Nuclear Multipole Transitions in Inelastic Electron Scattering

Abstract

Expressions are obtained for the differential cross sections for inelastic scattering of fast electrons with excitation of various nuclear multipole transitions. The most probable transitions are those that involve collective motion of many nucleons, and in this case the term arising from the transition charge density dominates those that come from the current and magnetization densities. There is then a close relation between the probability for inelastic electron scattering and the probability for the corresponding radiative electric multipole transition, although an assumption must be made as to the shape of the transition charge density. This is illustrated with a detailed discussion of the collective electric quadrupole transitions, using the model of Bohr and Mottelson. When the transition is produced by one or a small number of nucleons, or when it is of magnetic multipole type, there is likely to be little relation between inelastic scattering and radiation probabilities. The electric monopole transition (0+→0+) is also discussed. It is shown how the elastic scattering can be corrected for unresolved inelastic scattering as well as elastic quadrupole scattering before an analysis is made in terms of the spherically symmetric part of the static nuclear charge density, and also how the strength as well as the shape of the transition charge density can be determined experimentally when only relative measurements of inelastic scattering are available.