Disappearance of Roton Propagation in SuperfluidH4eatTλ

Using neutron scattering, we determine the dynamic structure factor $S(q,\nu )$ of liquid ${}^4\mathrm{He}$ for the roton wave number $q=2.0\mathrm{}{Å}^{-1\mathrm{}}$ as a function of frequency $\nu$ at constant density $0.1715\mathrm{g}{\mathrm{cm}}^{-3\mathrm{}}$ and for ten temperatures in the range $1.08\le T\le 2.00\mathrm{K}$, primarily near the superfluid transition temperature $T_{\lambda }=1.9202\mathrm{}\mathrm{K}$. The superfluid transition is marked by a complete softening of the roton mode and a rapid decrease in lifetime. This change is continuous with temperature, and we find no evidence for a new mode appearing as one enters the superfluid phase, as has been proposed on the basis of theoretical considerations.