The correlated motion of a positron surrounded by electrons is a fundamental many-body problem. We approach this by modeling the momentum density of annihilating electron-positron pairs using the framework of reduced density matrices, natural orbitals and natural geminals (electron-positron pair wave functions) of the quantum theory of many-particle systems. We find that an expression based on the natural geminals provides an exact, unique and compact expression for the momentum density. The natural geminals can be used to define and determine enhancement factors for enhancement models going beyond the independent-particle model for a better understanding of results of positron annihilation experiments.
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