Signature of Fermi surface jumps in positron spectroscopy data

A subtractionless method for solving Fermi surface sheets ({\tt FSS}), from measured $n$-axis-projected momentum distribution histograms by two-dimensional angular correlation of the positron-electron annihilation radiation ({\tt 2D-ACAR}) technique, is discussed. The window least squares statistical noise smoothing filter described in Adam {\sl et al.}, NIM A, {\bf 337} (1993) 188, is first refined such that the window free radial parameters ({\tt WRP}) are optimally adapted to the data. In an ideal single crystal, the specific jumps induced in the {\tt WRP} distribution by the existing Fermi surface jumps yield straightforward information on the resolved {\tt FSS}. In a real crystal, the smearing of the derived {\tt WRP} optimal values, which originates from positron annihilations with electrons at crystal imperfections, is ruled out by median smoothing of the obtained distribution, over symmetry defined stars of bins. The analysis of a gigacount {\tt 2D-ACAR} spectrum, measured on the archetypal high-$T_c$ compound $YBa\sb{2}Cu\sb{3}O\sb{7-\delta}$ at room temperature, illustrates the method. Both electronic {\tt FSS}, the ridge along $\Gamma X$ direction and the pillbox centered at the $S$ point of the first Brillouin zone, are resolved.