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Elementary quantum mechanics of the neutron with an electric dipole 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 non-relativistic description of these two phenomena, in which the dipole moment operator, $\vec{\cal D}$, is not constrained to lie along the spin operator. Although the expectation value of $\vec{\cal D}$ in the neutron is less than $10^{-13}$ of the neutron radius, $r_n$, the expectation value of $\vec {\cal D}\,^2$ 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.