Vibrational Modes of a Negative Ion in Liquid Helium

A general expression is obtained for the breathing mode and the surface-distortion modes of a negative ion or electron bubble in liquid ${\mathrm{He}}^4$ at low temperatures. The electron is assumed to be in a spherical potential well of finite depth. The modes are damped because of the excitation of compressional waves in the surrounding fluid. Numerical calculations indicate that the breathing mode gives rise to a broad resonance in the vicinity of ${10}^{11}$ ${\sec }^{-1\mathrm{}}$ and that there is a rather sharp quadrupole distortion mode with frequency varying from 1.6 × ${10}^{11}$ to 5.6 × ${10}^{11}$ ${\sec }^{-1\mathrm{}}$ as the external pressure varies from 0 to 20 atm.