# 7.1. XSPROC: The Material and Cross Section Processing Module for SCALE

*M. L. Williams, L. M. Petrie, R. A. Lefebvre, K. T. Clarno, J. P. Lefebvre, U. Merturyek, D. Wiarda, and B. T. Rearden*

ABSTRACT

The material and cross section processing module of SCALE (XSProc) was improved for the 6.2 release to prepare data for continuous-energy and multigroup calculations. XSProc expands material input from Standard Composition Library definitions into atom number densities and, for multigroup calculations, performs cross section resonance self-shielding, energy group collapse, and spatial homogenization. XSProc implements capabilities for problem-dependent temperature interpolation, calculation of Dancoff factors, resonance self-shielding using Bondarenko factors with full-range intermediate resonance treatment, as well as use of continuous energy resonance self-shielding in the resolved resonance region. The SCALE 6.3 XSProc maintains the same architecture with SCALE 6.2 which integrated and enhanced the capabilities previously implemented independently in BONAMI, CENTRM, PMC, WORKER, ICE, and XSDRNPM, along with some additional capabilities that were provided by MIPLIB and SCALELIB. The SCALE 6.3 XSProc development focuses on improving accuracy, applicability and stability for any advanced reactor analysis including Light Water Reactors (LWR), Pebble and Prismatic High Temperature Gas-cooled Reactors (HTGR), Molten Salt Reactors (MSR), Sodium- and Lead-cooled Fast Reactors (SFR and LFR) without any limitation.

ACKNOWLEDGMENTS

Development and maintenance of XSProc and related codes and methods have been sponsored by the US Nuclear Regulatory Commission (NRC) and the US Department of Energy (DOE).

VERSION INFORMATION

XSProc has evolved from the concept of a Material Information Processor library (MIPLIB) that used alphanumeric material specifications, which was initially proposed and developed by R. M. Westfall. J. R. Knight and J. A. Bucholz expanded and refined MIPLIB in early SCALE releases.

**SCALE 6.1 (2011) and 6.2 (2016)**:
M. L. Williams and L. M. Petrie led development and improvement for
XSProc and contributors include, R. A. Lefebvre, K. T. Clarno,
J. P. Lefebvre, U. Merturyek, D. Wiarda, B. T. Rearden, S. Goluoglu,
D. F. Hollenbach, N. F. Landers, J. A. Bucholz, C. F. Weber, and
C. M. Hopper. With the SCALE modernization initiative beginning in
SCALE 6.2, MIPLIB is no longer part of the XSProc analysis, but the
original concepts and input formatting were preserved in the new
implementation.

**SCALE 6.3 (2021)**:
K. S. Kim led responsibility and contributors include A. M. Holcomb,
D. Wiarda, R. Bostelmann, M. A. Jessee, and W. A. Wieselquist. The
SCALE 6.3 XSProc has been focused on improving accuracy, applicability
and stability for advanced reactor analysis including high temperature
gas cooled reactors and fast spectrum reactors.

## 7.1.1. Introduction

Self-shielding of multigroup cross sections is required in SCALE sequences for criticality safety, reactor physics, radiation shielding, and sensitivity analysis. In all previous versions of SCALE, resonance self-shielding calculations were done by executing a series of stand-alone executable codes, each dedicated to a specific aspect of the self-shielding operations. Each sequence had its own unique internal coding to launch the executable codes. Multigroup (MG) and continuous-energy (CE) cross sections and other data were passed between the individual executable codes by external I/O, which could require a substantial amount of clock time. In the modern version of SCALE, all self-shielding operations are consolidated into a single driver module named XSProc, and the stand-alone executable codes have been transformed into callable “computational modules” [XSProc-RLL+15]. The functions of XSProc are to (a) read input data, (b) generate in-memory data structures (objects) containing problem-definition information (compositions, cell geometries, computation options), as well as self-shielding information (MG and CE cross sections and fluxes), and (c) execute appropriate computational modules for the requested self-shielding option. Calculated results produced by one module may be stored in the internal data objects and passed to other modules through application program interfaces (APIs). At the completion of XSProc the self-shielded MG cross sections on the data objects can be passed along to transport solvers for continued execution of the control sequence or can be written to an external AMPX library file.

In the future, XSProc will be extended to parallel computations in which self-shielding calculations are done simultaneously for multiple types of unit cells. At the present time, however, XSProc is limited to serial computations; but even in serial mode it typically requires less time than older versions of SCALE to process shielded cross sections, and significant speedups have been observed for heavily I/O bound problems. Integrating the self-shielding capabilities into a single module has a number of additional benefits as well, including maintainability, extensibility, and the ability to easily replace an entire computational module with a future implementation containing new features. Additionally, the size of the problem-dependent MG library generated by XSProc may be greatly reduced compared to previous versions of SCALE because macroscopic cross sections are stored rather than a general-purpose library of microscopic data.

