Muon Capture in Oxygen-16

The muon capture rate in oxygen is used as a means for measuring the induced pseudoscalar coupling constant ($C_P$) of weak interactions. The capture rate between the $J^P=0^{+}$ ground state of ${\mathrm{O}}^{16}$ and the $0^{-}$, $1^{-}$, $2^{-}$, and $3^{-}$ states of ${\mathrm{N}}^{16}$ are calculated as a function of $C_P$ with different nuclear models. Using the experimental values of the transition rates, we then determine $C_P$. We find that the transition rate, and therefore $C_P$, depends strongly on the nuclear model. We conclude that $5<\mathrm{}\frac{C_P}{C_A}<20\mathrm{}$.