DISAPPEARANCE OF ROTON PROPAGATION IN SUPERFLUID HE-4 AT T-LAMBDA

Using neutron scattering, we determine the dynamic structure factor S( q, v) of liquid He-4 for the roton wave number q = 2.0 Angstrom(-1) as a function of frequency v at constant density 0.1715 g cm(-3) and for ten temperatures in the range 1.08 less than or equal to T less than or equal to 2.00 K, primarily near the superfluid transition temperatu re T-lambda = 1.9202 K. The superfluid transition is marked by a compl ete 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 pro posed on the basis of theoretical considerations.