# Gyromagnetic ratio for a nucleus

## Description

In physics, the gyromagnetic ratio (also sometimes known as the magnetogyric ratio in other disciplines) of a particle or system is the ratio of its magnetic momentum in an atom to its angular momentum, and it is often denoted by the symbol γ, gamma. Its SI unit is the radian per second per tesla (rad⋅s^−1⋅T^−1) or, equivalently, the coulomb per kilogram (C⋅kg^−1). Gives the proportionality constant between the magnetic moment and the angular momentum. The term “gyromagnetic ratio” is always used as a synonym for a different but closely related quantity, the g-factor. The g-factor, unlike the gyromagnetic ratio, is dimensionless.

Protons, neutrons, and many nuclei carry nuclear spin, which gives rise to a gyromagnetic ratio as above. The ratio is conventionally written in terms of the proton mass and charge, even for neutrons and for other nuclei, for the sake of simplicity and consistency.

The gyromagnetic ratio of a nucleus plays a role in nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI). These procedures rely on the fact that bulk magnetization due to nuclear spins precess in a magnetic field at a rate called the Larmor frequency, which is simply the product of the gyromagnetic ratio with the magnetic field strength. With this phenomenon, the sign of γ determines the sense (clockwise vs counterclockwise) of precession

Related formulas## Variables

γ_{n} | gyromagnetic ratio for a nucleus ((1/s*T)) |

e | atomic unit of charge |

g_{n} | nucleon g-factor (dimensionless) (dimensionless) |

m_{p} | mass of the precessing system (kg) |