Journal of Low Temperature Physics,Vol.36, Nos. 3/4, 1979 Tunneling from Electron Bubbles Beneath the Surface of Liquid Helium Milton W. Cole Department of Physics, The Pennsylvania State University, University Park, Pennsylvania and James R. Klein Department of Physics, Worthington Scranton Campus, The Pennsylvania State University, Dunmore, Pennsylvania (Received January 24, 1979) Schoepe and Rayfield have measured the lifetime ~'for escape of electrons from bubbles beneath a liquid He surface. We compute "r using the tunneling Hamiltonian method of Bardeen. If accepted bubble parameters are assumed, ~- is found to be approximately two orders of magnitude smaller than the measured value. Agreement with experiment can be obtained if the radius is taken to be 50% larger than currently believed. We consider the effects of diffuseness of the bubble boundary, diffuseness of the liquid-vapor interface, and polarizability of the bubble. A discrepancy remains which may be explicable in terms of surface deformation when the bubble is very close to the surface. 1. INTRODUCTION Ions have been used extensively to explore the properties of quantum fluids. One species which is particularly interesting is the electron bubble. 1,2 In liquid 4He, the electron is localized in a cavity of radius R = 18 A because of a repulsive exchange interaction with the He atoms. 3 This paper addresses a problem which may yield quite useful information about the nature of the bubble state. If an electric field F is applied in a direction such that it accelerates an electron toward the liquid-vapor interface, the electron's electrostatic potential energy is given by* V(z) = -Fez -A/z (1) A = eZ(et - Ev)/4~I(EI "[- Ev) (2) *The result of Buff and Goel 4 indicates that the finite bubble radius correction to this expression is negligible. 331 0022-2291/79/0800-o331503.00/0 ~ 1979 PlenumPublishing Corporation