By numerically investigating the nonlinear Schrödinger-Poisson eigenstates of acondensed Bose gas of charged particles that is confined in a two-dimensional axisymmetricparabolic potential ½meω2r2 (e.g. quantum-dot helium), it is shown that the probability amplitudebetween two nonlinear—and hence non-orthogonal—eigenstates displays an interferencepattern scaled (within 0.03 %) by Since α = e2/ℏc ~ 1/137 is the finestructure constant, this stunning result—indeed velocity of light c does not enter the presentnon-relativistic model—is tentatively explained by the existence of a "nonlinear" bound stateof the trapped particle-particle interaction Coulomb field whose energy defines the induced emission or absorption equilibrium processes between two appropriate chemical potentials.Besides, a non-decoherence quantum-classical transition with increasing nonlinearity ispointed out. As a possible experimental test for the present theory, the 0s2 → 1s2 nonlineartransition in an ℏω = 1.66meV GaAs quantum-dot helium is emphasized.