Understanding how electrons interact in a real solid is one of the important issues in solid-state physics. These electron-electron correlation phenomena and the consequences in the physical properties are studied in many systems, ranging from simple metals to complex compounds. The approach presented here is to investigate a rather simple model system, the free electron gas, where the experiment allows direct access to a theoretical model parameter: the free electron density. According to many-body calculations in such a system the electron-electron correlation only depends on the average intra-electron distance. In many cases the free electron theory serves for metals as a first order approximation and, with suitable corrections, it can be applied to more complex solid state systems.

Compton scattering (inelastic X-ray scattering at high momentum transfer) directly probes the electron ground state properties of matter. The behaviour of the electron density in a free electron system when external parameters are changed can be evaluated from the value of the Fermi momentum as derived from experimental Compton profiles. In earlier studies mainly alkali metals like Li, Na, K, Rb and Cs with different electron densities were investigated to evaluate the importance of electron-electron correlation. However, in the majority of these experiments, solid state effects modify the free electron behaviour and in general it is difficult to separate these two contributions. Therefore in the experiment presented here, the electron density was dynamically changed via the external pressure applied to the same sample. This type of experiment became feasible only recently thanks to the availability of sufficient photon flux of high energy X-rays and thanks to the development in high-pressure techniques.

The first pressure dependent Compton scattering data from sodium, which are almost free from contamination by the pressure cell, have been measured at the high-energy beamline ID15B. A solid state detector, and the recently developed large-volume cell of ID30 were used. Compton profiles under various pressures have been collected up to 4.2 GPa and the relative differences are shown in Figure 81. The experimental data clearly reflect the pressure induced increase in the electron density: the momentum density becomes broader and the Fermi momentum larger. The pressure dependence of the Fermi momentum also reveals the corresponding change of the electron-electron correlation: a simple free electron theory is not adequate while a proper RPA calculation including correlation effects agrees quite well with the data. A more detailed analysis to compare different theoretical correlation models is in progress.

The success of the work presented will also open up new possibilities for materials science as a possible use of high-pressure Compton scattering is to study phase transitions which are related to electronic topological transitions.

Authors
K. Hämäläinen (a), S. Huotari (a), J. Laukkanen (a), A. Soininen (a), S. Manninen (a), C.-C. Kao (b), T. Buslaps (c), M. Mezouar (c).

(a) University of Helsinki (Finland)
(b) NSLS (USA)
(c) ESRF