where ra is the electron gas parameter given by and n is the electron density. This behavior of 7(p) is quite sensitive to the construction of the many-body wave function. Experimentally, the peaking of 7(p) at pf should in principle be observable in alkali metals .
The Kahana theory in the plane-wave representation (corresponding to single particle wave functions in the HEG) can be generalized by using Bloch wave functions for a periodic ion lattice. This approach has been reviewed by Sormann . An important conclusion is that the state dependence of the enhancement factor is strongly modified by the inhomogeneity and the lattice effects. Therefore in materials, which are not nearly-free-electron like, the Kahana momentum dependence of is probably completely hidden.
The plane wave expansions used in the Bethe-Golstone equation can be slowly convergent to describe the cusp in the screening cloud. Choosing more appropriate functions depending on the electron-positron relative distance may provide more effective tools to deal with the problem. The Bethe-Golstone equation is equivalent to the Schrodinger equation for the electron-positron pair wave function F(ri, r2)
where y is a screened Coulomb potential. The Pluvinage approximation  for F(ri,r2) consists in finding twofunctions G(ri,r2) and /(ri,r2) such that F(ri,r2) = G(ri,r2) /(ri,r2) and such that the Schrodinger equation becomes separable. G(ri,r2) describes the orbital motion of the two particles ignoring each other, and /(ri,r2) describes the correlated motion. The correlated motion depends strongly on the initial electron state i (without the presence of the positron). Obviously, the core and the localized d and / valence electrons are less affected by the positron than the sp-type valence orbitals. On the basis of the Pluvinage approximation, one can develop a theory for the momentum density of annihilating electron-positron. In practice, this leads to a scheme in which one first determines the momentum density for a given electron state i within the IPM. When calculating the total momentum density this contribution is weighted by
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