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A simple formula has been derived for calculating root mean square (rms) radius of a proton pencil beam inside a body, where the body is approximated by a parallel, multiple-slab model. The derived rms radius expression was based on Brahme's formulation and Scott's approximation, while it eventually agrees with a special case resulting from Lax and Brahme's formulas for a multiple-slab model. A depth dose model was also constructed, taking into account the energy loss of protons, the range straggling, the momentum spread of the proton beams, and the flux reduction and local dose distributions were compared with previously reported experimental data, showing reasonable agreement between them.
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