Measurements of the rate nu at which negative ions nucleate charged vortex rings in isotopically pure superfluid He-4 for electric fields E, temperatures T and pressures P within the ranges 10^3 < E < 10^6 V/m, 75 < T < 500 mK, 12 < P < 23 bar show that the energy barrier impeding the tunneling process is strongly dependent on pressure. Minima observed in nu(T) are ascribed to phonon damping.