Molière's Theory of Multiple Scattering

Abstract

Mole\`ere's theory of multiple scattering of electrons and other charged particles is here derived in a mathematically simpler way. The differential scattering law enters the theory only through a single parameter, the screening angle ${{\ensuremath{\chi}}_{a}}^{\ensuremath{'}}$, Eq. (21). The angular distribution, except for the absolute scale of angles, depends again only on a single parameter $b$, Eq. (22). It is shown that $b$ depends essentially only on the thickness of the scattering foil in g/${\mathrm{cm}}^{2}$, and is nearly independent of $Z$.The transition to single scattering is re-investigated. An asymptotic formula is obtained which agrees essentially with that of Moli\`ere, Snyder, and Scott, but which remains accurate down to smaller angles, Eq. (38).The theory of Goudsmit and Saunderson has a close quantitative relation to that of Moli\`ere, and a good approximation to their distribution function can be obtained by multiplying Moli\`ere's function by ($\frac{\ensuremath{\theta}}{sin\ensuremath{\theta}}$). This relation holds until the scattering angles become so large that only very few terms in the series of Goudsmit and Saunderson need to be taken into account.