# Interpretation of the photon scattering rate?

The photon scattering rate $$\Gamma$$ describes the rate at which photons scatter off an atom$$^1$$. In a two-level system, the ansatz for the photon scattering rate often is given by

$$\begin{equation} \Gamma = \rho_{22}\gamma \end{equation}$$

where $$\rho_{22}$$ is the probability to find the atom in the excited state and $$\gamma$$ is the rate of spontaneous decay. However, I don't see the connection between the ansatz above and what the photon scattering rate is physically meant to be.

$$^1$$In my imagination, the photon scattering rate is the absorption rate for photons at a certain frequency $$\omega$$. Hence $$\Gamma(\omega)$$ shows the saturation broadened Lorentzian absorption line of the atom, centered around a resonance frequency.

Considering light as a stream of photons at energy hω, photon scattering is usually defined as cycles of absorption and subsequent spontaneous emission.

$$Γsc(r) = Pabs /hω = 1 /he0c*Im(α) I(r).$$

http://cds.cern.ch/record/380296/files/9902072.pdf

The photon scattering rate is the radiated power divided by the photon energy hω.

$$Rsc = Prad /ω$$

http://atomoptics-nas.uoregon.edu/~dsteck/teaching/quantum-optics/quantum-optics-notes.pdf

• This seems plausible, but I am struggling with the motivation of the ansatz $\Gamma=\rho_{22}\gamma$ as found in Foot, Atomic Physics. – faber Oct 23 at 7:05
• why the downvote? – Árpád Szendrei Oct 27 at 15:19