The basis set, scattering wavefunction and Schwinger variational principle: an application for low energy positron-atom scattering

Abstract

The quality of the positron wavefunction produced by applying the Schwinger variational principle (SVP) is scrutinized. An optical potential formalism is applied considering a semiempirical polarization potential. The positron wavefunction is expanded into a basis set formed by hydrogen-like atom eigenfunctions. Two different forms for the ansatz are tested out. The model is applied to positron scattering and annihilation by hydrogen, and by argon atoms as examples. The results are compared to the ones obtained through the direct integration of the Schrödinger equation. We found that the positron wavefunction generated by the SVP is of good quality only if the basis functions are mainly located inside the potential range. We also found that to provide the best scattering amplitude possible, the SVP may produce intentional deviations all along the positron wavefunction to compensate for local basis set deficiencies. We proposed a criterion based on the Lippmann–Schwinger equation to evaluate the accuracy of the positron wavefunction.