## 7.1.2. Techniques

XSProc integrates and enhances the capabilities previously implemented independently in BONAMI, CENTRM, PMC, WORKER, ICE, and XSDRNPM, as well as other capabilities formerly provided by MIPLIB and SCALELIB. It provides capabilities for problem-dependent temperature interpolation of both CE and MG nuclear data, calculation of Dancoff factors, and resonance self-shielding of MG cross sections using several available options. XSProc produces shielded microscopic data for each nuclide or macroscopic data for each material. Additionally, a flux-weighting spectrum can be applied to collapse cross sections to a coarser group structure and/or to integrate over volumes for homogenized cross sections. The flux-weighting spectrum can be input by the user or calculated using one-dimensional (1-D) coupled neutron/gamma transport model. These operations are performed by the sequences CSAS-MG, CSAS1, CSASI, and T-XSEC described in Sect. 7.1.3.2.

### 7.1.2.1. Overview of XSProc procedures

XSProc reads the COMPOSITION and CELL DATA blocks of the SCALE input,
which are described in the following sections. After reading the user
input data, XSProc loads the specified MG library to be self-shielded
and, depending on the selected self-shielding method, additional CE data
files for nuclides appearing in the problem specification. Finally
XSProc performs MG self-shielding calculations for all compositions by
calling APIs to computational modules such as BONAMI (**BON**darenko
**AM**PX **I**nterpolator), CRAWDAD (**C**ode to **R**ead
**A**nd **W**rite **DA**ta for **D**iscretized solution), CENTRM
(**C**ontinuous **EN**ergy **TR**ansport **M**odule), PMC
(**P**roduce **M**ultigroup **C**ross sections), CHOPS
(**C**ompute **HO**mogenized **P**ointwise **S**tuff), CAJUN
(**C**E **AJ**AX **UN**iter), WAX (**W**orking
**A**JA**X**), XSDRNPM (**X**-**S**ection **D**evelopment
for **R**eactor **N**ucleonics with **P**etrie
**M**odifications), and/or MIXMACRO to provide a problem-dependent
cross section library. Many computational modules have been modernized
compared to earlier executable codes distributed in previous versions of
SCALE.

Like earlier versions of SCALE, XSProc provides several options for
self-shielding an input MG library [XSProc-Wil11]. The first, based on the
Bondarenko method [XSProc-IB64], uses the computational module BONAMI. BONAMI is
always used to compute self-shielded cross sections for all energy
groups. If *parm=bonami* is specified, the shielded cross sections
provided by BONAMI are the final values output from XSProc. However the
Bondarenko method has several limitations, especially in the resolved
resonance range. Therefore XSProc provides another self-shielding
method, with several computation options, which often produces more
accurate MG data in the resolved resonance and thermal energy ranges. If
*parm=centrm* or *parm=2region* is specified on the sequence line,
XSProc calls APIs for the modules CRAWDAD, CENTRM, and PMC to compute CE
flux spectra for processing problem-specific, self-shielded cross
sections “on the fly [XSProc-WA95]. CENTRM performs MG transport calculations in
the fast and lower energy ranges, coupled to pointwise (PW) transport
calculations that use CE cross sections in the resonance range. PMC uses
the PW flux spectra from CENTRM to compute MG values, which replace the
previous values obtained from BONAMI over the specified range of the CE
calculation. The original BONAMI shielded cross sections are retained
for all other groups.

The CENTRM/PMC approach is the default for criticality and lattice physics calculations, while the BONAMI-only method is default for radiation shielding calculations. The end results of an XSProc calculation are self-shielded macroscopic and/or microscopic MG cross sections stored in memory for subsequent transport calculations; or alternatively a shielded MG AMPX library can be written to an external file and saved for future use.

### 7.1.2.2. Standard composition material processing

A primary function of the XSProc module is to expand user input in the COMPOSITION block into nuclear number densities (nuclei/b-cm) for every nuclide in each defined mixture. Mixtures can be specified through the direct use of materials presented in the Standard Composition Library, which includes individual nuclides, elements with natural abundances, numerous compounds, alloys and mixtures found in engineering practice, as well several variations of fissile solutions. Additionally, users may define their own materials as atom percent or weight percent combinations. Nuclear masses and theoretical densities are provided in the Standard Composition Library, and methods are available to determine equilibrium states for fissile solutions. Input options for composition data are described in Sect. 7.1.3.3 with several examples provided in Appendix A.

