Fermi contact interaction

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The Fermi contact interaction is the magnetic interaction between an electron and an atomic nucleus when the electron is inside that nucleus.

The parameter is usually described with the symbol A and the units are usually megahertz. The magnitude of A is given by this relationships


where A is the energy of the interaction, μn is the nuclear magnetic moment, μe is the electron magnetic dipole moment, and Ψ(0) is the value of the electron wavefunction at the nucleus.[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]

Use in magnetic resonance spectroscopy[edit]

Within an atom, only s-orbitals have non-zero electron density at the nucleus, so the contact interaction only occurs for s-electrons. Its major manifestation is in electron paramagnetic resonance and nuclear magnetic resonance spectroscopies, where it is responsible for the appearance of isotropic hyperfine coupling. 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.[3]


The interaction was first derived by Enrico Fermi in 1930.[4] A classical derivation of this term is contained in "Classical Electrodynamics" by J. D. Jackson.[5] In short, the classical energy may be written in terms of the energy of one magnetic dipole moment in the magnetic field B(r) of another dipole. This field acquires a simple expression when the distance r between the two dipoles goes to zero, since


  1. ^ 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.
  2. ^ 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.
  3. ^ Drago, R. S. (1992). Physical Methods for Chemists (2nd ed.). Saunders College Publishing. ISBN 978-0030751769.
  4. ^ Fermi, E. (1930). "Über die magnetischen Momente der Atomkerne". Zeitschrift für Physik. 60 (5–6): 320. Bibcode:1930ZPhy...60..320F. doi:10.1007/BF01339933.
  5. ^ Jackson, J. D. (1998). Classical Electrodynamics (3rd ed.). Wiley. p. 184. ISBN 978-0471309321.