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The interaction of an electromagnetic wave with an electron bound in an atom or molecule can be described by time-dependent [[Perturbation theory (quantum mechanics)|perturbation theory]]. Magnetic dipole transitions describe the dominant effect of the coupling to the magnetic part of the electromagnetic wave. They can be divided into two groups by the frequency at which they are observed: Optical magnetic dipole transitions can occur at frequencies in the infrared, optical or ultraviolet  between sublevels of two different electronic levels, Magnetic Resonance transitions can occur at microwave or radio frequencies between angular momentum sublevels within a single electronic level. The latter are called [[Electron Paramagnetic Resonance]] (EPR) transitions if they are associated with the electronic angular momentum of the atom or molecule and [[Nuclear Magnetic Resonance]] (NMR) transitions if they are associated with the nuclear angular momentum.<ref name="Cohen">{{cite book|last=C.Cohen Tannoudji|coauthors=B.Diu;F.Laloe|title=Quantum mechanics|publisher=Wiley|year=1999|isbn=978-0-471-56952-7}}</ref>


== Theoretical description ==


The Hamiltonian of an electron bound in an atom  interacting with an electromagnetic field is given by (the theoretical description follows <ref name="Siegman">{{cite book|last=A. E. Siegman|title=LASERS|publisher=University Science Books|year=1986|isbn=0-935702-11-3}}</ref>):
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<math>H=\frac{1}{2m}[\mathbf{P}-q\mathbf{A}(\mathbf{R},t)]^2+V(R)-\frac{q}{m}\mathbf{S} \cdot \mathbf{B}(\mathbf{R},t)</math>
 
The Hamiltonian can be split into a time independent and a time dependent part:
 
<math> H=H_0+W(t) </math>
 
with
 
<math>H_0=\mathbf{P}^2/(2m) +V(R)</math>
 
the atomic Hamiltonian and the interaction with the electromagnetic wave (time-dependent):
 
<math>W(t)=-q/m \mathbf{P}\cdot \mathbf{A}(\mathbf{R},t)-q/m \mathbf{S}\cdot \mathbf{B}(\mathbf{R},t)+q^2/(2m) \mathbf{A}^2(\mathbf{R},t)</math>
 
Since the last term is quadratic in A it can be neglected for small fields.
The time-dependent part can be expanded in terms belonging to electric dipole, magnetic dipole, electric quadropole and higher order terms. The term belonging to the magnetic dipole transitions is:
 
<math>W_{DM}(t)=-q/(2m)(\mathbf{L}+2\mathbf{S})\cdot\mathbf{B}(\mathbf{R},t)</math>
 
== Selection rules ==
 
The [[selection rule]]s for allowed magnetic dipole transitions are:
 
1. <math>\Delta J=0,\pm 1 (\text{except } J=0 \rightarrow J=0)</math> (J: [[total angular momentum quantum number]])
 
2. <math>\Delta M_J=0,\pm 1</math> (<math>M_J</math>: projection of the [[total angular momentum]] along a specified axis)
 
3. No parity change
 
== Comparison to electric dipole transitions ==
 
*[[Electric dipole transition]]s only have a non-vanishing matrix element between quantum states with different parity. Magnetic dipole transitions and electric quadrupole transitions in contrast couple states with the same parity.<ref name="Cohen" />
*The response of these two transitions is much weaker than that of electric dipole transitions.
*The electronic states of atoms and molecules normally don't have a static electric dipole moment but many states have a static magnetic dipole moment. The classical magnetized top model can be used to describe magnetic resonances for atoms with static magnetic dipole moment between different Zeeman-split-sublevel in a sufficient way without needing a full quantum mechanical description.<ref name="Siegman" />
 
== References ==
 
{{reflist}}
 
== External links ==
*[http://physics.nist.gov/Pubs/AtSpec/node17.html National Institute of Standards and Technology]
[[Category:Magnetism]]
{{physics stub}}

Revision as of 16:40, 4 February 2014


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