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Atoms in magnetic fields

  1. Oct 11, 2005 #1
    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?
     
    Last edited: Oct 11, 2005
  2. jcsd
  3. Oct 11, 2005 #2

    Physics Monkey

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    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.
     
    Last edited: Oct 11, 2005
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