Attosecond time delays at Cooper minima in valence-shell photoionization of alkali-metal and alkaline-earth-metal atoms

Ji et al. [New J. Phys. 26, 093014 (2024)] established a direct link between the photoionization cross section and the attosecond time delay near Cooper minima (CM) in the valence shells of noble-gas atoms. This link is based on the analytic properties of the ionization amplitude in the complex plane of the photoelectron energy, and is particularly sensitive to the winding number of the amplitude around the origin of the complex energy plane. Here, we demonstrate an analogous relation for photoionization of the valence $ns$ shells of alkali-metal atoms (AMA), from Na $(n=3)$ to Cs $(n=6)$, as well as alkaline-earth-metal atoms (AEMA), from Mg $(n=3)$ to Ba $(n=6)$. To this end, we employ a fully relativistic formalism that separates the two complementary $n{s}_{1/2}\ensuremath{\rightarrow}E{p}_{1/2}$ and $E{p}_{3/2}$ ionization channels. Each of these channels exhibits a phase variation close to $\ensuremath{\pi}$, but in opposite directions, near their respective Cooper minima. This phase variation vanishes in a nonrelativistic formulation, where the two channels become degenerate. For AMA, due to the threshold proximity of the CM, the universal Coulomb contribution to the time delay must be subtracted. The remaining component of the time delay is target-specific, angular-dependent, and accessible through comparative measurements.