On the nuclear halo of a proton pencil beam stopping in water
  The dose distribution of a pencil beam in water consists of a core, a halo, an aura and (possibly) spray. The core is due to primary protons which suffer multiple Coulomb scattering (MCS) and slow down by multiple collisions with atomic electrons (Bethe-Bloch theory). The halo is due to charged secondaries, many of them protons, from elastic interactions with H, elastic and inelastic interactions with O, and nonelastic interactions with O. We show that the halo radius is roughly one third of the beam range. The aura is due to neutral secondaries (neutrons and gamma rays). Spray denotes dose, avoidable in principle, coming in from the beam line.   We have measured the absolute dose at 177 MeV using a test beam in a water tank. The beam monitor was a PPIC 'proton counter' and the field IC a dose calibrated Exradin T1. We took depth-dose scans at ten displacements from the beam axis ranging from 0 to 10 cm. The dose spans five orders of magnitude, and the transition from halo to aura is obvious.   We present model-dependent (MD) and model-independent (MI) fits to these data. The MD fit has 25 parameters, and the goodness of fit (rms (measurement/fit) - 1) is 15%. The MI fit uses cubic spline fits in depth and radius. The goodness of fit is 9%. This fit is more portable and conceptually simpler.   We discuss the prevalent parameterization of the core/halo originated by the PSI group. We argue that its use of T(w), a mass stopping power which includes energy deposited by nuclear secondaries, is incorrect. The electromagnetic (Bethe-Bloch) mass stopping power should be used instead. In consequence, 'Bragg peak chamber' measurements and associated corrections are, in our view, irrelevant. Furthermore, using T(w) leads to spurious excess dose on the axis of the core around midrange, which may be significant in fields involving relatively few pencil beams. 
Bernard Gottschalk, Ethan W. Cascio, Juliane Daartz and Miles S.   Wagner
physics.med-ph physics.ins-det