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ps7 - Physics 212 Problem Set 7 Spring 2010 1 The Zeeman...

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Physics 212 – Problem Set 7 – Spring 2010 1. The Zeeman Effect with Nuclear Spin An external magnetic field is applied to a system with nuclear spin ~ I and electron total spin ~ J . The zeroth order Hamiltonian then gains the term H (1) = A ~ I · ~ J - J · ~ B - I · ~ B. Applying the magnetic field in the ˆ z direction yields H (1) = A ~ I · ~ J + g J μ B J z B z - g 0 I μ B I z B z , where J = g J μ B ~ J and I = g 0 I μ B ~ I define the new g-factors. Consider a system where the nuclear spin i =3 (like Boron 10) and the electron total spin j =3/2 (for instance, an electron in a p state). Calculate the shifts in the energy levels caused by H (1) in (a) the weak field limit:
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