The isospin dependent nucleon–nucleon inelastic cross section in the nuclear medium

Qingfeng Li,Zhuxia Li

doi:10.1016/j.physletb.2017.09.013

Qingfeng Li, Zhuxia Li

Open Access

https://doi.org/10.1016/j.physletb.2017.09.013

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Abstract

The calculation of the energy-, density-, and isospin-dependent Δ production cross sections in nucleon–nucleon (NN) scattering σNN→NΔ⁎ has been performed within the framework of the relativistic BUU approach. The NΔ cross sections are calculated in Born approximation taking into account the effective mass splitting of the nucleons and Δs in asymmetric matter. Due to the different mass splitting for neutron, proton and differently charged Δs, it is shown that, similar to the NN elastic ones, the reductions of NΔ inelastic cross sections in isospin-asymmetric nuclear medium are different from each other for all the individual channels and the effect is largest and of opposite sign for the Δ++ and Δ− states. This approach is also compared to calculations without effective mass splitting and with splitting derived from Dirac–Brueckerner (DB) calculations. The isospin dependence of the NΔ cross sections is expected to influence the production of π+ and π− mesons as well as their yield ratio, and thus affect the use of the latter quantity as a probe of the stiffness of the symmetry energy at supranormal densities.

Highlights

In addition to the isovector part of the mean field, i.e., the symmetry potential term, the isospin dependence of the medium-modified cross sections of the collision term should be considered simultaneously [4,5,6] for a real non-equilibrium process of heavy ion collisions, which is often simulated by microscopic transport models such as Boltzmann-Uehling-Uhlenbeck (BUU) or quantum molecular dynamics (QMD)
In the current work, based on the effective Lagrangian within the framework of the relativistic BUU (RBUU) microscopic transport theory [4, 17, 18] in which the σ, ω, δ[a0(983)], ρ, and π mesons are coupled to both nucleons and ∆(1232) resonances, we focus on the medium modifications of NN inelastic scatterings and especially in isospin-asymmetric circumstances
Theoretical calculations on the energy, density, and isospindependent nucleon-nucleon (NN) inelastic cross sections σN∗ N→N∆(s, ρ, α) are accomplished with the help of the RBUU microscopic transport theory in which the σ, ω, δ[a0(980)], ρ, and π mesons are coupled by density-dependent coefficients to both nucleons and ∆(1232) resonances

Summary

MOTIVATION

In addition to the isovector part of the mean field, i.e., the symmetry potential term, the isospin dependence of the medium-modified cross sections of the collision term should be considered simultaneously [4,5,6] for a real non-equilibrium process of heavy ion collisions, which is often simulated by microscopic transport models such as Boltzmann-Uehling-Uhlenbeck (BUU) or quantum molecular dynamics (QMD). In a more recent paper [16], Song and Ko have considered this issue by investigating the effect of the isospin-dependent medium modification of the pion-production threshold on the total pion yield and their ratio with the help of the relativistic Vlasov-Uehling-Uhlenbeck (RVUU) approach, based on mean fields from the nonlinear relativistic NLρ and NLρδ models.

THEORETICAL FRAMEWORK

NUMERICAL RESULTS

SUMMARY AND OUTLOOK