### 7.1.2.3. Unit cells for MG resonance self-shielding

XSProc utilizes a unit cell description to provide information for
resonance self-shielding calculations of the input mixtures. As many
unit cells as needed to describe the problem may be specified; however,
each mixture (other than 0 for a void mixture) can appear only in one
unit cell in the CELLDATA block. If a nuclide appears in more than one
mixture, multiple sets of self-shielded cross sections are calculated
for the nuclide-one for each mixture in each unit cell. Four types of
cells are available for self-shielding calculations: **INFHOMMEDIUM**,
**LATTICECELL**, **MULTIREGION**, and **DOUBLEHET**. The default
calculation type is CENTRM/PMC for CSAS, TRITON,
and TSUNAMI sequences and BONAMI for MAVRIC.
All materials not specified in a unit cell are treated as infinite
homogeneous media and shielded with BONAMI only, unless the mixture
contains a fissionable nuclide, in which case an infinite medium
CENTRM/PMC model is used. Note that previous versions of SCALE used
infinite medium CENTRM/PMC calculations for all unassigned mixtures. The
default type of self-shielding calculation can be overridden, as
described in Sect. 7.1.3.2. The following is a brief description of
the types of unit cells that can be input in CELLDATA and the
computation procedures used.

#### 7.1.2.3.1. INFHOMMEDIUM (infinite homogeneous medium) Treatment

The **INFHOMMEDIUM** treatment is best suited for large masses of
materials where the size of each material is large compared with the
average mean-free path of the material or where the fraction of the
material that is a mean-free path from the surface of the material is
very small. When **INFHOMMEDIUM** cell is specified, the material in the
unit cell is treated as an infinite homogeneous lump. Systems composed
of small fuel lumps or resonance nuclides sandwiched between moderating
regions should not be treated as infinite homogeneous media. In these
cases a MULTIREGION or LATTICECELL geometry should be used.

#### 7.1.2.3.2. LATTICECELL Treatment

The **LATTICECELL** model is appropriate for arrays of resonance
absorber mixtures-with or without clad-arranged in a square or a
triangular pitch configuration within a moderator. Annular fuel (e.g.,
with an internal moderator in the center) can also be addressed. Input
data for the **LATTICECELL** treatment are described in Sect. 7.1.3.5.
Self-shielded cross sections are generated for each material zone in a
unit cell of the lattice. If a nuclide appears in more than one zone,
self-shielded cross sections are produced for each zone where the
nuclide is present. Limitations of the **LATTICECELL** treatment are
listed below.

The cell description is limited to unit cells for arrays of spherical, plate (slab), or cylindrical fuel bodies. In the case of cylindrical pins in a square-pitch lattice, the default (

*parm=centrm*) self-shielding calculation uses the CENTRM method of characteristics (MoC) option to represent the 2D rectangular unit cell with reflected boundary conditions. By default, self-shielding for all other arrays uses a CENTRM 1D S_{N}calculation for the unit cell (spherical and cylindrical geometries use Wigner-Seitz cells). If*parm=bonami*is specified, heterogeneous self-shielding effects are treated by equivalence theory [XSProc-Wil11] The computation option*parm=2region*, described in Sect. 7.1.3.1, can also be used for self-shielding lattice cells.Only predefined choices of cell configurations are available. The available options are described in detail in Sect. 7.1.3.5.

The basic treatment for

**LATTICECELL**assumes an infinite, uniform array of unit cells. This assumption is a good approximation for interior fuel regions within a large, uniform array. The approximation becomes less rigorous for fuel regions on the periphery of the array or adjacent to a nonuniformity (e.g., control rod, water hole, etc.) in the lattice. For some cases it may be desirable to address this issue by specifying a different lattice cell for this type of fuel pin and using a modified procedure to define an effective unit cell, as described below.

****** LATTICECELL treatment for nonuniform arrays*.

Nonuniform lattice effects may be treated in CENTRM calculation by
specifying the keyword **DAN2PITCH=***dancoff* in the optional CENTRM
DATA (see Sect. 7.1.3.9). In this approach, the SCALE standalone code
MCDancoff must be run prior to the self-shielding calculation in order
to compute Dancoff factors for the fuel regions of interest in the
nonuniform lattice configuration. MCDancoff performs a simplified
one-group Monte Carlo calculation to compute Dancoff factors for complex
geometries (see Sect. 7.8). The Dancoff value for the fuel region of
interest is assigned to the DAN2PITCH keyword in the input for the
corresponding cell. Using an iterative procedure, CENTRM computes the
pitch of a uniform lattice that has the same Dancoff value as the
nonuniform lattice.

