Effective Mass in Quantum Hadrodynamics-I and its Impact on the Equation of State of Neutron Matter

Abstract

The effective nucleon mass (M^*) plays a central role in Quantum Hadrodynamics-I (QHD-I), linking scalar meson interactions at the microscopic level to the macroscopic properties of dense nuclear matter. In this work, we re-derive the scalar density integral in detail and validate it numerically using Gaussian quadrature. The numerical and analytic results are found to be in excellent agreement, confirming the robustness of both approaches. We then investigate the sensitivity of M^* to different parameter sets, highlighting its strong influence on nuclear saturation, compressibility, and the resulting equation of state (EoS). The analysis shows that variations in meson-nucleon couplings propagate directly into differences in pressure and energy density, affecting the stiffness of the EoS. While QHD-I produces characteristically stiff EoS, the effective mass evaluation provides a transparent framework for connecting microscopic meson dynamics to macroscopic neutron star properties. These findings underline the relevance of M^* as a microscopic-macroscopic bridge and demonstrate the utility of numerical methods for extending relativistic mean-field models in nuclear astrophysics.