= Spin-three-halves pair spectrum
{title2=$\mathbf S_1\cdot\mathbf S_2/\hbar^2\in\{-15/4,-11/4,-3/4,9/4\}$}
For $s_1=s_2=3/2$, <angular momentum addition> gives one copy of $j=0,1,2,3$. The identity $2\mathbf S_1\cdot\mathbf S_2=\mathbf J^2-\mathbf S_1^2-\mathbf S_2^2$ gives the four <eigenvalues> in the title, with <state degeneracy> $1,3,5,7$. These exhaust the $4\times4$ spin space. If the particles are identical <fermions>, an appropriate spatial exchange parity accommodates each sector; only a specified spatial restriction can remove sectors.
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