A fundamental many-particle theory of temperature-dependent spectral moments is developed for the enhanced optical absorption bands attributed to solvated electrons in various polar solvents. Several new results are obtained (expressed in atomic units): (1)n₀ƒ= 1, where n₀ is a mean index of refraction of the solvent and ƒ is the empirical oscillator strength of the band; (2)〈∣Δr_e∣²〉=(1/ω)_av, where 〈∣Δr_e∣²〉 is an equilibrium-averaged dispersion-in-position of the solvated electron and (1/ω)_av is the mean reciprocal absorption frequency of the band; (3)µ_e–¾ω_av, where µ_e is the standard chemical potential of the solvated electron and ω_av is the mean absorption frequency of the band; (4)ω_th⩽¾ω_av, where ω_th is the (vertical) photoejection threshold frequency of the solvated electron.

For solvated-electron spectra in ammonia, water and a number of other solvents, no more than about 25 % of the pertinent absorption band can be ascribed to bound–bound transitions involving excited states with energies less than that of the photoejection threshold of the solvated electron.