New Skyrme parametrizations to describe finite nuclei and neutron star matter with realistic effective masses. II. Adjusting the spin-dependent terms

TL;DR

The paper addresses ferromagnetic instabilities and unrealistic spin-dependent behavior in common Skyrme functionals by treating the functional as a density functional and independently constraining the spin sector. It introduces Sky3s and Sky4s, where the spin-dependent terms are fitted to microscopic Landau parameters $G_0$ and $G'_0$ and to spin-mass splittings, with a refitted spin-orbit term $W_0$ to maintain finite-nucleus properties. The resulting functionals yield positive $G_0$ and $G'_0$ at relevant densities, exhibit stable behavior in spin-1 channels, and provide realistic spin-related response functions. The work further computes RPA responses and neutrino scattering rates in neutron-star matter, showing notable differences from the unconstrained variants and enabling more reliable astrophysical applications, albeit with remaining uncertainties from three-body forces in the underlying microscopic inputs.

Abstract

Many common Skyrme functionals present ferromagnetic instabilities or unrealistic density dependence of the spin-dependent Landau parameters. To solve these problems, we consider the Skyrme interaction as a density-functional rather than a density-dependent two-body force. This allows us to adjust the spin-dependent terms of the new extended Skyrme functionals of our previous paper [M. Duan and M. Urban, Phys. Rev. C 110, 065806 (2024)] independently without altering the properties of spin saturated matter. The parameters of the spin-dependent terms are determined by fitting the Landau parameters $G_0$ and $G'_0$ in neutron matter and symmetric nuclear matter and the effective-mass splitting of up and down particles in spin polarized matter to the results of microscopic calculations. Using the new parametrizations, called Sky3s and Sky4s, the spin-related properties of nuclear matter are in good agreement with the microscopic results. As an application, we compute response functions and neutrino scattering rates of neutron-star matter with the new functionals having realistic effective masses and Landau parameters.

Figures (9)

• Figure 1: (Top) Neutron effective mass in PNM, (middle) proton effective mass in PNM (= isovector effective mass), and (bottom) nucleon effective mass in SNM (= isoscalar effective mass) from the BHF calculations of Ref. Baldo2014 (dash-dot lines) and the corresponding ones of Sky3 and Sky4 Duan2024 (solid lines).
• Figure 2: The Landau parameters $G_0$ in pure neutron matter (top panel) and $G_0$ and $G_0^{\prime}$ in symmetric nuclear matter (middle and bottom panels). The results are computed with Skyrme interactions Sky3, Sky4 Duan2024, SLy4 Chabanat1998, BSk20 Goriely2010, SLy5st Margueron2009, BSk17st Margueron2009b, and SAMi Roca-Maza2012. The square symbols represent the microscopic BHF results of Refs. Zuo2003PNMZuo2003communicationsZuo2003SNM.
• Figure 3: Equations of state of fully spin-polarized and unpolarized neutron matter computed with Sky3 and Sky4. The vertical red and steel-blue dotted lines represent the critical densities in pure neutron matter described using Sky3 and Sky4, respectively.
• Figure 4: Fits to microscopic results of Bombaci2006Bigdeli2009Bigdeli2024Vidana2024 for $C^{sT}$ as functions of density in pure neutron matter (red) and symmetric nuclear matter (blue). The scattering of the microscopic results for fixed densities comes from deducing $C^{sT}$ at different values of the polarization.
• Figure 5: The Landau parameters $G_0$ in pure neutron matter (upper panel) and $G_0$ and $G_0^{\prime}$ in symmetric nuclear matter (lower panel) computed with Sky3s and Sky4s. The $G_0$ in pure neutron matter recomputed from the results of Refs. Zuo2003PNMZuo2003communications as explained in Sec. \ref{['subsec:strategies']}, and the results for symmetric nuclear matter from Ref. Zuo2003SNM are also shown.