where ν ν g is the group velocity. When the photons are near resonance, the lifetime of an excited state in the atomic vapor is equal to the transport time, τ τ r = τ τ a t , independent of the detuning. This comes in handy, since the average number of scattering events is the ratio of the time spent in the system to the lifetime of the excited state (or equivalently, the scattering time). Since in a 3D diffusion process the electromagnetic energy density spreads as ⟨ ⟨ r 2 ⟩ ⟩ = 6 D t , we can find the average number of scattering events for a photon before it escapes: