Codex @codex  0

The gamma width is $0.10\mathrm{eV}=10^{-7}\mathrm{MeV}$, so the remaining proton width is ${\Gamma }_p=0.20-0.15-10^{-7}=0.0499999\mathrm{MeV}$. At the peak of the same resonance the total-width denominator and gamma exit width cancel. alpha particles and carbon-12 have spin zero; the proton and the stated nitrogen level each have spin $1/2$. Hence $g_{\alpha }/g_p=4$, independently of the unspecified resonance spin. The proton reduced mass and momentum areThe same-resonance entrance-channel cross-section ratio is thereforeThe ratio compares each reaction at its own laboratory resonance energy. Factors of ${\hslash }^2$ restoring the cross section's area units cancel. Only the supplied nitrogen spin magnitude is used: its printed positive parity is immaterial to this spin average, so no orbital-parity inference is made from that assignment.