Neutron magnetic moment

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The neutron magnetic moment is the intrinsic magnetic dipole moment of the neutron, symbol μn. Protons and neutrons, both nucleons, comprise the nucleus of atoms, and both nucleons act as small magnets whose strength is measured by their magnetic moments. The neutron interacts with normal matter primarily through the nuclear force and through its magnetic moment. The existence of the neutron's magnetic moment indicates the neutron is not an elementary particle. For an elementary particle to have an intrinsic magnetic moment, it must have both spin and electric charge. While the neutron has spin 1/2 ħ, it has no net charge.

Description[edit]

Schematic diagram depicting the spin of the neutron as the black arrow and magnetic field lines associated with the neutron's negative magnetic moment. While the spin of the neutron is upward in this diagram, the magnetic field lines at the center of the dipole are downward.

The best available measurement for the value of the magnetic moment of the neutron is μn = −1.91304272(45) μN.[1] Here μN is the nuclear magneton, a physical constant and standard unit for the magnetic moments of nuclear components. In SI units, μn = −9.6623640×10−27 J·T−1. A magnetic moment is a vector quantity, and the direction of the neutron's magnetic moment is defined by its spin. The negative value for the magnetic moment means that the neutron's spin and magnetic moment are antiparallel. The torque on the neutron resulting from the influence of an external magnetic field will tend to orient the spin of the neutron antiparallel to the magnetic field lines.

The nuclear magneton is the spin magnetic moment of a Dirac particle, a charged, spin 1/2 elementary particle, with a proton's mass mp. In SI units, the nuclear magneton is

\mu_\mathrm{N} = {{e \hbar} \over {2 m_\mathrm{p}}}

where e is the elementary charge and ħ is the reduced Planck constant. The magnetic moment of this particle is parallel to its spin. Since the neutron has no charge, it should have no magnetic moment by this expression. The non-zero magnetic moment of the neutron indicates that it is not an elementary particle. Similarly, the fact that the magnetic moment of the proton, μp = 2.793 μN, is not equal to 1 μN indicates that it too is not an elementary particle.[2] Protons and neutrons are composed of quarks, and the magnetic moments of the quarks can be used to compute the magnetic moments of the nucleons.

Measurement[edit]

Soon after the neutron was discovered in 1932, indirect evidence suggested the neutron had a non-zero value for its magnetic moment. Groups led by Otto Stern in Hamburg and I. I. Rabi in New York independently measured the magnetic moments of the proton and deuteron in 1934.[3][4][5] While the measured values for these particles were only in rough agreement between the groups, both groups found the magnetic moment for the proton to be unexpectedly large.[6][7] Since a deuteron is composed of a proton and a neutron with aligned spins, the neutron's magnetic moment could be inferred by subtracting the deuteron and proton magnetic moments. The resulting value was not zero and had sign opposite to that of the proton. A value for the magnetic moment of the neutron was also determined by I.Y. Tamm and S.A. Altshuler in the Soviet Union in 1934 in a study of the hyperfine structure of atomic spectra.[8] Although Tamm and Altshuler's estimate had the correct sign and order of magnitude as the present day value, the result was met with skepticism.[6][9] By the late 1930's the measurements by the Rabi and Stern groups were reconciled, allowing a more accurate value for the magnetic moment of the neutron to be deduced.[7] The large value for the proton's magnetic moment and the inferred negative value for the neutron's magnetic moment were unexpected and raised many questions.[6] The anomalous values for the magnetic moments of the proton and neutron would remain a puzzle until the the quark model was developed in the 1960s.

The breakthrough that allowed the Stern and Rabi measurements to be reconciled was the discovery in 1939 that the deuteron also possessed an electric quadrupole moment.[7][10] This electrical property of the deuteron had been interfering with the measurements by the Rabi group. The discovery meant that the physical shape of the deuteron was not symmetric, which provided valuable insight into the nature of the nuclear force binding nucleons.

The value for the neutron's magnetic moment was first directly measured by Luis Alvarez and Felix Bloch at Berkeley, California in 1940,[11] using magnetic resonance methods developed by Rabi. Alvarez and Bloch measured the magnetic moment of the neutron to be μn=−1.93(2) μN. By directly measuring the magnetic moment of free neutrons, or individual neutrons free of the nucleus, Alvarez and Bloch resolved all doubts and ambiguities about this anomalous property of neutrons.

