Dirac-Foldy term and the electromagnetic polarizability of the neutron

We reconsider the Dirac-Foldy contribution ${\mu }^2/m$ to the neutron electric polarizability. Using a Dirac equation approach to neutron-nucleus scattering, we review the definitions of Compton continuum $\left(\overline{\alpha }\right)$, classical static $\left({\alpha }_E^n\right)$, and Schrödinger $\left({\alpha }_{\mathrm{Sch}}\right)$ polarizabilities and discuss in some detail their relationship. The latter ${\alpha }_{\mathrm{Sch}}$ is the value of the neutron electric polarizability as obtained from an analysis using the Schrödinger equation. We find in particular ${\alpha }_{\mathrm{Sch}}=\overline{\alpha }-{\mu }^2/m$, where $\mu$ is the magnitude of the magnetic moment of a neutron of mass $m$. However, we argue that the static polarizability ${\alpha }_E^n$ is correctly defined in the rest frame of the particle, leading to the conclusion that twice the Dirac-Foldy contribution should be added to ${\alpha }_{\mathrm{Sch}}$ to obtain the static polarizability ${\alpha }_E^n.$