Lifetime of surface-state electrons on liquid<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">He</mml:mi></mml:mrow><mml:mprescripts/><mml:mrow/><mml:mrow><mml:mn>4</mml:mn></mml:mrow><mml:mrow/><mml:mrow/></mml:mmultiscripts></mml:mrow></mml:math>. I. Free electron

Electrons trapped on the surface of liquid $^{4}\mathrm{He}$ by the image potential can escape into the gas by thermal ionization. We have calculated the rate of ionization on the assumption that the electrons are strongly coupled to each other and weakly coupled to the liquid and gas. The first electrons to leave the surface extract their ionization energy from the kinetic energy of the electrons that remain behind. This adiabatic cooling effect rapidly lowers the electron temperature to a small fraction of the temperature of the surrounding gas and liquid. Above about 1.2 K gas-atom collisions determine the ionization rate and below 1 K it is determined by ripplon scattering. It is only for temperatures below 1 K that the lifetime measurement can be used to determine the surface-state binding energy.

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