Vol. 14, issue 09, article # 12

pdf Kruglova T. V., Bykov A. D., Naumenko O. V. Application of generalized Euler transformation to summation of Dunham series for diatomic molecules. // Atmospheric and oceanic optics. 2001. V. 14. No. 09. P. 748-752.
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The well known generalized Euler transformation of divergent series is applied to summation of Dunham series for diatomic molecules. The equation for the energy of a Kratzer oscillator, which is an exactly solvable problem of quantum mechanics, is used as an approximation function that is needed for series transformation. The transformed series consists of a main part, which is asymptotically correct for high values of vibrational and rotational quantum numbers, and an additional part depending on new variables, which are less than unity for all values of quantum numbers. New representation of the Dunham series may prove useful for calculation of highly excited rotational-vibrational states of diatomic molecules, for which only several first coefficients of the perturbation series are known.