Semiempirical Study of Perturbations of the Landé g Factors of the Electronic-Vibrational-Rotational Levels of Hydrogen: I. Theory

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Abstract

Theoretical analysis of perturbations of the Lande g factors of the electronic-vibrational-rotational levels of a diatomic molecule is performed for the case of interactions between electronic states whose number is arbitrary finite and that are not limited by the smallness of the parameter describing these interactions, with regard for the interaction of rovibrational states with an arbitrary finite number of vibrational-rotational levels of individual perturbing electronic states. The spin-multiplet interaction between rovibrational states was disregarded. As a result of general consideration, formulas are obtained for the g factors of rovibrational levels for the following cases: (i) mutual perturbation of a pair of levels; (ii) an nl complex of terms; and (iii) the interaction between an arbitrary number of vibrational-rotational levels of electronic states (whose number is also not limited) considered in the first order of the perturbation theory. The formulas obtained are given in the form of dependences on differences in observed (perturbed) values of rovibrational terms and matrix elements of vibrational wave functions dependent on the internuclear distance, which, in turn, are matrix elements of the electron wave functions of different operators that take into account the interaction between the electrons and nuclei of a molecule. The possibilities of using the obtained expressions in semiempirical study of perturbations and of determining the absolute dependences of the g factors of rovibrational levels of the electronic states of diatomic molecules (in particular, the hydrogen molecule) on the vibrational and rotational quantum numbers are analyzed.

Original languageEnglish
Pages (from-to)25-34
Number of pages10
JournalOptics and Spectroscopy (English translation of Optika i Spektroskopiya)
Volume96
Issue number1
DOIs
StatePublished - 1 Jan 2004

Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Atomic and Molecular Physics, and Optics

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