Low-momentum interactions with Brown-Rho-Ericson scalings and the density dependence of the nuclear symmetry energy

TL;DR

This paper investigates the density dependence of nuclear symmetry energy using low-momentum interactions with Brown-Rho and Ericson scalings, finding that nonlinear Ericson scaling aligns well with empirical data.

Contribution

It introduces the use of nonlinear Ericson scaling and three-nucleon forces to improve the modeling of nuclear symmetry energy at high densities.

Findings

Linear BR scaling yields overly stiff EOS.

Nonlinear Ericson scaling matches empirical symmetry energy.

Adding three-nucleon forces improves high-density predictions.

Abstract

We have calculated the nuclear symmetry energy $E_{sym}(\rho)$ up to densities of $4 \sim 5 \rho_0$ with the effects from the Brown-Rho (BR) and Ericson scalings for the in-medium mesons included. Using the $V_{low-k}$ low-momentum interaction with and without such scalings, the equations of state (EOS) of symmetric and asymmetric nuclear matter have been calculated using a ring-diagarm formalism where the particle-particle-hole-hole ring diagrams are included to all orders. The EOS for symmetric nuclear matter and neutron matter obtained with linear BR scaling are both overly stiff compared with the empirical constraints of Danielewicz {\it et al.} \cite{daniel02}. In contrast, satisfactory results are obtained by either using the nonlinear Ericson scaling or by adding a Skyrme-type three-nucleon force (TNF) to the unscaled $V_{low-k}$ interaction. Our results for $E_{sym}(\rho)$ obtained with the nonlinear Ericson scaling are in good agreement with the empirical values of Tsang {\it et al.} \cite{tsang09} and Li {\it et al.} \cite{li05}, while those with TNF are slightly below these values. For densities below the nuclear saturation density $\rho_0$, the results of the above calculations are nearly equivalent to each other and all in satisfactory agreement with the empirical values.