Direct bulk sensitive probe of 5f symmetry in URu2Si2

The second-order phase transition into a hidden order phase in URu$_2$Si$_2$ goes along with an order parameter which is still a mystery, despite 30 years of research. However, it is understood that the symmetry of the order parameter must be related to the symmetry of the low lying local electronic $f$-states. Here we present results of a novel spectroscopy, namely core-level non-resonant inelastic x-ray scattering (NIXS). This method allows for the measurement of local high-multipole excitations and it is bulk sensitive. The observed anisotropy of the scattering function unambiguously shows that the 5$f$ ground state wave function is composed mainly, but essentially not purely, of the $\Gamma_1$ with majority $J_z$ =$|4\rangle$ + $|-4\rangle$ and/or $\Gamma_2$ singlet states.