  The interaction of an electron with a polar molecule is shown to be the
simplest realization of a quantum anomaly in a physical system. The existence
of a critical dipole moment for electron capture and formation of anions, which
has been confirmed experimentally and numerically, is derived. This phenomenon
is a manifestation of the anomaly associated with quantum symmetry breaking of
the classical scale invariance exhibited by the point-dipole interaction.
Finally, analysis of symmetry breaking for this system is implemented within
two different models: point dipole subject to an anomaly and finite dipole
subject to explicit symmetry breaking.
