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.
Highlights
Electromagnetic fields polarize nucleons by coupling to the electric charges of their quark constituents
For sufficiently weak fields, such effects are quantified through polarizabilities, which characterize the linear response of the nucleon to the electromagnetic field; in terms of an effective Hamiltonian, polarizabilities are coefficients of terms quadratic in the electromagnetic field
The fields can be classified according to their space-time variation, starting with the most basic case of constant electric and magnetic fields that induce the socalled dipole polarizabilities; generalizing to space-time dependent fields, the effective Hamiltonian can be organized into a derivative expansion
Summary
Electromagnetic fields polarize nucleons by coupling to the electric charges of their quark constituents. It should be emphasized that these corrections depend on further details of the environment in which the neutron is placed, such as boundary conditions, and do not constitute intrinsic electromagnetic properties of the neutron on the same footing as the Foldy contributions As indicated by this preliminary discussion, the emphasis of the present study lies as much on ascertaining the boundaries of a description in terms of a local effective Hamiltonian of the form (1) as it does on extracting concrete results for the Foldy contributions associated with the polarizabilities in (1) to the extent possible. These limitations will become apparent in more than one aspect, and to exhibit them is as much a goal of this investigation as is the determination of those Foldy-type effects that are accessible in a such a framework
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