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.

 

[denian]

I can understand how the concepts of selection rules and related transitions can be confusing. Let me try to explain these concepts in a simpler way.

The selection rules are a set of guidelines that determine which transitions are allowed between different energy levels in an atom or molecule. These rules are based on the conservation of quantum numbers, which are fundamental properties of particles such as energy, angular momentum, and spin.

The reason why dipole transitions are specifically mentioned is because they are the most common type of transition that occurs in atoms and molecules. A dipole transition involves the absorption or emission of a photon by an electron, causing it to move from one energy level to another.

Now, let's look at the two examples you provided. In the first case, the electron absorbs a photon and jumps to a higher energy level. This is an example of an electric dipole transition, as it involves the absorption of a photon by an electron.

In the second case, where an rf (radio frequency) is applied to a system and causes the electron spin to flip, this is an example of a magnetic dipole transition. This is because the rf energy is interacting with the magnetic properties of the electron, rather than its electric properties.

The other types of transitions you mentioned, such as electric quadrupole, magnetic quadrupole, and quadrupole transitions, are less common and involve more complex interactions between particles. For example, an electric quadrupole transition involves the interaction between an electric quadrupole moment (a measure of the distribution of electric charge) and an external electric field.

To understand the selection rules better, it may be helpful to think about them in terms of symmetry. Each type of transition has a specific symmetry associated with it, and the selection rules state that the initial and final states of the transition must have the same symmetry. This is why certain transitions are allowed while others are not.

While it may be necessary to refer to a table of selection rules for specific cases, understanding the underlying principles and symmetry can help in understanding and remembering the rules. I hope this explanation has helped to clarify some of the confusion.