Nucleon magnetic moment

The nucleus of an atom comprises protons and neutrons, both nucleons that behave as small magnets.

The proton's magnetic moment was directly measured in 1933 by Otto Stern team in University of Hamburg.

Their magnetic moments were puzzling and defied a valid explanation until the quark model for hadron particles was developed in the 1960s.

[13] The magnetic moments of the antiproton and antineutron have the same magnitudes as their antiparticles, the proton and neutron, but they have opposite sign.

[22] Values for the magnetic moment of the neutron were independently determined by R. Bacher[23] at the University of Michigan at Ann Arbor (1933) and I. Y. Tamm and S. A. Altshuler[24] in the Soviet Union (1934) from studies of the hyperfine structure of atomic spectra.

[21][7]: 73–75 By 1934 groups led by Stern, now at the Carnegie Institute of Technology in Pittsburgh, and I. I. Rabi at Columbia University in New York had independently measured the magnetic moments of the proton and deuteron.

[28] The value for the neutron's magnetic moment was first directly measured by L. Alvarez and F. Bloch at the University of California at Berkeley in 1940.

[21] The unexpected values for the magnetic moments of the nucleons would remain a puzzle until the quark model was developed in the 1960s.

[31] The refinement and evolution of the Rabi measurements led to the discovery in 1939 that the deuteron also possessed an electric quadrupole moment.

[28] 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.

[28] Rabi was awarded the Nobel Prize in 1944 for his resonance method for recording the magnetic properties of atomic nuclei.

[12] The magnetic moment of the neutron has therefore been exploited to probe the properties of matter using scattering or diffraction techniques.

[53][52] One technique employs the fact that cold neutrons will reflect from some magnetic materials at great efficiency when scattered at small grazing angles.

In 1930, Enrico Fermi showed that the magnetic moments of nuclei (including the proton) are Ampèrian.

Based on Fermi's arguments, the intrinsic magnetic moments of elementary particles, including the nucleons, have been shown to be Ampèrian.

The arguments are based on basic electromagnetism, elementary quantum mechanics, and the hyperfine structure of atomic s-state energy levels.

[57][60][61][62] The anomalous values for the magnetic moments of the nucleons presented a theoretical quandary for the 30 years from the time of their discovery in the early 1930s to the development of the quark model in the 1960s.

[31] Considerable theoretical efforts were expended in trying to understand the origins of these magnetic moments, but the failures of these theories were glaring.

[31] Much of the theoretical focus was on developing a nuclear-force equivalence to the remarkably successful theory explaining the small anomalous magnetic moment of the electron.

G. C. Wick suggested that the magnetic moments could be caused by the quantum-mechanical fluctuations of these particles in accordance with Fermi's 1934 theory of beta decay.

[63] By this theory, a neutron is partly, regularly and briefly, disassociated into a proton, an electron, and a neutrino as a natural consequence of beta decay.

[65] The theory proved to be untenable, however, when H. Bethe and R. Bacher showed that it predicted values for the magnetic moment that were either much too small or much too large, depending on speculative assumptions.

[69] The one-loop contribution to the anomalous magnetic moment of the electron, corresponding to the first-order and largest correction in QED, is found by calculating the vertex function shown in the diagram on the right.

[67][70] Computed to fourth order, the QED prediction for the electron's anomalous magnetic moment agrees with the experimentally measured value to more than 10 significant figures, making the magnetic moment of the electron one of the most accurately verified predictions in the history of physics.

As noted by A. Pais, "between late 1948 and the middle of 1949 at least six papers appeared reporting on second-order calculations of nucleon moments".

[9][72][73] These theoretical approaches were incorrect because the nucleons are composite particles with their magnetic moments arising from their elementary components, quarks.

[75] 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:

[11] In one of the early successes of the Standard Model (SU(6) theory), in 1964 M. Beg, B. Lee, and A. Pais theoretically calculated the ratio of proton-to-neutron magnetic moments to be ⁠−+3/ 2 ⁠, which agrees with the experimental value to within 3%.

[79] 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 O. Greenberg in 1964.

The discrepancy stems from the complexity of the Standard Model for nucleons, where most of their mass originates in the gluon fields, virtual particles, and their associated energy that are essential aspects of the strong force.