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Journal of Physics B Atomic and Molecular Physics

Minima in the emission oscillator strengths of alkali Rydberg states

Constantine E. Theodosiou

Published Jan 14, 1980• 26 citations
Publisher

Abstract

Minima have been found in the calculated emission oscillator strengths of excited Rydberg states of the alkali atoms. These minima appear only in the D states of potassium and F states of caesium. Their origin and implications are discussed.
DOI
10.1088/0022-3700/13/1/001

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The structure of the Cooper minima in the transition probabilities and photoionization cross-sections for low-excited and Rydberg nS, nP, nD and nF states of alkali-metal atoms has been studied using a Coulomb approximation and a quasiclassical model. The range of applicability of the quasiclassical model has been defined from comparison with available experimental and theoretical data on dipole moments, oscillator strengths, and photoionization cross-sections. A new Cooper minimum for transitions between rubidium Rydberg states has been found.
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.
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.
Recent absorption measurements of the self-broadening of Rb principal series lines [C. H. Greene, E. L. Hamilton, H. Crowell, C. Vadla, and K. Niemax, Phys. Rev. Lett. 97, 233002 (2006)] verified the existence of minima in highly excited long-range potentials of Rb2{\text{Rb}}_{2}Rb2​ which were predicted theoretically as bound Rydberg molecule [C. H. Greene, A. S. Dickinson, and H. R. Sadeghpour, Phys. Rev. Lett. 85, 2458 (2000)]. The present paper reports on the extension of these experimental studies to principal series lines of K broadened by K as well as Cs broadened by Cs. In addition, the broadening of some lower members of the K, Rb, and Cs principal line series due to heteroatomic interactions was investigated. The analysis of the measured satellite structures in the quasistatic line wings and their comparison to the previously published analogous data for ${\text{Rb}}^{\ensuremath{\ast}}+\text{Rb}$ system lead to the conclusion that one can expect existence of potential minima in homo- and heteroatomic alkali-metal ${A}^{\ensuremath{\ast}}+B$ systems in a wide range of principal quantum numbers, starting with K, Rb, and Cs excited to the third resonance states. The positions and strengths of the satellite structures indicate that the potential minima are due to scattering of the valence electron by ground-state perturbers.
The authors describe practical methods for calculating the Stark structure of Rydberg states of the alkali metals based on diagnolization of the energy matrix. A survey of Stark structures is presented for all of the alkali metals in the vicinity of n=15n=15n=15. Topics discussed include general methods for evaluating radial matrix elements, the treatment of fine structure, oscillator-strength distribution, scaling laws, the structure of a level anticrossing, and sources of error. Experimental Stark maps are compared with calculated results for lithium and cesium. Experimental studies of the oscillator-strength distribution within a Stark manifold and the structure of a level anticrossing are also presented.