Selection Rules and Light with Orbital Angular Momentum

• zen loki
In summary, the conversation discusses selection rules for atomic transitions and the impact of photon angular momentum on these rules. It is noted that while electrons can only change states with a difference of 1ħ in angular momentum, photons can have higher integer quantities of orbital angular momentum. This suggests that different transitions and selection rules may be possible in certain circumstances, and that light with orbital angular momentum may absorb differently than light without it. However, due to the long wavelength of light and the dominance of dipole transitions, transitions involving higher angular momentum have significantly lower intensity.
zen loki
When we first learn of selection rules for atomic transitions, we learn that electrons have to change between states that differ in angular momentum by at most 1ħ, because photons have 1 unit of spin angular momentum.

However, photons can have arbitrarily high integer quantities of orbital angular momentum, meaning the total angular momentum available can be more than 1. So, would we expect that different transitions and selection rules are possible? In specific circumstances, would light with orbital angular momentum absorb differently than the same frequency without orbital angular momentum?

The point is that due to the long wavelength of light as compared with atomic dimensions, by far the strongest transitions are dipole transitions. Transitions corresponding to the absorption of light with higher angular momentum have a much lower intensity. Specifically, the eigenstates of light angular momentum are the vector spherical harmonics and e.g. a plane wave can be decomposed into them.

1. What are selection rules?

Selection rules refer to the set of criteria that determine which transitions are allowed and which are forbidden in a physical system. These rules are based on the conservation of energy, momentum, and other quantum numbers.

2. How do selection rules relate to light with orbital angular momentum?

Light with orbital angular momentum carries angular momentum in addition to its linear momentum. Therefore, the selection rules for such light are more complex and involve the conservation of both orbital and spin angular momentum.

3. Can selection rules be violated?

Yes, selection rules can be violated in certain cases. This can happen through processes such as virtual transitions or tunneling, which allow forbidden transitions to occur. However, these violations are typically very rare and require specific conditions to be met.

4. How do selection rules affect spectroscopy?

In spectroscopy, selection rules play a crucial role in determining which transitions can be observed and which cannot. This helps in identifying and characterizing different energy levels and their corresponding transitions in a physical system.

5. Are selection rules the same for all physical systems?

No, selection rules can vary depending on the physical system being studied. For example, the selection rules for atomic transitions differ from those for molecular transitions. Additionally, selection rules can also be influenced by external factors such as the presence of a magnetic field.

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