A Many-Body Theory for Nearly-Free Electrons and Its Application to Annihilation of Positrons in a Periodic Field

抄録

A many-body theory for nearly-free electrons has been constructed by introducing “ Bloch-pair operators,” α_k and β_k, which are related to free-particle operators through the transformation
(Remark: Graphics omitted.)
where h is 2π times a reciprocal lattice vector, and θ_h is the sign of the relevant Fourier component, v_h, of the periodic field. This theory has been then applied to the annihilation of positrons in the periodic field. The interaction between a positron and a Bloch electron, has been, for the first time, taken into account through a few simplest diagrams. The result shows that a fairly sharp break of the angular-correlation curve occurs a the hexagonal-zone-face position in copper just as expected from the experiments previously made by the present author and his collaborator.