Equation of State of Dense Supermova Matter and Newborm Hot Neutron Stays

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In this project, we aimed to obtain realistic results of the thermo-dynamic quantities and the equation of state (EOS) for dense supernova matter and to discuss the characteristics of newborn hot neutron stars. Also, we aimed to investigate the properties of neutron-rich nuclear matter relevant to supernova matter, in connection with the underlying physics of unstable nuclei.(1) As a way to approach nucleon matter at finite temperature, we have proposed the method to solve a set of finite-temperature Hartree-Fock equations with the effective uncleon interaction V and shown the validity as well as the workability. In particular, the "separation method" to separate V into a realistic two-nucleon part and a phenomenological part is very effective to see how the results are affected by the present theoretical uncertainties.(2) We have tabulated the thermodynamic quantities of dense supernova matter for wide ranges of temperature T, denisty rho and lepton fraction y_l and given the explanations to the findings such as the constant population of the constituents, the large proton fraction Y_p and the stiffened EOS.It is remarked that Y_p is represented within 3% accuracy by the formula Y_p=/Y_l+0.05.(3) We have systematically investigated the rho-, T- and alpha (asymmetry)- dependences of the bulk and the single-particle quantities of neutron-rich nuclear matter and discussed the T- and the aipha- dependence of nuclear incompressibility k. It is found that the coexistent region for the Liquid-Gas phase transition becomes narrower as aipha increases.(4) We have ramarked that newborn neutron stars are "fat" and hence the spin-up and the release of binding energy are expected in the early cooling stage. The released energy is discussed in relation to the neutrino burst of SN1987A.It is found that hot neutron stars at birth bring about new constraints on the maximum mass and the maximum rotation rate of usual cold neutron stars.