# Many-body calculations of two-photon, two color matrix elements for attosecond delays

## TL;DR

This paper presents advanced many-body calculations of atomic delays in noble gas photoionization, demonstrating gauge invariance and examining the validity of common delay interpretations, with findings relevant for attosecond physics.

## Contribution

It introduces a comprehensive two-color two-photon Random-Phase Approximation with Exchange approach for calculating atomic delays, highlighting gauge invariance and convergence properties.

## Key findings

- Gauge invariance of atomic delays is demonstrated.
- Universal continuum--continuum contribution is generally valid.
- Special cases like the 3s Cooper minimum show deviations.

## Abstract

We present calculations for attosecond atomic delays in photoionization of noble gas atoms based on full two-color two-photon Random-Phase Approximation with Exchange in both length and velocity gauge. Gauge invariant atomic delays are demonstrated for the complete set of diagrams. The results are used to investigate the validity of the common assumption that the measured atomic delays can be interpreted as a one-photon Wigner delay and a universal continuum--continuum contribution that depends only on the kinetic energy of the photoelectron, the laser frequency and the charge of the remaining ion, but not on the specific atom or the orbital from which the electron is ionized. Here we find that although effects beyond the universal IR--photoelectron continuum--continuum transitions are rare, they do occur in special cases such as around the $3s$ Cooper minimum in argon. We conclude also that in general the convergence in terms of many-body diagrams is considerably faster in length gauge than in velocity gauge.