Fermi contact interactionfermi contact interaction physics, fermi contact interaction
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 relationshipsA = − 8 3 π ⟨ μ n ⋅ μ e ⟩ | Ψ 0 | 2 cgs }\pi \left\langle }_\cdot }_\right\rangle |\Psi 0|^\qquad }}
andA = − 2 3 μ 0 ⟨ μ n ⋅ μ e ⟩ | Ψ 0 | 2 , SI }\mu _\left\langle }_\cdot }_\right\rangle |\Psi 0|^,\qquad }}
where A is the energy of the interaction, μn is the nuclear magnetic moment, μe is the electron magnetic dipole moment, and Ψ0 is the value of the electron wavefunction at the nucleus
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 "Classical Electrodynamics" by 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 Br of another dipole This field acquires a simple expression when the distance r between the two dipoles goes to zero, since∫ S r B r d 3 r = − 2 3 μ 0 μ \mathbf \mathbf \,d^\mathbf =-}\mu _}}
- ^ 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:2000EJPh2119B doi:101088/0143-0807/21/1/303
- ^ Soliverez, C E 1980 "The contact hyperfine interaction: An ill-defined problem" Journal of Physics C 13 34: L1017 Bibcode:1980JPhC131017S doi:101088/0022-3719/13/34/002
- ^ 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:1930ZPhy60320F doi:101007/BF01339933
- ^ Jackson, J D 1998 Classical Electrodynamics 3rd ed Wiley p 184 ISBN 978-0471309321
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