Dirac-Foldy term and the electromagnetic polarizability of the neutron

Abstract

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