Correlations between bulk parameters in relativistic and nonrelativistic hadronic mean-field models

TL;DR

This paper investigates correlations among bulk parameters in relativistic and nonrelativistic hadronic mean-field models, providing analytical insights and exploring how these correlations manifest in different model frameworks and conditions.

Contribution

It introduces analytical correlations among bulk parameters in the nonrelativistic limit and compares them with relativistic models, highlighting conditions for linearity and the impact of scalar self-interactions.

Findings

Analytical correlations among bulk parameters in the nonrelativistic limit.

Relativistic models with scalar self-interactions reproduce some nonrelativistic correlations.

Crossing points in density dependence indicate linear correlations between parameters.

Abstract

In this work, we study the arising of correlations among some isoscalar ($K_o$, $Q_o$, and $I_o$) and isovector ($J$, $L_o$, $K_{sym}^o$, $Q_{sym}^o$, and $I_{sym}^o$) bulk parameters in nonrelativistic and relativistic hadronic mean-field models. For the former, we investigate correlations in Skyrme and Gogny parametrizations, as well as in the nonrelativistic (NR) limit of relativistic point-coupling models. We provide analytical correlations among bulk parameters for the NR limit, discussing the conditions in which they are linear ones. Based on a recent study [B. M. Santos et al., Phys. Rev. C 90, 035203 (2014)], we also show that some correlations presented in the NR limit are reproduced for relativistic models presenting cubic and quartic self-interactions in the scalar field $\sigma$, mostly studied in this work in the context of the relativistic framework. We also discuss how the crossing points, observed in the density dependence of some bulk parameters, can be seen as a signature of linear correlations between the specific bulk quantity presenting the crossing, and its immediately next order parameter.