Variational approach to nuclear matter

We calculated the energies of asymmetric nuclear matter at zero and finite temperatures with the cluster variational method. At zero temperature, the expectation value of the two-body Hamiltonian composed of the kinetic energies and the AV18 two-body forces is calculated with the Jastrow wave function in the two-body cluster approximation. The obtained two-body energy is in good agreement with the result with the Fermi Hypernetted Chain (FHNC) calculation by Akmal et al. The energy caused by the UIX three-body forces is treated somewhat phenomenologically so that the total energy reproduces the empirical saturation point. Furthermore, the parameters included in the three-body energy are readjusted so that the Thomas-Fermi (TF) calculations with use of the obtained energy of nuclear matter reproduce the gross feature of the experimental data on atomic nuclei. The nuclear species in the neutron star crust obtained by the TF calculation are reasonable. The free energies of asymmetric nuclear matter at finite temperatures are calculated with an extension of the method proposed by Schmidt and Pandharipande. The obtained free energies are in good agreement with those with the FHNC method, and it is also found that the present variational method is self-consistent. It is remarkable that the symmetry free energy is not proportional to (1 -2x)², where x is the proton fraction. With use of the obtained thermodynamic quantities, we are constructing a new nuclear equation of state for supernova simulations.