#### 7.1.2.3.3. MULTIREGION Treatment

The **MULTIREGION** treatment is appropriate for 1-D geometric regions
where the geometry effects may be important, but the limited number of
zones and boundary conditions in the **LATTICECELL** treatment are not
applicable. The **MULTIREGION** unit cell allows more flexibility in the
placement of the mixtures but requires all regions of the cell to have
the same geometric shape (i.e., slab, cylinder, sphere, buckled slab, or
buckled cylinder). Lattice arrangements can be approximated by
specifying a non-vacuum boundary condition on the outer boundary. See
Sect. 7.1.3.6 for more details. Limitations of the **MULTIREGION**
cell treatment are listed below.

A

**MULTIREGION**cell is limited to a 1-D approximation of the system being represented. An exact 1D model can be defined for the following multizone geometries with vacuum boundary conditions: spheres, infinitely long cylinders, and slabs; and for an infinite array of slabs with reflected or periodic boundaries.The shape of the outer boundary of the

**MULTIREGION**cell is the same as the shape of the inner regions. Cells with curved outer surfaces cannot be stacked physically to create arrays; however, arrays can be approximated by a Wigner-Sietz cell with a white outer boundary condition, where the outer radius is defined to preserve the area of the true rectangular or hexagonal unit cell.Boundary conditions available in a

**MULTIREGION**problem include vacuum (eliminated at the boundary), reflected (reflected about the normal to the surface at the point of impact), periodic (a particle exiting the surface effectively enters an identical cell having the same orientation and continues traveling in the same direction), and white (isotropic return about the point of impact). Reflected and periodic boundary conditions on a slab can represent real physical situations but are not valid on a curved outer surface. A single, non-interacting cell has a vacuum outer boundary condition. If the cell outer boundary condition is not a vacuum boundary, the unit cell approximates some type of array.When using the CENTRM/PMC self-shielding method, the MULTIREGION cell model must include fissionable material. This can be accomplished by adding a trace amount of a fissionable material to one or more mixtures, or by modeling a region of homogenized fuel and water, or by adding a thin (e.g., 1e-6 cm-thick) layer containing at least a trace of a fissionable nuclide on the periphery of the problem.

#### 7.1.2.3.4. DOUBLEHET Treatment

**DOUBLEHET** cells use a specialized CENTRM/PMC calculational approach
to treat resonance self-shielding in “doubly heterogeneous” systems. The
fuel for these systems typically consists of small, heterogeneous,
spherical fuel particles (grains) embedded in a moderator matrix to form
the fuel compact. The fuel-grain/matrix compact constitutes the first
level of heterogeneity. Cylindrical(rod). spherical (pebble), or slab
fuel elements composed of the compact material are arranged in a
moderating medium to form a regular or irregular lattice, producing the
second level of heterogeneity. The fuel elements are also referred to as
“macro cells.” Advanced reactor fuel designs that use TRISO
(tri-material, isotopic) or fully ceramic microencapsulated (FCM) fuel
require the **DOUBLEHET** treatment to account for both levels of
heterogeneities in the self-shielding calculations. Simply ignoring the
double-heterogeneity by volume-weighting the fuel grains and matrix
material into a homogenized compact mixture can result in a large
reactivity bias.

In the **DOUBLEHET** cell input, keywords and the geometry description
for grains are similar to those of the **MULTIREGION** treatment, while
keywords and the geometry for the fuel element (macro-cell) are similar
to those of the **LATTICECELL** treatment. The following rules apply to
the **DOUBLEHET** cell treatment and must be followed. Violation of any
rules may cause a fatal error.

As many grain types as needed may be specified for each unique fuel element. Note that grain type is different from the number of grains of a certain type. For example, a fuel element that contains both UO

_{2}and PuO_{2}grains has two grain types. The same fuel element may contain 10000 UO_{2}grains and 5000 PuO_{2}grains. In this case, the number of grains of type UO_{2}is 10000, and the number of grains of type PuO_{2}is 5000.As many fuel elements as needed may be specified, each requiring its own

**DOUBLEHET**cell. This may be the case for systems with many fuel elements at different fuel enrichments, burnable poisons, etc. Each fuel element may have one or more grain types.Since the grains are homogenized into a new mixture to be used in the fuel element (macro-cell) cell calculation, a unique fuel mixture number must be entered. XSProc creates a new material with the new mixture number designated by the keyword f

