Relativistic mean-field study of the neutron star inner crust using the asymmetric finite difference method

The ground-state properties of neutron-rich nuclear clusters in the inner crust of neutron stars are investigated within the Wigner-Seitz approximation using a relativistic mean-field framework. The radial Dirac equations are solved with an asymmetric finite-difference scheme, by which the hermiticity is preserved and spurious states are eliminated. Calculations are performed for representative Wigner-Seitz cells employing TM1-based interactions with different symmetry-energy slope parameters $L$, as well as a parametrization with a larger nucleon effective mass. It is found that the binding energy per nucleon decreases systematically with increasing $L$, while a larger effective mass leads to further reduction, particularly at higher densities. Quantum shell effects, which are absent in the Thomas-Fermi approximation, give rise to oscillatory density distributions and modify neutron properties. Within the Wigner-Seitz cell, the resulting neutron root-mean-square radius and chemical potential are shown to be sensitive to both $L$ and the effective nucleon mass, underscoring their important roles in determining the microscopic structure of the neutron-star inner crust.