arXiv 2108.043882021-08-10quant-phhep-th

相对论库仑问题的有限微扰理论

Finite perturbation theory for the relativistic Coulomb problem

Scott E. Hoffmann

备注：: 11 pages, 5 figures. Submitted to Physics Letters B

摘要：

我们提出了一种新形式的相对论性量子力学，并演示了如何解决它使用最近导出的酉微扰理论，在分波分析。该理论是测试一个相对论性的问题，两个无自旋，质量相等的粒子，其中的相互作用是完全由库仑势。因此，它并不意味着再现两个电子散射的实验结果，而是为了测试我们的计算方法。我们发现，这种微扰理论给出了有限的结果，在二阶。这与其他版本的微扰理论不同，后者在二阶和所有高阶上都有不同的结果。我们计算微分截面在非相对论制度，我们发现很好的协议与卢瑟福公式。然后，在相对论范围内，我们发现微分截面的形状与莫勒公式相似，与莫勒公式相差不到一个数量级。

英文摘要：

We present a novel form of relativistic quantum mechanics and demonstrate how to solve it using a recently derived unitary perturbation theory, within partial wave analysis. The theory is tested on a relativistic problem, with two spinless, equal mass particles, in which the interaction is entirely given by a Coulomb potential. As such, it is not meant to reproduce experimental results for the scattering of two electrons, but is intended as a test of our calculation methods. We find that this perturbation theory gives finite results at second order. This is unlike other versions of perturbation theory, which find divergent results at second and all higher orders. We calculate differential cross sections in the nonrelativistic regime, where we find excellent agreement with the Rutherford formula. Then, well into the relativistic regime, we find differential cross sections with similar shapes to the Møller formula and differing from that formula by less than an order of magnitude.

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英文摘要：

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