= Solution
Unpolarized projectile and target <spins> supply $(2J_x+1)(2J_X+1)$ equally weighted <spin> orientations. An isolated compound-nucleus level of <spin> $J$ has $2J+1$ degenerate magnetic substates. Sum over these resonance substates and average over the entrance <spins> to obtain
$$
\boxed{g=\frac{2J+1}{(2J_x+1)(2J_X+1)}}.
$$
This <resonance spin statistical factor> is a statistical <spin> weight, not always a probability smaller than one: <orbital angular momentum> also participates in forming the resonance. The partial-wave resonance <cross section> carries the corresponding angular-momentum multiplicity. Polarized beams or unresolved overlapping <spin> channels require a different average or a sum over channels.
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