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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

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