## 4 2001-2007: The Memory Function-Based Modeling of IXS Spectra of Noble Gases
### Microscopic vs. Structural Relaxations  
The results discussed in [6] indicate that the relaxation phenomenon causing the viscoelastic response of neon has a microscopic origin as opposite to the structural character of relaxations routinely observed in associated and/or highly viscous fluids. It should be emphasized that structural and microscopic relaxations have different physical origin and phenomenology: the former are cooperative in character and involve readjustments of the structure in response to a mechanical or a scattering-induced perturbation. Consequently, they are prevalent in glass-forming systems or associated fluids, _i.e._, fluids with extended network of bonds, this is, e.g., liquid water [93; 12; 94; 95], hydrogen fluoride [14], glycerol [17]. Since collective rearrangements of the structure are hampered by  
Figure 11: Lower panel: the generalized specific heat ratio as derived from \(MD\) computations for [PERSON] models simulating deeply supercritical neon ([66], red dots). The unit value is reported as a dashed line for reference. Lower panel: the thermal diffusivity, as derived from \(MD\) simulations in [66], while using the simplified hydrodynamic expression in Equations (3c). In all plots horizontal dashed line indicate the macroscopic values (from National Institute of Standards and Technology NIST database [72] of the symbols having corresponding color. viscous processes, the timescale of structural relaxation follows a temperature dependence roughly as steep as the one of viscosity. Conversely, microscopic relaxations are induced by single molecules' motions in the \(10^{-13}\) s window and are dominating in simple systems, such as dense gases and non-associated, weakly viscous, fluids. These fast motions can be naturally identified with vibration-like cage oscillations. Due to their non-cooperative nature, microscopic relaxations are not significantly slowed down by viscosity and their timescale exhibits only a weak dependence on thermodynamic conditions. To quantitatively assess the hypothesized microscopic nature of viscoelastic processes in neon, sensible variable to take as a reference is the mean free time between interatomic collisions, \(\tau_{c}\). This depends on atomic size, mass and shape, as well as on the interaction potential and thermodynamic state of the system. Without sophisticated calculations, a reasonable estimate can be obtained assuming as model a hard sphere gas following the Maxwell-Boltzmann statistics. For this system the inter-collision time can be easily calculated as:  
\[\tau_{c}=\sqrt{\frac{M}{16\pi d^{4}k_{B}T}} \tag{14}\]  
where \(d\) is the hard sphere diameter. In this context \(\tau_{c}\) can be identified as the characteristic timescale of interatomic interactions and for microscopic, or collisional, relaxations is reasonable that the relaxation time \(\tau_{\alpha}\) and \(\tau_{c}\) have comparable values. In Figure 12 the \(Q\)-dependence of the reduced relaxation time \(\Psi=\tau_{\alpha}/\tau_{c}\) is reported as obtained using \(\tau_{\alpha}\) values measured in neon in Ref. In spite of the important scattering of data, it is clear that for \(Q\) larger than about 8 nm\({}^{-1}\)\(\Psi\) approaches the unit value, as expected in the merely collisional limit. In this perspective, data in Figure 12 lead to the conclusion that for \(Q\) > 8 nm\({}^{-1}\)_THz_ relaxation processes of neon are intimately related to interatomic collisions. This may be an expected conclusion, particularly since relaxation processes are activated by the coupling of density fluctuations with some internal degree of freedom of the system. Given that microscopic components of a monatomic fluid lack internal degrees of freedom, it seems natural to identify local cage oscillations as the internal degree of freedom that density fluctuations couple to. At this stage, _THz_ viscoelastic data available in literature can be used to compare the case of Ne to the one even more studied of water.