A new quantum-dynamical theory for three dimensional atom-diatom reactions of the light-heavy-light type is described. The method involves applying the energy sudden approximation to the entrance arrangement channel hamiltonian, and the centrifugal sudden approximation to the exit arrangement channel hamiltonian. Expressions relating the S matrix elements of the method to differential and integral, vibrational-rotational, reaction cross sections are derived. A description is also given of how the method is implemented within the framework of the close-coupling, R matrix propagator method.