Attosecond delay of xenon $4d$ photoionization at the giant resonance and Cooper minimum

A Kohn-Sham time-dependent local-density-functional scheme is utilized to predict attosecond time delays of xenon $4d$ photoionization that involves the $4d$ giant dipole resonance and Cooper minimum. The fundamental effect of electron correlations to uniquely determine the delay at both regions is demonstrated. In particular, for the giant dipole resonance, the delay underpins strong collective effect, emulating the recent prediction at ${\mathrm{C}}_{60}$ giant plasmon resonance [T. Barillot et al., Phys. Rev. A 91, 033413 (2015)]. For the Cooper minimum, a qualitative similarity with a photorecombination experiment near argon $3p$ minimum [S. B. Schoun et al., Phys. Rev. Lett. 112, 153001 (2014)] is found. The result should encourage attosecond measurements of Xe $4d$ photoemission.

Figure 1

LDA and TDLDA channel cross sections of the photoionization of Xe $4d$. The TDLDA $4d$ total cross section is compared with the experiment [48].

Figure 2

(a) LDA scattering phases ($\eta$) and TDLDA phases ($\mathrm{\Gamma }$) for the Xe $4d$ photoemission channels. The positions of the giant dipole resonance (GDR) at 101 eV and the Cooper minimum (CM) at 172 eV are indicated. (b) Real and imaginary components of the $4d\to kf$ radial matrix element in TDLDA where a very weak minimum at 80 eV in the imaginary part is pointed out. The real LDA radial matrix element is also shown.

Figure 3

(a) LDA and TDLDA $4d$ photoionization phase of Xe. The inset carries the $4d$ TDLDA cross section in the GDR region. (b) The corresponding Wigner-Smith time delays. The TDLDA delay for the $5s\to kp$ channel is also shown. The vertical arrow at 97.5 eV photon energy indicates 19.3-as TDLDA delay of the $4d$ emission relative to $5s$ which closely agrees with the relative delay of 18 as observed in streaking measurements [38]. (c) Published emission delays of the ${\mathrm{C}}_{60}$ highest occupied molecular orbital electron at the plasmon resonance [28] and Ar $3p$ electron near $3p$ CM [24], both in TDLDA, are shown for the comparison.