Two-particle atomic coalescences

The two-electron Schrodinger equation at the two-particle coalescences was studied for atomic three-body systems in S states. The general differential equation in three variables was reduced to the centrally symmetric field problem for the case of electron-nucleus and electron-electron coalescence lines. Specific potentials describing attractive and repulsive interactions between the coalesced pair of the electron and nucleus and the two coalesced electrons, respectively, were derived and studied. Interesting features of these potentials in the vicinity of the triple-coalescence point were found. The ground states of the helium atom, the negative ion of hydrogen, and the positive ion of lithium were explored as the typical examples of the helium isoelectronic sequence.