Theory of Multiple Coulomb Scattering from Extended Nuclei

Two independent methods are described for calculating the multiple scattering distribution for projected angle scattering resulting when very high-energy charged particles traverse a thick scatterer. The single scattering law for projected angle scattering is taken to be the Rutherford scattering law for projected angle scattering modified at small angles by electron shielding and at large angles by a nuclear form factor ${\mathcal{F}}_n\left(\frac{\varphi }{{\varphi }_0}\right)$ which gives the effect of the finite nuclear size. The calculations can be carried through for any reasonable choice of ${\mathcal{F}}_n$ and have been carried through for two suggested choices of ${\mathcal{F}}_n$ for the examples of fast $\mu$-meson scattering in lead slabs of thickness 2 cm and 5 cm, with good agreement for the two methods of calculation. The results are compared with the theories of Molière and Olbert.