Stability of Three Unit Charges. Necessary Conditions

Abstract

We consider the stability of three Coulomb charges $\{+1, -1, -1 \}$ with finite masses in the framework of nonrelativistic quantum mechanics. A simple physical condition on masses is derived to guarantee the absence of bound states below the dissociation thresholds. In particular this proves that certain negative muonic ions are unstable, thus extending the old result of Thirring \cite{thirring} to the actual values of all masses. The proof is done by reducing the initial problem to the question of binding of one particle in some effective potential.