Quasiclassical calculations of blackbody-radiation-induced depopulation rates and effective lifetimes of Rydberg $nS$, $nP$, and $nD$ alkali-metal atoms with $n\le 80$

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 $n\le 80$ 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.

Figure 1

(Color online) The rates of spontaneous and BBR-induced transitions from the rubidium $30S$ state to $n^{\prime }P$ states.

Figure 2

(Color online) (a) Comparison of the numerically calculated BBR-induced depopulation rates of (a) Na $n{S}_{1/2}$, (b) Na $n{P}_{1/2}$, (c) Na $n{D}_{3/2}$, (d) Rb $n{S}_{1/2}$, (e) Rb $n{P}_{1/2}$, and (f) Rb $n{D}_{3/2}$ Rydberg states (this work) with numerical results of Farley and Wing [4].

Figure 3

(Color online) Comparison of our numerically calculated depopulation rates of Rb $nS$ states at $T=300\text{K}$ with (a) Eqs. (8, 13) and (b) Eqs. (13, 14), and comparison of our numerically calculated temperature dependences of BBR-induced depopulation rates of (c) Rb $10S$ and (d) Rb $30S$ states with Eqs. (13, 14).

Figure 4

(Color online) Comparison of the numerically calculated radiative and effective lifetimes of Na (a) $nS$, (b) $nP$, and (c) $nD$ and Rb (d) $nS$, (e) $nP$, and (f) $nD$ Rydberg states with available numerical data [8, 9].

Figure 5

(Color online) Comparison of the numerically calculated by us effective lifetimes of Rb (a) $nS$, (b) $nP$, and (c) $nD$ and Cs (d) $nS$, (e) $nP$, and (f) $nD$ Rydberg states at the ambient temperatures $T=77$, 300, and 600 K with Eq. (16).

Figure 6

(Color online) Comparison of the calculated effective lifetimes of Rb (a) $nS$, (b) $nP$, and (c) $nD$ Rydberg states with the experiments [13, 14] at $T=300\text{K}$.