ON USE OF RESONANT STATES IN EIGENFUNCTION EXPANSIONS OF SCATTERING AND REACTION AMPLITUDES

The orthogonality and completeness properties of the resonant states as defined by Humblet and Rosenfeld are investigated using a simple regularization method first suggested by Zel'dovich. It is found that at leat for finite-range potentials, the set of bound states and any finite number of proper resonant states can be completed by a set of continuum states. This makes it possible to expand the scattering and reaction amplitudes in such a way that their resonance behabiour is exhibited, and the dependence of the corresponding partial widths on the interaction becomes more explicit. © 1968.