Nuclear magneton

The nuclear magneton (symbol μ_N) is a physical constant of magnetic moment, defined in SI units by: $${\displaystyle \mu _{\text{N}}={{e\hbar } \over {2m_{\text{p}}}}}$$ and in Gaussian CGS units by: $${\displaystyle \mu _{\text{N}}={{e\hbar } \over {2m_{\text{p}}c}}}$$ where:

• e is the elementary charge,
• ħ is the reduced Planck constant,
• m_p is the proton rest mass, and
• c is the speed of light

The value of nuclear magneton

System of units	Value
SI	5.0507837393(16)×10−27 J⋅T−1‍[1]
Gaussian	5.05078374×10−24 erg·G−1[2]
eV	3.15245125417(98)×10−8 eV·T−1[3]
MHz/T (per h)	7.6225932188(24) MHz/T[4]

Its CODATA recommended value is:

μ_N = 5.0507837393(16)×10⁻²⁷ J⋅T⁻¹

In Gaussian CGS units, its value can be given in convenient units as

μ_N = 0.10515446 e⋅fm

The nuclear magneton is the natural unit for expressing magnetic dipole moments of heavy particles such as nucleons and atomic nuclei.

Due to neutrons and protons having internal structure and not being Dirac particles, their magnetic moments differ from μ_N:

μ_p = 2.793 μ_N

μ_n = −1.913 μ_N

The magnetic dipole moment of the electron, which is much larger as a consequence of much larger charge-to-mass ratio, is usually expressed in units of the Bohr magneton, which is calculated in the same fashion using the electron mass. The result is larger than μ_N by a factor equal to the proton-to-electron mass ratio, about 1836.

See also

• Nucleon magnetic moment