Elementary quantum mechanics of the neutron with an electric dipole moment

TL;DR

This paper provides a unified non-relativistic quantum mechanical framework for understanding both permanent and induced electric dipole moments of the neutron, analyzing their effects on spin motion and relating them to fundamental symmetry violations.

Contribution

It introduces a non-relativistic model where the neutron's dipole moment operator is not aligned with its spin, linking permanent dipole moments to T-violation and polarizability.

Findings

Expectation value of permanent dipole is very small, less than 10^{-13} of neutron radius.

Neutron electric polarizability does not influence spin motion in external fields.

Permanent dipole moment is proportional to T-violating coupling and neutron polarizability.

Abstract

The neutron, in addition to possibly having a permanent electric dipole moment as a consequence of violation of time-reversal invariance, develops an induced electric dipole moment in the presence of an external electric field. We present here a unified non-relativistic description of these two phenomena, in which the dipole moment operator, $\vec{\cal D}$, is not constrained to lie along the spin operator. Although the expectation value of $\vec{\cal D}$ in the neutron is less than $10^{-13}$ of the neutron radius, $r_n$, the expectation value of $\vec {\cal D}\,^2$ is of order $r_n^2$. We determine the spin motion in external electric and magnetic fields, as employed in past and future searches for a permanent dipole moment, and show that the neutron electric polarizability, although entering the neutron energy in an external electric field, does not affect the spin motion. In a simple non-relativistic model we show that the expectation value of the permanent dipole is, to lowest order, proportional to the product of the time reversal-violating coupling strength and the electric polarizability of the neutron.