21 April 2016 On calculations of two-electron atoms in spheroidal coordinates mapping on hypersphere
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Abstract
3D boundary-value problem (BVP) that arises in modelling the interactions of two-electron quantum systems (atoms or ions) with laser radiation, is formulated in the internal coordinate frame with the electrons placed in the focal points of the spheroidal system of coordinates with mapping on a hyper-sphere.1, 2 The wave function is sought for in the form of a decomposition in the basis of surface functions of the Coulomb two-center problem having the purely discrete spectrum and parametrically depending on the hyper-sphere hyper-radius. Surface functions are sought for in the form of an expansion in the basis of Legendre polynomials with unknown components calculated as solutions of the reduced problem. Efficiency of the approach in comparison with that of the conventional hyper-spherical one3, 4 is demonstrated by the example of helium atom.
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Sergue Vinitsky, Sergue Vinitsky, A. A. Gusev, A. A. Gusev, O. Chuluunbaatar, O. Chuluunbaatar, V. L. Derbov, V. L. Derbov, A. S. Zotkina, A. S. Zotkina, } "On calculations of two-electron atoms in spheroidal coordinates mapping on hypersphere ", Proc. SPIE 9917, Saratov Fall Meeting 2015: Third International Symposium on Optics and Biophotonics and Seventh Finnish-Russian Photonics and Laser Symposium (PALS), 99172Z (21 April 2016); doi: 10.1117/12.2229528; https://doi.org/10.1117/12.2229528
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