On LCAO positron wavefunctions in crystals

In this work we deal with the construction of delocalized positron wavefunctions in crystalline solids within the linear combination of atomic orbitals (LCAO) scheme. The present method leads to an accurate wavefunction of a positron, both in the core and in the interstitial region of a crystal. Furthermore, its representation by a superposition of atomic orbitals is simple enough for the application to calculations of expectation values, like e.g. of accurate electron-positron annihilation rates (high momentum components). The representation of the positron wavefunction can be optimized with respect to the two points of view: firstly, the number of orbitals in the LCAO representation can be minimized (e.g. within the localized spherical orbitals (LSO) method) or, secondly, the orbitals can be chosen to be well-localized around their atoms and vanishing near all others: this leads to the computational advantage, that three- or multicenter integrals arising during numerical calculations can be replaced by oneand two-center integrals which are treated using standard numerical techniques in spherical polar or elliptic coordinates. The transformation from the first into the second representation can be performed via a ''fuzzy'' cellular partitioning of the crystal volume via an analytically continuous shape-function. Finally we demonstrate our method in the case of a positron in lithium.