# Relative intensities of Zeeman components

• Acetylene5
In summary, the conversation discusses the calculation of the effect of a magnetic field on spectral lines, specifically focusing on the splitting of energy levels and the selection rules for allowed electric dipole transitions. The conversation also mentions the relevant equations from Condon and Shortley's Theory of Atomic Spectra and raises a question about the interpretation of these equations. The update from the person asking the question clarifies that if the relative intensity is 0, then that Zeeman component is not allowed to appear.
Acetylene5
Hi-

I'm trying to calculate the effect of a magnetic field on some spectral lines. I know that each energy level will split into 2J+1 sub levels (each denoted by Mj). I can calculate the energy level splitting and using the selection rules (dJ = 0, +/-1, dMj = 0, +/-1, dL = 0, +/-1), I can figure out which transitions are allowed electric dipoles. I know that the pi components (dMj = 0) are not emitted parallel to the magnetic field, while the sigma components (dMj = +/- 1) can be seen in both parallel and transverse directions.

So, I think I can calculate the zeeman splitting alright, but the problem arises when I try to calculate the relative intensities of each of the zeeman components. I found some relevant equations in Condon and Shortley's Theory of Atomic Spectra (Chapter 16, section 4), but I don't think I'm interpreting it right. It's been a while since I had a quantum class, so it's possible I'm forgetting something stupid.

"For the Zeeman pattern of any line in which there is no change in J, the strengths of the components in transverse observation are proportional to:
| < alpha J M| P | alpha' J M> |^2 = |<alpha J| P | alpha' J>|^2 M^2 (pi)
1/4*|<alpha J M | P | alpha' J M -/+ 1>|^2 = |<alpha J| P |alpha' J>|^2 1/4 (J +/- M)(J -/+ M+1) (sigma)

There are different (but very similar) formulas for delta J = +1, and -1, but I'm not going to type them out here (I can if others would find it useful).

My problem is when delta Mj = 0, and Mj = 0 as well. Does this mean that since Mj = 0, the pi component is not allowed? To put it another way, when the proportionality factor = zero, is that component forbidden? It doesn't seem to make sense, as you'd be missing the central pi component completely from both the transverse and longitudinal spectra.

I know there's a selection rule against delta J = 0 when J =0, but i didn't think that prohibited Mj from being zero when delta J = 0.

Where am I going wrong?

Thanks,
C.

Here's an update for anyone who's looking for an answer... It turns out that if the relative intensity = 0, then that Zeeman component does not appear. In effect, it's not allowed. Hope this helps.

## 1. What are Zeeman components?

Zeeman components refer to the splitting of spectral lines in the presence of a magnetic field. This effect was discovered by Dutch physicist Pieter Zeeman in 1896.

## 2. How do magnetic fields affect the relative intensities of Zeeman components?

The relative intensities of Zeeman components depend on the strength of the magnetic field. As the magnetic field increases, the spectral lines split into multiple components, each with its own intensity. The relative intensities of these components are determined by the quantum numbers of the energy levels involved.

## 3. What is the significance of studying relative intensities of Zeeman components?

Studying the relative intensities of Zeeman components can provide information about the atomic structure and energy levels of an element. It can also help in understanding the behavior of matter in the presence of magnetic fields.

## 4. How are relative intensities of Zeeman components measured?

The relative intensities of Zeeman components can be measured using spectroscopy techniques. By analyzing the intensities of different components, scientists can determine the energy levels involved and the strength of the magnetic field.

## 5. What are some applications of studying relative intensities of Zeeman components?

The study of relative intensities of Zeeman components has various applications in fields such as astronomy, plasma physics, and materials science. It can be used to analyze the composition and properties of celestial objects, study the behavior of particles in plasma, and investigate the electronic structure of materials.

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