A resonant inelastic X-ray scattering experiment has made it possible to observe the Lindhard continuum directly, the theoretical signature of collective electron excitations in a metal. It is the first direct detection of this structure, predicted decades ago by Jens Lindhard as part of his description of the interacting electron gas, but until now out of reach of conventional spectroscopic techniques.

The Lindhard continuum describes how an electron travelling through a conducting medium excites electron-hole pairs across a continuous range of energies and momenta. Although the theory is a pillar of condensed-matter physics and appears in any solid-state textbook, testing it experimentally proved difficult: the individual excitations overlap into a broad, weak background, easily masked by stronger signals such as plasmons or elastic scattering peaks.

The key was to combine hard X-rays with resonance: by tuning the incident photon energy to a specific electronic threshold of the material, the scattering cross-section increases enough for the continuum of individual electrons to stand out above the noise. The technique, resonant inelastic X-ray scattering (RIXS), also resolves the energy and momentum transferred to the system simultaneously, so that the two-dimensional shape of the continuum can be compared directly with the calculated Lindhard response function.

The results reproduce the shape and extent of the continuum predicted by theory, with quantitative agreement within experimental uncertainty. The measurement opens the door to studying how this continuum is modified in materials where electronic correlations or spin-orbit coupling alter the electron gas response, and to using it as a reference to separate contributions in more complex RIXS spectra.