Semiempirical study of perturbations of the Landé g factors of the electronic-vibrational-rotational levels of hydrogen: I. Theory
Tóm tắt
Theoretical analysis of perturbations of the Landé 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.
Tài liệu tham khảo
B. P. Lavrov and S. A. Astashkevich, Opt. Spektrosk. 86, 946 (1999) [Opt. Spectrosc. 86, 845 (1999)].
S. A. Astashkevich and B. P. Lavrov, Opt. Spektrosk. 92, 988 (2002) [Opt. Spectrosc. 92, 818 (2002)].
M. Mizushima, The Theory of Rotating Diatomic Molecules (Wiley, New York, 1975).
H. Lefebvre-Brion and R. W. Field, Perturbations in the Spectra of Diatomic Molecules (Academic, New York, 1986).
F. H. Crawford, Rev. Mod. Phys. 6, 90 (1934).
I. Kovacs, Rotational Structure in the Spectra of Diatomic Molecules (Akademiai Kiado, Budapest, 1969).
R. Jost, M. A. Marechal, and M. Lombardi, Phys. Rev. A 5, 732 (1972).
R. Jost, M. A. Marechal, and M. Lombardi, Phys. Rev. A 5, 740 (1972).
J. C. Lehmann, Rep. Prog. Phys. 41, 1609 (1978).
R. S. Freund and T. A. Miller, J. Chem. Phys. 56, 2211 c(1972).
S. V. Berdyugina and S. K. Solanki, Astron. Astrophys. 385, 701 (2002).
G. H. Dieke, S. P. Gunningham, and F. T. Byrne, Phys. Rev. 92, 81 (1953).
C. W. T. Chien, F. W. Dalby, and J. van der Linde, Can. J. Phys. 56, 827 (1978).
R. Jost, M. Lombardi, R. S. Freund, and T. A. Miller, Mol. Phys. 37, 1605 (1979).
T. A. Miller and R. S. Freund, J. Chem. Phys. 59, 4093 (1973).
R. S. Freund and T. A. Miller, J. Chem. Phys. 60, 4900 (1974).
R. S. Freund and T. A. Miller, J. Chem. Phys. 61, 2160 (1974).
R. Jost and M. Lombardi, Phys. Rev. Lett. 33 (2), 53 (1974).
T. A. Miller and R. S. Freund, J. Chem. Phys. 62, 2240 (1975).
T. A. Miller and R. S. Freund, J. Chem. Phys. 63, 256 (1975).
T. A. Miller and R. S. Freund, J. Mol. Spectrosc. 63, 193 (1976).
T. A. Miller, R. S. Freund, and B. R. Zegarski, J. Chem. Phys. 64, 1842 (1976).
T. A. Miller, R. S. Freund, and B. R. Zegarski, J. Chem Phys. 64, 4069 (1976).
R. S. Freund, T. A. Miller, R. Jost, and M. Lombardi, J. Chem. Phys. 68, 1683 (1978).
T. A. Miller, B. R. Zegarski, and R. S. Freund, J. Mol. Spectrosc. 69, 199 (1978).
J. van der Linde and F. W. Dalby, Can. J. Phys. 50 (3), 287 (1972).
R. Jost, Chem. Phys. Lett. 17, 393 (1972).
P. Quadrelli, K. Dressler, and L. Wolniewicz, J. Chem. Phys. 92, 7461 (1990).
S. O. Adamson, E. A. Pazyuk, N. E. Kuz’menko, et al., Phys. Rev. A 61, 052501 (2000).
E. A. Pazyuk, V. I. Pupyshev, A. V. Stolyarov, and T. Kiyoshima, J. Chem. Phys. 116, 6618 (2002).
S. A. Astashkevich, B. P. Lavrov, L. L. Pozdeev, and V. I. Ustimov, Opt. Spektrosk. 70, 285 (1991) [Opt. Spectrosc. 70, 164 (1991)].
R. Jost, M. Lombardi, J. Derouard, et al., Chem. Phys. Lett. 37, 507 (1976).
B. P. Lavrov, M. V. Tyutchev, and V. I. Ustimov, Opt. Spektrosk. 54, 4 (1983) [Opt. Spectrosc. 54, 2 (1983)].
B. P. Lavrov and V. I. Ustimov, Acta Phys. Hungy 67 (1–2), 3 (1990).
S. A. Astashkevich and B. P. Lavrov, Opt. Spektrosk. 76, 1994) [Opt. Spectrosc. 76, 30 (1994)].
S. A. Astashkevich, Opt. Spektrosk. 93, 546 (2002) [Opt.Spectrosc. 93, 501 (2002)].
L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 3: Quantum Mechanics: Non-Relativistic Theory, 4th ed. (Nauka, Moscow, 1989; Pergamon, New York, 1977).
W. Kolos and L. Wolniewicz, Rev. Mod. Phys. 35, 473 (1963).
D. A. Varshalovich, A. N. Moskalev, and V. K. Khersonski i, Quantum Theory of Angular Momentum (Nauka, Leningrad, 1975; World Sci., Singapore, 1988).
J. S. Millis, Phys. Rev. 38, 1148 (1931).
J. N. Van Vleck, Phys. Rev. 33, 467 (1929).
S. A. Astashkevich and B. P. Lavrov, Opt. Spektrosk. 76, 42 (1994) [Opt. Spectrosc. 76, 38 (1994)].
E. Reinhold, W. Hogervorst, and W. Ubachs, J. Chem. Phys. 112, 10754 (2000).
L. Li, Sh. Kasahara, Md. H. Kabir, et al., J. Chem. Phys. 114, 10805 (2001).