Refractive-index measurements of dense helium up to 16 GPa at<i>T=298</i>K: Analysis of its thermodynamic and electronic properties

Abstract

The refractive index of He as a function of pressure, n(P), has been measured with an accuracy of 3\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}3}$, in a diamond anvil cell up to 16 GPa at T=298 K, by an experimental procedure which couples two types of interferometric methods. These data permit us to obtain, from recent Brillouin scattering measurements, the fluid adiabatic sound velocity, so as to derive the equation of state of liquid He up to melting, the volume discontinuity at melting, and some related thermodynamic quantities. Under justified physical assumptions, the equation of state is extrapolated into the solid phase, in good agreement with recent single-crystal x-ray data. The comparison of these two equations of state with different calculations confirms the importance of many-body interactions in dense He. The refractive index of He, expressed as a function of density, is then related, through a Sellmeier formula, to the electronic properties of dense He: These are given in terms of the evolution with density of the excitonic ${1}^{1}$${S}_{0}$\ensuremath{\rightarrow}${2}^{1}$${P}_{1}$ energy level and of the contraction of the electronic cloud of the He atom.