The three-dimensional positron-electron momentum density study in Ge by means of a full-scale use of two-dimensional angular correlation of positron annihilation radiations

The positron-electron momentum density in germanium was studied by a full-scale use of the two-dimensional angular correlation of positron annihilation radiations (2D-ACAR). The term, a full-scale use of 2D-ACAR, means that the three-dimensional momentum-space density rho (p) of the annihilation positron-electron item is directly determined from a set of experimental 2D-ACAR spectra, followed by the reconstruction technique. The obtained electron momentum density, rho (p), showed, as a whole, good agreement with the electron momentum distribution of the fully filled Jones zone with the exception that a deep dip in the origin appears, which has been observed in the 1D-ACAR or semi-2D-ACAR integrated spectra in germanium. In the present work, the electron momentum density distribution shows a ridge along the (110) line and a vary deep valley exists along the (100) line, which is also the deviation from the Jones zone. In germanium, the valence 4p electrons are mainly participating in bonding sigma bonds, and the distribution in space is prominently anisotropic. This anisotropy is reflected on the electron momentum density distribution in the present work. The analysis based on group theory was performed by Saito et al. in order to investigate the origin of the anisotropy in the present work.