Behavior of the eigenphase sum near a resonance

Abstract

It is shown that for an isolated resonance in a multichannel problem the sum of the eigenphases ${\delta }_n$ satisfies the usual formula appropriate for the elastic phase shift: ${\Sigma }_n{\delta }_n={\Delta }^0+invtan\left[\frac{\Gamma }{2(E_0-E)}\right]$. The parameter $\Gamma$ is the total width of the resonance.