The triple- and quadruple-escape peaks of 6.128 MeV photons from the F ( p , α γ ) 19 O 16 nuclear reaction were observed in an HPGe detector. The experimental peak areas, measured in spectra projected with a restriction function that allows quantitative comparison of data from different multiplicities, are in reasonably good agreement with those predicted by Monte Carlo simulations done with the general-purpose radiation-transport code penelope . The behaviour of the escape intensities was simulated for some gamma-ray energies and detector dimensions; the results obtained can be extended to other energies using an empirical function and statistical properties related to the phenomenon.