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A determination of multiple scattering for a negative pion beam Watts, Larry James


The multiple Coulomb scattering of negative pions has significant effects on the dose distributions resulting from pion beams incident on thick targets. The use of negative pions in radiotherapy requires a detailed knowledge of the distribution of dose and biological effect. Thus it is important to have an accurate description for the lateral distributions of pions which result from multiple scattering. It has been proposed by Fowler and Perkins that these lateral distributions are of a Gaussian nature for incident pencil beams. In this study an attempt has been made to determine experimentally and theoretically the appropriate value for the standard deviation of the Gaussian in the pencil beam description. The experimental determination involved placing medical x-ray films in a homogeneous water phantom, perpendicular to the beam axis of the M8 biomedical channel at TRIUMF. The distributions recorded on film for circularly collimated beams were measured for optical density and compared to calculated distributions in order to extract the pencil beam information. The presence of contaminating electrons and muons as well as the difficulty in achieving a parallel beam complicated the determination of the standard deviation of the Gaussian for pions. The experimental determination at the end of a 20.1 cm range in water is only 7% greater than the preferred theoretical calculation for pions alone. This calculation is based on the first (Gaussian) term of Moliere’s theory modified for the Fano correction and energy loss and yields results 20% lower than those of the "standard reference" of Fowler and Perkins. The agreement between the theory for pions and the experiment for a real beam in water indicates that the theory presented should be adequate for treatment planning calculations.

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