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.
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.
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 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.
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.
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.
Once created, an ensemble of atoms in their identical Rydberg states immediately experiences significant variations of its structure and corresponding properties. The variation is caused by the inevitable radiation transitions of highly excited states into different states of higher or lower energies. In particular, the change of a uniform definite-state population for another kind of population of different states will change the long-range interaction between atoms, even transforming the van der Waals interaction, Δ E vdW =− C 6 / R 6 , into dipole–dipole interaction with a different dependence on the interatomic distance, Δ E d−d =− C 3 / R 3 . In this paper, the most important—dipole radiation transitions from Rydberg states to higher- or lower-energy | n ′ 1 P 1 ⟩ states—are considered, both spontaneous and induced by the blackbody radiation (BBR) of the environment. The total transition probability rate, which is usually determined as the natural width, equals the imaginary part of the Rydberg-state energy Γ n S /2=−Im E n S . The probabilities of the | n ′ 1 P 1 ⟩-state populations W n S ( n ′ P, T ), which depend on the BBR temperature T , on the lifetime scale are also rather important optical characteristics of the ensemble of the Rydberg-state atoms. The value of W n S ( n ′ P, T ) is determined as the ratio of a particular transition probability rate Γ n S→ n ′ P sp +Γ n S→ n ′ P BBR ( T ) to the sum of all possible radiative transition rates, which include spontaneous and BBR-induced rates, where the latter depend on the temperature T of the environment. Numerical values of W n S ( n ′ P, T ) are calculated and presented in wide regions of the principal quantum numbers n , n ′ , and BBR temperatures T .
Rates of depopulation by blackbody radiation (BBR) and effective lifetimes of alkali-metal nS, nP, and nD 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.