On highly accurate computations of the Coulomb two-center systems with unit charges

Abstract

Results of our recent highly accurate computations of the Coulomb two-center systems with the unit electrical charges $X^{+}{X}^{+}{e}^{-}$ and $X^{+}{Y}^{+}{e}^{-}$ are discussed. In particular, we have determined (to very high accuracy) the total energies of the ground $1s\sigma -$states in the two-center adiabatic (or molecular) H${}_2^{+}$, D${}_2^{+}$, HD${}^{+}$, HT${}^{+}$, T${}_2^{+}$ and DT${}^{+}$ ions. In these computations we applied the new masses of hydrogen isotopes, which have been measured in the recent high-energy experiments. We also derived (and tested) our accurate mass-interpolation formula for the total energies of the model two-center $X^{+}{X}^{+}{e}^{-}$ ions with very heavy masses of the point $X^{+}$ particles ($M_X\ge$ 100,000 $m_e$). By using this formula we analyze the overall accuracy and validity of the adiabatic two-center approximation in application to the three-body atomic (or Coulomb) systems.

arXiv commentPACS number(s): 36.10.-k and 36.10.Dr