= Solution
Both particles can occupy $l=0$ with opposite <spins>, giving a unique <singlet state> at \b[$E=0$, <quantum degeneracy> 1]. At the next distinct <energy> $\epsilon_R$, one orbital is $l=0$ and the other is $l=+1$ or $-1$. For each orbital choice there is one symmetric spatial state paired with the <singlet state>, and one antisymmetric spatial state paired with three <triplet state> <spin> projections. Hence
$$
\boxed{g(E=\epsilon_R)=2(1+3)=8}.
$$
Swapping particle labels adds no independent state after the required exchange symmetry is imposed.
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