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.
Camblong, Horacio E., "Quantum Anomaly in Molecular Physics" (2001). Physics and Astronomy. Paper 2.