The nucleon magnetic moments are the intrinsic magnetic dipole moments of the proton and neutron, symbols and The nucleus of an atom comprises protons and neutrons, both nucleons that behave as small magnets. Their magnetic strengths are measured by their magnetic moments. The nucleons interact with normal matter through either the nuclear force or their magnetic moments, with the charged proton also interacting by the Coulomb force.
The proton's magnetic moment was directly measured in 1933 by Otto Stern team in University of Hamburg. While the neutron was determined to have a magnetic moment by indirect methods in the mid-1930s, Luis Alvarez and Felix Bloch made the first accurate, direct measurement of the neutron's magnetic moment in 1940. The proton's magnetic moment is exploited to make measurements of molecules by proton nuclear magnetic resonance. The neutron's magnetic moment is exploited to probe the atomic structure of materials using scattering methods and to manipulate the properties of neutron beams in particle accelerators.
The existence of the neutron's magnetic moment and the large value for the proton magnetic moment indicate that nucleons are not elementary particles. For an elementary particle to have an intrinsic magnetic moment, it must have both spin and electric charge. The nucleons have but the neutron has no net charge. Their magnetic moments were puzzling and defied a valid explanation until the quark model for hadron particles was developed in the 1960s. The nucleons are composed of three quarks, and the magnetic moments of these elementary particles combine to give the nucleons their magnetic moments.
Description
The CODATA recommended value for the magnetic moment of the proton is The best available measurement for the value of the magnetic moment of the neutron is Here, μN is the nuclear magneton, a standard unit of measure for the magnetic moments of nuclear components, and μB is the Bohr magneton, an alternate unit from spectroscopy, both being physical constants. In SI units, these values are and A magnetic moment is a vector quantity, and the direction of the nucleon's magnetic moment is determined by its spin. The torque on the neutron that results from an external magnetic field is towards aligning the neutron's spin vector opposite to the magnetic field vector.
The nuclear magneton is the spin magnetic moment of a Dirac particle, a charged, elementary particle, with a proton's mass p, in which anomalous corrections are ignored. The nuclear magneton is
where is the elementary charge, and is the reduced Planck constant. The magnetic moment of such a particle is parallel to its spin. Since the neutron has no charge, it should have no magnetic moment by the analogous expression. The non-zero magnetic moment of the neutron thus indicates that it is not an elementary particle. The sign of the neutron's magnetic moment is that of a negatively charged particle. Similarly, that the magnetic moment of the proton, is not almost equal to indicates that it too is not an elementary particle. 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.
Although the nucleons interact with normal matter through magnetic forces, the magnetic interactions are many orders of magnitude weaker than the nuclear interactions. The influence of the neutron's magnetic moment is therefore only apparent for low energy, or slow, neutrons. Because the value for the magnetic moment is inversely proportional to particle mass, the nuclear magneton is about as large as the Bohr magneton. The magnetic moment of the electron is therefore about 1000 times larger than that of the nucleons.
The magnetic moments of the antiproton and antineutron have the same magnitudes as their antiparticles, the proton and neutron, but they have opposite sign.
Measurement Proton The magnetic moment of the proton was discovered in 1933 by Otto Stern, Otto Robert Frisch and Immanuel Estermann at the University of Hamburg. The proton's magnetic moment was determined by measuring the deflection of a beam of molecular hydrogen by a magnetic field. Stern won the Nobel Prize in Physics in 1943 for this discovery.
Neutron
The neutron was discovered in 1932, and since it had no charge, it was assumed to have no magnetic moment. Indirect evidence suggested that the neutron had a non-zero value for its magnetic moment, however, until direct measurements of the neutron's magnetic moment in 1940 resolved the issue.
Values for the magnetic moment of the neutron were independently determined by R. Bacher at the University of Michigan at Ann Arbor (1933) and I. Y. Tamm and S. A. Altshuler in the Soviet Union (1934) from studies of the hyperfine structure of atomic spectra. Although Tamm and Altshuler's estimate had the correct sign and order of magnitude (), the result was met with skepticism.
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. The measured values for these particles were only in rough agreement between the groups, but the Rabi group confirmed the earlier Stern measurements that the magnetic moment for the proton was unexpectedly large. 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 a sign opposite to that of the proton. By the late 1930s, accurate values for the magnetic moment of the neutron had been deduced by the Rabi group using measurements employing newly developed nuclear magnetic resonance techniques.
