Exploring the Parameter Space of pvCD-Bonn Potentials under Constraints from Nuclear Saturation Properties

Abstract

We explore the parameter space of the pvCD-Bonn B potential within the relativistic Brueckner--Hartree--Fock framework under the constraints from the empirical saturation properties of symmetric nuclear matter. We first examine the effects of the scalar-meson and pion coupling constants. Changing the $σ$-meson couplings in the $^{1}S_0$ and $^{3}S_1$--$^{3}D_1$ channels alone cannot reproduce the empirical saturation density and binding energy at the same time, whereas increasing $g_π$ moves the saturation point toward the empirical region. However, changing $g_π$ alone also affects the deuteron properties and tensor-sensitive observables. We therefore extend the parameter search by varying the $ρ$-meson tensor coupling $f_ρ/g_ρ$ and readjusting the effective $σ$-meson couplings in the $^{1}S_0$ and $^{3}P_0$ channels. Four representative parameter sets with $g_π^2/4π=14.7$--15.0 give deuteron properties close to the experimental values and maintain a reasonable description of the main neutron--proton phase shifts and differential cross sections at $E_{\rm lab}=50$ and 212 MeV. Their saturation densities lie in the range $0.159$--$0.161~\mathrm{fm}^{-3}$, with saturation energies between $-15.00$ and $-15.38~\mathrm{MeV}$. For the interactions obtained by varying $g_π$, the neutron-star mass--radius relations show only a weak dependence on the pion coupling, with maximum masses of about $2.24$--$2.28\,M_\odot$ and radii of about $12.3$--$12.6~\mathrm{km}$ at $1.4\,M_\odot$. These results show that including the $ρ$-meson tensor coupling and partial-wave-dependent $σ$-meson couplings provides a better balance between free-space two-nucleon observables and nuclear-matter saturation properties than varying the pion coupling alone.