Semiclassical quantization of Bohr orbits in the helium atom |
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Authors: | V V Belov V A Maksimov |
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Institution: | (1) Moscow State Institute of Electronics and Mathematics, Moscow, Russia |
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Abstract: | We use the complex WKB-Maslov method to construct the semiclassical spectral series corresponding to the resonance Bohr orbits
in the helium atom. The semiclassical energy levels represented as the Rydberg tetra series correspond to the doubly symmetrically
excited states of helium-like atoms. This level series contains the Rydberg triple series reported by Richter and Wintgen
in 1991, which corresponds to the Z2+e−e− configuration of electrons observed by Eichmann and his collaborators in experiments on the laser excitation of the barium
atom in 1992. The lower-level extrapolation of the formula obtained for the semiclassical spectrum gives the value of the
ground state energy, which differs by 6% from the experimental value obtained by Bergeson and his collaborators in 1998. We
also calculate the fine structure of the semiclassical spectrum due to the spin-orbit and spin-spin interactions of electrons.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 151, No. 2, pp. 261–286, May, 2007. |
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Keywords: | semiclassical quantization spectral series complex WKB-Maslov method generalized action-angle variable generalized harmonic oscillator variable |
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