Journal of Physical Studies 10(1), 1–11 (2006)
DOI: https://doi.org/10.30970/jps.10.1

THE TWO DIMENSIONAL TWO COULOMB CENTERS PROBLEM AT SMALL INTERCENTRE SEPARATION

D. Bondar^{1}, V. Lazur^{1}, M. Hnatič^{2}
¹Department of Theoretical Physics, Uzhgorod National University,
Voloshin Str. 54, 88 000 Uzhgorod, Ukraine
²Institute of Experimental Physics Slovak Academy of Sciences,
Watsonova 47, 043 53 Košice, Slovakia

An elliptic motion integral for the planar two Coulomb center problem \ZeZtwo is obtained by the method of separation of variables. Discrete spectrum of \ZeZtwo problem is analyzed by asymptotic methods in the case of united atom ($R\ll 1$). Asymptotic expansions for the energy terms and the quantum defect of the system \ZeZtwo are obtained to order $O\left(R^6\right)$. Influence of the dimensional factor to the energy spectrum of hydrogen molecular ion ${\rm H}^+_2$ is studied.

PACS number(s): 02.60.Lj, 02.30.Mv, 02.30.Gp, 03.65.Ge