Elementary quantum mechanics of the neutron with an electric dipole moment

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, $\vec{\mathcal{D}}$, is not constrained to lie along the spin operator. Although the expectation value of $\vec{\mathcal{D}}$ in the neutron is less than $10^{-13}$ of the neutron radius, $r_n$, the expectation value of $\vec{\mathcal{D}}{}^2$ 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.

References in corpus (11)

• An Improved Experimental Limit on the Electric Dipole Moment of the Neutron
• Electric dipole moments as probes of new physics
• Degenerate Quantum Gases with Spin-Orbit Coupling
• Electric Dipole Moments of Nucleons, Nuclei, and Atoms: The Standard Model and Beyond
• The angular momentum controversy: What's it all about and does it matter?
• Electromagnetic and spin polarisabilities in lattice QCD
• Full QCD calculation of neutron electric dipole moment with the external electric field method
• Quasi-free Compton Scattering and the Polarizabilities of the Neutron
• Dispersion Relations and the Nucleon Polarizability
• Radiative corrections to real and virtual muon Compton scattering revisited
• Nucleon Polarizabilities: Theory

Cited by in corpus (3)

• Predicting outcomes of electric dipole and magnetic moment experiments
• A quest for new physics inside the neutron
• Computing Nucleon Electric Dipole Moment from lattice QCD