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Optics and Spectroscopy

Radiative lifetime and photoionization cross-section for Rydberg states in alkali-metal atoms

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

Published Jul 1, 2011• 9 citations
Publisher

Abstract

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.

DOI
10.1134/s0030400x11070162

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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.
Approximation formulae in the form of quadratic polynomials in combination with Planck's distribution are proposed for the thermal ionization rates of Rydberg states in helium and alkali atoms. The coefficients of the polynomials were determined by fitting the data for the rates calculated by integrating the photoionization cross sections obtained in the model potential approach for the S, P and D states with the principal quantum number ranging from n = 10 to n = 45, in product with Planck's frequency distribution for the flux of blackbody photons at temperatures from 100 K to 2000 K. Tables of the polynomial coefficients are presented for the atoms indicated. The deviations of the data given by the approximation formula from that of the straightforward integration of cross sections is less than 7% for states with n from 20 up to 55 in the temperature range from 70 K to about 1000 K, not exceeding 40–50% for states with n = 20–100 in the temperature range extending up to 10 000 K, thus providing rather simple and accurate estimates for experiments and for practical applications.
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.
Rates of depopulation by blackbody radiation (BBR) and effective lifetimes of alkali-metal nSnSnS, nPnPnP, and nDnDnD Rydberg states have been calculated in a wide range of principal quantum numbers $n\ensuremath{\le}80$ at the ambient temperatures of 77, 300, and 600 K. Quasiclassical formulas were used to calculate the radial matrix elements of the dipole transitions from Rydberg states. Good agreement of our numerical results with the available theoretical and experimental data has been found. We have also obtained simple analytical formulas for estimates of effective lifetimes and BBR-induced depopulation rates, which well agree with the numerical data.
General properties are considered of three different terms in the imaginary part of the Stark effect on n S, n P and n D Rydberg states of alkali atoms in the field of environmental blackbody radiation with temperature in the ranges between T = 100 K and T = 3000 K. The terms are equal to the rates of decay P d nl ( T ), excitation P e nl ( T ) and ionization P ion nl ( T ) and may be separated and determined independently of each other. Corresponding numerical data calculated together with the rates of spontaneous decay P sp nl in the region of principal quantum numbers n from n = 10–1000 are transformed into fractional rates R d(e, ion) nl ( T ) = P d(e, ion) nl ( T )/ P nl sp . The asymptotic dependences on T and n display an essential difference between the fractional rates of ionization R ion nl ( T )∝ Tn 2/3 and the rates of decay (excitation) R d(e) nl ( T )∝ Tn , approximated by two different asymptotic formulae, one for R ion nl ( T ) and another one for R d(e) nl ( T ). The approximation polynomials with coefficients, determined from the curve-fitting polynomial interpolation procedure for three values of n between n = 15 and n = 150 at three values of temperature T = 100, 300, 1000 K, reproduce the calculated values with fractional departures below 2–3% in the regions from n = 10 to n = 1000 at temperatures from T = 100 K to T = 3000 K.
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