Geodesic
Two-dimensional problem of two Coulomb centers at small intercenter distances
Teoretičeskaâ i matematičeskaâ fizika, Tome 148 (2006) no. 2, pp. 269-287

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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
Mots-clés : confluent Heun equation, Mathieu functions, Ince equation. 
@article{TMF_2006_148_2_a7,
     author = {D. I. Bondar and M. Gnatich and V. Yu. Lazur},
     title = {Two-dimensional problem of two {Coulomb} centers at small intercenter distances},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {269--287},
     publisher = {mathdoc},
     volume = {148},
     number = {2},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2006_148_2_a7/}
}
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D. I. Bondar; M. Gnatich; V. Yu. Lazur. Two-dimensional problem of two Coulomb centers at small intercenter distances. Teoretičeskaâ i matematičeskaâ fizika, Tome 148 (2006) no. 2, pp. 269-287. http://geodesic.mathdoc.fr/item/TMF_2006_148_2_a7/