diff --git a/docs/source/methods/cross_sections.rst b/docs/source/methods/cross_sections.rst index 9c11d3626d..869040f5df 100644 --- a/docs/source/methods/cross_sections.rst +++ b/docs/source/methods/cross_sections.rst @@ -75,7 +75,7 @@ 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 -Python API :ref:`_notebook_mgxs_part_iv` example notebook. This multi-group +: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. @@ -83,9 +83,10 @@ 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\arrow\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 +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. @@ -113,8 +114,8 @@ reaction has occurred: .. math:: - multiplicity_{g \arrow g'} = \frac{\nu_{scatter}\sigma_{s,g \arrow g'}}{ - \sigma_{s,g \arrow g'}} + multiplicity_{g \rightarrow g'} = \frac{\nu_{scatter}\sigma_{s,g \rightarrow g'}}{ + \sigma_{s,g \rightarrow g'}} If this scattering multiplication information is not provided in the library then no weight adjustment will be performed. This is equivalent to neglecting @@ -130,7 +131,7 @@ follows: .. math:: - \sigma_{a,g} = \sigma_{t,g} - \sum_{g'}{\nu_{scatter}\sigma_{s,g \arrow g'}} + \sigma_{a,g} = \sigma_{t,g} - \sum_{g'}\nu_{scatter}\sigma_{s,g \rightarrow g'} The above method is the same as is usually done with most deterministic solvers. Note that this method is less accurate than using the scattering multiplication diff --git a/docs/source/methods/physics.rst b/docs/source/methods/physics.rst index e08965371c..bb26ffec53 100644 --- a/docs/source/methods/physics.rst +++ b/docs/source/methods/physics.rst @@ -87,7 +87,7 @@ Elastic Scattering Note that the multi-group mode makes no distinction between elastic or inelastic scattering reactions. The spceific multi-group scattering -implementation is discussed in the multi-group-scatter_ section. +implementation is discussed in the :ref:`multi-group-scatter` section. Elastic scattering refers to the process by which a neutron scatters off a nucleus and does not leave it in an excited. It is referred to as "elastic" @@ -182,7 +182,7 @@ Inelastic Scattering Note that the multi-group mode makes no distinction between elastic or inelastic scattering reactions. The spceific multi-group scattering -implementation is discussed in the multi-group-scatter_ section. +implementation is discussed in the :ref:`multi-group-scatter` section. The major algorithms for inelastic scattering were described in previous sections. First, a scattering cosine is sampled using the algorithms in @@ -202,7 +202,7 @@ secondary photons from nuclear de-excitation are tracked in OpenMC. Note that the multi-group mode makes no distinction between elastic or inelastic scattering reactions. The specific multi-group scattering -implementation is discussed in the multi-group-scatter_ section. +implementation is discussed in the :ref:`multi-group-scatter` section. These types of reactions are just treated as inelastic scattering and as such are subject to the same procedure as described in :ref:`inelastic-scatter`. For @@ -229,13 +229,13 @@ incoming energy group is to select a random number (:math:`\xi`) between 0 and produced from the outgoing group (`g'`) data for the given incoming group (`g`): .. math:: - CDF = \sum_{g'=0}^{h}\Sigma_{s,g \arrow g'} + CDF = \sum_{g'=0}^{h}\Sigma_{s,g \rightarrow g'} If the scattering data is represented as a Legendre expansion, then the -value of :math:`\Sigma_{s,g \arrow g'}` above is simply the 0th order for the +value of :math:`\Sigma_{s,g \rightarrow g'}` above is the 0th order forthe given group transfer. If the data is provided as tabular or histogram data, then -the value of :math:`\Sigma_{s,g \arrow g'}` is the sum of all bins of data for a -given `g` and `g'` pair. +:math:`\Sigma_{s,g \rightarrow g'}` is the sum of all bins of data for a given +`g` and `g'` pair. Now that the outgoing energy is known the change-in-angle, :math:`\mu` can be determined. If the data is provided as a Legendre expansion, this is done by