Energy of a point-like neutron in an external electromagnetic field

TL;DR

This paper derives the energy shift of a point-like neutron in an external electromagnetic field using a Foldy-Wouthuysen transformation, distinguishing it from effects due to neutron structure and calculating contributions for different neutron states.

Contribution

It generalizes the Foldy result for electric polarizability to include a derivative expansion and computes the leading contributions for zero-momentum and zero-velocity neutrons.

Findings

Derived energy shift expressions for a point-like neutron.

Identified ten Foldy contributions for zero-momentum neutron.

Determined eight contributions for zero-velocity neutron due to operator ambiguities.

Abstract

A point-like neutron in an external electromagnetic field experiences a shift in energy that mimicks the effect of an actual structural deformation of an extended neutron, i.e., a proper polarizability. In order to be able to differentiate between the former and the latter, a Foldy-Wouthuysen transformation is constructed which yields the energy shift of a point-like neutron quadratic in the external field in a derivative expansion, generalizing a long-known result for the dipole electric polarizability due to Foldy. The ten leading Foldy contributions to the energy are determined for a zero-momentum neutron. In addition, eliminating the momentum operator in favor of the velocity operator, analogous results are derived for a zero-velocity neutron. In this case, operator ordering ambiguities are encountered that permit only a determination of eight of the ten Foldy terms.