Time Delay in the Recoiling Valence Photoemission of Ar Endohedrally Confined in ${\mathrm{C}}_{60}$

The effects of confinement and electron correlations on the relative time delay between the $3s$ and $3p$ photoemissions of Ar confined endohedrally in ${\mathrm{C}}_{60}$ are investigated using the time-dependent local density approximation—a method that is also found to mostly agree with recent time delay measurements between the $3s$ and $3p$ subshells in atomic Ar. At energies in the neighborhood of $3p$ Cooper minimum, correlations with ${\mathrm{C}}_{60}$ electrons are found to induce opposite temporal effects in the emission of Ar $3p$ hybridized symmetrically versus that of Ar $3p$ hybridized antisymmetrically with ${\mathrm{C}}_{60}$. A recoil-type interaction model mediated by the confinement is found to best describe the phenomenon.

Figure 1

Schematic for probing the effects of correlations from the confinement on the relative time delay in the emission of an atom encaged endohedrally inside ${\mathrm{C}}_{60}$.

Figure 2

Top: TDLDA $3p$, $3s$ and total photoionization cross sections for atomic Ar are compared with experiments for $3s$ [21] and total [22]. For $3s$ the computed cross section is scaled to reproduce the measurement at the Cooper minimum. Bottom: The relative TDLDA time delay between $3s$ and $3p$ of Ar and its comparison with measurements (solid black circles, Ref. 16; open red squares, Ref. 15). RPAE results [14] at three experimental energies are also cited.

Figure 3

TDLDA quantum phases for ionization via $d$-waves from bonding $3p[\mathrm{Ar}+{\mathrm{C}}_{60}]$ and antibonding $3p[\mathrm{Ar}-{\mathrm{C}}_{60}]$ levels and via $p$-wave from Ar $3s@$ are compared with their counterparts in free Ar.

Figure 4

Top: Absolute time delay for ionizations in $3p[\mathrm{Ar}\pm {\mathrm{C}}_{60}]\to kd@$ and $3s@\to kp@$ channels. For the two hybrid channels, results modified by incorporating $s$-wave delays are also shown. Bottom: Relative delays ${\tau }_{3s@}-{\tau }_{3p[\mathrm{Ar}\pm {\mathrm{C}}_{60}]}$, including the $s$-wave contributions; ${\tau }_{3s}-{\tau }_{3p}$ of free Ar is also shown for comparison.