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The measurements of microwave (μw) and radio-frequency (RF) radiation quantitative parameters may be based on the quantum–optical approach to determine the spectral characteristics of radiation transitions between the Rydberg states of atoms. Frequencies and matrix elements are calculated for dipole transitions between opposite-parity Rydberg states nL 1L and n′L±1 1L±1 (where n′= n,n±1,n±2) of the singlet series in the alkaline–earth–metal-like atoms of group IIb (Zn, Cd, Hg) and Yb. The matrix elements determine the shifts of Rydberg-state energy levels in the field of resonance μw or RF radiation, splitting the resonance of electromagnetically induced transparency (EIT) for intensely absorbed probe radiation. Numerical computations based on the single-electron quantum defect method (QDM) and the Fues’ model potential (FMP) approach with the use of the most reliable data from the current literature on quantum defect values are performed for frequencies and matrix elements of transitions between singlet Rydberg states of 1S0-, 1P1-, 1D2-, and 1F3-series in Zn, Cd, Hg, and Yb atoms. The calculated data are approximated by polynomials in the powers of the principal quantum numbers. The polynomial coefficients are determined with the use of a standard curve-fitting interpolation polynomial procedure for numerically calculated functions. These approximation expressions provide new possibilities for accurately evaluating the frequencies and matrix elements of dipole transitions between Rydberg states over a wide range of quantum numbers n >> 1, accompanied by the emission and absorption of μw and RF photons.

The measurements of microwave (μw) and radio-frequency (RF) radiation quantitative parameters may be based on the quantum–optical approach to determine the spectral characteristics of radiation transitions between the Rydberg states of atoms. Frequencies and matrix elements are calculated for dipole transitions between opposite-parity Rydberg states  n L   1 L  and  n ′ L ± 1   1 L ± 1  (where  n ′ =   n , n ± 1 , n ± 2 ) of the singlet series in the alkaline–earth–metal-like atoms of group IIb (Zn, Cd, Hg) and Yb. The matrix elements determine the shifts of Rydberg-state energy levels in the field of resonance μw or RF radiation, splitting the resonance of electromagnetically induced transparency (EIT) for intensely absorbed probe radiation. Numerical computations based on the single-electron quantum defect method (QDM) and the Fues' model potential (FMP) approach with the use of the most reliable data from the current literature on quantum defect values are performed for frequencies and matrix elements of transitions between singlet Rydberg states of 1S0-, 1P1-, 1D2-, and 1F3-series in Zn, Cd, Hg, and Yb atoms. The calculated data are approximated by polynomials in the powers of the principal quantum numbers. The polynomial coefficients are determined with the use of a standard curve-fitting interpolation polynomial procedure for numerically calculated functions. These approximation expressions provide new possibilities for accurately evaluating the frequencies and matrix elements of dipole transitions between Rydberg states over a wide range of quantum numbers n >> 1, accompanied by the emission and absorption of μw and RF photons. [ABSTRACT FROM AUTHOR]

Background of the electromagnetically induced transparency (EIT) resonance splitting by millimeter-wave radiation was investigated and so were calculated frequencies and amplitudes of radiation transitions between Rydberg states in alkaline earth atoms of IIA group elements, which are necessary for precise measurements of electric field magnitude at millimeter-wave (mmw) frequencies. Numerical values of the frequencies and matrix elements are approximated by asymptotic polynomials and tabulated for dipole transitions between singlet nS, nP, nD, and nF states with large values of principal quantum number n. [ABSTRACT FROM AUTHOR]

First evaluations of the blackbody-radiation (BBR)-induced shift and broadening of highly excited Rydberg states were based on the account of only the first term of the expansion for the Planck's distribution in powers of the ratio of the BBR-photon energy to the environmental thermal energy. The corresponding asymptotic expression for the shift is proportional to a sum rule for the oscillator strengths, which is identical for all states, independently of their principal and angular-momentum quantum numbers. The broadening appeared proportional to the sum of the oscillator-strength first moments, which is dependent on only the principal quantum number, being independent of the state's angular momentum. In this article, we demonstrate that the account of higher-order terms of the Planck's distribution expansion provides corrections revealing the dependence of asymptotic shift and broadening on the Rydberg-state principal and angular-momentum quantum numbers. The strongest corrections are observed for states with low angular momenta, in agreement with earlier performed numerical calculations. Sum rules for higher moments of oscillator strengths are used for evaluating the corrections for the BBR-induced broadening and shift of Rydberg-state energy levels in neutral atoms and ions of arbitrary nuclear charge Z. [ABSTRACT FROM AUTHOR]

