Zeeman effect sign of circular polarization

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Discussion Overview

The discussion revolves around the Zeeman effect and the relationship between circular polarization and wavelength in the context of a magnetic field directed toward the observer. Participants explore the energy levels associated with circularly polarized emissions and their respective wavelengths.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant expresses uncertainty about whether the counterclockwise (CCW) polarized emission is at a higher or lower wavelength than the clockwise (CW) polarized emission when the magnetic field is directed toward the observer.
  • Another participant states that the ##\sigma^-## line has higher energy than the ##\sigma^+## line, implying a relationship between energy and polarization.
  • A different participant questions the clarity of the energy or magnetic field direction in the provided picture, suggesting a lack of information.
  • One participant clarifies that the magnetic field is uniform and pointing in the positive z direction, providing a formula for energy levels in the presence of the magnetic field and explaining the frequency of transitions based on changes in magnetic quantum numbers.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the relationship between the circular polarization and wavelength, as there are differing interpretations of the energy levels and the implications of the magnetic field direction.

Contextual Notes

The discussion includes assumptions about the uniformity of the magnetic field and the definitions of the transitions associated with the circular polarization, which may not be universally accepted or clarified among participants.

Khashishi
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I'm unsure about the sign of the circular polarization.
Assume the magnetic field is pointed toward the observer.
In the Zeeman effect spectrum, is the CCW polarized emission at higher or lower wavelength than the CW polarized emission.

I think the CCW polarized emission is higher, and this is reversed if we change the direction of the magnetic field.
 
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In the picture below ##\sigma^-## line has higher energy than ##\sigma^+##.
 

Attachments

  • Zeeman effect longitudinal.png
    Zeeman effect longitudinal.png
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I don't see any indication of energy or direction of magnetic field in that picture.
 
Sorry I forgot to mention that the field is uniform pointing in the positive z direction.
The explanation about the energy is given in the text, there I took the snapshot of the picture only. In the presence of uniform magnetic field the energy level is given by
$$
E = E_n +\mu_B B_z(m_l+2m_s)
$$
The frequency corresponding to down-transition ##n\to n'## is then ##\nu = (E-E')/\hbar = \frac{E_n-E_{n'}}{\hbar} - \frac{\mu_B B_z}{\hbar}(m_{l'}-m_l) = \nu_{nn'} - \frac{\mu_B B_z}{\hbar}\Delta m_l## where ##E>E'## and ##\Delta m_l = m_{l'}-m_l##. The ##\sigma^+## line which is defined to be the transition with ##\Delta m_l = -1## hence has higher frequency than ##\sigma^-## line which is defined by ##\Delta m_l = 1##.
 
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