We have observed two critical velocity levels for phase slips in super
fluid He-4 at temperatures between 14 and 44 mK, due to microparticles
formed in the cell at low temperature. We interpret these observation
s as evidence for pinning and unpinning events of single vortices of n
anometric size. From a study of the lifetime and unpinning velocities
of the pinned vortices, we are led to conclude that unpinning takes pl
ace by quantum tunneling. [S0031-9007(98)07420-1].