Evidence for soft-mode behavior of the roton at high density

Results for the temperature dependence of the inelastic neutron scattering at the roton wavevector, q=2.0A˚ ^-1, in liquid ⁴He at a constant density of 0.1715 g·cm ^-3 are presented. The superfluid transition temperature, T _λ=1.9202±0.0002K (at P=20.05 bar), is approached to within 0.0026 K (0.014 K) from below (above). Analysis in terms of the relaxation function ν ^-1χ″(q, ν) shows that, as T _λ is approached from below, there is an increasingly rapid decrease (increase) in the roton propagation frequency (intrinsic width). This “softening” is complete at T _λ where there is a collapse to the non-propagating behavior (central modes only) characteristic of ordinary fluids.