  The development of high-brightness free-electron lasers (FEL) has
revolutionised our ability to create and study matter in the
high-energy-density (HED) regime. Current diagnostic techniques have been very
successful in yielding information on fundamental thermodynamic plasma
properties, but provide only limited or indirect information on the detailed
quantum structure of these systems, and on how it is affected by ionization
dynamics. Here we show how the electronic structure of solid-density nickel,
heated to temperatures of 10's of eV on femtosecond timescales, can be studied
by resonant (Raman) inelastic x-ray scattering (RIXS) using the Linac Coherent
Light Source FEL. We present single-shot measurements of the valence density of
states in the x-ray-heated transient system, and extract simultaneously
electron temperatures, ionization, and ionization potential energies. The RIXS
spectrum provides a wealth of information on the valence structure of the HED
system that goes beyond what can be extracted from x-ray absorption or emission
spectroscopy alone.
