Elementary quantum mechanics of the neutron with an electric dipole moment

Gordon Baym, D. H. Beck

Research output: Contribution to journalArticlepeer-review


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 D2 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.

Original languageEnglish (US)
Pages (from-to)7438-7442
Number of pages5
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number27
StatePublished - Jul 5 2016


  • Electric dipole moment
  • Nuclear physics
  • Time-reversal violation

ASJC Scopus subject areas

  • General


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