*uelmix=*, containing all the nuclides that are homogenized. The user must assign the new mixture number in the transport solver geometry (e.g., KENO) input unless a cell-weighted mixture is created.The type of lattice or array configuration for the fuel-element may be spheres on a triangular pitch (

**SPHTRIANGP**), spheres on a square pitch (**SPHSQUAREP**), annular spheres on a triangular pitch (**ASPHTRIANGP)**, annular spheres on a square pitch (**ASPHSQUAREP)**, cylindrical rods on a triangular pitch (**TRIANGPITCH**), cylindrical rods on a square pitch (**SQUAREPITCH**),annular cylinderical rods on a triangular pitch (**ATRIANGPITCH)**, annular cylindrical rods on a square pitch (**ASQUAREPITCH)**, a symmetric slab (**SYMMSLABCELL)**, or an asymmetric slab (**ASYMSLABCELL)**.If there is only one grain type for a fuel element, the user must enter either the pitch, the aggregate number of particles in the element, or the volume fraction for the grains. The code needs the pitch and will directly use it if entered. If pitch is not given, then the volume fraction (if given) is used to calculate the pitch. If neither the pitch nor the volume fraction is given, then the number of particles is used to calculate the pitch and the volume fraction. The user should only enter one of these items.

If the fuel matrix contains more than one grain type, all types are homogenized into a single mixture for the compact. As for the one grain type case, the pitch is needed for the spherical cell calculations. However, the pitch by itself is not sufficient to perform the homogenization. Since each grain’s volume is known (grain dimensions must always be entered), entering the number of particles for each grain type essentially provides the total volume of each grain type and therefore enables the calculation of the volume fraction and the pitch. Likewise, entering the volume fraction for each grain type essentially provides the total volume of each grain type and therefore enables the calculation of the number of particles and the pitch. Therefore, one of these two quantities must be entered for multiple grain types. In these cases, since pitch is not given, the available matrix material is distributed around the grains of each grain type proportional to the grain volume and is used to calculate the corresponding pitch. Over-specification is allowed as long as the values are not inconsistent to greater than 0.01%.

For cylindrical rods and for slabs, fuel height must also be specified. For slabs the slab width must also be specified.

The CENTRM calculation option must be S

_{n}.

### 7.1.2.4. Cell weighting of MG cross sections

Cell-weighted self-shielded cross sections are created when
**CELLMIX**= is specified in a **LATTICECELL** or **MULTIREGION** cell
input. In this case, after finishing the self-shielding calculations for
all mixtures in the cell, XSProc calls the computational module XSDRNPM,
which solves the 1-D MG transport equation to obtain k_{∞} and
space-dependent MG fluxes for the cell. The resultant fluxes are used to
compute MG flux disadvantage factors for processing cell-weighted
cross sections of all nuclides in the cell. When the cell-weighted
cross sections are used with *homogenized* number densities of the cell
nuclides, the reaction rates of the homogenized mixture preserve the
spatially averaged reactions rates of the heterogeneous configuration.
The user must input a new mixture ID to identify the homogenized mixture
associated with the cell-weighted cross sections. **This homogenized
mixture should not be used in the heterogeneous geometry data for other
transport codes such as KENO, NEWT, etc.** Instead, the cell-homogenized
mixture that is created should be used at the location of the original
cell. Also, cell weighted homogenized cross sections should not be used
in MG sensitivity data calculations performed using the TSUNAMI
sequences.

## 7.1.3. XSPROC Input Data Guide

XSProc input data are entered in free form, allowing alphanumeric data,
floating-point data, and integer data to be entered in an unstructured
manner. Up to 252 characters per line are allowed. Data can usually
start or end in any column. Each data entry must be followed by one or
more blanks to terminate the data entry. For numeric data, either a
comma or a blank can be used to terminate each data entry. Integers may
be entered for floating values. For example, 10 will be interpreted as
10.0 if a floating point value is required. Imbedded blanks are not
allowed within a data entry unless an E precedes a single blank as in an
unsigned exponent in a floating-point number. For example, 1.0E 4 would
be correctly interpreted as 1.0 × 10^{4}. A number with a negative
exponent must include an “E”. For example 1.0-4 cannot be used for
1.0E-4.

