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Title: Constraining transfer cross sections using Bayes' theorem

Background: Being able to rigorously quantify the uncertainties in reaction models is crucial to moving this field forward. Even though Bayesian methods are becoming increasingly popular in nuclear theory, they have yet to be implemented and applied in reaction theory problems. Purpose: The purpose of this work is to investigate, using Bayesian methods, the uncertainties in the optical potentials generated from fits to elastic-scattering data and the subsequent uncertainties in the transfer predictions. We also study the differences in two reaction models where the parameters are constrained in a similar manner, as well as the impact of reducing the experimental error bars on the data used to constrain the parameters. Method: We use Bayes' theorem combined with a Markov chain Monte Carlo to determine posterior distributions for the parameters of the optical model, constrained by neutron-, proton-, and/or deuteron-target elastic scattering. These potentials are then used to predict transfer cross sections within the adiabatic wave approximation or the distorted-wave Born approximation. Results: We study a number of reactions involving deuteron projectiles with energies in the range 10–25 MeV/nucleon on targets with mass A = 48–208. The case of 48Ca(d,p) 49Ca transfer to the ground state is described in detail. Amore » comparative study of the effect of the size of experimental errors is also performed. Five transfer reactions are studied, and their results are then compiled in order to systematically identify trends.« less
Authors:
 [1] ;  [2]
  1. Michigan State Univ., East Lansing, MI (United States). National Superconducting Cyclotron Lab. and Dept. of Physics and Astronomy; Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
  2. Michigan State Univ., East Lansing, MI (United States). National Superconducting Cyclotron Lab. and Dept. of Physics and Astronomy
Publication Date:
Grant/Contract Number:
NA0002132; NA0002135; PHY-1403906; FG52-09NA29467
Type:
Accepted Manuscript
Journal Name:
Physical Review C
Additional Journal Information:
Journal Volume: 97; Journal Issue: 6; Journal ID: ISSN 2469-9985
Publisher:
American Physical Society (APS)
Research Org:
Michigan State Univ., East Lansing, MI (United States)
Sponsoring Org:
USDOE National Nuclear Security Administration (NNSA); National Science Foundation (NSF)
Country of Publication:
United States
Language:
English
Subject:
73 NUCLEAR PHYSICS AND RADIATION PHYSICS; Uncertainty Quanti cation; elastic scattering; inelastic scattering; transfer reactions; direct reaction theory; optical, coupled-channel & distorted wave models
OSTI Identifier:
1463318
Alternate Identifier(s):
OSTI ID: 1456272

Lovell, A. E., and Nunes, F. M.. Constraining transfer cross sections using Bayes' theorem. United States: N. p., Web. doi:10.1103/PhysRevC.97.064612.
Lovell, A. E., & Nunes, F. M.. Constraining transfer cross sections using Bayes' theorem. United States. doi:10.1103/PhysRevC.97.064612.
Lovell, A. E., and Nunes, F. M.. 2018. "Constraining transfer cross sections using Bayes' theorem". United States. doi:10.1103/PhysRevC.97.064612. https://www.osti.gov/servlets/purl/1463318.
@article{osti_1463318,
title = {Constraining transfer cross sections using Bayes' theorem},
author = {Lovell, A. E. and Nunes, F. M.},
abstractNote = {Background: Being able to rigorously quantify the uncertainties in reaction models is crucial to moving this field forward. Even though Bayesian methods are becoming increasingly popular in nuclear theory, they have yet to be implemented and applied in reaction theory problems. Purpose: The purpose of this work is to investigate, using Bayesian methods, the uncertainties in the optical potentials generated from fits to elastic-scattering data and the subsequent uncertainties in the transfer predictions. We also study the differences in two reaction models where the parameters are constrained in a similar manner, as well as the impact of reducing the experimental error bars on the data used to constrain the parameters. Method: We use Bayes' theorem combined with a Markov chain Monte Carlo to determine posterior distributions for the parameters of the optical model, constrained by neutron-, proton-, and/or deuteron-target elastic scattering. These potentials are then used to predict transfer cross sections within the adiabatic wave approximation or the distorted-wave Born approximation. Results: We study a number of reactions involving deuteron projectiles with energies in the range 10–25 MeV/nucleon on targets with mass A = 48–208. The case of 48Ca(d,p) 49Ca transfer to the ground state is described in detail. A comparative study of the effect of the size of experimental errors is also performed. Five transfer reactions are studied, and their results are then compiled in order to systematically identify trends.},
doi = {10.1103/PhysRevC.97.064612},
journal = {Physical Review C},
number = 6,
volume = 97,
place = {United States},
year = {2018},
month = {6}
}