Supersymmetry between deep and shallow optical potentials for {sup 16}O+{sup 16}O scattering
- Physique Nucleaire Theorique et Physique Mathematique, C.P. 229, Universite Libre de Bruxelles, B-1050 Brussels (Belgium)
Pairs of supersymmetric transformations allow one to remove square-integrable solutions from a complex potential without modifying its complex phase shifts. This technique is applied to {sup 16}O+{sup 16}O scattering where deep and shallow optical potentials provide essentially similar fits of excitation functions over the 10{endash}35 MeV range in the center-of-mass system. After removing complex normalizable solutions from the deep optical potential of Kond{bar o} {ital et} {ital al}., the resulting potential resembles the shallow potential of Chatwin {ital et} {ital al}., except for the fact that it is singular at the origin. The transformation succeeds in removing bound states and also narrow resonances from the real part of the deep potential. Different theoretical aspects of scattering with complex potentials are also discussed such as the behavior of complex phase shifts in the vicinity of a resonant or normalizable state, and the Levinson theorem. In order to explain phase-shift behaviors, resonance locations are calculated by the complex rotation method, combined with numerical methods valid for determining square-integrable solutions of a Schr{umlt o}dinger equation involving a complex potential. In phase-equivalent pairs of supersymmetric transformations, the apparent contradiction between removing a square-integrable solution which corresponds to a pole of the scattering matrix, and keeping this {ital S} matrix unchanged is explained with the Jost function. {copyright} {ital 1996 The American Physical Society.}
- OSTI ID:
- 383341
- Journal Information:
- Physical Review, C, Vol. 54, Issue 3; Other Information: PBD: Sep 1996
- Country of Publication:
- United States
- Language:
- English
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