The word “END” is a special data item. An END may have a name or label
associated with it. The name or label associated with an END is
separated from the END by a single blank and is a maximum of
12 characters long. *At least two blanks or a new line MUST follow every
labeled and unlabeled END. WARNING: It is the user’s responsibility to
ensure compliance with this restriction. Failure to observe this
restriction can result in the use of incorrect or incomplete data
without the benefit of warning or error messages.*

Multiple entries of the same data value can be achieved by specifying the number of times the data value is to be entered, followed by either R, *, or $, followed by the data value to be repeated. Imbedded blanks are not allowed between the number of repeats and the repeat flag. For example, 5R12, 5*12, 5$12, or 5R 12, etc., will enter five successive 12’s in the input data. Multiple zeros can be specified as nZ where n is the number of zeroes to be entered.

### 7.1.3.1. XSProc data checking and resonance processing options

To check the XSProc input data, run CSAS-MG and specify PARM=CHECK or PARM=CHK after the sequence specification as shown below.

```
=CSAS-MG PARM=CHK
```

In this case the actual XSProc cross section processing calculations are not performed. The input data are checked, the problem description is printed, appropriate error and warning messages are printed, and a table of additional data is printed.

Resonance processing will automatically be performed by the default
method for the sequence selected. The default methods are CENTRM/PMC for
CSAS, TRITON, and TSUNAMI sequences and BONAMI for the MAVRIC sequences.
Alternatively, a resonance processing procedure may be chosen by
entering PARM=*option*, where *option* CENTRM selects the recommended
CENTRM/PMC transport method for each cell type, *option* 2REGION selects
the CENTRM/PMC two-region calculation, and *option* BONAMI applies full
range Bondarenko factors to all energy groups without utilizing
CENTRM/PMC. For example, to run CSAS1X sequence using only BONAMI for
self-shielding, rather than the default CENTRM/PMC method, enter the
computational sequence specification shown below.

```
=CSAS1X PARM=BONAMI
```

Multiple PARM options are specified by enclosing parameters in parenthesis, such as

```
=CSAS1X PARM=(CHK, BONAMI)
```

XSProc resonance self-shielding options are summarized below.

PARM=BONAMI.

This is the fastest MG processing method. It performs resonance self-shielding for all energy groups using the Bondarenko method. BONAMI computes the appropriate background cross section of a given unit cell and then interpolates the corresponding shielding factor from Bondarenko factors on the MG library. Dancoff factors needed to evaluate the background cross section for lattices are computed internally, but these can be overridden by input values in the MORE DATA block. More details on this method are given in the BONAMI section of the manual.

PARM=CENTRM.

This executes the CENTRM/PMC modules to process shielded MG cross sections using CE flux spectra calculated with the recommended type of CE transport solver for the designated type of cell. The CENTRM-recommended CE transport solvers are (a) infinite homogeneous medium calculation for INFHOMMEDIUM cells; (b) 2D MoC transport calculation for a LATTICECELL consisting of cylindrical fuel pins in a square lattice; and (c) 1-D discrete S

_{n}transport for all other LATTICECELLs and for all MULTIREGION cells. The recommended type of transport solver can be overridden for individual cells, as well as for selected energy ranges, by using the CENTRM DATA block described in Sect. 7.1.3.9.

PARM=2REGION.

The CENTRM two-region (2R) option computes the PW flux using a simplified collision probability method for an absorber (e.g., fuel) region surrounded by an external moderator region which has an asymptotic energy spectrum. To account for the heterogeneous effects of a lattice, a correction known as the Dancoff factor is applied to the escape probabilities in the 2R calculation (see the CENTRM chapter of the SCALE manual). These Dancoff factors are calculated internally by XSProc for a uniform array of mixtures in slab, spherical, or cylindrical geometries. These mixture-dependent Dancoff factors can be modified by user input using the DAN parameters contained in the MORE DATA block, as defined in Sect. 7.1.3.8.

*Note on CENTRM/PMC self-shielding options:*

The energy range of the CENTRM flux calculation is subdivided into three
sections: fast, PW, and low energy. PMC only computes self-shielded
cross sections for groups within the PW range defined by parameters
*demax* and *demin*, which, respectively, define the upper and lower
energies of the CENTRM PW flux calculation. Problem-dependent cross
sections for groups in the fast and low energy ranges are obtained with
the more approximate BONAMI method. Default values for parameters
*demax* and *demin* are defined appropriately for self-shielding of
important resonance materials in thermal reactor systems. The PW
self-shielding range can be extended or decreased for individual cells
by modifying these parameters using CENTRM DATA.

