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Journal of Physics B Atomic Molecular and Optical Physics

Model-potential calculation of lifetimes of Rydberg states of alkali atoms

Xinghong He, Baiwen Li, Aiqiu Chen, Chengxiu Zhang

Published Feb 28, 1990• 61 citations
Publisher

Abstract

A comprehensive set of transition probabilities and radiative lifetimes of Rydberg states of alkali atoms (for Na, K, Cs, n<or=30; and for Rb, n<or=50) is obtained by using a simple, exactly solvable potential model for atoms. The results agree well with the available experimental values and other theoretical ones. Scaling relations for evaluating transition probabilities and lifetimes of high Rydberg states are also discussed. The well known (n*) -5 scaling law of the transition probabilities A n(inf) not=n(inf) / with n' approximately=n>>1 is generally valid; however, the authors also find deviations from this law for some d to p and f to d transitions for Rb. A third-power polynomial is found to be better than the currently used exponential scaling law in predicting the lifetimes of even higher excited states.

DOI
10.1088/0953-4075/23/4/001

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The analytical wavefunctions and oscillator strengths between highly excited states of alkali atoms over a wide range of principal quantum number n(10<or=n<or=40, and for Na, n<or=60) are calculated straightforwardly by using a simple, one-parameter, exactly soluble model for atoms. The valence electron of the atom is assumed to be in a potential of the following form: V(r)=-e/r1+ delta + alpha '/r+ gamma '+ beta '/(r+ gamma ') 2 where alpha ', beta ', gamma ' are the parameters to be determined and delta is the ionicity. Analytical solutions can be obtained by solving the Schrodinger equation containing V(r). The parameters in the potential and the wavefunction, which are dependent on the atomic states, can be expressed in terms of a single parameter, the quantum defect. The wavefunctions of the alkali atoms were obtained, and their general behaviour and the number of nodes agree with Hartree-Fock-Slater theory. This model is well suited for studying the behaviour of atoms that are mainly dependent of the outer region of high Rydberg states.

Journal of Physics B Atomic Molecular and Optical Physics•Jun 28, 1988•4 citations
A comprehensive set of transition probabilities and radiative lifetimes of Rydberg states of alkali atoms (for Na, K, Cs, n<or=30; and for Rb, n<or=50) is obtained by using a simple, exactly solvable potential model for atoms. The results agree well with the available experimental values and other theoretical ones. Scaling relations for evaluating transition probabilities and lifetimes of high Rydberg states are also discussed. The well known (n*) -5 scaling law of the transition probabilities A n(inf) not=n(inf) / with n' approximately=n>>1 is generally valid; however, the authors also find deviations from this law for some d to p and f to d transitions for Rb. A third-power polynomial is found to be better than the currently used exponential scaling law in predicting the lifetimes of even higher excited states.
We report a comprehensive set of calculations of the lifetimes of Rydberg states in alkali-metal atoms, using realistic potentials to represent the atomic core. The effects due to core polarizability, spin-orbit interaction, and blackbody radiation are explicitly included. A complete cross reference listing of all available experimental lifetimes is also attempted. The results compare well with experiment for all principal quantum numbers nnn examined and should provide guidance for future experimental investigations. The relation of the present approach to other works is discussed.
General properties were determined and asymptotic approximation formulas for probabilities of spontaneous decay and photoionization cross-sections were derived on the basis of numerically calculated amplitudes of bound-bound and bound-free radiation transitions from Rydberg nS -, nP - and nD -states of alkali atoms with high principal quantum numbers, up to n = 1000. The departure of data from the asymptotic formulas for states with principal quantum numbers in the range between n = 10 and n = 2000 from originally calculated data does not exceed 0.1–1%, and may be useful for estimations of natural radiation widths for arbitrary high Rydberg levels.
General properties were determined and asymptotic approximation formulas for probabilities of spontaneous decay and photoionization crosssections were derived on the basis of numerically calculated amplitudes of boundbound and boundfree radiation transitions from Rydberg nS�, nPand nDstates of alkali atoms with high principal quantum numbers, up to n = 1000. The departure of data from the asymptotic formulas for states with principal quantum numbers in the range between n = 10 and n = 2000 from originally calculated data does not exceed 0.1-1%, and may be useful for estimations of natural radiation widths for arbitrary high Rydberg levels.
The analytical wavefunctions and oscillator strengths between highly excited states of alkali atoms over a wide range of principal quantum number n(10<or=n<or=40, and for Na, n<or=60) are calculated straightforwardly by using a simple, one-parameter, exactly soluble model for atoms. The valence electron of the atom is assumed to be in a potential of the following form: V(r)=-e/r1+ delta + alpha '/r+ gamma '+ beta '/(r+ gamma ') 2 where alpha ', beta ', gamma ' are the parameters to be determined and delta is the ionicity. Analytical solutions can be obtained by solving the Schrodinger equation containing V(r). The parameters in the potential and the wavefunction, which are dependent on the atomic states, can be expressed in terms of a single parameter, the quantum defect. The wavefunctions of the alkali atoms were obtained, and their general behaviour and the number of nodes agree with Hartree-Fock-Slater theory. This model is well suited for studying the behaviour of atoms that are mainly dependent of the outer region of high Rydberg states.