Electrons in superfluid helium form cavities that displace hundreds of atoms. These ``electron bubbles'' characteristically emit rotons in pairs when accelerated by an electric field. As no symmetry prevents the emission of single rotons, this has long been a mystery. We use a recent theory, which correctly predicts roton pair emission, to calculate its rate. The values that we obtain are four orders of magnitude smaller than experiment. This discrepancy can be linked to tunneling amplitudes associated with the bubble geometry that are sensitive to details of the helium wave function.