ELECTRON IN THE FIELD OF 3 COULOMB CENTERS - ASYMPTOTIC SOLUTIONS

A system formed of one electron and three nuclei with charges Z(a) = Z(b) = 1 and Z(c) = Z = 1, 2, 3... is analysed. The asymptotic expansions of the solutions for the systems (Z + H-2+) and (p+p+A+(z-1)) are found when the distances between the particles are large. The quadrupole moments and the polarizability of the hydrogen molecular ion H-2+ are calculated for the equilibrium internuclear distance R = 2 a0. The asymptotic formula obtained for the energy terms of the system formed from the hydrogen-like ion A+(Z-1) and two protons transforms into the well known formula for two Coulomb centres when R = 0.