  An experimental and computational investigation of the space-charge effects
occurring in ultrafast photoelectron spectroscopy from the gas phase is
presented. The target sample CF$_3$I is excited by ultrashort (100 fs)
far-ultraviolet radiation pulses produced by a free-electron laser. The
modification of the energy distribution of the photoelectrons, i.e. the shift
and broadening of the spectral structures, is monitored as a function of the
pulse intensity. The experimental results are compared with computational
simulations which employ a Barnes-Hut algorithm to calculate the effect of
individual Coulomb forces acting among the particles. In the presented model, a
survey spectrum acquired at low radiation fluence is used to determine the
initial energy distribution of the electrons after the photoemission event. The
spectrum modified by the space-charge effects is then reproduced by $N$-body
calculations that simulate the dynamics of the photoelectrons subject to the
individual mutual Coulomb repulsion and to the attractive force of the positive
ions. The employed numerical method accounts for the space-charge effects on
the energy distribution and allows to reproduce the complete photoelectron
spectrum and not just a specific photoemission structure. The simulations also
provide information on the time evolution of the space-charge effects on the
picosecond scale. Differences with the case of photoemission from solid samples
are highlighted and discussed. The presented simulation procedure, although it
omits the analysis of angular distribution, constitutes an effective simplified
model that allows to predict and account for space-charge effects on the
photoelectron energy spectrum in time-resolved photoemission experiments with
high-intensity pulsed sources.
