The Relativistic Thomas-Fermi Atom

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Abstract
The Thomas-Fermi equation determining the inner atomic potential and the charge distribution is generalized to take care of the relativistic change of mass with velocity. The relativistic equation is then solved numerically by means of a first order perturbation method and with the help of the differential analyzer. The solution is applied to the case of mercury and it is shown that while the atomic potential changes only slightly, the charge density is appreciably increased in the immediate vicinity of the nucleus and slightly decreased at larger distances.

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