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 $\sigma$-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 $g_{\pi }$ moves the saturation point toward the empirical region. However, changing $g_{\pi }$ alone also affects the deuteron properties and tensor-sensitive observables. We therefore extend the parameter search by varying the $\rho$-meson tensor coupling $f_{\rho }/g_{\rho }$ and readjusting the effective $\sigma$-meson couplings in the ${}^1{S}_0$ and ${}^3{P}_0$ channels. Four representative parameter sets with $g_{\pi }^2/4\pi =14.7$--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 $E_{\mathrm{lab}}=50$ 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 $g_{\pi }$, the neutron-star mass--radius relations show only a weak dependence on the pion coupling, with maximum masses of about $2.24$--$2.28M_{\odot }$ and radii of about $12.3$--$12.6\mathrm{km}$ at $1.4M_{\odot }$. These results show that including the $\rho$-meson tensor coupling and partial-wave-dependent $\sigma$-meson couplings provides a better balance between free-space two-nucleon observables and nuclear-matter saturation properties than varying the pion coupling alone.

Comments: 31 pages, 18 figures, 5 table, has been accepted by Atoms