Neutron g-factor[edit]

The magnetic moment of a nucleon is sometimes expressed in terms of its g-factor. The conventional formula is

 \boldsymbol{\mu} = \frac{g \mu_\mathrm{N}}{\hbar}\boldsymbol{I}

where μ is the intrinsic magnetic moment of the nucleon, I is the nuclear spin angular momentum, and g is the effective g-factor. For the neutron, I is 1/2 ħ, so that the neutron's g-factor, symbol gn, is −3.82608545(90).[12]

Physical significance[edit]

When a neutron is put into a magnetic field produced by an external source, it is subject to a torque tending to orient its magnetic moment parallel to the field (hence its spin antiparallel to the field).[13] Like any magnet, the amount of this torque is proportional both to the magnetic moment and the external magnetic field. Since the neutron has spin, hence angular momentum, this torque will cause the neutron to precess with a well-defined frequency, called the Larmour frequency. It is this phenomenon that enables the measurement of nuclear properties through nuclear magnetic resonance.

The magnetic moment of the neutron has been exploited to probe the properties of matter using scattering or diffraction techniques. These methods provide information that is complementary to X-ray spectroscopy. In particular, the magnetic moment of the neutron is used to determine magnetic properties of materials at length scales of 1–100 Å using cold or thermal neutrons.[14] Bertram Brockhouse and Clifford Shull won the Nobel Prize in physics in 1994 for the development of these scattering techniques.[15]

Since neutrons are neutral particles, they do not have to overcome Coulomb repulsion as they approach charged targets, as experienced by protons or alpha particles. Neutrons can deeply penetrate matter. On the other hand, without an electric charge, neutron beams cannot be controlled by the conventional electromagnetic methods employed for particle accelerators. The magnetic moment of the neutron allows some control of neutrons using magnetic fields, however,[16][17] including the formation of polarized neutron beams.

Since an atomic nucleus consists of a bound state of protons and neutrons, the magnetic moments of the nucleons contribute to the nuclear magnetic moment, or the magnetic moment for the nucleus as a whole. The nuclear magnetic moment also includes contributions from the orbital motion of the nucleons. The deuteron has the simplest example of a nuclear magnetic moment, with measured value 0.857 µN. This value is within 3% of the sum of the moments of the proton and neutron, which gives 0.879 µN. In this calculation, the spins of the nucleons are aligned, but their magnetic moments offset because of the neutron's negative magnetic moment.

Magnetic moment, quarks, and the Standard Model[edit]

Within the quark model for hadrons, such as the neutron, the neutron is composed of one up quark (charge +2/3 e) and two down quarks (charge −1/3 e).[18] The magnetic moment of the neutron can be modeled as a sum of the magnetic moments of the constituent quarks,[19] although this simple model belies the complexities of the Standard Model of particle physics.[20]

In one of the early successes of the Standard Model (SU(6) theory), in 1964 Mirza A. B. Beg, Benjamin W. Lee, and Abraham Pais theoretically calculated the ratio of proton to neutron magnetic moments to be −3/2, which agrees with the experimental value to within 3%.[21][22][23] The measured value for this ratio is −1.45989806(34).[24] A contradiction of the quantum mechanical basis of this calculation with the Pauli exclusion principle, led to the discovery of the color charge for quarks by Oscar W. Greenberg in 1964.[21]

From the nonrelativistic, quantum mechanical wavefunction for baryons composed of three quarks, a straightforward calculation gives fairly accurate estimates for magnetic moments of neutrons, protons, and other baryons.[19] The calculation assumes that the quarks behave like pointlike Dirac particles, each having their own magnetic moment, as computed using an expression similar to the one above for the nuclear magneton. For a neutron, the end result of this calculation is that the magnetic moment of the neutron is given by μn = 4/3 μd − 1/3 μu, where μd and μu are the magnetic moments for the down and up quarks, respectively. This result combines the intrinsic magnetic moments of the quarks with their orbital magnetic moments.

Baryon Magnetic moment
of quark model
Computed
(\mu_\mathrm{N})
Observed
(\mu_\mathrm{N})
p 4/3 μu − 1/3 μd 2.79 2.793
n 4/3 μd − 1/3 μu −1.86 −1.913

While the results of this calculation are encouraging, the masses of the up or down quarks were assumed to be 1/3 the mass of a nucleon,[19] whereas the masses of these quarks are only about 1% that of a nucleon.[20] The discrepancy stems from the complexity of the Standard Model for nucleons, where most of their mass originates in the gluon fields and virtual particles that are essential aspects of the strong force.[20] Further, the complex system of quarks and gluons that constitute a neutron requires a relativistic treatment. A calculation of nucleon magnetic moments from first principles is not yet available.

