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Hyperfine Hamiltonian

  • Thread starter TFM
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  • #1
TFM
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Homework Statement



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].

Homework Equations



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

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?

TFM
 
Last edited:

Answers and Replies

  • #3
TFM
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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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