Multiple Scattering of Electrons

The series developed in a previous paper representing the distribution for the multiple scattering of electrons has been evaluated numerically for a large number of cases; the results are given in Table I. An approximate expression is found for the value of $sin \ensuremath{\theta}$ averaged over the distribution per unit solid angle, $f(\ensuremath{\theta})$. This expression, which agrees within a few percent with the exact computation, is $w{〈sin \ensuremath{\theta}〉}_{\mathrm{Av}}\ensuremath{\sim}1.76{A}^{\frac{1}{2}}{(5.60\ensuremath{-}\frac{1}{3} log Z+\frac{1}{2} log A)}^{\frac{1}{2}},$ in which $w$ is the energy in units $m{c}^{2}$ and $A=24.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}26}{Z}^{2}\mathrm{Nt}$. For the scattering intensity per unit solid angle at 0\ifmmode^\circ\else\textdegree\fi{}, that is $f(0)$, an approximate relation is $\frac{4\ensuremath{\pi}f(0)}{{w}^{2}}\ensuremath{\sim}\frac{0.43}{A(5.60\ensuremath{-}\frac{1}{3} log Z+\frac{1}{2} log A)}.$ The accurate calculations show also that $\frac{f(\ensuremath{\theta})}{{w}^{2}}$ is almost independent of the energy. A series formula is derived for the projected scattering distribution as observed in a cloud chamber. The averages of $w sin \ensuremath{\alpha}$, $\ensuremath{\alpha}$ being the projected angle, are given in Table VI. These averages are smaller than the values computed by Williams and show a variation with energy. It is believed that the largest inaccuracy remaining in the results given is due to uncertainties in the single scattering law.