The Thomas-Fermi-gombas atom models in which the electrons are grouped into n- and nl-shells and a calculation of the atomic form factor

摘要

This article, considers in detail P. Gombas's idea of grouping electrons into n- and nl-shells in the Thomas-Fermi theory of free atoms briefly, the TFG n- and TFG nl-models respectively. Using these models, exact analytical expressions for the total energy E and the atomic form factor F(K) are obtained. All integrals of the TFG nl-model are computed by means of the hypergeometric functions F-2(1)(x), F-3(2)(x), F-2(x,y) and F-A(x1,..., x(6)) for the first time. In particular, Weizsacker's gradient correction to the kinetic energy of the nl-th shell E-w((nl)) generates a new numerical triangle T-w((nl)) with coefficients bw = n + 2l(n - l - 1).