Scattering of High Velocity Electrons in Hydrogen as a Test of the Interaction Energy of two Electrons

摘要

1. The electronic scattering of high velocity electrons is considered as a test of the formulas for the interaction energy of two electrons. Three formulas for the interaction energy of two Dirac electrons are considered: I, the simple electrostatic interaction, II, the Gaunt formula, III, the Breit formula.\ud\ud2. The Dirac transition probability method is reviewed briefly.\ud\ud3. The cross-section of free electrons at rest for scattering high velocity electrons is calculated by the Dirac transition probability method, using each of the three formulas for interaction energy. Random distribution of spins is assumed. Relativistic variation of mass with velocity is taken into account, removing the symmetry about 45° of the classical scattering formula. Expanded to terms in β^2 the formulas obtained are compared with the classical Darwin formula and the recent formula of Mott. They differ from Mott's formula and from each other by terms of order β^2.\ud\ud4. For high-velocity electrons, the scattering by hydrogen may be considered as the sum of nuclear and electronic scattering. A criterion for the validity of this procedure is obtained. The advantage of using hydrogen as the scatterer in experiments to test these formulas is discussed.