diff --git a/docs/source/methods/cross_sections.rst b/docs/source/methods/cross_sections.rst index b9043a944d..9f677bac43 100644 --- a/docs/source/methods/cross_sections.rst +++ b/docs/source/methods/cross_sections.rst @@ -183,45 +183,43 @@ Multi-Group Data The data governing the interaction of particles with various nuclei or materials are represented using a multi-group library format specific to the OpenMC code. -The format is described in the :ref:`mgxs_lib_spec`. -The data itself can be prepared via traditional paths or directly from a -continuous-energy OpenMC calculation by use of the Python API as is shown in the -:ref:`notebook_mgxs_part_iv` example notebook. This multi-group -library consists of meta-data (such as the energy group structure) and multiple -`xsdata` objects which contains the required microscopic or macroscopic -multi-group data. +The format is described in the :ref:`mgxs_lib_spec`. The data itself can be +prepared via traditional paths or directly from a continuous-energy OpenMC +calculation by use of the Python API as is shown in the +:ref:`notebook_mg_mode_part_i` example notebook. This multi-group library +consists of meta-data (such as the energy group structure) and multiple `xsdata` +objects which contains the required microscopic or macroscopic multi-group data. At a minimum, the library must contain the absorption cross section (:math:`\sigma_{a,g}`) and a scattering matrix. If the problem is an eigenvalue -problem then all fissionable materials must also contain either -a fission production matrix cross section -(:math:`\nu\sigma_{f,g\rightarrow g'}`), or -both the fission spectrum data (:math:`\chi_{g'}`) and a fission production -cross section (:math:`\nu\sigma_{f,g}`), or, . The library must also contain -the fission cross section (:math:`\sigma_{f,g}`) or the fission energy release -cross section (:math:`\kappa\sigma_{f,g}`) if the associated tallies are -required by the model using the library. +problem then all fissionable materials must also contain either a fission +production matrix cross section (:math:`\nu\sigma_{f,g\rightarrow g'}`), or both +the fission spectrum data (:math:`\chi_{g'}`) and a fission production cross +section (:math:`\nu\sigma_{f,g}`), or, . The library must also contain the +fission cross section (:math:`\sigma_{f,g}`) or the fission energy release cross +section (:math:`\kappa\sigma_{f,g}`) if the associated tallies are required by +the model using the library. After a scattering collision, the outgoing particle experiences a change in both energy and angle. The probability of a particle resulting in a given outgoing -energy group (`g'`) given a certain incoming energy group (`g`) is provided -by the scattering matrix data. The angular information can be expressed either -via Legendre expansion of the particle's change-in-angle (:math:`\mu`), a -tabular representation of the probability distribution function of :math:`\mu`, -or a histogram representation of the same PDF. The formats used to -represent these are described in the :ref:`mgxs_lib_spec`. +energy group (`g'`) given a certain incoming energy group (`g`) is provided by +the scattering matrix data. The angular information can be expressed either via +Legendre expansion of the particle's change-in-angle (:math:`\mu`), a tabular +representation of the probability distribution function of :math:`\mu`, or a +histogram representation of the same PDF. The formats used to represent these +are described in the :ref:`mgxs_lib_spec`. Unlike the continuous-energy mode, the multi-group mode does not explicitly track particles produced from scattering multiplication (i.e., :math:`(n,xn)`) reactions. These are instead accounted for by adjusting the weight of the particle after the collision such that the correct total weight is maintained. The weight adjustment factor is optionally provided by the `multiplicity` data -which is required to be provided in the form of a group-wise matrix. -This data is provided as a group-wise matrix since the probability of producing -multiple particles in a scattering reaction depends on both the incoming energy, -`g`, and the sampled outgoing energy, `g'`. This data represents the average -number of particles emitted from a scattering reaction, given a scattering -reaction has occurred: +which is required to be provided in the form of a group-wise matrix. This data +is provided as a group-wise matrix since the probability of producing multiple +particles in a scattering reaction depends on both the incoming energy, `g`, and +the sampled outgoing energy, `g'`. This data represents the average number of +particles emitted from a scattering reaction, given a scattering reaction has +occurred: .. math::