Extended momentum-dependent interaction for transport models and neutron stars

TL;DR

This work extends the momentum-dependent interaction (MDI) by introducing three finite-range Yukawa terms and three zero-range density-dependent terms (MDI3Y), enabling flexible momentum and density behavior of the single-nucleon and symmetry potentials. Six interactions are constructed with the same isoscalar properties but different momentum dependence of the symmetry potential $U_{\mathrm{sym}}$ and symmetry-energy slope $L$ ($L=35,55,75$ MeV), including both monotonic and non-monotonic $U_{\mathrm{sym}}$ forms, calibrated to optical potentials, SNM/PNM data, and neutron-star constraints. The exchange part of the finite-range interaction is mapped to a Skyrme-like energy-density functional via density-matrix expansion, furnishing a HF-like framework for cold nuclear matter and neutron-star modeling. The resulting EOSs and neutron-star properties (e.g., $R_{1.4}$ and $\Lambda_{1.4}$) reveal sensitivity to $U_{\mathrm{sym}}$ and high-density symmetry-energy behavior, offering a versatile tool for transport-model analyses of heavy-ion collisions and multimessenger neutron-star signals, with future extensions to hyperons and dense-matter phenomenology.

Abstract

The momentum-dependent interaction (MDI) model, which has been widely used in microscopic transport models for heavy-ion collisions (HICs), is extended to include three different momentum-dependent terms and three zero-range density-dependent terms, dubbed as MDI3Y model. Compared to the MDI model, the single-nucleon potential in the MDI3Y model exhibits more flexible momentum-dependent behaviors. Furthermore, the inclusion of three zero-range density-dependent interactions follows the idea of Fermi momentum expansion, allowing more flexible variation for the largely uncertain high-density behaviors of nuclear matter equation of state (EOS), especially the symmetry energy. Moreover, we also obtain the corresponding Skyrme-like energy density functional through density matrix expansion of the finite-range exchange interactions. Based on the MDI3Y model, we construct four interactions with the same symmetry energy slope parameter $L=35$ MeV but different momentum dependence of $U_{\mathrm{sym}}$, by fitting the empirical nucleon optical potential, the empirical properties of symmetric nuclear matter, the microscopic calculations of pure neutron matter EOS and the astrophysical constraints on neutron stars. In addition, two interactions with $L=55$ and $75$ MeV are also constructed for comparison. Using these MDI3Y interactions, we study the properties of nuclear matter and neutron stars. These MDI3Y interactions, especially those with non-monotonic momentum dependence of $U_{\mathrm{sym}}$, will be potentially useful in transport model analyses of HICs data to extract nuclear matter EOS and the isospin splitting of nucleon effective masses.

Figures (13)

• Figure 1: The energy dependence of single-nucleon potential in cold SNM with $\Lambda_3=700$, $1318$, and $3000$ MeV/$c$, respectively, in the MDI3Y model. Also shown are the nucleon optical potential (Schrödinger equivalent potential, $\mathrm{U}_{\mathrm{sep}}$) in SNM at $\rho_0$ obtained by Hama et al.Hama:1990vrCooper:1993nx.
• Figure 2: The predicted values of $U_{0}^{\infty}$ for different $\Lambda_3$ in the MDI3Y model. Note $U_{0}^{\infty}=55$ MeV with $\Lambda_3=1318$ MeV/$c$.
• Figure 3: The predicted values of $m_{s,0}^{\ast}$ for different $\Lambda_3$ with the MDI3Y interaction. The dashed line indicates $\Lambda_3=1318$ MeV/$c$ with $m_{s,0}^{\ast}/m=0.763$.
• Figure 4: Momentum dependence of the single-nucleon potential in SNM $U_{0}(\rho,p)$, at $\rho=\rho_0/4$, $\rho_0/2$, $\rho_0$, and $2\rho_0$, respectively. The vertical lines indicate the corresponding Fermi momenta.
• Figure 5: The isoscalar nucleon effective mass $m_{s}^{\ast}(\rho)$ as a function of nucleon density. The results for interactions SLy4 Chabanat:1997un, SkSP.1 Farine:2001oac, and M3Y-P7 Nakada:2012sq are also shown for comparison.