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A correlation function for a positron-electron pair within a metal is obtained by solving an extended Bethe-Goldstone equation which includes the short range positron-electron hole interaction besides the short range positron-electron interaction. The computed lifetimes of positrons are longer than those calculated by Kahana. The effects of the long range Coulomb interaction on the annihilation rates are investigated. It is pointed out that the two-photon annihilation process accompanied by a plasmon emission in metals with low electron densities may not be neglected.
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Kanazawa et al. (1965) studied this question.
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