Fractal generalization of Thomas-Fermi model

摘要

The Thomas-Fermi model is developed for a multielectron neutral atom at an arbitrary metric dimension of the electron cloud. It has been shown that the electron cloud with the reduced dimension should be located in the close vicinity of the nucleus. At a metric dimension of the electron cloud of 2, the differential equation of the model admits an analytical solution. In this case, the screening parameter does not depend on the charge of the nucleus.