Reconstruction techniques in angular correlation of positron annihilation experiments

Abstract

Various techniques for the reconstruction of momentum densities from 2D-ACPAR and ID-ACPAR (angular correlation of positron annihilation radiation) data are reviewed. Emphasis is placed on spherical harmonic reconstruction techniques. Results of the reconstruction of the Fermi surface of vanadium are included. The possibility of obtaining wave-function or quantum density matrix information from the momentum density is also mentioned.

Positron annihilation study of the Fermi surface of Ni2MnGa

“…In addition to the benefits detailed in Kontrym-Sznajd's original paper [54], our practical experience of using Cormack's method for FS measurement has shown one further great advantage over Fourier-transform based methods connected with those methods introducing strong oscillations into the reconstructed densities at low momentum. For examples of these low momentum artefacts, coming from the final inverse Fourier transform, see [55,56]. It is also worth noting the recent attempts to avoid this problem by explicitly removing the contribution from the first Brillouin zone in the data analysis [57].…”

“…It is also worth noting the recent attempts to avoid this problem by explicitly removing the contribution from the first Brillouin zone in the data analysis [57]. An early review of reconstruction algorithms can be found in [55] and a more recent summary can be found in [58,59]. Cormack's method has been applied by us in a wide range of materials and to momentum densities coming not only from positron annihilation but also x-ray Compton scattering [40,41,44,47,60].…”

Methods of Extracting Electron-Positron Enhancement Factors from Experimental ACAR Data

“…Alternative reconstruction techniques for 1D and 2D ACAR data were described by Pecora [8] as well as by Cormack [9] and Reiter and Silver [10]. We recommend techniques of Refs.…”

On the possible identification of defects using the autocorrelation function approach in double Doppler broadening of annihilation radiation spectroscopy

“…ρ 2γ j (p)) [18]. The main use of B 2γ (r) has in the past been in reconstructing full three-dimensional momentum densities ρ 2γ (p) for perfect (non-defected) crystals from the one and two dimensional projections that DBAR and ACAR spectroscopies provide [19,20]. The point emphasized here is that, with regard to positron annihilation radiation originating from vacancy traps, B 2γ (r) also presents itself as a function with useful application, being probably the best real-space visualization of the defect's atomic structure that quantum mechanics will allow.…”