Quantum defect analysis of the eigenvalue spectrum of the Newton-Schroedinger equation

We point out that quantum defect theory is the appropriate framework to explain and understand the behavior of the solutions of the Newton-Schroedinger equation. We find that, beyond ordinary quantum defect theory, the nonlinearity of the equation induces novel features, in particular a strong state dependence of the quantum defects. We show how this can be compensated by a rescaling of the energy unit