Revealing the temperature effect on the nucleon-nucleon inelastic cross section in isospin-asymmetric nuclear medium

TL;DR

This work addresses how finite temperature affects the in-medium NN→NΔ inelastic cross section in both isospin-symmetric and asymmetric nuclear matter. It employs a self-consistent relativistic Boltzmann–Uehling–Uhlenbeck framework with an effective Lagrangian that includes $σ$, $ω$, $δ$, $ρ$, and $π$ mesons and compares two coupling schemes, DD-MEδ and OMEG. The main findings show that increasing temperature enhances $σ^{*}_{NN→NΔ}$, especially at higher densities, while density suppresses the cross section due to reduced baryon effective masses, with stronger density/temperature sensitivity in the OMEG model; isospin asymmetry further modifies these trends by reducing temperature sensitivity and introducing channel- and model-dependent isospin effects. These results inform the thermal treatment of Δ-related processes in transport models and have implications for high-density EoS in astrophysical contexts, with upcoming experiments at HIAF, FAIR, and others expected to tighten constraints on the underlying interactions.

Abstract

The nucleon-nucleon ($NN$) inelastic cross section plays an important role in constraining the nuclear equation of state at high baryon density and in describing the formation and evolution of compact astrophysical objects. In this study, the temperature $T$ dependence of the $Δ^{++}$ and $Δ^{-}$ production cross sections in the isospin-symmetric and -asymmetric nuclear medium is investigated within the self-consistent and relativistic Boltzmann--Uehling--Uhlenbeck (RBUU) framework. Two relativistic mean-field parameterizations are employed: the density-dependent parameterization (called DD-ME$δ$) and the nonlinear-dependent parameterization (called OMEG). Both parameterizations yield similar $T$-dependent baryon effective masses and mass splittings, although the OMEG set exhibits a stronger density dependence, particularly at higher densities ($> 1.5ρ_{0}$). Consequently, at lower densities, the energy, density, temperature, and isospin dependence of both $Δ^{++}$ and $Δ^{-}$ production cross sections are comparable for both sets, whereas at higher densities, the OMEG set predicts a stronger temperature and density sensitivity. Moreover, the $T$ dependence of the $NN$ inelastic cross section is enhanced with increasing density, but is suppressed in isospin-asymmetric nuclear matter compared to that in isospin-symmetric nuclear matter. The isospin dependence of the cross section remains nearly $T$-independent at small asymmetries, yet becomes more intricate in highly asymmetric systems. These findings provide valuable testing inputs for improving the thermal treatment of $Δ$-related dynamical processes in transport models and offer insights into the behavior of $Δ$ in astrophysical environments, such as core-collapse supernovae and binary neutron star mergers.

Figures (8)

• Figure 1: (Color online) Nucleon effective mass with respect to DD-ME$\delta$ set (top panels) and OMEG parameter set (bottom panels). The left panels depict the density dependence of nucleon effective mass at $\alpha$=0 (solid lines) and $\alpha$=0.3 (dashed lines) in cold nuclear matter. The right panels show the temperature dependence of nucleon effective mass at densities of $\rho_{0}$ (solid lines), 2$\rho_{0}$ (dotted lines), 3$\rho_{0}$ (dashed lines) at $\alpha$=0.3.
• Figure 2: (Color online) The energy, density, and temperature dependence of the $\sigma^{*}_{NN\rightarrow N\Delta}$ in the isospin-symmetric nuclear matter calculated with the DD-ME$\delta$ parameter set.
• Figure 3: (Color online) Same as Fig. \ref{['alpha=0 cross section DD-ME']}, but for the results calculated with OMEG parameter set.
• Figure 4: (Color online) Ratios $R(\alpha=0, T)=\sigma^{*}(\alpha = 0, T)/\sigma^{*}(\alpha = 0, T=0)$ for the $\Delta$ production channels as functions of temperature $T$ at $\sqrt{s} = 2.326$ GeV and densities of $\rho_{0}$, 1.5$\rho_{0}$, 2$\rho_{0}$, and 3$\rho_{0}$. The horizontal gray dotted line represents the reference value 2.
• Figure 5: (Color online) The energy, density, isospin, and temperature dependence of the $\sigma^{*}_{NN\rightarrow N\Delta}$ in the isospin-asymmetric nuclear matter calculated with the DD-ME$\delta$ parameter set. The top and bottom panels correspond to the individual $pp\rightarrow n\Delta^{++}$ and $nn \rightarrow p \Delta^{-}$ cross sections, respectively.