The empirical regularities in the variation of the radiative lifetimes τ k of excited states of atoms are reviewed. A quasiclassical theory of radiation damping processes is constructed. The formalism of quantization of the natural width A k = τ k −1 of the excited states of atoms and ions is presented. The question of how to describe the serial dependences for a perturbed series is investigated. It is demonstrated that the radiation emission of atomic systems is sharply reduced when the classical factors in the radiative processes are suppressed. Schemes are proposed for extrapolating lifetimes from the lower terms of a series to the upper Rydberg states, right up to the continuum. Recommended values of τ k for group I, II, and VIII atoms are given in a form that is convenient for inclusion in a computerized data base.
The empirical regularities in the variation of the radiative lifetimes τ k of excited states of atoms are reviewed. A quasiclassical theory of radiation damping processes is constructed. The formalism of quantization of the natural width A k = τ k −1 of the excited states of atoms and ions is presented. The question of how to describe the serial dependences for a perturbed series is investigated. It is demonstrated that the radiation emission of atomic systems is sharply reduced when the classical factors in the radiative processes are suppressed. Schemes are proposed for extrapolating lifetimes from the lower terms of a series to the upper Rydberg states, right up to the continuum. Recommended values of τ k for group I, II, and VIII atoms are given in a form that is convenient for inclusion in a computerized data base.
We present the results of relativistic calculation of the radiative transition probabilities and excited states lifetimes for a heavy Rydberg atomic systems in a black-body (thermal) radiation field on example of the rubidium. As theoretical approach we apply the combined generalized relativistic energy approach and relativistic many-body perturbation theory with ab initio Dirac zeroth approximation. There are obtained the calculational data for the radiative transition probabilities and excited states lifetimes, in particular, the rubidium atom in the Rydberg states with principal quantum number n=10-100. It is carried out the comparison of obtained theoretical data on the effective lifetime for the group of Rydberg nS states of the rubidium atom at a temperature of T = 300K with experimental data as well as data of alternative theoretical calculation based on the improved quasiclassical model. It is shown that the accuracy of the theoretical data on the radiative transition probabilities and excited states lifetimes is provided by a correctness of the corresponding relativistic wave functions and accounting for the exchange-correlation effects.
So far we have treated the energy levels of an atomic system as stable states with infinite lifetimes. The presence of an electromagnetic field changes this picture. Absorption of photons will excite atoms and ions to higher levels, while stimulated emission will make excited ones decay. Einstein (1917) showed, using purely statistical arguments, that an excited ion will decay through spontaneous emission in the absence of an electromagnetic field. This process can also be derived by using a rigorous quantum electrodynamic treatment, where the field is quantized. In this chapter we start by discussing transitions between atomic levels in a general sense, postulating the operators responsible for the decay. After the first few sections we will concentrate on the most important few multipoles or terms in the expansion of the electromagnetic field. We will introduce a number of different properties describing the transition, and eventually arrive at the measurable transition rate and, directly linked to it, the lifetime of an excited state. We will start, however, with the most basic property, the component strength. Our aim is to arrive at computationally useful expressions as soon as possible. For a more thorough treatment of the theory of radiative transitions we refer to the book by Sobelman (1972). For a brief review of the many factors affecting spectra of atoms, see Martin and Wiese (1996) .
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 .
The radiative lifetimes τrad of the highly excited 4f7/2136s1/2(4)np3/2[11/2](n=21−31) Rydberg Tm states have been measured with the method of multistep laser excitation and electric field ionization. The lifetime values have been obtained with an accuracy of better than 15%. The influence of blackbody radiation on the states with n ≥ 27 has been observed. The experimental results are in good agreement with our previously calculated values obtained by relativistic perturbation theory with a zero-order model approximation. It has been shown that the τrad-versus-n* dependence (n* is the effective principal quantum number) is best described by the relation τrad = 0.0022.(n*)2.46 (μsec). This property may be attributed to the strongly expressed nonhydrogenlike behavior of the investigated states, which is caused by the essentially non-Coulombic core potential acting on the Rydberg electron.
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.
We examine the exponential decay law for an excited quantum system in the case where the state amplitude has a “memory,” that is, where the rate at which the amplitude is decaying at a particular time depends to some extent on values of the amplitude at previous times. For a particular choice of memory, characterized by a memory time τ, the amplitude obeys the differential equation of a damped harmonic oscillator. When τ is greater than a certain critical memory time τc, comparable to the natural lifetime of the state, the amplitude becomes an exponentially damped oscillation in time. When τ is less than τc, the decay is nearly exponential with a decay rate somewhat greater than that calculated from standard theory. By comparing theory with experiment, we can place an upper limit on the memory time for the radiative decay of atoms.