We express the photoionization cross section of an atomic or molecular shape resonance in the form $\sigma \propto {sin}^2{\delta }_{\ell }$ which connects the cross section with the photoelectron scattering phase in the dominant partial wave $\ell$. This expression allows us to relate the cross section with the photoelectron group delay (Wigner time delay) ${\tau }_{\mathrm{W}}=\partial {\delta }_{\ell }/\partial E$ 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.

• Received 28 November 2022
• Accepted 15 February 2023

DOI:https://doi.org/10.1103/PhysRevA.107.L021102