This article is cited in 11 papers

Two-dimensional problem of two Coulomb centers at small intercenter distances

D. I. Bondar^a, M. Gnatich^b, V. Yu. Lazur<sup>a

a</sup> Uzhgorod National University
^b Institute of Experimental Physics, Slovak Academy of Sciences

Abstract: We use analytic methods to analyze the discrete spectrum for the problem $(Z_1eZ_2)_2$ in the united-atom limit $(R\ll1)$ and obtain asymptotic expansions for the quantum defect and energy terms of the system $(Z_1eZ_2)_2$ at small intercenter distances $R$ up to terms of the order $O(R^6)$. We investigate the effect of the dimensionality factor on the energy spectrum of the hydrogen molecular ion H$^+_2$.

Keywords: planar problem of two Coulomb centers, boundary layer phenomena, confluent Heun equation, Mathieu functions, Ince equation.

Received: 28.11.2005
Revised: 19.12.2005

DOI: 10.4213/tmf2085

 English version: Theoretical and Mathematical Physics, 2006, 148:2, 1100–1116

Bibliographic databases:

• 
• 
• 
• 
•