# Electric dipole transition

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

Following, 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

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

$W_{DE}(t)={\frac {qE_{0}}{m\omega }}p_{z}\sin \omega t.\,$ 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.

$W_{DM}(t)={\frac {q}{2m}}(L_{x}+2S_{x})B_{0}\cos \omega t\,$ and describes magnetic dipole transitions.

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