Abstract: A new formulation of the theory of nuclear reactions based on the properties of a generalized “optical” potential is presented. The real and imaginary part of this potential satisfy a dispersion type relation while its poles give rise to resonances in nuclear reactions. A new derivation of the Breit-Wigner formula is given in which the concept of channel radius is not employed. This derivation is extended to the case of overlapping resonances. These results can then be employed to obtain the complex potential well model for pure elastic scattering. This potential well is shown to become real as the average width of the resonances increases. Reactions as well as elastic scattering are treated. Considering the former process in an isolated resonance, we obtain a nonresonant term analogous to the familiar potential scattering term of elastic scattering. This is just the direct interaction term which thus appears automatically in this formalism. Upon performing the appropriate energy averages over resonances, the complex potential well model is generalized so as to include inelastic scattering. The effects of the identity of nucleons is investigated. It is shown that our formalism is valid as long as the exit channels can at most contain one nucleon.
Publication Year: 1958
Publication Date: 1958-12-01
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 2812
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