Shape resonances in photoionization cross sections and time delay

Shape resonances in photoionization of atoms and molecules arise from a particular geometry of the ionic potential which traps the receding photoelectron in a quasi-bound state in a particular partial wave. This mechanism allows us to connect the photoionization cross section in the resonant region with the photoelectron scattering phase in this partial wave by a simple formula \(\sigma \propto \sin^2\delta_\ell\). Due to this relation, the phase \(\delta_\ell\) can be extracted from an experimentally known cross section and then converted to the photoelectron group delay (Wigner time delay) \(\tau_{\rm W} = \partial \delta_\ell/\partial E\) which is measurable by recently developed laser interferometric techniques. Such a direct connection of the photoionization cross section and the time delay is a fundamental property of shape resonances which provides a comprehensive test of novel measurements against a large body of older synchrotron data.