Electron capture and scaling anomaly in polar molecules

We present a new analysis of the electron capture mechanism in polar molecules, based on von Neumann's theory of self-adjoint extensions. Our analysis suggests that it is theoretically possible for polar molecules to form bound states with electrons, even with dipole moments smaller than the critical value D0=1.63×10−18 esu cmD0=1.63×10−18 esu cm. We argue that the quantum mechanical scaling anomaly is responsible for the formation of these bound states.