  The analysis of correlation energy of the simplest first approximation of a
variational method for the intrashell states of two-electron atoms is the
purpose of the present work. This method allows to divide energy of atom on
Coulomb and additional not - Coulomb correlation parts with very high accuracy.
Thus all the Coulomb interaction completely is taken into account in
calculation and not-Coulomb terms enter only in additional correlation energy.
The general formula for energy of additional correlation interaction is
obtained and the constant of this interaction is determined. The algorithm of
calculation of total energy of two-electron atoms is offered. The outcomes of
calculations for intra-shell states are adduced and compared to the
experimental data . The arguments for the capability of existence of the
analytical solution for a three-body problem in atomic physics are presented.
Some reasons about probable practical consequences are presented. Most
interesting of them is the discovery that under certain conditions additional
electron-electron attraction can exceed classical electron-electron repulsion.
