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Journal of Physics B Atomic Molecular and Optical Physics

Thermal photoionization of Rydberg states in helium and alkali-metal atoms

Igor L. Glukhov, Vitalii D Ovsiannikov

Published Mar 20, 2009• 16 citations
Publisher

Abstract

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.

DOI
10.1088/0953-4075/42/7/075001

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Journal of Physics B Atomic Molecular and Optical Physics•Jun 1, 2010•30 citations
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.
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.
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.
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.
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
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.