Reactive scattering of rotationally excited target molecules with adiabatic theory

Abstract

We present a formulation of the three-dimensional quantum mechanical reactive scattering of an atom and a rotationally excited diatomic target molecule within the framework of adiabatic distorted wave theory. This is an extension of previous work where only the rotationally ground initial state was treated while the final molecule could be in any state. The importance of the present formulation lies in the fact that the population of the rotationally excited target molecules is significant under ordinary experimental conditions. A method of obtaining exact and approximate adiabatic wave functions and energies is developed through the use of the body-fixed formulation of atom–diatomic molecule scattering. The integration in transition matrix with rotationally excited adiabatic wave function is again reduced to the three-dimensional integral by separating out the angular variables for the rigid motion of the plane for the atom–molecule system. Explicit integration formula is presented for the reactive transition matrix element. The computational feature of the present formulation is illustrated by evaluating the reactive cross section of the (D,H2) system. For 0→1 rotational transition, present calculations reproduced earlier results. For 1→1 rotational transition, for which no previous result of the adiabatic distorted wave theory is available, the present calculations yield qualitatively similar but quantitatively different angular dependence in the differential cross sections, as in those of the rotationally ground target molecule. Physical significances and further implication of the present formulation are discussed.