Photoemission-time-delay measurements and calculations close to the 3$s$-ionization-cross-section minimum in Ar

We present experimental measurements and theoretical calculations of photoionization time delays from the $3s$ and $3p$ shells in Ar in the photon energy range of 32–42 eV. The experimental measurements are performed by interferometry using attosecond pulse trains and the infrared laser used for their generation. The theoretical approach includes intershell correlation effects between the $3s$ and $3p$ shells within the framework of the random-phase approximation with exchange. The connection between single-photon ionization and the two-color two-photon ionization process used in the measurement is established using the recently developed asymptotic approximation for the complex transition amplitudes of laser-assisted photoionization. We compare and discuss the theoretical and experimental results, especially in the region where strong intershell correlations in the $3s\to kp$ channel lead to an induced “Cooper” minimum in the 3s ionization cross section.

Figure 1

Schematic illustration of our experimental setup.

Figure 2

Electron spectrum obtained by ionizing Ar with four harmonics of orders 21, 23, 25, and 27. The ionization channels are shown on the top.

Figure 3

Electron spectrum as a function of time delay between the attosecond pulses and the IR laser. The signal strength is indicated by colors. The spectrum on the right ($3p$) follows that on the left ($3s$) with a factor of 6 reduction in the color code and a slight overlap in energy.

Figure 4

Energy-level scheme of the processes discussed in the present work: (a) RABBIT principle and (b) different channels in two-photon ionization from the $3s$ and $3p$ subshells.

Figure 5

Continuum-continuum delay ${\tau }_{cc}$ as a function of excitation photon energy for subshells $3s$ (red solid line) and $3p$ (blue dashed line) for an IR photon energy of 1.55 eV (800-nm wavelength).

Figure 6

Feynman-Goldstone diagrams representing (a) one-photon and (b) two-photon ionization processes. (c) Diagrammatic representation of the RPAE equations. The second and third diagrams on the right-hand side refer to time forward and time reversed, respectively. (d) Two-photon ionization including intershell correlation effects. (e) Two-photon ionization with the XUV photon absorbed after the IR photon.

Figure 7

(top) The photoionization cross sections ${\sigma }_{3p\to kd}$ calculated in the HF (blue dotted line) and RPAE (red solid line) approximations are compared with the ${\sigma }_{3p\to ks}$ cross sections (HF, green open circles; RPAE, purple dashed line). The experimental data for the ${\sigma }_{3p}$ cross section are from Ref. [31]. (middle) Photoionization cross sections ${\sigma }_{3s}$ calculated in the HF (blue dotted line) and RPAE (red solid line) approximations are compared with experimental data [10]. (bottom) Correlation-induced phase shifts for the $3s$ and $3p$ dipole matrix elements.

Figure 8

Ionization delay for the three angular channels: $3p\to kd$ (blue dotted line), $3p\to ks$ (green dashed line), and $3s\to kp$ (red solid line).

Figure 9

Comparison between our theoretical calculations (dashed blue line, HF; red solid line, RPAE) and experiments (circles, Ref. [8]; crosses, present work)