When talking about selection rules in atomic physics, many books state that the photon interacts with the electrons angular momentum such that that $\Delta l=\pm 1$. Absorbed/emitted photons exchange angular momentum with the electrons of the atom. For example: When an incoming circular polarised photon with spin $1\hbar$ is absorbed by the atom, an electron has to change its angular momentum $\vec{l}$ by $1\hbar$.
But why is there no such interaction between the electrons spin $\vec{s}$ and photons? What is the origin of the selection rule $\Delta S=0$?
I'm interested in both mathematical and especially intuitive explanations 🙂
Best Answer
The selection rule $\Delta S=0$ is an approximation, nothing more, and in suitable circumstances it can easily break. One prominent example of this is the hydrogen 21cm line.
Electromagnetic atomic and molecular transitions are arranged into a series in order of multipolarity, which describes the atomic operators that enact the interaction hamiltonian, with higher multipolarities scaling down in coupling strength as powers of $a/\lambda$, i.e. the ratio between the system's size and the radiation's wavelength, which is generally small. Thus, you get
Generally, the no-spin-flips rule holds only for electric dipole transitions, for which the interaction hamiltonian is the electric dipole operator $\hat{\mathbf d}$, which does not couple sectors with different spin (unless you have strong spin-orbit coupling).
However, it is perfectly possible to have magnetic dipole transitions between states of spin that differ by $\Delta S=1$. Here the coupling is weaker (so you will need a higher intensity, or longer pulse times, to excite them), and thus typically the linewidth is smaller (so you will require a sharper laser), also giving a longer decay lifetime, but those are things that make the transition harder to observe, not impossible.