Uncertainty quantification due to optical potentials in models for ( d,p ) reactions

Abstract

Recent work has studied the uncertainty in predictions for A(d,p)B reactions using the distorted-wave Born approximation (DWBA), coming from the parameterization of the effective dA interactions [Lovell et al., Phys. Rev. C 95, 024611]. There are different levels of sophistication in theories for one-nucleon transfer reactions, including the adiabatic wave approximation (ADWA) which takes deuteron breakup into account to all orders. In this work, we quantify the uncertainties associated with the ADWA method that come from the parameterization of the NA interactions, and compare ADWA with DWBA. We use nucleon elastic-scattering data on a wide variety of targets to constrain the optical potential input to the ADWA theory. Pulling from the $\chi^2$-distribution, we obtain 95% confidence plots for the elastic distributions. From the resulting parameters, we predict 95% confidence bands for the (d,p) transfer cross sections. Results obtained with the uncorrelated $\chi^2$ are compared to those using the correlated $\chi^2$ of Lovell et al. We also repeat the DWBA calculations for the same reactions for comparison purposes. We find that NA elastic scattering data provides a significant constraint to the interactions, and, when the uncertainties are propagated to the transfer reactions using ADWA, predictions are consistent with the transfer data. The angular distributions for ADWA differ from those predicted by DWBA, particularly at small angles. Confidence bands obtained using the uncorrelated $\chi^2$-function are unrealistically narrow and become much wider when the correlated $\chi^2$-function is considered. For most cases, the uncertainty bands obtained in ADWA are narrower than DWBA, when using elastic data of similar quality and range. However, given the large uncertainties predicted from the correlated $\chi^2$-function, the transfer data cannot discriminate between these two methods.