ANALYTIC EVALUATION OF THE BORN-OPPENHEIMER AMPLITUDE FOR REARRANGEMENT COLLISIONS

We present a closed-form expression for the Born-Oppenheimer amplitude for arbitrary initial state to arbitrary final state transition. So f ar these amplitudes have been evaluated analytically for transitions a mong some low-lying states (1s,2s,2p) with the help of parametric diff erentiations which is rather tedious. The present method offers an ele gant way to avoid these parametric differentiations to calculate the J ackson-Schiff transition amplitudes between states of arbitrary quantu m numbers. Analytic expressions of our basic integral are checked agai nst a well known result for a special case. We demonstrate numerically the need for the analytic evaluation of these amplitudes especially f or the transition between states of large quantum numbers.