  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 D_0 given by 1.63\times10^{-18} esu cm. This prediction is consistent
with the observed anomalous electron scattering in H_2S and HCl, whose dipole
moments are smaller than the critical value D_0. We also show that for a polar
molecule with dipole moment less than D_0, typically there is only a single
bound state, which is in qualitative agreement with observations. We argue that
the quantum mechanical scaling anomaly is responsible for the formation of
these bound states.
