Two Contributions to the Theory of Annihilation of Positrons in Metals. I. Determination of the True Fermi Surface

Abstract

The theory of positron annihilation in metals, including electron-positron and electron-electron interaction, is discussed. It is well known that the Coulomb force of the positron causes very major changes in the motion of the electrons. Nevertheless, it is established that a sharp "break" in the angular-correlation curve of the two $\ensuremath{\gamma}$ rays resulting from the singlet-state annihilation occurs at precisely those angles where it should be expected in the absence of electron-positron interaction. The break is an image of the discontinuity in the momentum distribution present in "normal" metals. Positron annihilation in metals is therefore a useful tool for the investigation of the true Fermi surface. It is also demonstrated that the slope of the angular-correlation curve at the Fermi momentum is related to the Gaussian curvature of the Fermi surface.