# 4. Multi-Group Cross Section Library Format¶

OpenMC can be run in continuous-energy mode or multi-group mode, provided the nuclear data is available. In continuous-energy mode, the cross_sections.xml file contains necessary meta-data for each dataset, including the name and a file system location where the complete library can be found. In multi-group mode, the multi-group meta-data and the nuclear data itself is contained within an mgxs.h5 file. This portion of the manual describes the format of the multi-group data library required to be used in the mgxs.h5 file.

The multi-group library is provided in the HDF5 format. This library must provide some meta-data about the library itself (such as the number of energy groups, delayed groups, and the energy group structure, etc.) as well as the actual cross section data itself for each of the necessary nuclides or materials.

The current version of the multi-group library file format is 1.0.

## 4.1. MGXS Library Specification¶

/

Attributes
• filetype (char[]) – String indicating the type of file; for this library it will be ‘mgxs’.

• version (int[2]) – Major and minor version of the multi-group library file format.

• energy_groups (int) – Number of energy groups

• delayed_groups (int) – Number of delayed groups (optional)

• group structure (double[]) – Monotonically increasing list of group boundaries, in units of eV. The length of this array should be the number of groups plus 1.

/<library name>/

The data within <library name> contains the temperature-dependent multi-group data for the nuclide or material that it represents.

Attributes
• atomic_weight_ratio (double) – The atomic weight ratio (optional, i.e. it is not meaningful for material-wise data).

• fissionable (bool) – Whether the dataset is fissionable (True) or not (False).

• representation (char[]) – The method used to generate and represent the multi-group cross sections. That is, whether they were generated with scalar flux weighting (or reduced to a similar representation) and thus are angle-independent, or if the data was generated with angular dependent fluxes and thus the data is angle-dependent. Valid values are either “isotropic” or “angle”.

• num_azimuthal (int) – Number of equal width angular bins that the azimuthal angular domain is subdivided if the representation attribute is “angle”. This parameter is ignored otherwise.

• num_polar (int) – Number of equal width angular bins that the polar angular domain is subdivided if the representation attribute is “angle”. This parameter is ignored otherwise.

• scatter_format (char[]) – The representation of the scattering angular distribution. The options are either “legendre”, “histogram”, or “tabular”. If not provided, the default of “legendre” will be assumed.

• order (int) – Either the Legendre order, number of bins, or number of points (depending on the value of scatter_format) used to describe the angular distribution associated with each group-to-group transfer probability.

• scatter_shape (char[]) – The shape of the provided scatter and multiplicity matrix. The values provided are strings describing the ordering the scattering array is provided in row-major (i.e., C/C++ and Python) indexing. Valid values are “[Order][G][G’]” or “[Order][G’][G]” where “G’” denotes the secondary/outgoing energy groups, “G” denotes the incoming energy groups, and “Order” is the angular distribution index. This value is not required; if not the default value of “[Order][G][G’]” will be assumed.

/<library name>/kTs/

Datasets
• <TTT>K (double) – kT values (in eV) for each temperature TTT (in Kelvin), rounded to the nearest integer

/<library name>/<TTT>K/

Temperature-dependent data, provided for temperature <TTT>K.

Datasets
• total (double[] or double[][][]) – Total cross section. This is a 1-D vector if representation is “isotropic”, or a 3-D vector if representation is “angle” with dimensions of [polar][azimuthal][groups].

• absorption (double[] or double[][][]) – Absorption cross section. This is a 1-D vector if representation is “isotropic”, or a 3-D vector if representation is “angle” with dimensions of [groups][azimuthal][polar].

• fission (double[] or double[][][]) – Fission cross section. This is a 1-D vector if representation is “isotropic”, or a 3-D vector if representation is “angle” with dimensions of [polar][azimuthal][groups]. This is only required if the dataset is fissionable and fission-tallies are expected to be used.

• kappa-fission (double[] or double[][][]) – Kappa-Fission (energy-release from fission) cross section. This is a 1-D vector if representation is “isotropic”, or a 3-D vector if representation is “angle” with dimensions of [polar][azimuthal][groups]. This is only required if the dataset is fissionable and fission-tallies are expected to be used.

• chi (double[] or double[][][]) – Fission neutron energy spectra. This is a 1-D vector if representation is “isotropic”, or a 3-D vector if representation is “angle” with dimensions of [polar][azimuthal][groups]. This is only required if the dataset is fissionable and fission-tallies are expected to be used.

• nu-fission (double[] to double[][][][]) – Nu-Fission cross section. If chi is provided, then nu-fission has the same dimensionality as fission. If chi is not provided, then the nu-fission data must represent the fission neutron energy spectra as well and thus will have one additional dimension for the outgoing energy group. In this case, nu-fission has the same dimensionality as multiplicity matrix.

• inverse-velocity (double[] or double[][][]) – Average inverse velocity for each of the groups in the library. This dataset is optional. This is a 1-D vector if representation is “isotropic”, or a 3-D vector if representation is “angle” with dimensions of [polar][azimuthal][groups].

/<library name>/<TTT>K/scatter_data/

Data specific to neutron scattering for the temperature <TTT>K

Datasets
• g_min (int[] or int[][][]) – Minimum (most energetic) groups with non-zero values of the scattering matrix provided. If scatter_shape is “[Order][G][G’]” then g_min will describe the minimum values of “G’” for each “G”; if scatter_shape is “[Order][G’][G]” then g_min will describe the minimum values of “G” for each “G’”. These group numbers use the standard ordering where the fastest neutron energy group is group 1 while the slowest neutron energy group is group G. The dimensionality of g_min is: g_min[g], or g_min[num_polar][num_azimuthal][g]. The former is used when representation is “isotropic”, and the latter when representation is “angle”.

• g_max (int[] or int[][][]) – Similar to g_min, except this dataset describes the maximum (least energetic) groups with non-zero values of the scattering matrix.

• scatter_matrix (double[]) – Flattened representation of the scattering moment matrices. The pre-flattened array corresponds to the shape provied in scatter_shape, but if representation is “angle” the dimensionality in scatter_shape is prepended by “[num_polar][num_azimuthal]” dimensions. The right-most energy group dimension will only include the entries between g_min and g_max. dimension has a dimensionality of g_min to g_max.

• multiplicity_matrix (double[]) – Flattened representation of the scattering moment matrices. This dataset provides the code with a scaling factor to account for neutrons being produced in (n,xn) reactions. This is assumed isotropic and therefore is not repeated for every Legendre moment or histogram/tabular bin. This dataset is optional, if it is not provided no multiplication (i.e., values of 1.0) will be assumed. The pre-flattened array is shapes consistent with scatter_matrix except the “[Order]” dimension in scatter_shape is ignored since this data is assumed isotropic.