In-medium nucleon-nucleon cross sections from relativistic ab initio calculations

TL;DR

The paper addresses the challenge of computing ab initio in-medium nucleon-nucleon cross sections by implementing relativistic Brueckner-Hartree-Fock theory in the full Dirac space with the Bonn A potential. It constructs the in-medium $G$-matrix via the Thompson equation, derives the $S$-matrix and scattering amplitudes, and obtains phase shifts, differential cross sections, and total cross sections for $pp$, $nn$, and $np$ in dense nuclear matter. The results reveal general medium suppression of cross sections, with pronounced near-Fermi-surface enhancements for certain channels at zero total momentum, and distinct angular patterns between $np$ and $pp$ scattering; isospin asymmetry effects are comparatively weak. These findings provide a robust microscopic basis for transport-model parametrizations and have implications for heavy-ion collisions and neutron-star matter, with future work aiming at parameterizations, inclusion of $\Delta$ degrees of freedom, higher densities, asymmetric matter, and relativistic chiral forces.

Abstract

The in-medium nucleon-nucleon scattering cross section is a pivotal quantity for studying the medium effects of strong interaction, and its precise knowledge is critical for understanding the equation of state for dense matter, intermediate-energy heavy-ion collision dynamics, and related phenomena. In this work, we perform a microscopic investigation of in-medium nucleon-nucleon scattering cross sections, by utilizing the relativistic Brueckner-Hartree-Fock (RBHF) theory with the Bonn potential. The fully incorporation of both positive- and negative-energy states in the RBHF solutions allows us to determine the single-particle potentials, the effective G matrix, and the scattering cross section uniquely. The momentum, density, and isospin dependence of the cross section for pp, nn, and np scattering are studied in detail. Our results provide a solid foundation for future parametrization studies of multiparameter dependency of total scattering cross sections.

Figures (9)

• Figure 1: The $np$ scattering phase shifts for the $^{1}S_{0}$ and $^{3}S_{1}$ channels, and $pp$ scattering phase shifts for the $^{3}P_{1}$ channel as functions of the laboratory energy. In each panel, the green short-dashed, red solid, and blue short-dotted lines represent the results at densities $\rho=0.5\rho_0, \rho_0$, and $1.5\rho_0$, respectively. For comparison, the phase shifts in free space are shown as black dashed lines. The total momentum and isospin asymmetry are set as $P=0$ and $\alpha=0$.
• Figure 2: The $np$ scattering phase shifts for the $^{3}S_{1}$ channel as functions of the laboratory energy. The red solid, green short-dotted, blue short-dashed, and pink short-dash-dotted lines correspond to the total momenta $P=0, 0.1, 1.0$, and $2.0\ \text{fm}^{-1}$, respectively. The phase shifts in free space are also given as black dashed lines for comparison. The density is fixed at $\rho=\rho_0$.
• Figure 3: The $np$, $pp$, and $nn$ scattering phase shifts for the $^{1}S_{0}$ channels as functions of the laboratory energy. In each panel, the red solid, green short-dashed, and blue short-dotted lines represent the results at isospin asymmetries $\alpha = 0, 0.4$, and $0.8$, respectively. The density and total momentum are fixed at $\rho = \rho_0$ and $P=1.0\ \text{fm}^{-1}$. The phase shifts in free space are also given as black dashed lines for comparison.
• Figure 4: The $np$ differential scattering cross sections in symmetric nuclear matter as functions of scattering angle at laboratory energy $E_\text{lab.}=50$ and $300$ MeV. Each panel displays results for baryon densities $\rho=0.5\rho_0, \rho_0$, and $1.5\rho_0$, represented by green short-dashed, red solid, and blue short-dotted curves, respectively. The total momentum is fixed at $P=1.0\ \text{fm}^{-1}$. For comparison, free-space phase shifts are included as black dashed lines, while pink symbols with error bars denote experimental data from Ref. 1977-Montgomery-PhysRevC.16.499.
• Figure 5: Same as in Fig. \ref{['Fig4']}, but for $pp$ differential cross sections.