Electron Capture and Scaling Anomaly in Polar Molecules

TL;DR

This paper analyzes how polar molecules can form bound electron states below a critical dipole moment, explaining observed anomalies through quantum scaling effects using von Neumann's theory.

Contribution

It introduces a theoretical framework based on self-adjoint extensions to explain electron binding in polar molecules with subcritical dipole moments.

Findings

Bound states can form even below the critical dipole moment D_0.

Typically only a single bound state exists for subcritical dipoles.

Quantum scaling anomaly explains the formation of these bound states.

Abstract

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.