Different ways of dealing with Compton scattering and positron annihilation experimental data

Different ways of dealing with one-dimensional (1D) spectra, measured e.g. in the Compton scattering or angular correlation of positron annihilation radiation (ACAR) experiments are presented. On the example of divalent hexagonal close packed metals it is shown what kind of information on the electronic structure one can get from 1D profiles, interpreted in terms of either 2D or 3D momentum densities. 2D and 3D densities are reconstructed from merely two and seven 1D profiles, respectively. Applied reconstruction techniques are particular solutions of the Radon transform in terms of orthogonal Gegenabauer polynomials. We propose their modification connected with so-called two-step reconstruction. The analysis is performed both in the extended p and reduced k zone schemes. It is demonstrated that if positron wave function or many-body effects are strongly momentum dependent, analysis of 2D densities folded into k space may lead to wrong conclusions concerning the Fermi surface. In the case of 2D ACAR data in Mg we found very strong many-body effects. PACS numbers: 71.18.+y, 13.60.Fz, 87.59.Fm