Analytical expressions for spontaneous and induced by blackbody radiation energy shifts and widths of atomic circular states are derived. The features of asymptotic behavior of the total width and energy shifts for highly excited Rydberg circular states in the blackbody radiation field are described. Approximate equations are proposed for simple evaluations of energy characteristics and an absence of temperature-independent spontaneous contribution to the total energy width in a range of high temperatures and principal quantum numbers is demonstrated. [ABSTRACT FROM AUTHOR]

• The quantitative data for contribution of continuum to Rydberg-state energy-level shift and broadening is determined for group IIb ions • Asymptotic equations for the rates of the blackbody radiation (BBR) induced ionization and energy-level shifts are presented analytically in terms of Rydberg-states binding energy and photoionization cross section • Quantitative analysis is given for angular-momentum dependence of photoionization cross section of Rydberg-state atoms and ions • Analytic equations for amplitudes of bound-bound transitions from Rydberg states in the quantum defect approach are written in terms of generalized hypergeometric polynomials. General properties of n -dependence at the threshold and regularities of above-threshold ionization cross sections for states with high principal quantum numbers n and arbitrary angular momenta l are determined and used for evaluating the blackbody-radiation(BBR)-induced ionization broadening of n S, n P, n D and n F Rydberg-state energy levels of the group IIb ions Zn + , Cd + , Hg + at temperatures from T = 100 K to T = 3000 K. The contributions to the energy level shifts from transitions into continuum are also determined with the use of the ionization cross sections. The single-electron quantum defect method (QDM) was used, which appears rather precise and suitable for calculating the amplitudes of radiation transitions from Rydberg states, and specifically for summation of matrix-element-dependent terms over infinite number of discrete states. The dependencies on temperature and binding energy are determined and approximate analytic equations are proposed for simplified evaluations of the BBR-induced ionization broadening and shifts. Numerical parameters of approximate equations are tabulated for S, P, D and F Rydberg states of the group IIb ions. [ABSTRACT FROM AUTHOR]

On the basis of analytical expressions in the Fues model potential approach for the second-order Stark effect on single-electron Rydberg states in atoms and ions, general equations are derived for coefficients of polynomials in powers of the principal quantum number n in asymptotic presentations of static scalar and tensor dipole polarizabilities. The power dependence for polarizabilities of isolated Rydberg states |nl〉 at n ≫ 1 scales as n7, in contrast with that of polarizabilities for hydrogenic states, degenerate in the orbital quantum number l ⩽ n − 1, which scales as n6. This difference is demonstrated analytically in the asymptotic dependencies of the second-order matrix elements, determining the Stark shifts of the isolated and degenerate states. Analytical equations for polynomial coefficients use the data on quantum defects determined from the level energies of corresponding series of states. Numerical values of coefficients are presented for S-, P- and D-series of Rydberg states in neutral atoms of alkali-metal elements and helium in comparison with existing data of the literature. The analytical equations are also used for determining numerical values of coefficients in asymptotic polynomials for polarizabilities of Rydberg states in positive ions of alkaline-earth-metal elements. [ABSTRACT FROM AUTHOR]

The static hyperpolarizabilities, oscillator-strength-distribution moments S[?]3 and polarizabilities for S-, P- and D-series of helium and alkali atoms in Rydberg states with principal quantum numbers n between 30 and 70 were calculated in the single-electron Fues' model potential approach. On the basis of the numerical data, three-term polynomials in powers of the effective principal quantum number have been proposed for rapid and accurate evaluations of the indicated characteristics for atoms in arbitrary highly excited states. Numerical values of the fourth-order coefficients in the field-power-series expansions for energies of S1/2-, P1/2,3/2- and D3/2,5/2-states were determined in satisfactory agreement with available data of experiments and theory for rubidium atoms. The numerical data for sodium atoms were used for evaluating the second-order and fourth-order contributions to the electric field magnitude which can tune into double resonance the two-photon transitions between Stark sublevels of the nPJ- and (n+1){\rm P}_{J^{\prime}} - states via the (n + 1)S1/2-state. [ABSTRACT FROM AUTHOR]