## 2 Measurements of the _THz_ Spectrum of Noble Gases up to the 1990s
### 1998: First IXS Measurements of the THz Spectrum of Noble Gases  
The only _THz_ spectroscopic technique available until the mid-90s was _INS_, a method intrinsically hampered by kinematic constraints (see, e.g., [63] pp. 63-101) limiting the accessible portion of dynamic plane (\(Q\),\(\omega\)). These limitations are particularly penalizing at low \(Q\)s, where the collective nature of structural rearrangements become dominating, as well as at large \(\omega\) values, where instead short-time, collisional events have a visible influence on density fluctuations.  
These problems were successfully overcome after the development of the first high resolution _IXS_, a spectroscopic technique virtually free from kinematic limitations [2; 64].  
Figure 5: Two representative _INS_ spectral lineshapes of Ar measured by [PERSON] _et al._ [62] at low exchanged momenta.  
The first _IXS_ measurement on a dense noble gas was performed on deeply supercritical neon (\(T\) = 295 K, \(n\) = 29.1 atoms/nm\({}^{3}\)) and discussed in combination of a _MD_ simulation on a Lennard-Jones model representative of the same sample [65]. In Figure 7, two representative _IXS_ spectra (upper panels) and corresponding _MD_ simulations (lower panels) are compared (middle panels) after the former have been multiplied with the detailed balance factor and convoluted with the instrumental energy resolution function. The good agreement between measured and computed line-shapes suggests that the Lennard-Jones model provides a consistent description of the spectrum. Furthermore, it is apparent that even at \(Q\) values extending well above 1 nm\({}^{-1}\), the inelastic peaks are visible in the _MD_ simulated line-shapes and, in spite of some resolution limitations, in the experimental spectra as well.  
Figure 6: Relevant shape parameters of the S(Q,\(\omega\)) of supercritical Ne and Ar as measured, at the indicated thermodynamic conditions, in [40; 62], respectively. The reported solid and dashed lines are the hydrodynamic predictions referring to symbols of corresponding color as derived from the lowest Q expansion in Equation (3a–c).  
At this stage, a pending question relates to the \(Q\)-threshold, \(Q_{h}\), defining the limit of validity for the \"extended hydrodynamic\" regime. Based on the fit of \(M\)\(D\) spectra reported in Figure 8 and discussed in Refs. [65; 66; 67], one could conclude that, at least for dense supercritical neon, \(Q_{h}\) is as high as 7.5 nm\({}^{-1}\). According to the plot, the transport parameters derived from best-fit results through Equation (3a-c) are essentially consistent with the macroscopic, or hydrodynamic, limit at least for \(Q\) lower than the values included in the shadowed area. Thanks to the high statistical accuracy of \(Q\)-dependent data in Figure 8, one may infer that the simple hydrodynamic approximation is not accurate for the thermal diffusivity. In fact, low-\(Q\) values of \(D_{T}\) seem slightly lower than the macroscopic value.  
Figure 7: Upper panels: low Q inelastic X-ray scattering _IXS_ spectra measured on deeply supercritical neon (\(T=\)295 K, \(n=\) 29.1 atoms/nm\({}^{3}\)). The raw data (open circles) are compared with corresponding resolution functions (dashed lines). Lower panels: corresponding \(M\)\(D\) spectra computed on a Lennard Jones model representative of the same sample (blue lines). Middle panels: Comparison between _IXS_ spectra (open circles) and the corresponding molecular dynamics (\(M\)\(D\)) ones convoluted with the resolution functions (red lines). Data are redrawn with permission from [65], which is copyrighted bt the American Physical Society.