Third-order coulomb wave function and single quantum annihilation

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An expression for the third-order Coulomb wave function, correct to order (αZ)3 for all momenta and energies, is derived. Using this wave function the total cross section for single-photon emission resulting from a positron annihilating with a K-shell electron (single quantum annihilation), valid to relative order (αZ)2, is calculated numerically. The results for lead are compared to the exact answer of Jaeger and Hulme, and the results for silver are also given graphically. The effect of the third-order term in the cross section is found to be significant, especially for low and intermediate positron energies. The cross section for lead is found to be qualitatively correct while that for silver is essentially exact. The question of how to treat the normalization factors of the various wave functions is also discussed. © 1963 The American Physical Society.

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Physical Review

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