Theory of Nuclear Matter for Neutron Stars and ... - Graduate Physics

141210Phase diagram, Y p =0.45SLy4FRTF ModifiedFRTF TruncatedT (MeV)864201e-06 1e-05 0.0001 0.001 0.01 0.1 1ρ (fm -3 )Figure 6.9: This figure shows the phase boundaries of dense matter when Y p = 0.45.6.7 ConclusionsThe liquid droplet approach is the most promising method to generate thermodynamicallyconsistent nuclear EOS table. The nuclear force model should be tested before making anEOS table so that the table represents both nuclear experiments on Earth and astrophysicalobservations.To make the EOS consistent with the nuclear physics aspect, we have to use one nuclearforce model to calculate the energy contribution from heavy nuclei, nucleons outside, andsurface tension. In the thermodynamical sense, the derivatives in liquid droplet approachare written analytically and can be compared with numerical derivatives.We treat electrons and photons separately since they interact weakly. But we add themto calculate total energy, pressure, entropy and their derivative with respect to temperature,density, and proton composition.For finite temperature, we have to calculate the Fermi integral (F 1/2 , F 3/2 ) to obtain numberdensity and momentum density. The interpolation from the table cannot give enough accuracyat low temperature (T ≤ 1 MeV). JEL is a successful scheme to give enough accuracyfor all domains (relativistic vs. non-relativistic, degenerate and non-degenerate).Phase transitions around half of nuclear saturation density (1/2ρ 0 ) can be achieved when weemploy the geometric function D and changing the dimension d continuously.We should be able to combine the liquid droplet approach with a relativistic mean fieldmodel in the near future if we handle the large L with acceptable values so new parameters102