Abstract
Taking into account the structure and the size of localized electrons the density matrix of localized electrons is analytically derived. In the framework of Kohn's approximation the analytical expression is used for the density matrix, and the additional potential for the three-body Coulomb systems is determined. Our result shows that, the consideration of the structure and size of localized electrons leads to an additional potential. If the size parameter is small, then the additional potential is the oscillator one. This gives a possibility to explain experimental results.