Analytic Solutions of the Ultra-relativistic Thomas-Fermi Equation

Details Analytic Solutions of the Ultra-relativistic Thomas-Fermi Equation Analytic Solutions of the Ultra-relativistic Thomas-Fermi Equation

2009-03-24

arxiv.org/abs/0903.4095v1

Astronomy and Astrophysics

Astrophysics

Solar and Stellar Astrophysics

5 pages, 1 figure, 2 tables, to appear in the Proceedings of the Third Stueckelberg Workshop on Relativistic Field Theories, C

Scientific paper

It is well known that the ultra-relativistic Thomas-Fermi equation, amply adopted in the study of heavy nuclei, admits an exact solution for a constant proton distribution within a spherical core of radius Rc. Here exact solutions of a generalized ultra-relativistic Thomas-Fermi equation are presented, assuming a Wood-Saxon-like proton distribution and its further generalizations. These solutions present an overcritical electric field close to their surface. The variation of the electric fields as a function of the generalized Wood-Saxon parameters are studied.

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