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

The theory of multiple Coulomb scattering discussed in Part I has been applied to some specific problems in the analysis of data obtained with a multiplate cloud chamber. In particular, the problem of estimating the momentum (or, more exactly, the quantity Π=pcβ) for a single particle is discussed, and a procedure for determining mass using scattering and residual range is given for the case of a group of particles homogeneous in mass. In the case of an inhomogeneous group of particles, it is shown that the distribution function for values of the mean square angle of scattering in n plates can sometimes be used as a basis of separation into nearly homogeneous mass groups. In addition the distribution of the mean square angles provides an estimate of the error in II or in the value of the mass. These methods are illustrated by a determination of the masses of the proton and meson using a mixture of these particles observed in a multiplate cloud chamber. In the theory developed in Part I it was assumed that the probability for single Coulomb scattering goes abruptly to zero for angles greater than ϕ₀=ϕ_mar_n, where ϕ_m is the screening angle as given by Molière, a is the Thomas-Fermi atomic radius, and r_n is the nuclear radius. As a result of this assumption the mean value of the scattering angles, for means of order two and higher, remains finite as contrasted with the result of Molière or Snyder and Scott where the mean square angle of scattering is infinite. Consequently either the mean of the absolute values of the scattering angles or the rms angle of scattering can be used in the above applications. Both cases are given. The above assumption as to the cut-off angle for single scattering affects the value of the rms angle of scattering only slightly; it is shown, however, that the behavior of the "tail" of the distribution function depends critically on the choice of ϕ₀. Consequently, the value of Π or of the mass is not greatly dependent on the particular theory of multiple scattering used, but the probability of scattering through angles large compared with the rms angle is. The difficulty of identifying a nuclear scattering by this method is emphasized.