Coupling of positron annihilation and compton scattering: A theoretical possibility to analyze positron distribution through atom-like local patterns appearing in positron annihilation A(r)- and compton scattering B(r)-functions

Areal space function A(r) has been introduced as the Fourier inversion transform of the electron-positron pair momentum density function in solids. It corresponds to the Compton scattering B(r) function defined in the same way from the electron momentum density function. The correlation theorem shows that the A(r) and B(r) can be described in terms of autocorrelation among the pair-and among the electron- wave functions, respectively. An electron weight function F(r`,r) has been introduced. The r'-averaging transforms a positron autocorrelation function P(r) exactly into the ratio A(r)/B(r). The ratio function, therefore, has a theoretical possibility of drawing information of positron distribution by reducing an electron distribution effect in an "averaged" form. In a pseudopotential framework for Si and Ge in which the core-orthogonality (CO) of the valence electronic states is fully taken into account, atom-like local patterns appear on contour maps of A(r) and B(r). The patterns become clearer on the maps of anisotropic parts of the CO contributions DeltaA(r) and DeltaB(r). The centre position of the pattern in DeltaB(r) is just on the unit-cell atom site and the shape and size also well correspond to those of the atom. In DeltaA(r) an electron coupling with positron distribution modifies the atom-like pattern in position, shape and size. The ratio A(r)/B(r) becomes an interesting candidate as a probe probiding us with an information of positron distribution around the electronic bonding center.