Alignment creation by elastic electron scattering. A quantum treatment

Alignment creation by elastic heavy particle scattering has been studied by many authors. A formula for the alignment creation cross section by elastic scattering is obtained by quantum-mechanical methods. The formula obtained differs from the analogous formula relevant for inelastic electron scattering. In the case of a J=1 to J=1 transition according to the inelastic formula, the alignment created is proportional to the quantity σ (1) - σ (0) where σ (M) is the excitation cross section of the M magnetic sublevel and thus σ (1) = (σ1-1 + σ10 + σ11)/3 and σ (0) = (σ0-1+σ00 + σ01)/3 where σMM' refers to the cross section of the electron impact induced M' to M transition. In the elastic scattering alignment creation formula obtained in the case of a J=1 to J=1 elastic scattering, the alignment created is proportional to the quantity q(1) - q(0) where q(1) σ (1) - σ11/3 and q(0) = σ00/3. Thus in obtaining q(M), the elastic scattering cross section by the M magnetic sublevel, σMM', is subtracted. This derivation considered only direct scattering, i.e. the incident electron was considered distinguishable from the target electrons. (Y.Kazumata)