Off-line analysis of positron annihilation spectra. I. Signature of crystal symmetry

While the technique of 2-D angular correlation of the electron-positron annihilation radiation (2D-ACAR) yields data in the laboratory frame, consistent off-line data analysis requires their reformulation in the crystal frame. In the case of an n-axis projected 2D-ACAR spectrum (where n denotes a principal crystallographic axis) of a high-Tc superconductor, the crystal frame derivation needs enhancement of information on spectrum symmetry. The concept of signature of crystal symmetry (SCS) in a 2D-ACAR histogram discussed in this paper is a basic ingredient to the consistent solution of the problem. The SCS in a row 2D-ACAR histogram is defined as a collection of chi-square sums over Mmax + 1 sets of sites inside the detector-defined histogram plane. The number Mmax is fixed by choice of the principal crystallographic axis n-vector and the angular aperture of the setup. The necessity of this concept is discussed in Section 2. The correct understanding of the meaning of the SCS results heavily relies of that of the various sources contributing to the symmetry a 2D-ACAR spectrum. This point is discussed in Section 3. The quantitative definition of the SCS is detailed in Section 4. Finally, Section 5 is devoted to a short consideration of the computation of the SCS numerical values