Breit-Wigner phase shift

Equations (15) and (16) are Breit-Wigner s one-level formula for the phase shift. If the pole lies close to the real E axis, i.e., if T is very small, the part 5r of the phase shift increases very rapidly with E by tt/2 within the energy region of width T and centered at Er. It increases by nearly it within several times T. This is a resonance phenomenon. 

If there is only one open channel, a resonance (of either type) is characterized by a sharp change in the phase shift Sl, which increases sharply by k across the width of the resonance. The phase shift follows a Breit-Wigner form as a function of energy. 

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 ... 

Unlike the case of a direct collision, a delay requires that the phase shift increases with energy. A long delay requires a steep increase and this behavior is often represented by a Breit-Wigner form... 

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