Physics

Magnetic dipole moment of an odd-odd nucleus

Step-by-step physics solution: Magnetic dipole moment of an odd-odd nucleus

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1. What the problem is asking

  • Part A – Explain why the ground state of (^{40}!{\rm K}) has the quantum numbers

[ J^{\pi}=4^{-} ]

  • Part B – Using the nuclear shell model, obtain a theoretical value for the magnetic dipole moment (\mu) of this state.
    (The nucleus is odd‑odd: one unpaired proton and one unpaired neutron.)

2. Shell‑model picture of (^{40})K

Nucleus Closed‑core Valence nucleons
(^{40})Ca (core) (Z=20,\;N=20) – doubly magic, ({\rm 0s,0p,0d,1s,0f,1p}) filled –
(^{40})K (Z=19,\;  

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