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This article is cited in 11 scientific papers (total in 11 papers)
Two-dimensional problem of two Coulomb centers at small intercenter distances
D. I. Bondara, M. Gnatichb, V. Yu. Lazura a 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
Citation:
D. I. Bondar, M. Gnatich, V. Yu. Lazur, “Two-dimensional problem of two Coulomb centers at small intercenter distances”, TMF, 148:2 (2006), 269–287; Theoret. and Math. Phys., 148:2 (2006), 1100–1116
Linking options:
https://www.mathnet.ru/eng/tmf2085https://doi.org/10.4213/tmf2085 https://www.mathnet.ru/eng/tmf/v148/i2/p269
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