Universality in the Critical Broadening of Spectral Lines in Simple Fluids

Nonlinear mode-coupling hydrodynamics is used to study the broadening of spectral lines near a liquid-gas critical point. The critical contribution to the line shape is given by a universal line-shape function. For values of $\epsilon =\left|\frac{(T-T_c)}{T_c}\right|$ which are not too small, the line assumes a Lorentzian form and the width $\hat{\Gamma }$ increases as $\sim {\epsilon }^s$ with the critical exponent $s=\gamma +\nu =-0.607\mathrm{}$. Very close to the critical point the line changes into a Levy distribution [the Fourier transform of $\exp (-t^r)$ where $\mathcal{r}=\frac{(3-\eta )}{2}$] and the line shape becomes independent of $\epsilon$ ($s=0\mathrm{}$).