Oscillator Strengths, Polarizabilities, and Hyperpolarizabilities of Rydberg States

WKB-approximation in the Quantum Defect Method (WKB-QDM-approximation) - providing simple theoretical calculations of spectroscopic and polarization characteristics in Rydberg-state atoms and ions - is systematically presented in this paper. The analytical expressions for the dipole and quadrupole matrix elements between the Rydberg states are derived. The table of parameters for numerical calculations with the help of these formulas and the method for determining these parameters in some limiting and particular cases are presented. The method is used in calculating the polarizabilities a alpha(n/m) and hyperpolarizabilities gamma(n/m) for highly excited atoms. Simple formulas for calculating the irreducible parts of tensors a alpha(n/m) (omega) and gamma(n/m) (omega) in dc and resonant fields are derived. In the high frequency limit, we present the asymptotic expansion in power series of parameter 1/omega for a alpha(n/m). The analytical expressions are given both for the coefficients of the asymptotic series and for the sums of the generalized radial oscillator strengths used in their derivation. The application of the results, obtained for atoms, to the description of properties of Rydberg states in two-atomic dipole molecules is also discussed.