Many-body perturbation theory and phosphorescence: Application to CH ₂

A diagrammatic formalism is derived which facilitates the calculation of phosphorescent lifetimes. This formalism uses double perturbation theory where the spin-own-orbit interaction and the two electron fluctution potential are the perturbations. The transition amplitude between the ground state and the phosphorescent state is calculated to first order in both perturbations. The phosphorescent lifetime of the ¹A₁, state of methylene is evaluated, by way of illustration, and is predicted to be in the range of 40-100 s. The transition amplitude, in this case, is due primarily to the direct spin-orbit mixing of the ¹A₁, state with the ³B₁ ground state.