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When L and S are parallel and pointing in the same direction, they add together to J = 2. When L and S are parallel and pointing in the opposite direction, they are subtracted and J = 0. When L and S are perpendicular they sum to J = 1. The perturbing term depends on the J = (L+S), L and S operators. You can imagine the eigenvalues of these operators as vectors in space. The alignment of the vectors then determines the energy difference.
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