Elementary quantum mechanics of the neutron with an electric dipole moment

Significance A permanent electric dipole moment of the neutron, a manifestation of the violation of time-reversal symmetry in nature, is an important clue to physics beyond the standard model, and is the subject of a number of ongoing large-scale experimental efforts. Although, in the absence of external electric fields, the dipole moment must lie along the neutron spin, the neutron dipole moment and spin are independent; e.g., the external electric field in Compton scattering on the neutron induces a component of the dipole moment parallel to the field. How then should one think generally about the neutron electric dipole moment, including time-reversal violation, within elementary quantum mechanics, and in particular when interpreting experimental searches for a permanent moment? 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 nonrelativistic description of these two phenomena, in which the dipole moment operator, D→, is not constrained to lie along the spin operator. Although the expectation value of D→ in the neutron is less than 10−13 of the neutron radius, rn, the expectation value of D→ 2 is of order rn2. We determine the spin motion in external electric and magnetic fields, as used 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 nonrelativistic 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.