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

Figure 2.11: The same as Fig. 2.10 except for an asymmetric case with a dense phase protonfraction x I = 0.3. In this case, the critical temperature is T c ≃ 16.1 MeV. The dashed lineshows the neutron skin thickness R n −R p in fm.2.6 Isolated Nuclei and Nuclei in Dense MatterFor the computation of finite nuclei, spherical symmetry and zero temperature are assumedin this model. These restrictions will be relaxed in a future publication. The main pointof this model is to demonstrate the feasibility of efficiently computing the thermodynamicproperties of nuclei in a consistent Thomas-Fermi approximation without the simplificationsassociated with the liquid droplet model. In contrast to the case of a semi-infinite interface,it is preferable in the finite nucleus case to choose values for N and Z, together with thetemperature. The additional two constraints in Eq. (2.65) then determine the chemicalpotentials of the isolated nucleus, i.e., a nucleus in a zero density environment.2.6.1 Isolated NucleiThe total energy of a nucleus must include the electrostatic Coulomb energy∫ ∫E Coul = e2d 3 r d 3 r ′[ρ p(r)−ρ e (r)][ρ p (r ′ )−ρ e (r ′ )], (2.94)2|r −r ′ |VVwhere the spatial integrals are over the entire volume. In the case of an isolated nucleus,ρ e = 0, and the integrand is finite only within the nucleus. The contribution of the Coulombenergy to the proton chemical potential can be found from a variation of E Coul with respect32