Pressure dependence of the negative ion effective mass in He II

The breakdown of superfluidity in liquid 4 He. IV. Influence of 3 He isotopic impurities on the nucleation of quantized vortex rings

We have investigated the rate v at which negative ions nucleate charged vortex rings in a series of extremely dilute superfluid 3 He/ 4 He solutions. Measurements of v were made at a pressure P = 23 bar (23 x 105 Pa) for temperatures, T , electric fields, E , and 3 He/ 4 He isotopic ratios, x 3 , within the ranges: 0.33 < T <0.61 K, 1.0 x 10 4 < E < 1.5 x 10 6 V m -1 , 2.1 x 10 -8 < x 3 < 1.7 x 10 -7 . A few data were also recorded at other pressures within the range 19 < P < 25 bar. For each concentration, and also for nominally pure 4 He ( x 3 = 1.9 x 10 -10 ), v was measured for the same set of E and T . For all the chosen values of x 3 and P , the form of v ( E, T ) was qualitatively much the same, and considerably more complicated than for pure 4 He. It was found that v became equal to the nucleation rate in pure 4 He for large , but that for smaller values of E at low T . The 3 He-influenced contribution to the overall nucleation rate, A v = v — v 0 , passed through a pronounced maximum at a value of E that increased with increasing T ; but the magnitude of A v itself decreased rapidly with increasing T . Plots of v against x 3 for fixed P, E and T show a marked upward curvature for the lower values of E and T , but become linear within experimental error above ca . 0.5 K. A model is proposed (in two variants) in which the complicated behaviour of v ( E, T ) is accounted for in terms of changes in the average occupancy by 3 He atoms of trapping states on the surface of the ion, it being proposed that the nucleation rate v 1 , due to ions each having one trapped 3 He atom, is very much greater than v 0 for bare ions. The nonlinearities in v ( x 3 ) are interpreted in terms of the simultaneous trapping of two (or more) 3 He atoms on a significant fraction of the ions. It is shown that the model can be fitted closely to the experimental data, thereby yielding numerical values of v 1 )of the 3 He binding energy on the ion, and of a number of other relevant quantities. From the form of v 1 ( E ), it is deduced that the addition of a 3 He atom to a bare ion affects its propensity to create vortex rings in two ways: the critical velocity for the process is reduced by ca . 4 m s -1 , and the rate constant is increased by a factor of ca . 10 3 . The implications of these results for microscopic theories of the vortex nucleation mechanism are discussed.