Electron bubbles in cryogenic liquids

For electrons in nonpolar liquids, a simple criterion was derived by Springett et al. (1968) which allowed a prediction of the energetically most favorable state. The energy of the localized state, E, is compared to the energy of the delocalized state, Vn, such that 

For the estimation of E, it is usually assumed that the electron resides in an empty bubble of radius R. The energy of localization is then given by the electronic energy 

The energy of bubble creation consists of a term describing the creation of the inner surface, AEg, and of the volume work, AEp, done against the external pressure, p  

Y denotes the surface tension of the liquid. Bubble formation is fostered in liquids with small surface tension and where the atoms or molecules repel the electron. 

The ground state of the electron, Ej, is the electronic part of the localization energy, AEg. The magnitudes of Vq and Rb determine if excited states exist in the well. With C given by 

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