GENERALIZATION OF THE PSEUDOPOTENTIAL TO AN INTERACTION WITH NONZERO RANGE

The resonance properties of certain arrays of potentials defined by a self-adjoint integral operator of finite rank are studied. It is shown that a uniformly spaced infinite linear array of such potentials can admit zero-width resonances, and that a uniformly spaced circular array can admit resonances whose widths tend to zero exponentially, as the number of potentials tends to infinity while the arc-length spacing remains constant-properties that have previously been studied for the Fermi pseudopotential (point interaction). Additionally, it is demonstrated that the pseudopotential can be derived from such an integral-operator potential as an appropriate limit. The relevance of these calculations to the study of arrays of cylindrical dipoles in classical electromagnetism is discussed.