Calculations of the frequencies and damping of the normal modes of ion pools in liquid 4He

For crystalline ion pools trapped just beneath the surface of superfluid He-4, we present a new calculation of the phonon frequencies, and extend this calculation to motion normal to the ion plane. We calculate the damping due to the cubic anharmonicity associated with each in-plane normal mode. We find well defined transverse modes, but difficulties associated with the damping of long wavelength longitudinal modes. Simple arguments are presented to discuss these problems.