  The emergence of a multiplet structure of the helium-like ions is studied
within Relativistic Schr\"odinger Theory (RST), a fluid-dynamic approach to the
relativistic quantum theory of the many-particle systems. The fluid-dynamic
character of RST demands to specify the electronic current densities $\jmu$ for
any $N$-particle configuration which is exemplified here by considering the
helium singlet (${}^1S_0$) and triplet (${}^3S_1$) states in great detail.
Since the use of densities in RST is based upon the concept of wave functions,
the new theory appears as a certain kind of (relativistic) unification of the
conventional wave function formalism and the density functional theory, which
both are the most prominent theoretical tools in atomic and molecular physics.
As a demonstration of the practical usefulness of RST, the energy difference
$\Delta E_{1\backslash 2}$ of the helium singlet states $2s^2 {}^1S_0$ and
$1s^2 {}^1S_0$ is calculated for a large range of nuclear charge numbers
$z_{ex}$ ($2\leq z_{ex}\leq 100$), whereas the corresponding experimental
values are available only up to $z_{ex}=42$ (molybdenum). The deviations of
these RST results from the observational data is less than $0,3
