The H2+_2^+ molecular ion: a solution

Combining the WKB expansion at large distances and Perturbation Theory at small distances it is constructed a compact uniform approximation for eigenfunctions. For lowest states 1s\si_{g} and 2p\si_{u} this approximation provides the relative accuracy $\lesssim 10^{-5}$ (5 s.d.) for any real $x$ in eigenfunctions and for total energy $E(R)$ it gives 10-11 s.d. for internuclear distances $R \in [0,50]$. Corrections to proposed approximations are evaluated. Separation constants and the oscillator strength for the transition 1s\si_{g} \rar 2p\si_{u} are calculated and compared with existing data.Comment: 16 pages, 4 figures, 6 tables, typos are corrected and small additions are inserted, to be published at JPB (fast track comm

Relativistic corrections of order m\alpha^6 to the two-center problem

Effective potentials of the relativistic m\alpha^6 order correction for the ground state of the Coulomb two-center problem are calculated. They can be used to evaluate the relativistic contribution of that order to the energies of hydrogen molecular ions or metastable states of the antiprotonic helium atom, where precision spectroscopic data are available. In our studies we use the variational expansion based on randomly chosen exponents that permits to achieve high numerical accuracy.Comment: 12 pages, 3 tables 2 figures; submitted to the Journal of Physics