Knowledge of range and type of secondary particles such as Auger electrons, photoelectrons or characteristic X-rays, and their variation with the primary photon energy is fundamental to develop a model delineating GNPs-photons interactions. Monte Carlo simulations were carried out using Geant4 simulation toolkit in which a 2 nm GNP placed at the center of a \(10^3\) \(\mu\text{m}^3\) cube of water was uniformly irradiated with different photon energies ranging from 50 keV to 15 MeV. Auger electrons, photoelectric emission, and interaction of secondaries in nearby atoms were simulated to evaluate the ionization density following irradiation. Energetic cutoff of 10 eV were used for the production of secondary particles.
The radial distribution of energy deposited from secondary electrons emitted from the nanoparticle was assumed symmetrical \cite{McMahon_2011}. The phase-space of secondary electrons was sampled on the GNP surface and the following energy deposits in the water volume surrounding the nanoparticle were histogrammed radially, putting the GNP at the origin, with a bin width of 1 nm up to a distance of 5000 nm. The actual shape of the radial dose profile to be found in realistic treatments was obtained through a weighted superposition of monoenergetic profiles, using specific photon spectra. For this work, spectra resulting from 160 kVp, 6 and 15 MV irradiation in water were analyzed to evaluate GNPs ionization rate (figure \ref{radial_dose}). The obtained dose distribution profiles were used as input to a radial function which was exploited to calculate the number of lethal events upon a determinate distance from the nanoparticles center.