Speaker
Description
This paper describes methods for processing and use of thermal neutron scattering data in OpenMC. OpenMC relies on NJOY to process thermal scattering ENDF evaluations into ACE files, which are then converted to HDF5 files by OpenMC's Python API. This process is fully automated with OpenMC producing an NJOY input deck containing appropriate options for each module and covering every temperature available on the original ENDF evaluation. OpenMC keeps a list of recognized thermal scattering evaluations for determining what isotopes should be associated with a particular evaluation as well as the number of atom types in a mixed moderator.
In many cases, NJOY processing results in probability distributions for the cosine of the scattering angle, $\mu$, and outgoing energy (for incoherent scattering) that are represented as a series of equally-likely discrete values. Without special treatment, these discrete values can produce unphysical artifacts in the observed angle and energy distributions of neutrons. For incoherent inelastic scattering, NJOY does support an option to produce a continuous distribution of outgoing energies. Both the older discrete format and newer continous format for incoherent inelastic scattering are supported in OpenMC.
For incoherent elastic scattering, NJOY does not have an option to produce a continuous distribution for the scattering cosine. Instead of using discrete cosines from the ACE file, OpenMC uses a novel, continuous sampling method based on the differential cross section, which can be expressed analytically as
$$
\frac{d\sigma}{dE' d\Omega} (E\rightarrow E', \mu, T) = \frac{\sigma_b}{4\pi} e^{-2EW'(T)(1 - \mu)} \delta(E - E')
$$
where $\sigma_b$ is the characteristic bound cross section and $W'(T)$ is the the Debye-Waller integral as a function of temperature, $T$. A probability density function for the cosine of the scattering angle can be sampled by using inverse transform sampling based on the above equation, resulting in the following algorithm:
$$
\xi \gets U(0,1)
$$
$$
\mu \gets \frac{1}{c} \log \left ( 1 + \xi \left ( e^{2c} - 1 \right ) \right) - 1
$$
where $U(0,1)$ is a uniformly distributed random number on the interval $[0,1)$ and $c = 2EW'$. Note that this method requires that $\sigma_b$ and $W'(T)$ be stored in the HDF5 data files; to support this, OpenMC pulls the appropriate data directly from ENDF files to augment the ACE data produced by NJOY. Comparisons of observed angular distributions for a variety of thermal neutron scattering evaluations with incoherent elastic scattering, to be presented in the full paper, demonstrate the advantages of this method.
OpenMC has several other attractive features related to thermal scattering. It supports the use of partial $S(\alpha,\beta,T)$ tables, wherein the user can indicate that thermal scattering data should only apply to some fraction of the atoms in a material. This makes it possible to spatially homogenize materials, some of which should use thermal scattering data and some of which should not. OpenMC has also recently been updated to support new ENDF-6 formatted evaluations that contain both coherent and incoherent elastic scattering (so-called ``mixed'' elastic scattering).