Effect of Mutual Distortion on Phase Shifts of Colliding Systems

Abstract

The box variational principle for scattering phase shifts is extended to one channel collisions of arbitrary angular momentum without exchange, and also to systems with many degrees of freedom, when the energies are nonrelativistic and insufficient to produce inelastic collisions. Under reasonable assumptions of continuity it is proved that the commonly used one state and many state approximations always reduce the scattering phase shift from its correct value, so long as no further approximations have to be made, and thus provide lower bounds to the exact scattering phase shift. The distorted wave approximation is an example. The inclusion of more states into a many state approximation never makes the estimated phase any worse, and generally improves it. Mutual distortion of colliding systems never reduces the phase shift and generally increases it, thus producing an effective attraction between the systems.