The detailed description of electron terms in the field of two stationary Coulomb centers of charges Z and Z ' separated by a distance R is one of the most fundamental problems in quantum mechanics. When the charges Z and Z ' approach each other and share the only one electron that they have, they form a quasimolecule. Such quasimolecules are encountered in various kinds of plasmas and play an important role in theoretical and experimental studies of charge exchange. When the electron is in a highly-excited state, it is a one-electron Rydberg quasimolecule (OERQ). There are extensive analytical studies of the OERQ by the methods of classical mechanics (which are appropriate for Rydberg states). In one of our previous papers we studied the OERQ subjected to a laser field in the situation where the laser frequency was much smaller than the highest frequency of the unperturbed system. In the present paper we consider the situation where the OERQ is subjected to a laser field whose frequency is much greater than the highest frequency of the unperturbed system. For obtaining analytical results we use a generalization of the method of effective potentials. We show that as the amplitude of the laser field increases, in the case of the linearly-polarized laser field, the structure of the energy terms becomes more complex. Moreover the number of the energy terms increases in this case. We also calculated analytically the shift of the radiation frequency of OERQ caused by the laser field. As the amplitude of the laser field increases, so does the shift. The radiation frequency is shifted to the blue in the case of the linearly-polarized laser field, and to the red in the case of the circularly-polarized laser field. For a known amplitude of the laser field, by measuring the relative shift of the radiation frequency it should be possible to determine experimentally the distance of the orbital plane of the electron from the nucleus of the smaller nuclear charge.
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