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Journal of Physics B Atomic Molecular and Optical Physics

Blackbody-radiation-induced shifts and the broadening of Rydberg states in the ions of group IIa elements

Igor L. Glukhov, E A Nikitina, Vitalii D Ovsiannikov

Published Jan 21, 2016• 9 citations
Publisher

Abstract

Abstract The rates of blackbody-radiation(BBR)-induced transitions from excited n S, n P, n D and n F states into bound states and into continua of the group IIa ions Ca + , Sr + , Ba + at temperatures from T = 100 K to T = 3000 K are calculated in consecutive comparison of the Fues model potential (FMP) with quantum defect method (QDM). The temperature and binding-energy dependencies are determined and analytical asymptotic approximations are proposed for evaluating numerically the contributions of the bound states and continua to the Rydberg-level widths and positions. The general properties of n -dependence at the threshold and regularities of above-threshold ionization cross sections for states with high principal quantum numbers n are used for determining the rates of BBR-induced ionization. Relations are determined between deviations from general regularities for the sum rules of oscillator- strengths and specific non-local dependence of the FMP on optical-electron angular momentum. The QDM appears preferable in comparison with the FMP approach for calculating the amplitudes of radiation transitions from Rydberg states, and specifically sums of matrix-element-dependent terms over very large (in particular, infinite) numbers of discrete states. The fractional (related to natural decay) rates of BBR-induced decay into lower bound states, excitation into upper bound states and ionization transitions into the continuum are presented asymptotically with parameters tabulated for the S, P, D and F Rydberg states.

DOI
10.1088/0953-4075/49/3/035003

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Abstract The rates of blackbody-radiation(BBR)-induced transitions from excited n S, n P, n D and n F states into bound states and into continua of the group IIa ions Ca + , Sr + , Ba + at temperatures from T = 100 K to T = 3000 K are calculated in consecutive comparison of the Fues model potential (FMP) with quantum defect method (QDM). The temperature and binding-energy dependencies are determined and analytical asymptotic approximations are proposed for evaluating numerically the contributions of the bound states and continua to the Rydberg-level widths and positions. The general properties of n -dependence at the threshold and regularities of above-threshold ionization cross sections for states with high principal quantum numbers n are used for determining the rates of BBR-induced ionization. Relations are determined between deviations from general regularities for the sum rules of oscillator- strengths and specific non-local dependence of the FMP on optical-electron angular momentum. The QDM appears preferable in comparison with the FMP approach for calculating the amplitudes of radiation transitions from Rydberg states, and specifically sums of matrix-element-dependent terms over very large (in particular, infinite) numbers of discrete states. The fractional (related to natural decay) rates of BBR-induced decay into lower bound states, excitation into upper bound states and ionization transitions into the continuum are presented asymptotically with parameters tabulated for the S, P, D and F Rydberg states.
Abstract We present the derivation of simple analytical expressions for calculating the widths of Rydberg states with small orbital angular momenta in Zn+, Cd+, Hg+ ions of group IIb of the periodic system of elements induced by blackbody radiation (BBR) at ambient temperatures from 100 to 3000 K. The probabilities of radiative transitions from excited nS, nP, nD and nF states to all dipole-accessible states of ions are calculated. The wave functions of the quantum defect (QD) method for the initial and final states of the Rydberg electron are used to calculate the amplitudes of transitions between bound states. The dependences of the probabilities of induced decays and excitations on the BBR temperature, the principal and orbital quantum numbers of the Rydberg ion are determined. Analytical expressions are derived for numerical estimates of the contributions of the probabilities of thermally induced decays and excitations to the width of the Rydberg energy level. The numerical values of the coefficients of interpolation polynomials representing asymptotic expansions in powers of the principal quantum number n for the relative probabilities of decays and excitations of Rydberg states with large values of n and small orbital angular momenta l = 0, 1, 2, 3 are calculated.
New features of the blackbody-induced radiation processes on Rydberg atoms were discovered on the basis of numerical data for the blackbody-induced decay P d nl ( T ), excitation P e nl ( T ) and ionization P ion nl ( T ) rates of n S, n P and n D Rydberg states calculated together with the spontaneous decay rates P sp nl in neutral hydrogen, and singlet and triplet helium atoms for some values of the principal quantum number n from 10 to 500 at temperatures from T = 100 K to 2000 K. The fractional rates R d ( e , ion) nl ( T ) = P nl d ( e , ion) ( T )/ P sp nl equal to the ratio of the induced decay (excitation, ionization) rates to the rate of spontaneous decay were determined as functions of T and n in every series of states with a given angular momentum l = 0, 1, 2. The calculated data reveal an essential difference between the asymptotic dependence of the ionization rate P ion nl ( T ) and the rates of decay and excitation P d ( e ) nl ( T )∝ T / n 2 . The departures appear in each Rydberg series for n > 100 and introduce appreciable corrections to the formula of Cooke and Gallagher. Two different approximation formulae are proposed on the basis of the numerical data, one for R d ( e ) nl ( T ) and another one for R ion nl ( T ), which reproduce the calculated values in wide ranges of principal quantum number from n = 10 to 1000 and temperatures between T = 100 K and T = 2000 K with an accuracy of 2% or better. Modified Fues' model potential approach was used for calculating matrix elements of bound–bound and bound–free radiation transitions in helium.
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
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 n S, n P and n D 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 n S and n D Rydberg states with n =8–20 at 300 K. Good agreement for all states except n S with n >15 is observed. Useful analytical formulae for quick estimates of BBR ionization rates of Rydberg atoms are presented. Application of BBR-induced ionization signal to measurements of collisional ionization rates is demonstrated.
The effect of a thermal field on Rydberg states of the nS-, nP- and nD-series in beryllium ions Be+ is investigated. The blackbody radiation-induced depopulation rates caused by transitions to upper (excitations) and lower (decays) bound levels and to the continuum (ionization) are calculated in wide ranges of the principal quantum numbers n and ambient temperatures. Simple and reliable approximations for natural lifetimes and stimulated by thermal radiation depopulation rate components are proposed. The blackbody-radiation-induced shifts of Rydberg levels are also calculated and their qualitative and quantitative properties are analysed.
Abstract 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 .