Variational method with explicit energy functionals for hot nuclear matter with the tensor force

An equation of state for hot nuclear matter has been constructed with the AV6’ two-nucleon potential and the UIX three-nucleon potential by the variational method with explicit energy functionals. For neutron matter and symmetric nuclear matter at zero temperature, energies per nucleon are expressed as explicit functionals of spin-isospin-dependent radial distribution functions and tensor distribution functions. Then the Euler-Lagrange equations for these distribution functions are derived from the energy functionals and are solved numerically. The obtained energies per nucleon are reasonable as compared with those obtained by the Auxiliary Field Diffusion Monte Carlo method. In this presentation, we report on an extension of the above variational method to nuclear matter at finite temperatures following the method by Schmidt and Pandharipande. In this study, the isospin-dependent tensor distribution functions play a crucial role in treating the two-body tensor force and the two-pion-exchange three body force.  Furthermore, we will apply the obtained EOS for hot nuclear matter to proto-neutron stars.