### 7.1.3.2. XSProc input data

The types of input data required for XSProc are given in Table 7.1.1,
and individual entries are explained in the text following the table.
The title, cross section library name (either CE or MG), and standard
composition specification data (**READ COMP** input block) are required
for all sequences that use XSProc. The name of the cross section library
is used to determine if the transport solver is executed using CE or MG
data (e.g., CE or MG KENO calculations). The unit cell descriptions
(**READ CELL** input block) are only used for MG self-shielding
calculations. If the specified sequence executes in CE mode, the cell
data input can be omitted, or it will be skipped if present. If the cell
data information is omitted for MG calculations, all mixtures are
self-shielded using the infinite medium approximation.

There are seven standard SCALE sequences that run just XSProc, and produce a MG cross section library or libraries.

**=XSPROC** produces three libraries with an optional fourth library.

**sysin.microLib**is a self-shielded library of the individual nuclides in the problem for use in a later transport calculation,**sysin.macroLib**is a self-shielded library of the mixture cross sections in the problem for use in a later transport calculation,**sysin.smallMicroLib**is a self-shielded library of specific reaction rate cross sections and the elastic and total inelastic scattering transfer matrices for later use in calculating reaction rates and sensitivity values, and**sysin.xsdrnWeightedLib**is an optional library produced if the input specifies having**XSDRN**do a weighting calculation. This can be a cell weighted and/or a group collapse calculation. The library can be either individual nuclides or mixtures, depending on input.

**=CSAS-MG** produces an **ft04f001** library that is equivalent to the
**sysin.microLib**. With appropriate input it can also produce an
**ft03f001** which is equivalent to **sysin.xsdrnWeightedLib** above.

**=CSASI** or **=CSASIX** produce an **ft04f001** library that is
equivalent to **sysin.microLib**, and an **ft02f001** library that is
equivalent to **sysin.macroLib**. CSASIX will run an **XSDRN** on the
first cell without any MOREDATA input. With appropriate input they both
can produce an **ft03f001** that is the equivalent of
**sysin.xsdrnWeightedLib**.

**=CSAS1** or **=CSAS1X** produce an **ft04f001** library that is the
equivalent of **sysin.microLib**. Both sequences will run an **XSDRN**
on the first cell. With appropriate input, they both can produce an
**ft03f001** that is the equivalent of **sysin.xsdrnWeightLib**.

**=T-XSEC** produces an **ft04f001** library that is equivalent to
**sysin.macroLib**. and an **ft44f001** library that is equivalent to
sysin.microLib.

The reactions (MT numbers) written to each library are listed in the
`SequenceNeutronMT.txt`

file located in the etc directory installed with
SCALE.

TITLE. An 80-character maximum title is required. The title is the first 80 characters of the XSPROC data.

CROSS SECTION LIBRARY NAME. This item specifies the cross section library that is to be used in the calculation. See Table

*Standard SCALE cross-section libraries*in the XSLIB chapter of the SCALE manual for a discussion of the available libraries.The keywords

**READ COMP**followed by the standard compositions specifications. These data are used to define mixtures used in the problem. See Sect. 7.1.3.3 and Table 7.1.2 for a description of the standard composition specification data. These data are required for every problem. After all mixtures have been entered, the keywords**END COMP**must be entered.The keywords

**READ CELLDATA**followed by the input describing each unit cell as defined below. After all unit cells are described, the keywords**END CELLDATA**terminate this input block.

TYPE OF CALCULATION. The options are

INFHOMMEDIUM,LATTICECELL,MULTIREGION,DOUBLEHET, or nothing. A description of these cell types and the associated computational methods are provided in Sect. 7.1.2.3. If all input mixtures are to be treated as infinite homogeneous media, theCELLDATAblock can be omitted. In this case the self-shielding calculations will not account for any geometrical effects, so users should be careful in applying this approach. Similarly, mixtures not explicitly assigned to a cell are treated as infinite homogeneous media in the manner discussed in Sect. 7.1.2.3.CELL GEOMETRY SPECIFICATION. See Sect. 7.1.3.4 and Table 7.1.7 for an explanation of the optional unit cell data associated with an

INFHOMMEDIUMproblem. See Sect. 7.1.3.5 for an explanation of the data associated withLATTICECELLproblems. Sect. 7.1.3.6 explains the data required for aMULTIREGIONproblem. Sect. 7.1.3.7 explains the required data for aDOUBLEHETproblem. TheDOUBLEHETinput may be thought of as a combination ofMULTIREGIONinput for the fuel grains andLATTICECELLinput for the fuel element.OPTIONAL MORE PARAMETER DATA. This option allows certain defaulted parameters to be re-specified by the user. This block begins with

MORE DATAand is used by XSDRN. These data apply only to the unit cell immediately preceding them. Data placed prior to all unit cell data apply to all materials not listed in any unit cell and are treated as infinite homogeneous media. Omit these data unless they are needed. This block ends withEND MORE. See Sect. 7.1.3.8.OPTIONAL CENTRM PARAMETER DATA. This optional data block begins with

CENTRM DATAand ends withEND CENTRM. These data allow the user to override default data for CENTRM and PMC. These data apply only to the unit cell immediately preceding them. Data placed prior to all unit cell data apply to all materials not listed in any unit cell and are treated as infinite homogeneous media.

