Bayesian Analysis of the $^{70}$Zn$(d, ^3\!\text{He}) ^{69}$Cu Transfer Reaction

TL;DR

This paper integrates Bayesian methods with distorted wave Born approximation to quantify uncertainties in nuclear transfer reaction analysis, improving the reliability of spectroscopic factors and angular momentum assignments.

Contribution

It introduces a Bayesian framework to propagate uncertainties in transfer reaction analysis, enhancing the accuracy of spectroscopic factors and angular momentum transfer identification.

Findings

Large asymmetric uncertainties in spectroscopic factors (35-108%)

Bayesian model comparison confirms many angular momentum assignments

Data suggests reclassification of a state from ℓ=2 to ℓ=3 transfer

Abstract

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 $^{70}$Zn$(d, ^3\!\text{He}) ^{69}$Cu 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 is better characterized by an $\ell = 3$ transfer, rather than the previously reported $\ell = 2$.