Rotationally induced transitions in atomic collisions: two-state model

Time-dependent coupled Schrodinger equations in a two-state model are solved by the linearisation approximations to the Riccati equation derived from the original coupled equations. The methods proposed by Yagisawa (1976), and by Mehrotra and Boggs (1976) are shown to be equivalent to the approximations. By using the non-perturbative analytical formula thus obtained, transitions through rotational coupling are investigated. The uniform Airy approximation further simplifies the formula to give a useful analytical expression for the transition probability for the case of curve crossing at finite internuclear distance.