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.

中文翻译：

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基组、散射波函数和施温格变分原理：低能正电子原子散射的应用

仔细检查应用施温格变分原理 (SVP) 产生的正电子波函数的质量。考虑到半经验偏振势，应用光学势形式。正电子波函数被扩展为由类氢原子本征函数形成的基组。测试了 ansatz 的两种不同形式。该模型以氢原子和氩原子为例，应用于正电子散射和湮灭。将结果与通过直接积分薛定谔方程获得的结果进行比较。我们发现，只有当基函数主要位于势能范围内时，SVP 生成的正电子波函数才具有良好的质量。我们还发现，为了提供最佳的散射幅度，SVP 可能会沿着正电子波函数产生有意的偏差，以补偿局部基组的缺陷。我们提出了一个基于 Lippmann-Schwinger 方程的标准来评估正电子波函数的准确性。