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. Using an extension of the magnetic resonance methods developed by Rabi, Alvarez and Bloch determined the magnetic moment of the neutron to be . 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.
Unexpected consequences The large value for the proton's magnetic moment and the inferred negative value for the neutron's magnetic moment were unexpected and could not be explained. The unexpected values for the magnetic moments of the nucleons would remain a puzzle until the quark model was developed in the 1960s.
The refinement and evolution of the Rabi measurements led to the discovery in 1939 that the deuteron also possessed an electric quadrupole moment. 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. Rabi was awarded the Nobel Prize in 1944 for his resonance method for recording the magnetic properties of atomic nuclei.
Nucleon gyromagnetic ratios The magnetic moment of a nucleon is sometimes expressed in terms of its -factor, a dimensionless scalar. The convention defining the -factor for composite particles, such as the neutron or proton, is
where is the intrinsic magnetic moment, is the spin angular momentum, and is the effective -factor. While the -factor is dimensionless, for composite particles it is defined relative to the nuclear magneton. For the neutron, is so the neutron's -factor is while the proton's -factor is
The gyromagnetic ratio, symbol , of a particle or system is the ratio of its magnetic moment to its spin angular momentum, or
For nucleons, the ratio is conventionally written in terms of the proton mass and charge, by the formula
The neutron's gyromagnetic ratio is The proton's gyromagnetic ratio is The gyromagnetic ratio is also the ratio between the observed angular frequency of Larmor precession and the strength of the magnetic field in nuclear magnetic resonance applications, such as in MRI imaging. For this reason, the quantity called "gamma bar", expressed in the unit MHz / T, is often given. The quantities and are therefore convenient.
Physical significance
Larmor precession
When a nucleon 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 (in the case of the neutron, its spin is antiparallel to the field). As with any magnet, this torque is proportional the product of the magnetic moment and the external magnetic field strength. Since the nucleons have spin angular momentum, this torque will cause them to precess with a well-defined frequency, called the Larmor frequency. It is this phenomenon that enables the measurement of nuclear properties through nuclear magnetic resonance. The Larmor frequency can be determined from the product of the gyromagnetic ratio with the magnetic field strength. Since for the neutron the sign of γn is negative, the neutron's spin angular momentum precesses counterclockwise about the direction of the external magnetic field.
Proton nuclear magnetic resonance
Nuclear magnetic resonance employing the magnetic moments of protons is used for nuclear magnetic resonance (NMR) spectroscopy. Since hydrogen-1 nuclei are within the molecules of many substances, NMR can determine the structure of those molecules.
Determination of neutron spin The interaction of the neutron's magnetic moment with an external magnetic field was exploited to determine the spin of the neutron. In 1949, D. Hughes and M. Burgy measured neutrons reflected from a ferromagnetic mirror and found that the angular distribution of the reflections was consistent with spin . In 1954, J. Sherwood, T. Stephenson, and S. Bernstein employed neutrons in a Stern–Gerlach experiment that used a magnetic field to separate the neutron spin states. They recorded the two such spin states, consistent with a spin particle. Until these measurements, the possibility that the neutron was a spin particle could not have been ruled out.
Neutrons used to probe material properties Since neutrons are neutral particles, they do not have to overcome Coulomb repulsion as they approach charged targets, unlike protons and alpha particles. Neutrons can deeply penetrate matter. The magnetic moment of the neutron has therefore 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. B. Brockhouse and C. Shull won the Nobel Prize in physics in 1994 for developing these scattering techniques.
Control of neutron beams by magnetism As neutrons carry no electric charge, neutron beams cannot be controlled by the conventional electromagnetic methods employed in particle accelerators. The magnetic moment of the neutron allows some control of neutrons using magnetic fields, however, including the formation of polarized neutron beams. One technique employs the fact that cold neutrons will reflect from some magnetic materials at great efficiency when scattered at small grazing angles. The reflection preferentially selects particular spin states, thus polarizing the neutrons. Neutron magnetic mirrors and guides use this total internal reflection phenomenon to control beams of slow neutrons.
Nuclear magnetic moments