Nucleon magnetic moment
The nucleon magnetic moments are the intrinsic
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 spin ħ/2, 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
The nuclear magneton is the
Although the nucleons interact with normal matter through magnetic forces, the magnetic interactions are many orders of magnitude weaker than the nuclear interactions.[12] The influence of the neutron's magnetic moment is therefore only apparent for low energy, or slow, neutrons.[12] Because the value for the magnetic moment is inversely proportional to particle mass, the nuclear magneton is about 1/2000 as large as the Bohr magneton. The magnetic moment of the electron is therefore about 1000 times larger than that of the nucleons.[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.[14]
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.[15][16][17] The proton's magnetic moment was determined by measuring the deflection of a beam of molecular hydrogen by a magnetic field.[18] Stern won the Nobel Prize in Physics in 1943 for this discovery.[19]
Neutron
The neutron was discovered in 1932,[20] 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,[21] however, until direct measurements of the neutron's magnetic moment in 1940 resolved the issue.[22]
Values for the magnetic moment of the neutron were independently determined by
By 1934 groups led by Stern, now at the
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.[22] Using an extension of the magnetic resonance methods developed by Rabi, Alvarez and Bloch determined 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.[30]
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.[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][32] This electrical property of the deuteron had been interfering with the measurements by the Rabi group.[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.[33]
Nucleon gyromagnetic ratios
The magnetic moment of a nucleon is sometimes expressed in terms of its g-factor, a dimensionless scalar. The convention defining the g-factor for composite particles, such as the neutron or proton, is
The gyromagnetic ratio, symbol γ, 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 γn = 1.83247171(43)×108 s−1⋅T−1.
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).[43] 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.[44]
Proton nuclear magnetic resonance
Nuclear magnetic resonance employing the magnetic moments of protons is used for
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.[47] 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 1/2.[48] 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.[49] They recorded the two such spin states, consistent with a spin 1/2 particle.[49][47] Until these measurements, the possibility that the neutron was a spin 3/2 particle could not have been ruled out.[47]
Neutrons used to probe material properties
Since neutrons are neutral particles, they do not have to overcome
Control of neutron beams by magnetism
As neutrons carry no electric charge,
Nuclear magnetic moments
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.[47] The nuclear magnetic moment also includes contributions from the orbital motion of the charged protons.[47] The deuteron, consisting of a proton and a neutron, has the simplest example of a nuclear magnetic moment.[47] The sum of the proton and neutron magnetic moments gives 0.879 µN, which is within 3% of the measured value 0.857 µN.[56] In this calculation, the spins of the nucleons are aligned, but their magnetic moments offset because of the neutron's negative magnetic moment.[56]
Nature of the nucleon magnetic moments
A magnetic dipole moment can be generated by
Anomalous magnetic moments and meson physics
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.[31]
The problem of the origins of the magnetic moments of nucleons was recognized as early as 1935. 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.[64] By this idea, the magnetic moment of the neutron was caused by the fleeting existence of the large magnetic moment of the electron in the course of these quantum-mechanical fluctuations, the value of the magnetic moment determined by the length of time the virtual electron was in existence.[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.[63][66]
Similar considerations for the electron proved to be much more successful. In
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. The calculation was discovered by J. Schwinger in 1948.[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.[67]
Compared to the electron, the anomalous magnetic moments of the nucleons are enormous.[10] The g-factor for the proton is 5.6, and the chargeless neutron, which should have no magnetic moment at all, has a g-factor of −3.8. Note, however, that the anomalous magnetic moments of the nucleons, that is, their magnetic moments with the expected Dirac particle magnetic moments subtracted, are roughly equal but of opposite sign: μp − 1.00 μN = +1.79 μN, but μn − 0.00 μN = −1.91 μN.[71]
The Yukawa interaction for nucleons was discovered in the mid-1930s, and this nuclear force is mediated by pion mesons.[63] In parallel with the theory for the electron, the hypothesis was that higher-order loops involving nucleons and pions may generate the anomalous magnetic moments of the nucleons.[9] The physical picture was that the effective magnetic moment of the neutron arose from the combined contributions of the "bare" neutron, which is zero, and the cloud of "virtual" pions and photons that surround this particle as a consequence of the nuclear and electromagnetic forces.[7]: 75–80 [72] The Feynman diagram at right is roughly the first-order diagram, with the role of the virtual particles played by pions. 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".[31] These theories were also, as noted by Pais, "a flop" – they gave results that grossly disagreed with observation. Nevertheless, serious efforts continued along these lines for the next couple of decades, to little success.[9][72][73] These theoretical approaches were incorrect because the nucleons are composite particles with their magnetic moments arising from their elementary components, quarks.[31]
Quark model of nucleon magnetic moments
In the
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%.[76][77][78] The measured value for this ratio is −1.45989806(34).[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.[76]
From the nonrelativistic quantum-mechanical wave function for baryons composed of three quarks, a straightforward calculation gives fairly accurate estimates for the magnetic moments of neutrons, protons, and other baryons.[11] For a neutron, the magnetic moment 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 and assumes that the three quarks are in a particular, dominant quantum state.[11]
Baryon | Magnetic moment of quark model |
Computed () |
Observed () |
---|---|---|---|
p | 4 /3 μu − 1 /3 μd | 2.79 | 2.793 |
n | 4 /3 μd − 1 /3 μu | −1.86 | −1.913 |
The results of this calculation are encouraging, but the masses of the up or down quarks were assumed to be 1 /3 the mass of a nucleon. Furthermore, the complex system of quarks and gluons that constitute a nucleon requires a relativistic treatment.[81] Nucleon magnetic moments have been successfully computed from first principles, requiring significant computing resources.[82][83]
See also
- Aharonov–Casher effect
- LARMOR neutron microscope
- Neutron electric dipole moment
- Neutron triple-axis spectrometry
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External links
- Media related to Neutron magnetic moment at Wikimedia Commons