Abstract
We have performed numerical calculations to investigate the stability of multi-electron bubbles in liquid helium-4. In our calculations, for each bubble shape considered we find the equilibrium distribution of the electron gas on the inside surface of the bubble. For a stationary bubble, we find that whenever the pressure in the liquid is positive the bubble is unstable against fission into two bubbles. We find that a moving bubble can be stable within a certain region of the pressure-velocity plane. At the high pressure boundary of this region, the bubble undergoes fission, and on the low pressure boundary the bubble explodes.
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