Angular Momentum of Liquid Helium

Abstract

The difference in the angular momentum of liquid helium between an initial state in equilibrium with a steadily rotating cylindrical container and a final state with the container at rest has been measured both in He I and He II. If we denote this quantity by $L$ and the corresponding value for solid-body rotation of the liquid by $L_c$, then $\frac{L}{L_c}=1\mathrm{}$ for all temperatures and speeds used in the He I phase. In the He II region, however, and for speeds less than about 1 rad/sec, $\frac{L}{L_c}$ decreases monotonically from unity with decreasing initial angular velocity of the containing vessel apparently approaching the ratio $\frac{{\rho }_n}{\rho }$ as the initial angular velocity approaches zero. The results are compared with the Onsager-Feynman vortex model for He II and it is argued that concordance only can be obtained provided macroscopic rotational states of long lifetime can be shown to exist in this theory.