Molecular approach for the bound states of ABA Coulomb systems from H2+ to Ps-

Abstract

An alternative approach is introduced for adiabatic and nonadiabatic calculations in the ABA Coulomb systems from ${\mathrm{H}}_{2}^{+}$ to the positronium negative ion ${\mathrm{Ps}}^{\mathrm{\ensuremath{-}}}$ (${\mathit{e}}^{\mathrm{\ensuremath{-}}}$${\mathit{e}}^{+}$${\mathit{e}}^{\mathrm{\ensuremath{-}}}$) so that they are treated as molecular systems. The adiabatic vibrational solutions point out the most relevant ``nuclear'' configurations that should appear in the construction of the nonadiabatic wave function and reveal the importance of the AA vibrations at this stage. Applications provide evidence for the separability of the ground state of ${\mathrm{Ps}}^{\mathrm{\ensuremath{-}}}$ and give energy values for six S bound states of ${\mathrm{\ensuremath{\mu}}}^{+}$${\mathit{e}}^{\mathrm{\ensuremath{-}}}$${\mathrm{\ensuremath{\mu}}}^{+}$ that seem not to be reported so far.