Coupled Ripplon-Plasmon Modes in a Multielectron Bubble

In multielectron bubbles, the electrons form an effectively two-dimensional layer at the inner surface of the bubble in helium. The modes of oscillation of the bubble surface (the ripplons) are influenced by the charge redistribution of the electrons along the surface. The dispersion relation for these charge redistribution modes (`longitudinal plasmons') is derived and the coupling of these modes to the ripplons is analysed. We find that the ripplon-plasmon coupling in a multielectron bubble differs markedly from that of electrons a flat helium surface. An equation is presented relating the spherical harmonic components of the charge redistribution to those of the shape deformation of the bubble.