Breit-Wigner expression

Resonances in half and in full collisions have exactly the same origin, namely the temporary excitation of quasi-bound states at short or intermediate distances irrespective of how the complex was created. In full collisions one is essentially interested in the asymptotic behavior of the stationary wavefunction L(.E) in the limit R —> 00, i.e., the scattering matrix S with elements Sif as defined in (2.59). The S-matrix contains all the information necessary to construct scattering cross sections for a transition from state i to state /. In the case of a narrow and isolated resonance with energy Er and width hT the Breit- Wigner expression... 

The position and width of the resonance can be easily related to the derivatives with respect to k. Assuming the Breit-Wigner expression for the resonant part of the phase shift, the following equations result ... 

Because the cross section of a resonance process is expressed by the Breit-Wigner formula, the energy-integrated cross section is written as follows ... 

Substitution of the Breit-Wigner S matrix (34) into Eq. (48) for the Q matrix and the assumption of an energy-independent B, i.e., an energy-independent background Sb yield the expression... 

A simple expression may be readily obtained for the capture cross section, for 5-wave neutrons. To a first approximation the capture cross section is given by the one-level Breit-Wigner formula ... 

The most natural theoretical treatment of this mechanism is based on the notion of Breit-Wigner resonances [78, 80, 442]. This treatment yields an expression for kj. coinciding with that obtained from the simple kinetic scheme... 

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