A closed system of nonstationary equations for a multielectron atom is cons
tructed using a method previously developed for investigating multiparticle
fermion systems. The melt-known Thomas-Fermi--Dirac method is a particular
case of the system. The exchange spin-spin correlations are calculated usi
ng an improved spin-spin interaction Hamiltonian. The dependence of the ele
ctron concentration on the self-consistent electric field potential and a d
iscrete set of parameters determined by the total energy and the angular mo
mentum of the atom is derived for stationary atom states.