  Using inelastic x-ray scattering beyond the dipole limit and hard x-ray
photoelectron spectroscopy we establish the dual nature of the U $5f$ electrons
in UM$_2$Si$_2$ (M = Pd, Ni, Ru, Fe), regardless of their degree of
delocalization. We have observed that the compounds have in common a local
atomic-like state that is well described by the U $5f^2$ configuration with the
$\Gamma_1^{(1)}$ and $\Gamma_2$ quasi-doublet symmetry. The amount of the U
5$f^3$ configuration, however, varies considerably across the UM$_2$Si$_2$
series, indicating an increase of U5$f$ itineracy in going from M=Pd to Ni to
Ru, and to the Fe compound. The identified electronic states explain the
formation of the very large ordered magnetic moments in UPd$_2$Si$_2$ and
UNi$_2$Si$_2$, the availability of orbital degrees of freedom needed for the
hidden order in URu$_2$Si$_2$ to occur, as well as the appearance of Pauli
paramagnetism in UFe$_2$Si$_2$. A unified and systematic picture of the
U$M_2$Si$_2$ compounds may now be drawn, thereby providing suggestions for new
experiments to induce hidden order and/or superconductivity in U compounds with
the tetragonal body-centered ThCr$_2$Si$_2$ structure.
