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 magnetic resonance">magnetism">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
and
where A is the energy of the interaction, μn is the nuclear magnetic moment, μe is the electron [magnetic dipole moment], Ψ is the value of the electron wavefunction at the nucleus, and denotes the quantum mechanical spin coupling.
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.
File:J-coupling Fermi contact mechanism.svg|center|thumb|450px|Simplified view of the Fermi contact interaction in the terms of nuclear and electron spins. 1: in H2, 1H spin polarizes electron spin antiparallel. This in turn polarizes the other electron of the σ-bond antiparallel as demanded by Pauli's exclusion principle. Electron polarizes the other 1H. 1H nuclei are antiparallel and 1JHH has a positive value. 2: 1H nuclei are parallel. This form is unstable than the form 1. 3: vicinal 1H J-coupling via 12C or 13C nuclei. Same as before, but electron spins on p-orbitals are parallel due to Hund's 1. rule. 1H nuclei are antiparallel and 3JHH has a positive value.

Use in magnetic resonance spectroscopy

Roughly, the magnitude of A indicates the extent to which the unpaired spin resides on the nucleus. Thus, knowledge of the A values allows one to map the singly occupied molecular orbital.

History

The interaction was first derived by Enrico Fermi in 1930. A classical derivation of this term is contained in "Classical Electrodynamics" by John [David Jackson (physicist)|J. D. Jackson]. In short, the classical energy may be written in terms of the energy of one magnetic dipole moment in the magnetic field B of another dipole. This field acquires a simple expression when the distance r between the two dipoles goes to zero, since