Simple case of one resonance and zero angular momentum

1 Simple case of one resonance and zero angular momentum 

Note that this relation must anyway become valid at small detunings, i.e. sufficiently close to a resonance. Then S becomes the sum of (i) a hard sphere or potential scattering term and (ii) a second term whose denominator is E — E + (6 — ika). If we identify a width Ta = ka to yield the resonance form, and if we choose the shift Aa according to the physical criterion that Eres = E, then we are led to = 0 and 6 = 0. 

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