In this paper, the numerical results concerning different orbits of a 3D axisymmetric non-rotating galactic potential are presented. We use Paczynski's gravitational potential with different birth velocity distributions for the isolated old Neutron Star (NS) population. We note some smooth non-constant segments corresponding to regular orbits as well as the characterization of their chaoticity. This is strongly related to the effect of different kick velocities due to supernovae mass-loss and natal kicks to the newly- formed NS. We further confirm that the dynamical motion of the isolated old NSs in the gravitational field becomes obvious, with some significant diffraction in the symmetry of their orbital characteristics.

Recent discovery of 2M⊙ neutron stars in white dwarf-neutron star binaries, PSR J1614-2230 and PSR J0348+0432, has given strong constraints on the maximum mass of neutron stars. On the other hand, all well-measured neutron star masses in double neutron star binaries are still less than 1.5M⊙. These observations suggest that the neutron star masses in binaries may depend on the evolution process of neutron star binaries. In addition, recent works on LMXB (low-mass X-ray binaries) provides us the possibility of estimating the masses and radii of accreting neutron stars in LMXBs. In this talk, we discuss the implications of recent neutron star observations to the neutron star equation of states and the related astrophysical problems. For the evolution of neutron star binaries, we also discuss the possibilities of super-Eddington accretion onto the primary neutron stars.

We first deduce a uniform formula forthe Fermi energy of degenerate and relativistic electrons in the weak-magnetic field approximation. Then we obtain an expression of the special solution for the electron Fermi energy through this formula, and express the electron Fermi energy as a function of electron fraction and matter density. Our method is universally suitable for relativistic electron- matter regions in neutron stars in the weak-magnetic field approximation.

We have examined consequences of strong tidal encounters between a neutron star and a normal star using SPH as a possible formation mechanism of isolated recycled pulsars in globular clusters. We have made a number of SPH simulations for close encounters between a main-sequence star of mass ranging from 0.2 to 0.7 M⊙ represented by an n=3/2 polytrope and a neutron star represented by a point mass. The outcomes of the first encounters are found to be dependent only on the dimensionless parameter n'≡ (m/(m＋M))1/2(rmin/RMS)3/2(m/M)(1/6), where m and M are the mass of the main-sequence star and the neutron star, respectively, rmin the minimum separation between two stars, and RMS the size of the main-sequence star. The material from the (at least partially) disrupted star forms a disk around the neutron star. If all material in the disk is to be acctreted onto the neutron star's surface, the mass of the disk is enough to spin up the neutron star to spin period of 1 ms.