Relation between the Lifetime of the Excited State and the Energy of Excitation

Abstract

HEITLER¹ showed that in the absorption and emission of photons in resonance fluorescence, the scattering system “remembers” how it was excited; it always emits photons with the same energy as the absorbed photon. When a monochromatic line (Γ ≪ Γ₀) is scattered in the manner shown in Fig. 1, the intensity of the scattered photons is given by the Breit–Wigner equationI_r is the intensity of the scattered photons at the resonance E_r Γ₀ is the line width of the scattering system, and E is the energy of the incident (and scattered) photons. When resonance scattering takes place, the photon absorbed by the scatterer is delayed for a certain time before being emitted again. Messiah² showed that the delay depends on the energy of the incident photonswhere ħ is Planck's constant. No matter how the nuclei are excited, the lifetime of the excited state Δt always depends on ∣E−E_r∣. In this work I report another relation which also depends on ∣E−E_r∣and this equation can be verified experimentally.