Transition Moments in RPA-Like Approximations

We have investigated whether it is possible to approximate RPA transition probabilities by a standard state representation like <λ,app|M | v,app>. Using |HF> and 0_λ+ |HF> as the approximate eigenstates we find that the approximation seems to work best for transition between excited states. In this case only the first order correction, which involves a sum over all excited RPA states, gives an appreciable correction to the state representation of the transition probability. Parallel conclusions are obtained in both the dipole length and the dipole velocity formulation.