  In this paper we develop a new model for the electron emission of high-Z
nanoparticle irradiated by X-rays. This study is motivated by the recent
advances about the nanoparticle enhancement of cancer treatment by
radiotherapy. Our original approach combines a pure probabilistic analytical
model for the photon trajectories inside the nanoparticle and subsequent
electron cascade trajectories based here on a Monte-Carlo simulation provided
by the Livermore model implemented in Geant4. To compare the nanoparticle and
the plane surface electron emissions, we also develop our model for a plane
surface. Our model highlights and explains the existence of a nanoparticle
optimal radius corresponding to a maximum of nanoparticle electron emission. It
allows us to study precisely the nanoparticle photon absorption and electron
cascade production depth in the nanoparticle.