See also[edit]

References[edit]

  1. ^ Neutron particle listing in the 2013 update of the Review of Particle Physics.
  2. ^ Bjorken, J.D.; Drell, S.D. (1964). Relativistic Quantum Mechanics. McGraw-Hill, New York. ISBN 0070054932. 
  3. ^ Esterman, I.; Stern, O. (1934). "Magnetic moment of the deuton". Physical Review 45: 761(A109). 
  4. ^ Rabi, I.I.; Kellogg, J.M.; Zacharias, J.R. (1934). "The magnetic moment of the proton". Physical Review 46: 157. 
  5. ^ Rabi, I.I.; Kellogg, J.M.; Zacharias, J.R. (1934). "The magnetic moment of the deuton". Physical Review 46: 163. 
  6. ^ a b c Breit, G.; Rabi, I.I. (1934). "On the interpretation of present values of nuclear moments". Physical Review 46: 230. 
  7. ^ a b c John S. Rigden (2000). Rabi, Scientist and Citizen. Harvard University Press. ISBN 9780674004351. 
  8. ^ Tamm, I.Y.; Altshuler, S.A. (1934). "Magnetic Moment of the Neutron". Doklady Akad. Nauk SSSR 8: 455. 
  9. ^ Sergei Vonsovsky (1975). Magnetism of Elementary Particles. Mir Publishers. 
  10. ^ Kellogg, J.M.; Rabi, I.I.; Ramsey, N.F.; Zacharias, J.R. (1939). "An electrical quadrupole moment of the deuteron". Physical Review 55: 318. 
  11. ^ Alvarez, L. W; Bloch, F. (1940). "A quantitative determination of the neutron magnetic moment in absolute nuclear magnetons". Physical Review 57: 111. 
  12. ^ "CODATA values of the fundamental constants". NIST. 
  13. ^ B. D. Cullity, C. D. Graham (2008). Introduction to Magnetic Materials (2 ed.). Wiley-IEEE Press. p. 103. ISBN 0-471-47741-9. 
  14. ^ S.W. Lovesey (1986). Theory of Neutron Scattering from Condensed Matter. Oxford University Press. ISBN 0198520298. 
  15. ^ "The Nobel Prize in Physics 1994". Nobel Foundation. Retrieved 2015-01-25. 
  16. ^ Oku, T.; Suzuki, J.; et al. (2007). "Highly polarized cold neutron beam obtained by using a quadrupole magnet". Physica B 397: 188–191. 
  17. ^ Arimoto, Y.; Geltenbort, S.; et al. (2012). "Demonstration of focusing by a neutron accelerator". Physical Review A 86: 023843. doi:10.1103/PhysRevA.86.023843. 
  18. ^ Gell, Y.; Lichtenberg, D. B. (1969). "Quark model and the magnetic moments of proton and neutron". Il Nuovo Cimento A. Series 10 61: 27. Bibcode:1969NCimA..61...27G. doi:10.1007/BF02760010. 
  19. ^ a b c Perkins, Donald H. (1982), Introduction to High Energy Physics, Addison Wesley, Reading, Massachusetts, ISBN 0-201-05757-3 
  20. ^ a b c Cho, Adiran (2 April 2010). "Mass of the Common Quark Finally Nailed Down". http://news.sciencemag.org. American Association for the Advancement of Science. Retrieved 27 September 2014. 
  21. ^ a b Greenberg, O. W. (2009), "Color charge degree of freedom in particle physics", Compendium of Quantum Physics, Springer Berlin Heidelberg, p. 109–111, doi:10.1007/978-3-540-70626-7_32 
  22. ^ Beg, M.A.B.; Lee, B.W.; Pais, A. (1964). "SU(6) and electromagnetic interactions". Physical Review Letters 13: 514–517, erratum 650. 
  23. ^ Sakita, B. (1964). "Electromagnetic properties of baryons in the supermultiplet scheme of elementary particles". Physical Review Letters 13: 643–646. 
  24. ^ Mohr, P.J.; Taylor, B.N. and Newell, D.B. (2011), "The 2010 CODATA Recommended Values of the Fundamental Physical Constants" (Web Version 6.0). The database was developed by J. Baker, M. Douma, and S. Kotochigova. (2011-06-02). National Institute of Standards and Technology, Gaithersburg, Maryland 20899.