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

Abstract

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 twostep 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.

Calculating electron momentum densities and Compton profiles using the linear tetrahedron method

“…respectively. The momentum density (or spin density in momentum space) in two or three dimensions may be experimentally recovered by measuring a series of profiles along different crystallographic directions, and employing a suitable tomographic method [20].…”

Many body effects seen in the positron annihilation experiment

“…In a recent paper by one of us [14], the analysis of the experimental e-p momentum density in Mg led to the conclusion that there exist strong e-e dynamic correlations in this metal. Such conclusion was based on some model considerations.…”

Transform Methods of Computerized Tomography in Studying Electronic Structure and Fermi Surfaces of Solids

“…In this technique, applied in papers [76][77][78][79], one calculates the 1D FT of measured 2D spectra which represent the 3D FT of the 3D density. By expanding FT into the lattice harmonics, one reconstructs the 3D density according to the Fourier-Bessel method proposed for plane pro- 1D CP ⇒ 2D densities CM [29][30][31][32] DFT [70][71][72][73] 1D NS ⇒ 3D densities HP [41,42] jections [52,53]. This method is equivalent to the following procedure.…”

“…Cormack's method (CM), adopted for symmetry systems [12], has been applied many times for reconstructing electron-positron momentum densities from 2D ACAR data [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] as well as for reconstructing line dimensions of the Fermi surface from Compton scattering profiles (i.e. conversion: from 1D to 2D) [29][30][31][32].…”