# Magneton

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## Magneton

A unit of magnetic moment used to describe atomic, molecular, or nuclear magnets. More precisely, one unit, the Bohr magneton, is used at the atomic and molecular levels, and another unit, the nuclear magneton, is used at the nuclear level. Still another unit (which might be called the muon magneton, but is usually not named) is used to describe the magnetic moment of the muon.

The Bohr magneton μ_{B} is defined and its value given in Eq. (1), where -*e* and *m*

_{B}, but according to the theory of quantum electrodynamics the electron has a small anomalous magnetic moment. The experimental value of the electron magnetic moment μ

_{e}is given by Eq. (2), in agreement with the

The unit of magnetic moment to describe the muon is obtained from the Bohr magneton by replacing *m* in Eq. (1) by the muon mass *m*_{μ}. The experimental value of the muon magnetic moment is given in Eq. (3). The deviation

*See*Lepton

The nuclear magneton is obtained from the Bohr magneton by replacing *m* by the proton mass *m*_{p}. The value of the nuclear magneton is given in Eq. (4). The

*See*Neutron, Nuclear moments, Proton

According to present theory, the proton, neutron, and other hadrons have large anomalous magnetic moments because these particles are not elementary but composite. In the theory of quantum chromodynamics, the principal constituents of a baryon, such as the proton or neutron, are three quarks. *See* Baryon, Elementary particle, Fundamental constants, Quantum chromodynamics, Quarks

## Magneton

a unit of measurement of magnetic moment that has been adopted in atomic and nuclear physics.

The magnetic moment of atomic systems is due mainly to the motion of electrons and their spin and is measured in Bohr magnetons:

Here *ħ* is Planck’s constant, *e* and *m* are the absolute values of the charge and mass of an electron, and *c* is the speed of light.

In nuclear physics, magnetic moments are measured in nu-clear magnetons, which differ from *μ _{B}* in that the mass of the electron

*m*is replaced by the mass of the proton

*M:*

The physical meaning of the quantity *μ _{B}* may be understood easily on the basis of a semiclassical examination of the motion of an electron with velocity v in a circular orbit of radius

*r*. This system is analogous to a coil carrying a current whose strength I is equal to the charge divided by the period of rotation: I =

*ev/2π*. According to classical electrodynamics, in the Gaussian system the magnetic moment of a current-carrying coil that encompasses an area

_{r}*S*is

*μ = IS/c*=

*evr/2c*, or μ =

*eMi/2mc*, where

*M*is the orbital angular momentum of the electron. If we take into account the fact that, according to quantum laws, the orbital moment

_{1}— mvr*M*of an electron can assume only discrete values that are multiples of Planck’s constant,

_{i}*Mi*=

*lħ*where l = 0, 1, 2,…, then the following expression results:

Thus, the magnetic moment of an electron in a state with an orbital moment *M _{1}* is a multiple of the Bohr magneton. Consequently, in this case

*μ*plays the role of an elementary magnetic moment, a “quantum” of an electron’s magnetic moment.

_{B}In addition to the orbital angular momentum *M _{1}*, which results from rotation, the electron has an intrinsic mechanical moment, the spin, which is

*s =*1/2 (in units of ħ). The spin magnetic moment is μ

_{s}= 2

_{μB}—that is, it is twice as large as the quantity that would be expected on the basis of formula (3), but since s = 1/2 , μ

_{s}of an electron is also equal to the Bohr magneton: μ

_{s}= μ

_{B}This stems directly from the relativistic quantum theory of the electron, which is based on the Dirac equation.

The nuclear magneton has a similar meaning: it is the magnetic moment created by the motion of a proton (within the nucleus) having an orbital moment l = 1. However, the intrinsic magnetic moments of nuclear particles—the proton and neutron —which, like the electron, have a spin of 1/2, differ significantly from the values that would be expected according to Dirac’s theory. The anomalous magnetic moments of these particles are due to their strong interaction.

D. V. GAL’TSOV