 Solution

Both particles can occupy $l=0$ with opposite spins, giving a unique singlet state at $E=0$, quantum degeneracy 1. At the next distinct energy ${ϵ}_R$, 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. HenceSwapping particle labels adds no independent state after the required exchange symmetry is imposed.