Density and temperature dependence of nucleon-nucleon elastic cross section

Abstract

The in-medium neutron-proton, proton-proton (neutron-neutron) elastic scattering cross sections (σ * np , σ * pp(nn) ) are studied based on the effective Lagrangian of density dependent relativistic hadron theory in which the δ[a 0 (980)] meson is included. Our study shows that at low densities the σ * np is about 3 − 4 times larger than σ * pp(nn) and at densities higher than the normal density the isospin effect is almost washed out. Because of coupling to δ meson the σ * nn and σ * pp are different in isospin asymmetric medium following the splitting of the proton and neutron mass. The isospin effect on the density dependence of the in-medium nucleon elastic cross section is dominantly contributed by the isovector δ and ρ mesons. The temperature effect on the σ * np and σ * pp(nn) is studied. It is shown that the temperature effect is weaker compared with the density effect but it becomes obvious as density increases.

Medium modifications of the nucleon–nucleon elastic cross section in neutron-rich intermediate energy HICs

“…It was also seen from our previous work [7] that the density dependence of neutron-neutron (or proton-proton) and neutron-proton elastic cross sections is also different when we consider the isospin vector ρ-meson contribution. This effect is not considered here in order to observe more clearly the probable splitting effect which is originally from the isospin vector δ-meson contribution from the point of view of the extended QHD theory.…”

“…Li et al [15,16], in which the NR mass splitting was used. Again, it is seen that the effective cross sections are influenced contrarily by the different definitions of effective nuclear mass: based on the effective Lagrangian of density dependent relativistic hadron theory, our calculations [7] give the trend (in neutron-rich nuclear medium): σ * nn < σ * pp ; while, based on the DBHF model [11,12], the trend is on the contrary: σ * nn > σ * pp . For the effective np elastic cross section σ * np , two approaches give the similar result.…”

“…In [7] it was found that σ * nn is smaller than that of σ * pp since the effective neutron mass in neutronrich matter is smaller than that of proton after considering the contribution of δ meson [8].…”

“…The neutron-rich reactions 96 Zr + 96 Zr and 78 Ni + 96 Zr at a beam energy In this work, we suppose that the in-medium cross sections can be factorized as the product of a medium correction factor (F (u, α, p)) and the free NN elastic scattering cross sections (σ f ree ) based on present results of theoretical calculations in Refs. [7,11,12,16], which reads…”

“…The isospin dependence of the in-medium NN elastic cross sections was studied based on the extended QHD model in which ρ [6] as well as δ [7] mesons are included. In [7] it was found that σ * nn is smaller than that of σ * pp since the effective neutron mass in neutronrich matter is smaller than that of proton after considering the contribution of δ meson [8].…”