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