Relation between Multiple Coulomb Scattering and Residual Range in Nuclear Emulsion

Abstract

Measurements of multiple Coulomb scattering were carried out on 101 artificially produced stopping protons from the end of the track to a point where the residual range was 2500\ensuremath{\mu}. These measurements yield a new relation between range and multiple scattering which can be represented by a power law. The mass dependence was derived theoretically and checked by measuring 20 positive pions. The general relationship is: ${〈|\ensuremath{\eta}|〉}_{\mathrm{Av}}=(19.0\ifmmode\pm\else\textpm\fi{}0.3){R}^{\ensuremath{-}(0.607\ifmmode\pm\else\textpm\fi{}0.016)}{(\frac{{M}_{P}}{M})}^{(0.393\ifmmode\pm\else\textpm\fi{}0.016)}{(\frac{t}{50})}^{\frac{3}{2}},$ where ${〈|\ensuremath{\eta}|〉}_{\mathrm{Av}}$ is the mean absolute sagitta due to multiple scattering, $R$ is the range, $t$ the cell length, $M$ is the particle mass, and ${M}_{P}$ the mass of the proton. All lengths are measured in microns. This relationship leads to a set of schemes for making scattering measurements on stopping tracks in order to determine the mass of the particle with the maximal efficiency. The precision possible on an individual track is limited, but a sequence of tracks, each of which need not be too long, can give a very satisfactory precision, free from the systematic errors inherent in ionization measurements.