The Scattering of Fast Electrons by Heavy Elements. II

Abstract

If fast electrons impinge on a mercury atom, the external electrons will modify the nuclear scattering, at least for small angles. We have determined the amount of scattering to be expected, as a function of angle, for 100-kv electrons and for 230-kv electrons. For the former, shielding is effective below 60\ifmmode^\circ\else\textdegree\fi{}, and for the latter, below 15\ifmmode^\circ\else\textdegree\fi{}. For the determination of phase shifts, the electron may be pictured as moving in an effective (Dirac) field, which involves zero, first, and second derivatives of the ordinary (Hartree) field. Three methods were used: (1) integration with the differential analyzer, (2) the WKB procedure, and (3) the first-order Born approximation. Methods (1) and (2) lead to results in good agreement with each other for all angular momenta, and method (3) gives good results for large angular momenta, despite the fact that the first-order correction to the wave function is large. The summation of the series for the scattering amplitudes was accomplished by noting that the phase shifts decreased in an exponential manner for large values of the angular momentum.