QB_PH_SEC9_023: Nuclear Models & Decays

What is the maximum number of identical nucleons (degeneracy $2j+1$) that can occupy the $1g_{9/2}$ nuclear single-particle shell?

Correct Answer

### Step-by-Step Derivation & Verification: 1. **Angular Momentum Projection**: Each single-particle state with total angular momentum $j$ has projection $m_j$ taking values: $m_j \in \{-j, -j+1, \dots, +j\}$ 2. **Pauli Exclusion Subshell Capacity**: $N_{\text{max}} = 2j + 1$ 3. **Substitution for $j = 9/2$**: $N_{\text{max}} = 2\left(\frac{9}{2}\right) + 1 = 9 + 1 = 10$ 4. **Official Integer Answer**: 10.