Fermi contact interaction

The Fermi contact interaction is the magnetic interaction between an electron and an atomic nucleus. Its major manifestation is in electron paramagnetic resonance and nuclear magnetic resonance spectroscopies, where it is responsible for the appearance of isotropic hyperfine coupling.

This requires that the electron occupy an s-orbital. The interaction is described with the parameter A, which takes the units megahertz. The magnitude of A is given by this relationships

${\displaystyle A=-{\frac {8}{3}}\pi \left\langle {\boldsymbol {\mu }}_{n}\cdot {\boldsymbol {\mu }}_{e}\right\rangle |\Psi (0)|^{2}\qquad {\mbox{(cgs)}}}$

and

${\displaystyle A=-{\frac {2}{3}}\mu _{0}\left\langle {\boldsymbol {\mu }}_{n}\cdot {\boldsymbol {\mu }}_{e}\right\rangle |\Psi (0)|^{2},\qquad {\mbox{(SI)}}}$

where A is the energy of the interaction, μ_n is the nuclear magnetic moment, μ_e is the electron magnetic dipole moment, Ψ(0) is the value of the electron wavefunction at the nucleus, and ${\textstyle \left\langle \cdots \right\rangle }$ denotes the quantum mechanical spin coupling.^[1]

It has been pointed out that it is an ill-defined problem because the standard formulation assumes that the nucleus has a magnetic dipolar moment, which is not always the case.^[2]