# I Zeeman effect sign of circular polarization

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1. Jul 15, 2016

### Khashishi

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.

2. Jul 15, 2016

### blue_leaf77

In the picture below $\sigma^-$ line has higher energy than $\sigma^+$.

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• ###### Zeeman effect longitudinal.png
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3. Jul 18, 2016

### Khashishi

I don't see any indication of energy or direction of magnetic field in that picture.

4. Jul 19, 2016

### blue_leaf77

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 $\Delta m_l = 1$.