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arXiv:1207.3626

Cooper minima in the transitions from low-excited and Rydberg states of alkali-metal atoms

Ilya I. Beterov, Christopher Mansell, Elena A. Yakshina, I. I. Ryabtsev, Denis B. Tretyakov, Vasily M. Entin, C. MacCormick, Michał Piotrowicz, Anna Kowalczyk, S. Bergamini

Published Jul 16, 2012• 1 citation
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Abstract

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.

DOI
10.48550/arxiv.1207.3626

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Journal of Experimental and Theoretical Physics•Jul 1, 2008•10 citations
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.
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.
Abstract We present calculations of the photoionization (PI) cross sections of rubidium and cesium Rydberg atoms for light with wavelengths ranging from the infrared to the ultraviolet, using model potentials from Marinescu et al (1994 Phys. Rev. A 49 982). The origins of pronounced PI minima are identified by investigating the free-electron wavefunctions. These include broad PI minima in the nS to ϵP PI channels of both Rb and Cs, with free-electron energy ϵ , which are identified as Cooper minima. Much narrower PI minima in the nD to ϵF channels are due to shape resonances of the free-electron states. We describe possible experimental procedures for measuring the PI minima, and we discuss their implications in fundamental atomic physics as well as in practical applications. Measurements of PI cross sections of Rydberg atoms may serve as a sensitive probe for many-electron interactions of the Rydberg electron in the atomic core region.
The radial electric dipole moments of bound-bound, bound-free, and free-free transitions of high-lying (n>15)(n>15)(n>15) Rydberg states and low-lying continuum states $(\ensuremath{\epsilon}<400$ ${\mathrm{cm}}^{\ensuremath{-}1})$ are calculated for hydrogen and the alkali-metal atoms. All dipole matrix elements for the transitions between low-lll (s(s(s, ppp, ddd, and f)f)f) states of H, Li, and Rb are presented. Results of similar calculations for the other alkali-metal atoms (Na, K, and Cs) are summarized. These numerical results, using quantum defect theory, are compared with semiclassical approximations. The dipole matrix elements cross zero at certain combinations of initial and final states. The matrix elements at these so-called Cooper minima in Li, K, Rb, and Cs are presented in detail.
We have studied ionization of alkali-metal Rydberg atoms by blackbody radiation (BBR). The results of theoretical calculations of ionization rates of Li, Na, K, Rb and Cs Rydberg atoms are presented. The calculations have been performed for nS, nP and nD states for principal quantum numbers n=8-65 at ambient temperatures of 77, 300 and 600 K. The calculations take into account the contributions of BBR-induced redistribution of population between Rydberg states prior to photoionization and field ionization by extraction electric field pulses. The obtained results show that these phenomena affect both the magnitude of the measured ionization rates and their n-dependence. A Cooper minimum for BBR-induced transitions between bound Rydberg states of Li has been found. The calculated ionization rates are compared with our earlier measurements of BBR-induced ionization rates of Na nS and nD Rydberg states with n=8-20 at 300 K. A good agreement for all states except nS with n> 15 is observed. Useful analytical formulas for quick estimates of BBR ionization rates of Rydberg atoms are presented. Application of BBR-induced ionization signal to
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 results of theoretical calculations of the blackbody ionization rates of lithium, potassium, and cesium atoms residing in Rydberg states are presented. The calculations are performed for nS , nP , and nD states in a wide range of principal quantum numbers, n = 8−65, for blackbody radiation temperatures T = 77, 300, and 600 K. The calculations are performed using the known quasi-classical formulas for the photoionization cross sections and for the radial matrix elements of transitions in the discrete spectrum. The effect of the blackbody-radiation-induced population redistribution between Rydberg states on the blackbody ionization rates measured under laboratory conditions is quantitatively analyzed. Simple analytical formulas that approximate the numerical results and that can be used to estimate the blackbody ionization rates of Rydberg atoms are presented. For the S series of lithium, the rate of population of high-lying Rydberg levels by blackbody radiation is found to anomalously behave as a function of n . This anomaly is similar to the occurrence of the Cooper minimum in the discrete spectrum.