Virial theorem for inelastic molecular collisions. Atom–rigid rotor scattering

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Abstract
From the hypervirial theorem for a nonchemically reactive but otherwise arbitrary collision between two molecules, the virial theorem for the scattering of an atom by a nonvibrating (rigid rotor) diatomic molecule is derived and shown to be simply related to F. T. Smith’s collision lifetime matrix. It is found that there are two contributions to the collision lifetime: (1) The usual contribution due to the intermolecular potential and its derivative, and (2) a contribution due to the change in the internal energy of the molecule. The conditions under which the virial theorem is satisfied by the infinite order sudden (IOS), distorted wave (DW), and first Born (FB) approximations are also given.