Selection rules and related stuffs

[Weimin]

I'm quite confuse with some concepts here.

The selection rules are derived from the requirements that quantum numbers must be conserved. It's OK. Then I see they give rules for so-called electric dipole transitions. I just wonder why dipole comes in here. How do you classify these kinds of transitions:

1. An electron absorbs a photon and then jumps to the higher level.

2. In magnetic resonance, if we apply an rf with energy match to the separation between two energy levels, the electron spin can flip. The difference to case 1 is we have magnetic field involved.

Can you give me the examples of dipole-dipole, magnetic-dipole, electric quadrupole, magnetic quadrupole, quadrupole transitions? Is there any way to understand the selection rules rather than remember the table of selection rules?

 

[smallphi]

In semi-classical approximation of matter-light interaction, the atomic system (the matter) is quantized while the light is treated as a classical field. In that approximation, the probability for the atomic system to excite/deexcite is proportional to something like a series of matrix elements of certain operators between the initial and final states of the atomic system. The selection rules state when those matrix elements could be non-zero. The main term in the series is the electric dipole operator which gives rise to dipole transition rules. If that matrix element is zero, the probability for atomic transition is severely decreased, yet you have weaker operators in the series, like magnetic dipole, electric quadrupole etc. that can have non-zero matrix elements and still cause transition. Weaker transitions will show as fainter lines in the experimental atomic spectrum.

A full understanding why the matrix elements of a given operator between two sates are zero can be achieved only after you learn group theory.