  The stability of multielectron bubbles (MEBs) in liquid helium is
investigated using the liquid-drop model for fissioning nuclei. Whereas a
critical positive pressure can make the bubble unstable against fissioning, a
small negative pressure suffices to introduce a restoring force preventing any
small deformation of the bubble to grow. We also find that there exists an
energy barrier making MEBs metastable against fissioning at zero pressure. The
results obtained here overcome the difficulties associated with the
Rayleigh-Plesset equation previously used to study bubble stability, and shed
new light on the limits of achievable bubble geometries in recently proposed
experiments devised to stabilize MEBs.
