  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
