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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]

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]

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]

Simple analytical properties of ionization cross sections allow high-precision evaluations of contributions from integrals over continuum to sum rules for oscillator-strength moments and to the blackbody-radiation-induced shifts of atomic levels. The contributions from continuum and from infinite sums over discrete states are presented in terms of the cross section for the threshold photoionization. General properties of the indicated contributions are determined for bound states with small angular momenta (l ≼ 3) in hydrogen atoms. Asymptotic presentations for the contributions from continuum to the sums of oscillator-strength moments are proposed for highly excited Rydberg states. The estimate is given to the accuracy of determining the infinite sum over discrete states by a sum of a finite number of terms. [ABSTRACT FROM AUTHOR]

Rates of the blackbody radiation-induced excitation and decay were calculated for the S-, P-, D-series of the Rydberg states in sodium atoms with the Fues model potential method. Comparisons between three branches of the state depopulation mechanism (spontaneous decays, blakbody radiation-induced and excitations) were carried out. Simple analytical formulas were proposed for ratios of the blackbody radiation-induced decay and excitation rates to the spontaneous decay rate. [ABSTRACT FROM AUTHOR]

Quadratic Stark corrections to the wave functions, matrix elements, and probabilities of transitions between the singlet states 1 S 0 and 1 P 1 of helium atoms are calculated. The coefficients of the polynomials that depend on the effective principal quantum number of the upper level v f and that approximate the numerical values of the polarizabilities, the quadratic corrections to the wave functions, and the probabilities of transitions to highly excited Rydberg states with large v f are determined. The results of calculations testify that the probabilities of all σ transitions n i 1 S 0 → n f 1 P 1 and π transitions to the states with n f > n i /2 are decreased with increasing electric field strength, except for the transition 21 S 0 → 21 P 1, whose probability increases both for σ and for π transitions. [ABSTRACT FROM AUTHOR]

Perturbation theory for the wave function of a hydrogen-like atom in a homogeneous electric field of strength F makes it possible to obtain the Rayleigh-Schrödinger series with the coefficients of F[sup N] (N = 0, 1, 2, …) being linear combinations of the Sturm function, which represents the unperturbed state, with 8N² functions of the corresponding complete set with indices adjacent to the parabolic quantum number of the initial level. A method for recursive analytic calculation of the coefficients of the linear combination for any order N is developed. General expressions for corrections to the matrix elements and intensities of the radiation transitions between Stark sublevels are obtained. Analytic formulas and numerical values of the corrections up to the fourth order for the Lyman and Balmer series are presented. A comparison with the available data for transitions between the Stark components of Rydberg states is given. [ABSTRACT FROM AUTHOR]

Under the conditions of the total Paschen-Back effect the diamagnetic interaction determines the dependence of the intensity of the Zeeman components of atomic radiation lines on a magnetic field. The change in the matrix elements of the radiative transitions is due to the magnetically induced corrections to the wavefunctions of the initial and final states, whose contributions are of the same order of magnitude for the head lines of the optical series. For the high-frequency lines the positive corrections to the matrix element from the wavefunction of the upper level dominate. A magnetic field also induces dipole radiative transitions with selection rules for the orbital angular momentum Δl ≥ 3. The matrix elements of such transitions increase rapidly with the energy of the upper level, making possible efficient single-photon population of the dipole-inaccessible Rydberg states in moderate magnetic fields. [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]