A study of the momentum dependence of the phase shift for finite range and Coulomb potentials and its possible applications

✍ Scribed by W.J. Romo; S.R. Valluri

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 899 KB
• Volume: 636
• Category: Article
• ISSN: 0375-9474
• DOI: 10.1016/s0375-9474(98)00192-4

✦ Synopsis

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 can have a short range component as well as a long range Coulomb tail. Cut-off potentials, the Woods-Saxon potential, the Yukawa potentials, as well as potentials that behave like 1/r 4 or 1/r 6 as r tends to infinity fall into this category of short range potentials. Theoretical considerations like time delay and resonance widths are discussed, 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 analytic expressions for the partial derivative exists, such as in the case of a pure Coulomb potential or a square-well potential. This has facilitated a clear comparison of the numerical calculations. Possible applications of the formalism are discussed.