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
and
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
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]
History
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
References
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