Manifestation of Negative Compressibility in Low-Density Electron Liquids: Anomaly in the Ion-Pair Distribution Function in Supercritical Fluid Rb

It is a well-known fact that the electronic compressibility $\kappa$ diverges in the 3D electron gas as the density parameter $r_s$ approaches 5.25. A recent investigation clarifies that this divergence is due to the excitonic effect in the electron-hole pair excitation, in particular, to its zero-energy excitation [1]. For $r_s>5.25$, $\kappa$ becomes negative, leading to the negative static dielectric function $\varepsilon(q,0)$ for at least small $q$ owing to the compressibility sum rule. Then we can expect that two positive test charges do not repel but attract to each other in such a system. Keeping this situation in mind, we have calculated the ion-pair distribution function g(R) in the expanded Rb liquid metal by using the Monte Carlo method and found interesting features in g(R) characteristic to the negative $\varepsilon (q,0)$ [2]. Such features have been observed by the recent measurement of g(R) in the supercritical fluid Rb metal with continuously increasing $r_s$ from 5.25 [3]. This confirms the situation of $\kappa<0$ in the low-density 3D electron gas for the first time. [1] YT, J. Superconductivity {\bf 18}, No.3 (2005). [2] H. Maebashi and YT, to be submitted. [3] K. Matsuda and K. Tamura, private communication.