Radiative and Radiationless Rates

Fermi called eq. (15.36) the Golden Rule of time-dependent perturbation theory because of its prevalence in radiationless transitions. Sometimes it is referred to as Fermi s Golden Rule. 

Classically, charged particles radiate when they are accelerated. The strength of radiation is proportional to the square of the electric dipole moment, which is 

The absorption of light is mainly the result of the interaction between the oscillating electric vector of the electromagnetic radiation with the charged particles within the molecules. The transition probability coefficient in the absorption from a lower electronic state 1 to an upper electronic state 2 corresponds to Einstein s coefficient of absorption 

Eliminating n 2 and /12 using eqs. (15.3) and (15.38) in the above expression gives the absorption probability in the gas phase ( d=1) in terms of experimentally accessible quantities 

The radiative rate can now be expressed in terms of these quantities using eq. (15.9), 

---