Effect of the Nuclear Coulomb Field on the Capture of Slow Mesons

where sA„ is the average length of path for the electrons traversing the foil. The approximation involved in (1) is therefore equivalent to the assumption of linearity of the electron paths and the Goudsmit-Saunderson result is thus valid only for thin foils or for very fast electrons for which the scattering of the beam is small. Stated otherwise, the assumption of linear paths is equivalent to replacing cos 8 by unity in the convection term of the Boltzmann equation which describes the variation in the angular distribution with penetration into the foil. ' A calculation of the average path length of electrons which have penetrated a given distance into the scattering foil is of importance not only for the angular distribution but also for the evaluation of experiments on energy loss. ' The following is an attempt to make such a calculation. The restriction will be made to the case of foils thin enough, or electrons fast enough, so that back scattering is negligible. Thus, while the region of validity of (1) is to be extended, the extension is not to be made beyond the region of prediffusion, The average path is approximately given by