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

Chapter 7ConclusionsThe nuclear equation of state is needed to simulate supernovae explosions, proto-neutronstars, and compact binary mergers involving neutron stars. For these simulations, we needthermodynamic information for given baryon density, proton fraction, and temperature.Since the EOS should cover wide range of the above variables, we need to be careful whenwe choose a nuclear force model to make the EOS table. A good nuclear force modelshould represent both low and high densities nuclear phenomena as well as pure neutron andastrophysical matter.First of all, we study nuclear physics using Finite Range force model. In the Finite Rangeforce model, the nuclear interaction energy at density each point has the contribution fromevery spacial point with weight factor (e −r/a ). The first model that we investigated is thetruncated model (Chapter 2). To find the parameters in the truncated model, we use thestandard nuclear matter properties of symmetric nuclear matter , such as E/A = −B ≃ −16MeV, P = 0 MeV/fm 3 , S v ≃ 32 MeV, L ≃ 60MeV. a, which is a nuclear diffusenessparameter can be obtained from semi-infinite nuclear matter calculation. This truncatedmodel is improved by adding new density dependent interactions to fit optical potential,nuclear incompressibility, and pure neutron matter. To get optimized parameter set for themodified model, we compare the results of total binding energy of single nucleus from themodified model with experimental values. The recent constraints of S v and L [47] confirmthat our parameter set for the modified model is a good choice.Boththe truncated andmodified models model areused tocalculate energy per baryonofsingle nucleus and heavy nuclei in dense matter. Since the finite range model gives integralequations instead of differential equations, the boundary condition has no difficulty andthe numerical calculation in the unit (Wigner-Seitz) cell is much easier to perform thandifferential equations. Thomas-Fermi approximation is employed to find the nuclear densityprofile. In TF, we are seeking the local density at each point instead of finding the full wavefunctions. From the density profile, we find the plane wave so that we are able to calculatemomentum density to calculate Hamiltonian density or kinetic energy. At zero temperature,the relation between the number density and momentum density is simple since the Fermi-Diracdistributionfunctionisfrozento1. Atfinitetemperature, however, wehavetocalculatethe Fermi integral which is not an analytic function. For example, from the number density,we aresupposed tofind thedegeneracy parameter (φ)fromFermi integral, F 3/2 (φ)andto getthe momentum density from Fermi integral, F 5/2 (φ). JEL scheme provides polynomial fits104