Fermi contact interaction
The parameter is usually described with the symbol A and the units are usually megahertz. The magnitude of A is given by this relationship:
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.
Use in magnetic resonance spectroscopy
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.
The interaction was first derived by Enrico Fermi in 1930. A classical derivation of this term is contained in 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(r) of another. This field acquires a simple expression when the distance r between the two moments goes to zero, since:
- 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.
- 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.
- Drago, R. S. (1992). Physical Methods for Chemists (2nd ed.). Saunders College Publishing. ISBN 978-0030751769.
- Fermi, E. (1930). "Über die magnetischen Momente der Atomkerne". Zeitschrift für Physik 60 (5–6): 320. Bibcode:1930ZPhy...60..320F. doi:10.1007/BF01339933.
- Jackson, J. D. (1998). Classical Electrodynamics (3rd ed.). Wiley. p. 184. ISBN 978-0471309321.