A STUDY OF THE MOMENTUM DEPENDENCE OF THE PHASE-SHIFT FOR FINITE-RANGE AND COULOMB POTENTIALS AND ITS POSSIBLE APPLICATIONS

Closed form expressions for the partial derivative of the phase shift with respect to wave number k are obtained for a variety of potentials which call have a short range component as well as a long range Coulo mb tail. Cut-off potentials, the Woods-Saxon potential, the Yukawa pot entials, as well as potentials that behave like 1/r(4) or 1/r(6) as r tends 70 infinity fall into this category of short range potentials, T heoretical considerations like time delay and resonance widths are dis cussed. Numerical approximations based on the derived expressions for the partial derivative of the phase shift with respect to k are tested and compared with the exact value in those cases for which an analyti c expressions for the partial derivative exists, such as in the case o f a pure Coulomb potential or a square-well potential. This has facili tated a clear comparison of the numerical calculations. Possible appli cations of the formalism are discussed. (C) 1998 Elsevier Science B.V.