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.
Proceedings of the National Academy of Sciences