  Warm dense matter (WDM) is now routinely created and probed in laboratories
around the world, providing unprecedented insights into conditions achieved in
stellar atmospheres, planetary interiors, and inertial confinement fusion
experiments. However, the interpretation of these experiments is often filtered
through models with systematic errors that are difficult to quantify. Due to
the simultaneous presence of quantum degeneracy and thermal excitation,
processes in which free electrons are de-excited into thermally unoccupied
bound states transferring momentum and energy to a scattered x-ray photon
become viable. Here we show that such free-bound transitions are a particular
feature of WDM and vanish in the limits of cold and hot temperatures. The
inclusion of these processes into the analysis of recent X-ray Thomson
Scattering experiments on WDM at the National Ignition Facility and the Linac
Coherent Light Source significantly improves model fits, indicating that
free-bound transitions have been observed without previously being identified.
This interpretation is corroborated by agreement with a recently developed
model-free thermometry technique and presents an important step for precisely
characterizing and understanding the complex WDM state of matter.
