Causality with noncausal optical potentials

It is shown by way of a simplified model that the calculation of the time nonlocal potential resulting from an energy-dependent optical potential is not unique. Most choices result in a noncausal time-dependent potential, in spite of the inclusion of appropriate scattering boundary conditions in the...

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Bibliographic Details
Published in:Physical review. C, Nuclear physics Nuclear physics, 1995-04, Vol.51 (4), p.2011-2022
Main Authors: Madsen, VA, Goldman, KI
Format: Article
Language:English
Subjects:
663300 - Nuclear Reactions & Scattering, General- (1992-)
BOUNDARY CONDITIONS
CAUSALITY
DIFFERENTIAL EQUATIONS
ENERGY DEPENDENCE
ENERGY SPECTRA
EQUATIONS
FUNCTIONS
HAMILTONIANS
MATHEMATICAL OPERATORS
NONLOCAL POTENTIAL
NUCLEAR PHYSICS AND RADIATION PHYSICS
OPTICAL MODELS
PARTIAL DIFFERENTIAL EQUATIONS
POTENTIALS
QUANTUM OPERATORS
SCATTERING
SCHROEDINGER EQUATION
SPECTRA
TIME DEPENDENCE
WAVE EQUATIONS
WAVE FUNCTIONS
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Summary:It is shown by way of a simplified model that the calculation of the time nonlocal potential resulting from an energy-dependent optical potential is not unique. Most choices result in a noncausal time-dependent potential, in spite of the inclusion of appropriate scattering boundary conditions in the model. Similarly, potentials arising from the many-body treatment of the optical potential are typically noncausal. However, it is demonstrated that, because of the energy spectrum of the Hamiltonian, the appropriate wave equations for scattering and the wave-function solutions in both approaches are nevertheless causal.
ISSN:0556-2813
1089-490X
DOI:10.1103/PhysRevC.51.2011