Theory of energy relaxation in two-dimensional electron crystal at liquid helium surface

The theory of energy relaxation in a two-dimensional Wigner crystal on the free surface of liquid helium is developed. Using the self-consistent theory of coupled phonon-ripplon modes to describe the dynamic form-factor of the crystal, the time of the surface electron energy relaxation is found and shown to depend on the processes in which the transverse phonon of the two-dimensional lattice transforms into a pair of short-wavelength ripplons. The theory is compared with available experimental data