For protons in water the energy-loss variance accumulated per unit path is

PHYSICS · Subjective · Fermi University Physics · Nuclear Physics · Radiation interactions, detection and dosimetry · Radiation interactions, detection and dosimetry

The Nucleus Resolved, Ch Radiation in matter, computed: Bethe, Klein-Nishina and what they leave out

Problem

For protons in water the energy-loss variance accumulated per unit path is dσE2/dx=0.0871 MeV2 cm2 g−1\mathrm{d}\sigma_E^2/\mathrm{d}x = 0.0871\,\mathrm{MeV^2\,cm^2\,g^{-1}}, and the range follows the power law R=αEpR = \alpha E^{p} with p=1.75p=1.75 and R(100 MeV)=7.71 g cm−2R(100\,\mathrm{MeV}) = 7.71\,\mathrm{g\,cm^{-2}}. The accumulated variance gives a fractional range straggling σRR=0.0871 p3 R(3p−2) E02.\frac{\sigma_R}{R} = \sqrt{\frac{0.0871\,p^3\,R}{(3p-2)\,E_0^2}}. Estimate the absolute range straggling σR\sigma_R, in millimetres, for 100 MeV100\,\mathrm{MeV} protons in water (ρ=1.00 g cm−3\rho = 1.00\,\mathrm{g\,cm^{-3}}).

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