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# Electric dipole transition

Electric dipole transition is the dominant effect of an interaction of an electron in an atom with the electromagnetic field.

Following,[1] consider an electron in an atom with quantum Hamiltonian \( H_0 , interacting with a plane electromagnetic wave

\( {\mathbf E}({\mathbf r},t)=E_0 {\hat{\mathbf z}} \cos(ky-\omega t), \ \ \ {\mathbf B}({\mathbf r},t)=B_0{\hat{\mathbf x}} \cos(ky-\omega t). \)

Write the Hamiltonian of the electron in this electromagnetic field as

\( H(t) \ = \ H_0 + W(t).. \)

Treating this system by means of time-dependent perturbation theory, one finds that the most likely transitions of the electron from one state to the other occur due to the summand of W(t) written as

\( W_{DE}(t) = \frac{q E_0}{m\omega} p_z \sin \omega t. \, . \)

Electric dipole transitions are the transitions between energy levels in the system with the Hamiltonian \( H_0 + W_{DE}(t) .. \)

Between certain electron states the electric dipole transition rate may be zero due to one or more selection rules, particularly the angular momentum selection rule. In such a case, the transition is termed electric dipole forbidden, and the transitions between such levels must be approximated by higher-order transitions.

The next order summand in W(t) is written as

\( W_{DM}(t) = \frac{q}{2m} (L_x + 2S_x) B_0 \cos \omega t \, . \)

and describes magnetic dipole transitions.

Even smaller contributions to transition rates are given by higher electric and magnetic multipole transitions.

See also

Dipole

Electric dipole moment

Electromagnetism

Magnetic dipole transition

References

http://electron6.phys.utk.edu/QM2/modules/m10/time.htm

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