Nancolas, G. G. and Bowley, R. M. and McClintock, Peter V. E.
(1985)
*The breakdown of superfluidity in liquid He-4. IV. Influence of He-3 isotopic impurities on the nucleation of quantized vortex rings.*
Philosophical Transactions of the Royal Society of London A, 313.
pp. 537-606.
ISSN 0264-3820

## Abstract

We have investigated the rate nu at which negative ions nucleate charged vortex rings in a series of extremely dilute superfluid 3He/4He solutions. Measurements of nu were made at a pressure P = 23 bar (23 x 10^5 Pa) for temperatures, T, electric fields, E, and 3He/4He isotopic ratios, x3, within the ranges: 0.33 < T < 0.61 K, 1.0 x 1^04 < E < 1.5 x 10^6 V m^-1, 2.1 x 10^-8 < x3 < 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 4He (x3 = 1.9 x 10^-10), v was measured for the same set of E and T. For all the chosen values of x3 and P, the form of nu(E,T) was qualitatively much the same, and considerably more complicated than for pure 4He. It was found that nu became equal to the nucleation rate Vo in pure 4He for large E, but that v >> nu0 for smaller values of E at low T. The 3He-influenced contribution to the overall nucleation rate, Delta nu = nu - nu0 passed through a pronounced maximum at a value of E that increased with increasing T; but the magnitude of Delta nu itself decreased rapidly with increasing T. Plots of nu against x3 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 nu(E,T) is accounted for in terms of changes in the average occupancy by 3He atoms of trapping states on the surface of the ion, it being proposed that the nucleation rate nu1 due to ions each having one trapped 3He atom, is very much greater than nu0 for bare ions. The nonlinearities in nu(x3) are interpreted in terms of the simultaneous trapping of two (or more) 3He 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 nu1, of the 3He binding energy on the ion, and of a number of other relevant quantities. From the form of nu1(E), it is deduced that the addition of a 3He 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, 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.