Elastic and inelastic scattering of electrons by aligned light nuclei

Abstract

The contribution to the elastic and inelastic scattering cross sections, Δ, due to alignment of nuclei having axial symmetry was calculated for scattering of unpolarized, ultra-relativistic electrons by7Li atoms. This contribution turned out to be on the order of magnitude of the cross section σ0 previously calculated in the absence of nuclear alignment. For various nuclear orientations, the ratios Δ/σo were calculated as a function of the momentum transfer q, which may be useful, for example, in increasing the reliability of identification of quantum numbers of nuclear states and multipole transitions. In contrast with the expression for σo, the expression for Δ contains cross products of reduced matrix elements (RME), along with the squares of their moduli. This permits one, having previously experimentally found σ0 and Δ under various kinematical conditions but for fixed q (the RME depend only on q), to obtain a system of equations for the RME and the statistical tensor g2, which characterizes the degree of alignment of the nuclear target, along with the separation of the parallel and perpendicular cross sections as in the case of unaligned nuclei. Having solved the system of equations, one finds g2 both in terms of the moduli of the RME of each multipole transition individually, and also in terms of their relative phases. The additional information thus obtained for each nuclear transition may serve as a more strict criterion for checking models of nuclei used in calculations than measurement of σ0 alone.