Multiple Scattering of Electrons. II

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 $sin \theta$ averaged over the distribution per unit solid angle, $f\left(\theta \right)$. This expression, which agrees within a few percent with the exact computation, is $w{〈sin \theta 〉}_{\mathrm{Av}}\sim 1.76A^{\frac{1}{2}}{(5.60-\frac{1}{3} log Z+\frac{1}{2} log A)}^{\frac{1}{2}},$ in which $w$ is the energy in units $m{c}^2$ and $A=24.8\mathrm{}\times {10}^{-26\mathrm{}}{Z}^2\mathrm{Nt}$. For the scattering intensity per unit solid angle at 0°, that is $f\left(0\right)\mathrm{}$, an approximate relation is $\frac{4\pi f\left(0\right)\mathrm{}}{w^2}\sim \frac{0.43}{A(5.60-\frac{1}{3} log Z+\frac{1}{2} log A)}.$ The accurate calculations show also that $\frac{f\left(\theta \right)}{w^2}$ 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 $w sin \alpha$, $\alpha$ 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.