Neutron Capture Cross Sections from
Surrogate Reaction Data and Theory:
Connecting the Pieces with a
Markov-Chain Monte Carlo Approach
Oliver Gorton and Jutta E. Escher
Neutron capture cross sections can be measured by bombarding a sample of target
nuclei with neutrons and detecting decay products. Such measurements cannot be
completed in the laboratory when the target isotopes have half-lives that are short
compared to timescales relevant to the experiment. This leaves critical gaps in
nuclear data libraries. To predict the missing data, nuclear cross section calculations
can, in principle, be carried out using statistical Hauser-Feshbach (HF) models [1].
In compound nuclear reactions, a compound nucleus (CN) is formed, which then
decays through the available decay channels. These channels and the probability of
each being taken depend on the nuclear level densities and γ -ray strength function of
the CN. The general lack of nuclear structure information for medium to heavy mass
nuclei leads to the need for indirect constraints on the corresponding HF parameters.
The surrogate method [2] obtains these constraints using measurements of the same
CN decay observed in alternative reactions.
Specifically, in Ref. [3] the decay of the CN 91 Zr was modeled using
parametrized (phenomenological) forms for the level density and γ -ray strength
function. The parameters were fitted to measured 92 Zr(p, dγ ) data from a surrogate
experiment and subsequently used to calculate the desired 90 Zr(n, γ ) cross section.
A Bayesian Monte Carlo approach was employed, which provided an average (n, γ )
cross section, along with a variance, yielding an uncertainty band that is symmetric
around the mean. Here, we improve the parameter estimation by introducing a
Markov-Chain Monte Carlo (MCMC) approach for sampling the HF parameter
O. Gorton ()
San Diego State University, San Diego, CA, USA
e-mail: ogorton@sdsu.edu
J. E. Escher
Lawrence Livermore National Laboratory, Livermore, CA, USA
e-mail: escher1@llnl.gov
© This is a U.S. government work and not under copyright protection
in the U.S.; foreign copyright protection may apply 2021
J. Escher et al. (eds.), Compound-Nuclear Reactions, Springer Proceedings in
Physics 254, https://doi.org/10.1007/978-3-030-58082-7_28
229
Surrogate Reaction Data and Theory:
Connecting the Pieces with a
Markov-Chain Monte Carlo Approach
Oliver Gorton and Jutta E. Escher
Neutron capture cross sections can be measured by bombarding a sample of target
nuclei with neutrons and detecting decay products. Such measurements cannot be
completed in the laboratory when the target isotopes have half-lives that are short
compared to timescales relevant to the experiment. This leaves critical gaps in
nuclear data libraries. To predict the missing data, nuclear cross section calculations
can, in principle, be carried out using statistical Hauser-Feshbach (HF) models [1].
In compound nuclear reactions, a compound nucleus (CN) is formed, which then
decays through the available decay channels. These channels and the probability of
each being taken depend on the nuclear level densities and γ -ray strength function of
the CN. The general lack of nuclear structure information for medium to heavy mass
nuclei leads to the need for indirect constraints on the corresponding HF parameters.
The surrogate method [2] obtains these constraints using measurements of the same
CN decay observed in alternative reactions.
Specifically, in Ref. [3] the decay of the CN 91 Zr was modeled using
parametrized (phenomenological) forms for the level density and γ -ray strength
function. The parameters were fitted to measured 92 Zr(p, dγ ) data from a surrogate
experiment and subsequently used to calculate the desired 90 Zr(n, γ ) cross section.
A Bayesian Monte Carlo approach was employed, which provided an average (n, γ )
cross section, along with a variance, yielding an uncertainty band that is symmetric
around the mean. Here, we improve the parameter estimation by introducing a
Markov-Chain Monte Carlo (MCMC) approach for sampling the HF parameter
O. Gorton ()
San Diego State University, San Diego, CA, USA
e-mail: ogorton@sdsu.edu
J. E. Escher
Lawrence Livermore National Laboratory, Livermore, CA, USA
e-mail: escher1@llnl.gov
© This is a U.S. government work and not under copyright protection
in the U.S.; foreign copyright protection may apply 2021
J. Escher et al. (eds.), Compound-Nuclear Reactions, Springer Proceedings in
Physics 254, https://doi.org/10.1007/978-3-030-58082-7_28
229