Atoms in magnetic fields

In summary, the LS-coupling breaks down in a strong magnetic field due to the fact that the spin-orbit and Zeeman interactions have different strengths. In the case of a strong spin-orbit interaction, the good quantum numbers are J, M_J, L, and S, while in the case of a strong Zeeman interaction, the good quantum numbers are M_L, M_S, L, and S, but not J. This is because the Zeeman interaction is not proportional to J_z, as there are different g-factors associated with spin and orbital angular momentum. In weak fields, the spin-orbit splittings are much larger than the Zeeman splittings, allowing for the use of spin-orbit quantum numbers to
  • #1
jonas_nilsson
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A question concerning atoms in magnetic fields:

Why does the LS-coupling break down in a strong magnetic field (Paschen-Back effect)? I have until now only gotten this stated as a fact, but if anyone could give a few arguments it would be appreciated. Why aren't the individual components of [tex]\mu_s[/tex] and [tex]\mu_l[/tex] quantised in weak fields?
 
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  • #2
You have essentialy two limiting cases that define a set of good quantum numbers. In the case where the spin-orbit interaction is much stronger than Zeeman interaction, the good quantum numbers of the system are [tex] J,\,M_J, \,L,\, S [/tex]. In the opposite limit, where the Zeeman intereaction is much stronger than spin-orbit interaction, the good quantum numbers are [tex] M_L,\,M_S,\, L,\, S [/tex] but not [tex] J [/tex]. Why? The Zeeman interaction isn't proportional to [tex] J_z [/tex] because of the different g-factors associated with spin and orbital angular momentum which translates into the statement [tex] [J^2 , H_{Zeeman} ] \neq 0 [/tex]. When doing perturbation theory in a weak field (spin-orbit splittings much bigger than zeeman splittings), you can label the primary splittings with the spin-orbit quantum numbers and then treat the Zeeman effect as a perturbation on these states, but when doing perturbation theory in a strong magnetic field (zeeman splittings much bigger than spin-orbit splittings), you label the primary splittings using the Zeeman quantum numbers. Here is a good little site that has some nice diragrams: http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/paschen.html

Hope this helps.
 
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  • #3


There are a few key factors that contribute to the breakdown of LS-coupling in a strong magnetic field, resulting in the Paschen-Back effect. One of the main reasons is the Zeeman effect, which is the splitting of atomic energy levels in the presence of a magnetic field. This effect becomes more pronounced in a strong magnetic field, causing the LS-coupling to break down.

Additionally, the strength of the magnetic field can impact the relative strength of the spin-orbit interaction compared to the external magnetic field. In weak fields, the spin-orbit interaction dominates and causes the LS-coupling to hold, resulting in quantized values of the individual components of \mu_s and \mu_l. However, in strong fields, the external magnetic field becomes stronger and can overcome the spin-orbit interaction, leading to the breakdown of LS-coupling.

Furthermore, the electronic configuration of an atom can also play a role in the breakdown of LS-coupling in a strong magnetic field. For atoms with partially filled subshells, the presence of unpaired electrons can result in more complex energy level structures, making it more difficult for LS-coupling to hold.

Overall, the breakdown of LS-coupling in a strong magnetic field is a complex phenomenon that involves the interplay of various factors, such as the Zeeman effect, the strength of the magnetic field, and the electronic configuration of the atom. Further research and experimentation are needed to fully understand and explain this phenomenon.
 

What is the relationship between atoms and magnetic fields?

Atoms are made up of negatively charged electrons orbiting around a positively charged nucleus. When these atoms are placed in a magnetic field, the electrons will experience a force due to their charge and their motion in the field, resulting in a variety of phenomena.

How does a magnetic field affect the behavior of atoms?

A magnetic field can cause the electrons in an atom to either align or misalign their spin with the direction of the field. This can lead to changes in the energy levels of the electrons, affecting the atom's overall behavior and properties.

Can magnetic fields be used to manipulate atoms?

Yes, magnetic fields can be used to manipulate atoms in a variety of ways. For example, scientists can use magnetic fields to control the movement of atoms in a gas, or to trap and cool atoms for use in experiments or technology.

What is the significance of studying atoms in magnetic fields?

Studying atoms in magnetic fields allows scientists to better understand the fundamental properties and behaviors of matter. It also has practical applications in fields such as materials science, electronics, and medical imaging.

Are there any potential dangers associated with atoms in magnetic fields?

Highly powerful magnetic fields can have adverse effects on living organisms, including disrupting the body's electrical signals and causing discomfort or even injury. However, in most cases, the magnetic fields used in scientific research or medical applications are carefully controlled and pose minimal risk.

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