CALCULATIONS OF THE FREQUENCIES AND DAMPING OF THE NORMAL-MODES OF ION POOLS IN LIQUID-HE-4

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