Probabilities ofK-Electron Ionization of Silver by Cathode Rays

K-electron ionization by impact is treated here both experimentally and theoretically. The experimental work is on Ag in extremely thin films bombarded by cathode rays from constant potentials up to seven times the minimum ionizing potential. Ratios of probabilities of K ionization at different voltages are found as ratios of K line intensities after the latter have been corrected for minor perturbing factors. One of these is the slight retardation of the cathode rays within the film. Another is the effect of cathode-ray diffusion, in increasing the numbers of atoms penetrated. These effects occur in all films. In some of our films, which were backed with Be, there were two more corrections, both for K ionization of the Ag by the Be: one through rediffusion of cathode rays into the Ag, the other through continuous-spectrum x-rays. Altogether, films without backing appear more reliable at high voltages, and films with it at low voltages, though when corrected as described, the results agree well at all voltages in the range covered. An approximate empirical formula is probability=constant×U^-mlogU, where U is the ratio of tube voltage to minimum ionizing potential, and m is about 0.78. Among the theoretical formulas in the literature, those based on wave mechanics all depend on Born's approximation, which is invalid unless U is large, so they do not apply well to these data The classical quantum theory, considered as a possible temporary approximation, requires some further development, which is given here. The formula thus obtained seems to express the principles of classical quantum theory without seriously inaccurate approximations, but it agrees with the data only in the general type of the function: the ionization probability increases from zero at $U=1$ with a finite slope, attains a maximum value, and then declines. Quantitatively, the theory is far from the facts. A strictly heuristic modification of classical theory, changing the law of repulsion between the cathode ray and the K electron to an inverse cube, leads to a formula probability=constantU(π2invcosU^-1/2)²-1. This agrees fairly well with experiment, even though it contains no constant to change the shape of the graph, like the m in the other equation. But there is other evidence, as well as theoretical reason, for believing that the fundamental defect in the classical quantum theory lies not so much in any error in the inverse square law as in its dependence on contradictions of the uncertainty principle.