Equation of state for spin-polarized asymmetric nuclear matter with the cluster variational method

The nuclear equation of state (EOS) is one of the crucial ingredients in numerical simulations of core-collapse supernovae. Recently, we have constructed a new table of the nuclear EOS applicable to the core-collapse simulations by using the cluster variational method with realistic nuclear forces [1], and the resultant EOS table is available on the Web [2] for the use in various astrophysical simulations.

In this study, we generalize our cluster variational method to investigate spin-polarized asymmetric nuclear matter properties at zero and finite temperatures. As an extension of our supernova EOS, we calculate the free energies at various densities, proton fractions, temperatures, and spin-asymmetries within the two-body cluster approximation starting from the nuclear Hamiltonian composed of the Argonne v18 and Urbana IX nuclear potentials. The obtained free energy and related thermodynamic quantities are reasonable, and the spin susceptibility of pure neutron matter at zero temperature is in good agreement with that obtained with the auxiliary field diffusion Monte Carlo calculation.

In this talk, we will discuss properties of the present EOS for spin-polarized asymmetric nuclear matter in more details. The goal of our project is to obtain the neutrino-nucleon scattering rate in supernova matter with use of the spin susceptibility that is consistent with our supernova EOS, so we will also report possible new results of our project.