In cases with odd numbers of either or both protons and neutrons, the nucleus often has nonzero spin and magnetic moment.
The methods for measuring nuclear magnetic moments can be divided into two broad groups in regard to the interaction with internal or external applied fields.
For instance, the following techniques are aimed to measure magnetic moments of an associated nuclear state in a range of life-times τ: Techniques as Transient Field have allowed measuring the g-factor in nuclear states with life-times of few picoseconds or less.
[2] According to the shell model, protons or neutrons tend to form pairs of opposite total angular momentum.
Thus the real (measured) nuclear magnetic moment is between the values associated with the "pure" states, though it may be close to one or the other (as in deuterium).
Some isotopes in the human body have unpaired protons or neutrons (or both, as the magnetic moments of a proton and neutron do not cancel perfectly)[4][5][6] Note that in the table below, the measured magnetic dipole moments, expressed in a ratio to the nuclear magneton, may be divided by the half-integral nuclear spin to calculate dimensionless g-factors.
These g-factors may be multiplied by 7.622593285(47) MHz/T,[7] which is the nuclear magneton divided by the Planck constant, to yield Larmor frequencies (in MHz/T).
If divided instead by the reduced Planck constant, which is 2π less, a gyromagnetic ratio expressed in radians is obtained, which is greater by a factor of 2π.
The ratio of nuclei in the lower energy state, with spin aligned to the external magnetic field, is determined by the Boltzmann distribution.
[8] Thus, multiplying the dimensionless g-factor by the nuclear magneton and the applied magnetic field, and dividing by the product of the Boltzmann constant and the temperature.
has contributions both from the orbital angular momentum and the spin, with different coefficients g(l) and g(s): by substituting this back to the formula above and rewriting For a single nucleon