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This article is cited in 2 scientific papers (total in 2 papers)
Semiclassical Spectral Series of a Helium-like Atom in a Magnetic Field
V. V. Belov, V. A. Maksimov Moscow State Institute of Electronics and Mathematics
Abstract:
We apply the complex WKB method (the Maslov complex germ theory) to the model of two electrons in a field with a fixed center. We construct semiclassical spectral series of the Pauli operator eigenvalues in the external magnetic field with the spin-orbital and spin-spin interactions and the quadrupole moment of the nucleus taken into account. These series correspond to a new type of closed phase trajectories, the relative equilibrium positions of the corresponding classical nonintegrable system. Explicit effective formulas are derived for the fine (Zeeman effect) and the hyperfine splitting of semiclassical energy levels of a helium-like ion with an arbitrary nucleus charge $Z$ in the entire range of the magnetic field magnitude, including the extreme cases of weak and ultrastrong fields.
Received: 05.10.2000
Citation:
V. V. Belov, V. A. Maksimov, “Semiclassical Spectral Series of a Helium-like Atom in a Magnetic Field”, TMF, 126:3 (2001), 455–474; Theoret. and Math. Phys., 126:3 (2001), 378–395
Linking options:
https://www.mathnet.ru/eng/tmf441https://doi.org/10.4213/tmf441 https://www.mathnet.ru/eng/tmf/v126/i3/p455
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Abstract page: | 426 | Full-text PDF : | 195 | References: | 69 | First page: | 1 |
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