EGAS41 - Swansea University

41 st EGAS CP 121 Gdańsk 2009
Quasiclassical calculations of BBR-induced depopulation rates
and effective lifetimes of alkali-metal Rydberg atoms
I.I. Beterov ∗ , I.I. Ryabtsev, D.B. Tretyakov, V.M. Entin, N.N. Bezuglov
Institute of Semiconductor Physics SB RAS, Novosibirsk, Russia
∗ Corresponding author: beterov@isp.nsc.ru
Rates of depopulation by blackbody radiation (BBR) and effective lifetimes of all alkalimetal
nS, nP and nD Rydberg states have been numerically calculated for n = 10 −
80 at the ambient temperatures of 77, 300 and 600 K [1]. Quasiclassical formulas of
Dyachkov and Pankratov [2] were used to calculate the radial matrix elements of the
dipole transitions from Rydberg states. The advantage of the used quasiclassical model is
its relative simplicity that nevertheless provides a good agreement with more sophisticated
quantum-mechanical calculations.
We have also obtained a simple formula for estimates of BBR-induced depopulation
rates that is valid for both low and high values of n (in atomic units):
Γ BBR =
4
3n 5 eff c3 1
exp [ 1/(n 3 eff T)] − 1
(1)
Here n eff is the effective quantum number and c is the speed of light. For practical use
a modified Eq. (1) can be written in units of [s −1 ] for temperature taken in Kelvins:
Γ BBR = A
n D eff
2.14 × 10 10
exp [ 315780 × B/(n C eff T)] − 1
[
s
−1 ] . (2)
The scaling coefficients A, B, C and D, obtained for all alkali-metal atoms [1], were
introduced for better approximation of the numerical results. For high n ∼ 80 the error
of the approximation is less than 8%, while for n ∼ 50 it is as low as 3.5%. Good agreement
was observed with the recent experimental results [3] for Rb nS and nD states, while for
nP states the theoretical curve goes below the experimental points. This points towards
the need of new measurements in an extended n range.
Acknowledgment
This work was supported by the Russian Academy of Science and Russian Foundation for Basic
Research.
References
[1] I.I. Beterov, I.I. Ryabtsev, D.B. Tretyakov, V.M. Entin,
http://arxiv.org/abs/0810.0339
[2] L.G. Dyachkov, P.M. Pankratov, J. Phys. B: At. Mol. Opt. Phys. 27, 461 (1994)
[3] V.A. Nascimento, L.L. Caliri, A.L. de Oliveira, V.S. Bagnato and L.G. Marcassa,
Phys. Rev. A 74, 054501 (2006)
181