Relativistic Energy Levels of Para-Helium

Abstract

The practical usefulness of Relativistic Schr\"odinger Theory (RST) is tested by calculating approximately the energy difference between the excited singlet state $1s2s {}^1S_0$ and the ground state $1s^2 {}^1S_0$ of the helium-like ions with arbitrary charge number $z_{\rm ex} (2\le z_{\rm ex}\le 100)$. The results are compared to the corresponding predictions of other theoretical approaches in the literature and to the experimental data. Since the exact solutions of the RST energy eigenvalue problem are unknown, one has to resort to approximative methods. However the crudest approximation (``spherically symmetric approximation'') yields relatively accurate results so that it seems worth while to develop more powerful approximation techniques