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Update missing label in documentation

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Paul Romano 2017-03-20 06:24:19 -05:00
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docs/source/methods/cross_sections.rst
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@ -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::