Magnetic interaction between an electron and a nucleus
Not to be confused with Fermi's 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
and
where A is the energy of the interaction, μn is the nuclear magnetic moment, μe is the electron magnetic dipole moment, Ψ(0) is the value of the electron wavefunction at the nucleus, and 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]
Simplified view of the Fermi contact interaction in the terms of nuclear (green arrow) and electron spins (blue arrow). 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.[3]2: 1H nuclei are parallel. This form is unstable (has higher energy E) than the form 1.[4]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.[3]
^
Bucher, M. (2000). "The electron inside the nucleus: An almost classical derivation of the isotropic hyperfine interaction". European Journal of Physics. 21 (1): 19. Bibcode:2000EJPh...21...19B. doi:10.1088/0143-0807/21/1/303. S2CID 250871770.
^
Soliverez, C. E. (1980). "The contact hyperfine interaction: An ill-defined problem". Journal of Physics C. 13 (34): L1017. Bibcode:1980JPhC...13.1017S. doi:10.1088/0022-3719/13/34/002.
^ abM, Balcı (2005). Basic ¹H- and ¹³C-NMR spectroscopy (1st ed.). Elsevier. pp. 103–105. ISBN 9780444518118.
^Macomber, R. S. (1998). A complete introduction to modern NMR spectroscopy. Wiley. pp. 135. ISBN 9780471157366.
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