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

Abstract

We have calculated the nuclear symmetry energy ${E}_{\mathrm{sym}}(\ensuremath{\rho})$ up to densities of $4\ensuremath{-}5{\ensuremath{\rho}}_{0}$ with the effects from the Brown-Rho (BR) and Ericson scalings with the in-medium mesons included. Using the ${V}_{\mathrm{low} k}$ low-momentum interaction with and without such scalings, the equations of state (EOSs) of symmetric and asymmetric nuclear matter have been calculated using a ring-diagram formalism where the particle-particle-hole-hole ring diagrams are included to all orders. The EOSs for symmetric nuclear matter and neutron matter obtained with linear BR scaling are both overly stiff compared with the empirical constraints of Danielewicz et al. [Science 298, 1592 (2002)]. 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 ${V}_{\mathrm{low} k}$ interaction. Our results for ${E}_{\mathrm{sym}}(\ensuremath{\rho})$ obtained with the nonlinear Ericson scaling are in good agreement with the empirical values of Tsang et al. [Phys. Rev. Lett. 102, 122701 (2009)] and Li et al. [Phys. Rev. C 72, 064611 (2005)], while those with the TNF are slightly below these values. For densities below the nuclear saturation density ${\ensuremath{\rho}}_{0}$, the results of the above calculations are nearly equivalent to each other and all are in satisfactory agreement with the empirical values.