To be used in future
 Section 4.4: Landau Levels Up Chapter 4: Charged Particles and Electromagnetic Fields Section 4.6: Internal degrees of freedom: spin 

4.5 Coupling of light to atoms and nuclei: multipole couplings

If we consider light fields of wavelength much larger than the atom; also consider classical fields (we know we should quantise, since fields contain photons). Really geared towards the use of Fermi-Golden rule type calculations.
For the scalar potential we can make a multipole expansion
We assume the fields are weak, so we can perform a first order perturbation theory. The matrix elements we need to calculate are of the form In atoms we find that the dominant term is , this is linked to the strong dipole matrix elements in atoms, These are also called (electric, ) transitions.
In atomic nuclei we can’t have large dipoles (why?), but we often large quadrupole, so
Selection rules (parity)
Magnetic couplings (in expansion of , much more complicated).
Particle in laser fields: sytrong dipole interaction
 Section 4.4: Landau Levels Up Chapter 4: Charged Particles and Electromagnetic Fields Section 4.6: Internal degrees of freedom: spin