Transition from the upper state to the lower state in a two state system in fermis model where a term describing the radiation reaction force is added to the hamiltonian operator in Schrodinger equation. The additional term Vrr has the following form

Vrr = -(2e/3c³) (d³/dt³d ) r

Where d = e integral(Y₁^* r Y₂)dv

r and d are operators.

The system is initially almost in the upper state (|a₂|² = 0.9999 at t = 0) the contribution of the upper state decreases in time as |a₂(t)|² = (1 - |a₁(0)|²) /(1 - |a₁(0)|² + exp(At) |a₁(0)|² )

where A = (4e² / 3 c³h )[(E₂ - E₁)³/h³] (integral (Y₁^* r Y₂)dv)²

In the graphics it is taken as A = 1.