Decay of excited surface electron states in liquid helium and related relaxation phenomena induced by short-wavelength ripplons

Abstract

Decay rates of excited surface electron states on liquid helium are theoretically studied for different electron confinement potentials and in the presence of quantizing magnetic field. Contributions of both one-ripplon and two-ripplon scattering processes are analyzed. Regarding the decay rate of the first excited surface level (l=2), two-ripplon emission of short wave-length capillary waves is shown to dominate the conventional one-ripplon scattering in two distinct cases: the ambient temperature is low enough, or the surface state excitation energy Δ₂–Δ₁ does not match an excitation energy of the in-plane motion quantized under a strong magnetic field or in a quantum dot. In these cases, magnetic field and confinement cannot essentially reduce the decay rate which is of order of 10⁶ s⁻¹ and does not depend on temperature. Importance of these findings for a microwave resonance experiment is discussed.