[Paper Review] Photoemission time-delay measurements and calculations close to the 3s ionization minimum in Ar

Guenot, D., Klunder, K.+13 more|arXiv (Cornell University)|Apr 18, 2012

X-ray Spectroscopy and Fluorescence Analysis1 references3 citations

TL;DR

This study presents experimental attosecond time-delay measurements and theoretical calculations of photoionization from the 3s and 3p subshells in argon near the 3s ionization minimum (32–42 eV). Using attosecond pulse trains and RABBIT spectroscopy, combined with RPAE calculations including inter-shell correlation, it reveals that the 3s electron is delayed by up to ~70 as relative to 3p due to strong correlation effects, with excellent agreement between experiment and theory near the Cooper minimum.

ABSTRACT

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 (RPAE). 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.

Motivation & Objective

• To measure photoemission time delays from the 3s and 3p subshells in argon using attosecond pulse trains and RABBIT spectroscopy.
• To investigate the role of inter-shell correlation (3s–3p) in modifying ionization delays near the 3s ionization minimum.
• To compare experimental time delays with theoretical calculations that include electron correlation effects via the RPAE method.
• To assess the validity of the asymptotic approximation for laser-assisted two-photon ionization in extracting photoionization phase delays.
• To identify discrepancies between experiment and theory and explore their origins, particularly near the Cooper minimum.

Proposed method

• Employed a stabilized Mach-Zehnder interferometer to generate and measure attosecond pulse trains (XUV) and a weak IR laser field.
• Used the RABBIT technique to measure sideband amplitudes and extract time delays via interference between adjacent sidebands.
• Applied the asymptotic approximation for complex transition amplitudes in two-color, two-photon ionization to relate measured delays to one-photon matrix element phases.
• Performed theoretical calculations using the random phase approximation with exchange (RPAE) to include 3s–3p inter-shell correlation effects.
• Calculated ionization delays as the energy derivative of the phase of the photoionization matrix element, corrected for IR dressing effects.
• Used the Wigner time delay formalism extended to laser-dressed processes, with phase contributions from scattering (η), exchange (δ), and continuum-continuum coupling (φcc).

Experimental results

Research questions

• RQ1 How do inter-shell correlation effects between the 3s and 3p subshells influence photoemission time delays in argon near the 3s ionization minimum?
• RQ2 To what extent do experimental time-delay measurements using attosecond pulse trains agree with RPAE-based theoretical calculations including electron correlation?
• RQ3 How does the presence of a weak IR laser field affect the measured time delays, and can the asymptotic approximation accurately describe the two-photon ionization process?
• RQ4 Why is there a discrepancy between experiment and theory at the highest photon energy (sideband 26), particularly near the Cooper minimum?
• RQ5 What role do higher-order two-photon processes (e.g., IR-first absorption) play in modifying the measured time delays near a cross-section minimum?

Key findings

• The 3s photoionization delay increases significantly above 40 eV, reaching up to ~70 as relative to the 3p channel, due to strong inter-shell correlation and electron screening.
• Experimental time delays from the present work and prior measurements (from [8]) agree well across most of the energy range, except near the highest energy sideband (26), where a discrepancy is observed.
• Theoretical RPAE calculations reproduce the overall trend of increasing 3s delay with energy, particularly near the Cooper minimum at ~42 eV, where the 3s cross-section is minimized.
• The independent-electron HF calculation unexpectedly agrees better with experiment at higher sidebands than RPAE, suggesting possible limitations in the current theoretical treatment of correlation effects.
• The measured time delay for the 3p→kd channel is ~70 as, consistent with the angular momentum barrier effect, while 3p→ks is negligible.
• Discrepancies near the Cooper minimum may arise from the asymptotic approximation for continuum wave functions, neglected core effects, or unaccounted two-photon processes involving IR photon absorption first.