Application of the Multiple Scattering Theory to Cloud-Chamber Measurements. I

Some questions concerning the application of the multiple scattering theory to the analysis of cloud-chamber pictures are discussed from the theoretical point of view: (a) The Molière theory of multiple scattering is modified by the consideration of the finite nuclear dimensions. It is assumed that the probability of single scattering goes abruptly to zero for angles greater than ${\varphi }_0=\frac{{\varphi }_{m}a}{r_n}$, where $a$ is the radius of the statistical Thomas-Fermi atom, $r_n$ the radius of the nucleus, and ${\varphi }_m$ is the screening angle as derived by Molière. The distribution function for plural and multiple scattering is then derived for finite values of ${\varphi }_0$. It is shown that the cutoff affects especially the tail behavior of the distribution function as it was to be expected. While Molière's function decreases as ${\varphi }^{-3\mathrm{}}$ for projected angles of scattering large compared to the rms angle, the modified function decreases approximately as ($\frac{1}{\varphi }$) times a Gaussian function of ($\varphi -{\varphi }_0$) for angles large compared to the rms angle and the cut-off angle. (b) The distribution function for the mean value of the square angle of scattering in $n$ plates of a multiple-plate cloud chamber is derived and compared with the normal ${\chi }^2$-distribution. (c) The effect of observational errors on the distribution function for multiple scattering is estimated quantitatively and discussed in some detail for the case where the mean-square angle of real scattering is large compared to the variance of the noise level scattering.