Relativistic diffusion process around a slowly rotating neutron star has been studied. In this article, we formulated the relativistic Fokker-Planck equation to describe the dynamic of particles undergoing diffusion around slowly rotating neutron star. This equation is derived both Doni Andra et al. in the parametrization of phase space proper time and the coordinate time. The relativistic Fokker-Planck equation is expressed in the hyperbolic coordinate system since the observation that the velocity space in special relativity is a noncompact hyperbolic 3-dimensional Riemannian manifold embedded into the 4-dimensional velocity Minkowski space.
Electrons injected in NaCl crystal are studied using Thomas-Fermi-Dirac-von Weizsacker (TFDW) model. The external potential that contributes to the TFDW energy functional is not only due to the nuclei but also to the internal electrons. In order to obtain the potential term due to the internal electrons, the density of the internal electrons in the crystal is derived from the Fourier transformation of the structure factor equation. The external potential in the TFDW energy functional is equal to the summation of the potential owing to the internal electrons and the potential due to the nuclei. The external potential determines the 'umbrella' function that bounds the minimizer of the TFDW energy functional from above. In this present work, we assume that the density of the internal electrons is not affected by the injected external electrons.
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