The breakdown of superfluidity in liquid 4 He III. Nucleation of quantized vortex rings

Abstract

We have measured the rate v at which negative ions nucleate charged vortex rings in isotopically pure superfluid ⁴ He for pressures, P , temperatures, T , and electric fields, E , within the ranges: 15 < P T < 0.9 K; 5 x 10 ⁴ < E < 10 ⁶ V m ^-1 . The measurements were done by a novel electrostatic induction technique specially developed for the purpose, and this is described in some detail. It was found that: at fixed E and P , v increases rapidly with T for T ca. 0.5 K, but approaches a temperature-independent limiting value v _s for T < 0.5 K; at fixed P and T , v at first increases rapidly with E but then passes through a maximum at ca. 7 x 10 ⁵ V m ^-1 and decreases again for larger values of E ;at fixed E and T , v increases rapidly with decreasing P until, below ca. 15 bar, the signal becomes too small to use. In all cases, v was found to be considerably smaller than had been measured for low E by earlier workers using helium of the natural isotopic ratio ( ca. 2 x 10 ^-7 ). The same signals were also used for measuring ionic drift velocities, v for v < ca . 3 x 1O ⁴ s ^-1 . Values of the matrix element for roton pair emission have been deduced from the v ( E ) measurements for several pressures in the range 17 < P < 25 bar. The pressure dependence of the Landau critical velocity was measured and is compared with predictions based on accepted values of the roton parameters. Analysis of the nucleation data showed that, at fixed v and P ,( v — vs ) oc n _r ,where n _r is the thermal roton density, suggesting that v is the sum of contributions from two independent nucleation mechanisms: a spontaneous mechanism responsible for v _s and a roton driven mechanism responsible for the increase in v with T above 0.5 K. The existence of a maximum in v ( E ) appears to be inconsistent with the peeling model of vortex nucleation; but it is entirely to be expected on the basis of the quantum transition model. It is shown that all the nucleation rate measurements reported herein are consistent with the quantum transition model, provided that due account is taken of the possibility that roton absorption may give rise to a critical velocity v _r that is smaller than the critical velocity v _v characteristic of the spontaneous nucleation mechanism. Values of v _v and v _r are deduced from the experimental data for several pressures. The fact that exponential decay of the bare ion signal still occurs even when v > v _v (or v _r ) constitutes the first experimental evidence that the microscopic mechanisms responsible for vortex nucleation are probabilistic in nature.