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Hyperfine Hamiltonian

  1. May 17, 2009 #1


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    1. The problem statement, all variables and given/known data

    Derive the hyperfine Hamiltonian starting from [tex] \hat{H}_H_F = -\hat{\mu}_N \cdot \hat{B_L} [/tex]. Where [tex] \hat{\mu}_N [/tex] is the magnetic moment of the nucleus and
    [tex] \hat{B_L} [/tex] is the magnetic field created by the pion’s motion around the nucleon. Write down the Hamiltonian in the form [tex] \hat{H}_H_F = ... \vec{I} \cdot \vec{L} [/tex].

    2. Relevant equations

    [tex] \hat{B_L} = \frac{\mu_0e}{4\pi r^3}\vec{r} \times \vec{v}[/tex]

    3. The attempt at a solution

    Okay, I have tried putting everything together, and so far I currently have:

    [tex] \hat{H}_{hf} = g_n \mu_n \frac{\vec{I}}{\hbar}\cdot \frac{-\mu_0e}{4\pi r^3} \times V [/tex]

    but I am not sure where to go from here. Any suggestions?

    Last edited: May 18, 2009
  2. jcsd
  3. May 17, 2009 #2
  4. May 18, 2009 #3


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    Thanks for the linkj.

    I was koooking through my notes as suggested in the script, and they have a different version, my notes have [tex] \hat{H}_{HF} = -\hat{\mu}_N\hat{B}_j [/tex]

    the notes then go on to say that Bj is parallel to j

    is this useful?
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