  The mean free paths of low-energy electrons in liquid water are of
fundamental importance for modelling radiation damage and many related
physico-chemical processes. Neither theoretical predictions nor experimental
estimations have so far converged to yield reliable values for these
parameters. We therefore introduce a new approach to determine the elastic and
inelastic mean free paths (EMFP, IMFP) based on experimental data. We report
extensive ab-initio calculations of electron quantum scattering with water
clusters, which are brought to convergence with respect to the cluster size.
This provides a first-principles approach to condensed-phase scattering that
includes both multiple-scattering and condensation effects. The obtained
differential cross sections are used in a detailed Monte-Carlo simulation to
extract EMFP and IMFP from two recent liquid-microjet experiments that
determined the effective attenuation length (EAL) and the photoelectron angular
distribution (PAD) following oxygen 1s-ionization of liquid water. For electron
kinetic energies from 10 eV to 300 eV, we find that the IMFP is noticeably
larger than the EAL. The EMFP is longer than that of gas-phase water and the
IMFP is longer compared to the latest theoretical estimations, but both the
EMFP and IMFP are much shorter than suggested by experimental results for
amorphous ice. The Python module developed for the analysis is available at
https://gitlab.com/axelschild/CLstunfti and can be used to further refine our
results when new experimental data become available.
