Shape resonances in photoionization cross sections and time delay

We express the photoionization cross section of an atomic or molecular shape resonance in the form σ∝sin2δℓ which connects the cross section with the photoelectron scattering phase in the dominant partial wave ℓ. This expression allows us to relate the cross section with the photoelectron group delay (Wigner time delay) τW=∂δℓ/∂E which is measurable by recently developed laser interferometric techniques. Such a direct connection is a fundamental property of shape resonances which provides a comprehensive test of time delay measurements against a large body of older synchrotron cross-section data.