the established transport treatment that we have chosen to compare our medium-modified simulations to [17] does not contain any effective nucleon mass, as was utilized in the microscopic treatment of Ref. [12]. For this reason we have here ignored the effective mass in the microscopic calculations (i.e.…”

“…In this letter we present selected results from transport simulations that include in-medium quantities obtained from the π + NN −1 + ∆N −1 model of Ref. [12]. The present work constitutes an extension of Ref.…”