An Asymptotic Solution of the Fundamental Equation of the Statistical Atom Theory

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THE problem of atoms and ions with spherical symmetry as well as the problem of metals and ionic crystals seems to be dealt with quite satisfactorily by the Thomas – Fermi‘s statistical method1, with its modifications due to Dirac2, Jensen3 and Gombas4 respectively. But the fundamental equation of the modified theory having no solution in closed form, that is, in terms of elementary functions, one must apply for its solution, in each particular case, rather lengthy numerical methods. To avoid these difficulties, we propose an asymptotic method of solution which may be applied successfully in many cases.