Vortex rings and finite-wave-number superfluidity near theHe4λ transition

The superfluid response to a perturbation of wave number k is calculated using a vortex-ring theory of the ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ λ transition. Rings of diameter greater than ${\mathit{k}}^{\mathrm{-}1}$ cannot follow the perturbation, and this leads to a finite-size broadening of the superfluid density near ${\mathit{T}}_{\lambda }$. The vortex theory provides a new perspective on the Feynman-Onsager proposal that rotons are vortex rings of the smallest size.