## Abstract

We have investigated the rate $\nu $ at which negative ions nucleate charged vortex rings in a series of extremely dilute superfluid $^{3}$He/$^{4}$He solutions. Measurements of $\nu $ were made at a pressure P = 23 bar (23 $\times $ 10$^{5}$ 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 $\times $ 10$^{4}$ < E < 1.5 $\times $ 10$^{6}$ V m$^{-1}$, 2.1 $\times $ 10$^{-8}$ < x$_{3}$ < 1.7 $\times $ 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 $\times $ 10$^{-10}$), $\nu $ was measured for the same set of E and T. For all the chosen values of x$_{3}$ and P, the form of $\nu $(E,T) was qualitatively much the same, and considerably more complicated than for pure $^{4}$He. It was found that $\nu $ became equal to the nucleation rate $\nu _{0}$ in pure $^{4}$He for large E, but that $\nu \gg \nu _{0}$ for smaller values of E at low T. The $^{3}$He-influenced contribution to the overall nucleation rate, $\Delta \nu =\nu -\nu _{0}$, 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 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 $\nu $(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 $\nu _{1}$, due to ions each having one trapped $^{3}$He atom, is very much greater than $\nu _{0}$ for bare ions. The nonlinearities in $\nu $(x$_{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 $\nu _{1}$, of the $^{3}$He binding energy on the ion, and of a number of other relevant quantities. From the form of $\nu _{1}$(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.