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The soliton effect is defined in nonlinear physics by the transformation of anonlinear time-dependent dynamical system into an equivalent linear spectraleigenproblem whose invariant eigenvalues unambiguously define all the dynamicalproperties of the original system. We point out the existence of such an effectin a non-relativistic isotropic two-electron mean-field quantum-dot model. Ityields the prediction of observable modulation of radiation absorption betweenits two lowest-energy zero-angular-momentum nonlinear eigenstates (i.e.eigenstates which include electron-electron interaction: hence theirnon-orthogonality). Characteristic values for such a possible experiment aregiven in the case of GaAs. Furthermore it provides an intriguing nonlineardefinition of the fine-structure constant solely in terms of these eigenstates.

Observable eigenstate overlap in a nonlinear mean-field quantum model