Effect of Recoil on the Elastic Scattering of High-Energy Electrons by Zero-Spin Nuclei

Abstract

The effect of nuclear recoil on the elastic scattering of high-energy electrons or muons by zero-spin nuclei is studied by adapting the Breit two-particle Hamiltonian to the case that one of the two particles is of finite size, is spinless, and is nonrelativistic, the other being a normal point Dirac particle. A radial and angular separation of the Dirac equation is still possible. To leading order in the parameter (electron energy)/ (nuclear mass), the effect of the dynamic recoil terms is to rotate the scattering amplitude vectors in the complex plane without changing their magnitudes, a result which is independent of the shape and size of the nuclear charge distribution. To this order, the cross section is affected only by the kinematic recoil corrections. The dynamic recoil terms also influence the scattering amplitudes through terms of order (electron mass)/(nuclear mass). These corrections, owing to large amplification factors in going from phase shifts to cross section, may be of some significance in muon scattering, but are probably of no importance in the analysis of high-energy electron scattering. The dynamic effect is proportional to nuclear charge and therefore nearly as great for heavy as for light nuclei.