On the nuclear halo of a proton pencil beam stopping in water

The dose distribution of a proton beam stopping in water has components due to basic physics and may have others from beam contamination. We propose the concise terms core for the primary beam, halo (see Pedroni et al 2005 Phys. Med. Biol. 50 541-61) for the low dose region from charged secondaries, aura for the low dose region from neutrals, and spray for beam contamination. We have measured the dose distribution in a water tank at 177 MeV under conditions where spray, therefore radial asymmetry, is negligible. We used an ADCL calibrated thimble chamber and a Faraday cup calibrated integral beam monitor so as to obtain immediately the absolute dose per proton. We took depth scans at fixed distances from the beam centroid rather than radial scans at fixed depths. That minimizes the signal range for each scan and better reveals the structure of the core and halo. Transitions from core to halo to aura are already discernible in the raw data. The halo has components attributable to coherent and incoherent nuclear reactions. Due to elastic and inelastic scattering by the nuclear force, the Bragg peak persists to radii larger than can be accounted for by Molière single scattering. The radius of the incoherent component, a dose bump around midrange, agrees with the kinematics of knockout reactions. We have fitted the data in two ways. The first is algebraic or model dependent (MD) as far as possible, and has 25 parameters. The second, using 2D cubic spline regression, is model independent. Optimal parameterization for treatment planning will probably be a hybrid of the two, and will of course require measurements at several incident energies. The MD fit to the core term resembles that of the PSI group (Pedroni et al 2005), which has been widely emulated. However, we replace their T(w), a mass stopping power which mixes electromagnetic (EM) and nuclear effects, with one that is purely EM, arguing that protons that do not undergo hard single scatters continue to lose energy according to the Beth-Bloch formula. If that is correct, it is no longer necessary to measure T(w), and the dominant role played by the 'Bragg peak chamber' vanishes. For mathematical and other details we will refer to Gottschalk et al (2014, arXiv: 1409.1938v1), a long technical report of this project.