Angle-resolved Wigner time delay in atomic photoionization: The $4d$ subshell of free and confined Xe

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.

Figure 1

Channel-specific time delay as calculated using Eqs. (8)–(11) for the $4d_{3/2}$ initial state. Bold lines are the Wigner time delay for Xe@${\text{C}}_{60}$ (abbreviated by @ in the figures) and thin lines are for free Xe. Different colors correspond to different angles.

Figure 2

Channel-specific time delay as calculated using (12, 13, 14, 15) for $4d_{5/2}$. Bold lines are the Wigner time delay for Xe@${\text{C}}_{60}$ (abbreviated by @ in the figures) and thin lines are for free Xe. Different colors correspond to different angles.

Figure 3

Channel-specific time delay as calculated using (16, 17) for $4d_{5/2}$. Bold lines are the Wigner time delay for Xe@${\text{C}}_{60}$ and thin lines are for free Xe.

Figure 4

$m$ and final-state spin average time delay for $4d_{3/2}$ and $4d_{5/2}$ as calculated using Eq. (19). Bold lines are the Wigner time delay for Xe@${\text{C}}_{60}$ (abbreviated by @ in the figures) and thin lines are for free Xe. Different colors correspond to different angles.