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.

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


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

$$Rsc = Prad /ω$$


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

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