Muon dose distribution from a decaying pencil beam of pions

Increased interest in the use of negative pion beams for radiotherapy has led to a requirement for accurate knowledge of the extent and effect of beam contamination. Contaminating muons from the decay of pions upstream of the irradiation position cannot be easily identified by time-of-flight or range measurement techniques. A calculation of the stopping and dose distributions of these muons was performed. A monoenergetic pencil beam of 180 MeV/c pions, normally incident onto a semi-infinite water slab, was assumed to decay into muons over the one metre distance upstream of the water and in the water. Dose from the subsequent decay of muons to electrons was included. Contour maps of the stopping and dose distributions are presented as well as the stopping and depth-dose distributions for an infinite beam. The calculation clearly illustrates that muons from the decay of monoenergetic pions do not have a unique momentum and range, but rather include a wide spectrum of ranges and momenta. Since a muon dose contribution of 16% has been calculated at a depth of 8 cm, these muons could result in unexpected nonuniformities in dose in a clinical pion irradiation if they are ignored in pion treatment planning.