The angular dependence of photoemission time delay for the inner $n{d}_{3/2}$ and $n{d}_{5/2}$ subshells of free and confined Xe is studied in the dipole relativistic random phase approximation. A finite spherical annular well potential is used to model the confinement due to fullerene $C_{60}$ cage. Near cancellations in a variety of the dipole amplitudes, Cooper-like minima, are found. The effects of confinement on the angular dependence, primarily confinement resonances, are demonstrated and detailed.

Two decades ago, it was predicted [Y. S. Kim et al., Phys. Rev. Lett. 46, 1326 (1981)] that relativistic effects should alter the dynamics of the photoionization process in the vicinity of Cooper minima. The present experimental and theoretical study of the angular distributions of Xe ${4d}_{3/2}$ and ${4d}_{5/2}$ photoelectrons demonstrates this effect for the first time. The results clearly imply that relativistic effects are likely to be important for intermediate- $Z$ atoms at most energies.

It is remarkable that time delay is an experimentally measurable quantity, but time itself is not. Time delay in quantum collisions and in photoionisation/photodetachment of atomic and molecular systems is reviewed in this paper. Wigner–Eisenbud formalism of time delay in quantum collision of a wavepacket with a target is discussed. Its equivalence with Smith's formalism of time delay, based on an independent basis for time delay in terms of excess particle density in the collision zone, is demonstrated. Similarity and difference between quantum collision of an electron with a positive atomic/molecular ion and photoionisation/photodetachment of a neutral atom/molecule are discussed, and the underlying quantum dynamics involving the time-reversal symmetry between solutions with outgoing and ingoing wave boundary conditions is pointed out to interpret photoionisation/photodetachment as half-scattering. This relationship is subsequently taken advantage to extend the formalism of Wigner–Eisenbud–Smith time delay in photoionisation/photodetachment. The measurability of time delay is accounted for in terms of a self-adjoint quantum operator that characterises it, even if there is no such operator for time itself. A few illustrative examples of theoretical and experimental studies of time delay are given to indicate outstanding advances made in this field in the last two decades.

Using ${\mathrm{Cl}}^{-}$ as a test case, Wigner time delay in the photodetachment process has been investigated theoretically, along with the photoionization of the isoelectronic Ar atom, for the outer $3p$ shell using the relativistic-random-phase approximation (RRPA). Time delay was probed in these systems from threshold to 80 eV, to investigate threshold effects, the centrifugal barrier shape resonance, and the Cooper minimum region. This study focuses on ${\mathrm{Cl}}^{-}$ because, for negative ions, the phase of the photoemission process is not dominated by the Coulomb phase as it is in photoionization. The results show significant differences, both qualitative and quantitative, between the time delays for ${\mathrm{Cl}}^{-}$ and Ar photoemission at low photoelectron energy, but they are rather similar in the Cooper minimum region, where the Coulomb phase is small. In particular, the Wigner time delay in ${\mathrm{Cl}}^{-}$ exhibits a dramatic energy dependence just above threshold, and a rapidly increasing time delay in the vicinity of the shape resonance. A strong angular dependence of time delay has also been found near the threshold region for the ${\mathrm{Cl}}^{-}$ case, and is absent in the case of the photoionization of Ar. The origin of these phenomenologies is explained and a prospectus for future work is presented.