Blow-up Profile of Neutron Stars in the Chandrasekhar theory

We study the Chandrasekhar variational model for neutron stars, with or without an external potential. We prove the existence of minimizers when the attractive interaction strength $\tau$ is strictly smaller than the Chandrasekhar limit $\tau_c$ and investigate the blow-up phenomenon in the limit $\tau\uparrow \tau_{c}$. We show that the blow-up profile of the minimizer(s) is given by the Lane-Emden solution

Energies of the ground state and first excited 0+0^{+} state in an exactly solvable pairing model

Several approximations are tested by calculating the ground-state energy and the energy of the first excited $0^{+}$ state using an exactly solvable model with two symmetric levels interacting via a pairing force. They are the BCS approximation (BCS), Lipkin - Nogami (LN) method, random-phase approximation (RPA), quasiparticle RPA (QRPA), the renormalized RPA (RRPA), and renormalized QRPA (RQRPA). It is shown that, in the strong-coupling regime, the QRPA which neglects the scattering term of the model Hamiltonian offers the best fit to the exact solutions. A recipe is proposed using the RRPA and RQRPA in combination with the pairing gap given by the LN method. Applying this recipe, it is shown that the normal-superfluid phase transition is avoided, and a reasonably good description for both of the ground-state energy and the energy of the first excited $0^{+}$ state is achieved.Comment: 18 pages, 4 figure

Thermal pairing and giant dipole resonance in highly excited nuclei

Recent results are reported showing the effects of thermal pairing in highly excited nuclei. It is demonstrated that thermal pairing included in the phonon damping model (PDM) is responsible for the nearly constant width of the giant dipole resonance (GDR) at low temperature $T <$ 1 MeV. It is also shown that the enhancement observed in the recent experimentally extracted nuclear level densities in $^{104}$Pd at low excitation energy and various angular momenta is the first experimental evidence of the pairing reentrance in finite (hot rotating) nuclei. In the study of GDR in highly excited nuclei, the PDM has been extended to include finite angular momentum. The results of calculations within the PDM are found in excellent agreement with the latest experimental data of GDR in the compound nucleus $^{88}$Mo. Finally, an exact expression is derived to calculate the shear viscosity $\eta$ as a function of $T$ in finite nuclei directly from the GDR width and energy at zero and finite $T$. Based on this result, the values $\eta/s$ of specific shear viscosity in several medium and heavy nuclei were calculated and found to decrease with increasing $T$ to reach $(1.3 - 4)\times\hbar/(4\pi k_B)$ at $T =$ 5 MeV, that is almost the same value obtained for quark-gluon-plasma at $T >$ 170 MeV.Comment: 6 pages, 4 figures, invited lecture at the 11th Spring Seminar on Nuclear Physics, Ischia May 12 - 16, 201