The cancellation theorem in pseudopotential theory

The cancellation theorem of Cohen and Heine is derived in an exact form using a phase function approach. The new form of the theorem enables precise statements to be made about how far the zero to which we cancel the potential is arbitrary, and in certain circumstances to detect over cancellation. The latter phenomenon is ascribed to the influence of the core states and an expression derived for the maximum repulsive potential we can expect when we have over cancellation.