Bayesian analysis of the Zn 70 ( d , He 3 ) Cu 69 transfer reaction
Transfer reactions provide information about the single-particle nature of nuclear levels. In particular, the differential cross sections from these measurements are sensitive to the angular momentum of the transferred particle and the spectroscopic factor of the populated level. However, the process of extracting these properties is subject to uncertainties, both from experimental and theoretical sources. By integrating the distorted wave Born approximation into a Bayesian model, we propagate these uncertainties through to the spectroscopic factors and orbital angular momentum values. We use previously reported data of the proton pickup reaction Zn 70 ( d , He 3 ) Cu 69 as an example. By accounting for uncertainties in the experimental data, optical model parameters, and reaction mechanism, we find that the extracted spectroscopic factors for low-lying states of 69 Cu are subject to large, asymmetric uncertainties ranging from 35 to 108%. Additionally, Bayesian model comparison is employed to assign probabilities to each of the allowed angular momentum transfers. This method confirms the assignments for many states, but suggests that the data for a state lying at 3.70 MeV are better characterized by an ℓ =3 transfer, rather than the previously reported ℓ =2 .