Simple analytical expressions for the dose of point photon sources in homogeneous media

The contributions to the dose of a point photon source in homogeneous media due to primary and first, second, ..., nth scattered photons are investigated. Assuming a simple statistical model, an analytical form comes out for each of these contributions. It includes a polynomial and a single exponential and depends on three parameters which have a physical meaning. The values of these parameters for different energies and for water, as a test case, are obtained from numerical fits to the results of a Monte Carlo simulation with the code PENELOPE. The average differences between the model and the Monte Carlo results, after the fitting process, are below 1%. Our model permits to obtain improved versions of the classical approach of Berger in a straightforward way. The expressions obtained also describe the dose build-up of the primary photons.