where \langle f|H'|i \rangle is the matrix element (in bra–ket notation) of the perturbation between the final and initial states, and \rho(E_f) is the density of states (number of continuum states divided by dE in the infinitesimally small energy interval E to E + dE) at the energy E_f of the final states. This transition probability is also called "decay probability" and is related to the inverse of the mean lifetime. Thus, the probability of finding the system in state |i\rangle is proportional to e^{-\Gamma_{i \to f} t}.
