314 Appendix E: Raman and two-photon transitions
hydrogen the nearest level than can provide an intermediate state is
2p, which is almost degenerate with the 2s level (see Fig. 8.4); thus
ωiω 2 and ∆ ω =2π× 1015 s−^1 (or 4× 105 times larger than
the frequency detuning used in the example of a Raman transition in
the previous section). There are two important consequences of this
large frequency detuning: (a) in real atoms there are many levels with
comparable frequency detuning and taking these other paths (1→i→
2) into account leads to the summation overiin eqn E.16; and (b)
the rate of two-photon transitions is small even for high intensities (cf.(^10) A rough estimate of the two-photon allowed single-photon transitions). 10
rate can be made in a similar way to the
calculations for Raman transitions in
the previous section (Demtr ̈oder 1996).