The H${}_2^{+}$ molecular ion: a solution

Abstract

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.

16 pages, 4 figures, 6 tables, typos are corrected and small additions are inserted, to be published at JPB (fast track comm)

References in corpus (1)

• New Approach for the Electronic Energies of the Hydrogen Molecular Ion

Cited by in corpus (5)

• Nuclear critical charge for two-electron ion in Lagrange mesh method
• {H${}_2^{+}$, HeH and H${}_2$}: approximating potential curves, calculating rovibrational states
• The H${}_2^{+}$ molecular ion: low-lying states
• Static field-gradient polarizabilities of small atoms and molecules in finite temperature
• Quadrupole transitions in the bound rotational-vibrational spectrum of the tritium molecular ion