### 7.1.3.3. Standard composition specification data

Mixtures utilized in the problem are defined using standard composition
specification data. The standard composition input begins with the
keywords **READ COMP**, followed by standard composition specifications
for all mixtures in the problem. When all mixtures have been described,
enter the words **END COMP** to signal the completion of this block of
data. XSProc computes macroscopic cross sections for all mixtures
defined in the **COMP** block.

The required input for the standard composition specification data varies, depending on the type of standard composition material. However, every standard composition specification must include the following:

a standard composition material name.

a mixture number (MX) that contains this material, and

a terminator for the standard composition specification data (enter the word END).

The types of standard compositions in SCALE are (a) basic mixtures, (b) fissile solutions, (c) chemical compounds, and (d) alloys. The four general options for inputting these types of data are shown in Table 7.1.2. For some cases, more than one option could possibly be used to specify the mixture. The user may select whichever options are most convenient to define a particular mixture, and these may be entered in any order.

Names of the standard composition materials (the alphanumeric
identifiers) appearing in the **COMP** block input must be selected from
the tables of elements, compounds, solutions, and alloys given in the
SCALE manual section describing the Standard Composition Library. An
error message will be printed if the user enters an invalid standard
composition material name or if any isotopes in the compound do not
exist in the specified library

Input data to define each of the standard composition types in
Table 7.1.2 are summarized in Table 7.1.3 through Table 7.1.6. Optional input is
indicated by curly brackets { }. *Since some of the input is not keyword
based, the order of entries is important in the standard composition
specification*. The temperature specification is used for Doppler
broadening and/or determination of the proper thermal scattering data.
Input material densities are not modified for temperature effects.
Additional description of the standard composition input for each type
of material is given following all the tables. As in the tables, input
parameters enclosed by curly brackets { } indicate that these are
optional.

STANDARD COMPOSITION INPUT FOR BASIC MIXTURES (see Table 7.1.3).

Two input syntaxes are available for standard composition specifications
of basic mixtures in the **COMP** block. The first uses information
(e.g., densities, atomic weights, physical constants, etc.) contained in
the Standard Composition Library, along with user specified input, to
automatically compute the number densities for mixture components. In
the second option, the user computes the nuclide number densities, and
inputs these directly for each component of the mixture. XSProc
recognizes syntax 2 if the third entry of the composition specification
is zero, as shown below. It is allowable to use syntax 1 for some
standard composition specifications and syntax 2 for others. The two
syntaxes to define basic mixtures with the standard composition
specifications are shown below.

**syntax 1: Standard Composition Library data used to compute number
densities.**

scmxDEN=roth{VF=}vftempiza_{1}wtp_{1}…iza_{N}wtp_{N}END

**syntax 2: User input number densities**

scmx0adentempEND

The definitions for these input parameters are given below.

A1. **sc**

STANDARD COMPOSITION MATERIAL NAME. This corresponds to one of the material names given in the Standard Composition Library for isotopes, elements, thermal moderators and activity materials, chemical compounds, and alloys/mixtures. Some types of these materials require entering certain data such as the volume fraction or theoretical density and other engineering-type data. For standard compositions containing more than one isotope of an element (such as UO

_{2}), the user is free to specify the weight percent for each isotope, such that they total 100%. See the Basic standard composition specifications section for examples of basic standard compositions.

A2. *mx*

MIXTURE ID NUMBER. An arbitrary mixture number is required on every standard composition specification for both syntaxes. It defines the mixture that contains the material defined by the standard composition specification data. The mixture numbers are utilized in the CELLDATA block Cell Block for INFHOMMEDIUM, LATTICECELL, MULTIREGION, or DOUBLEHET problems and the geometry data.

A3. **DEN**=*roth*

MIXTURE DENSITY. The keyword

DENis assigned a value ofroth,whererothis the specified density of the mixture component in g/cm^{3}. It should always be entered for materials that contain enriched multi-isotopic nuclides. The effective density of the material component is equal to the product ofrothandvf.An example of this is demonstrated in Appendix A.

A4. {**VF**=}*vf*

VOLUME FRACTION. The keyword

VFis assigned a value ofvf. It is also allowable to omit the keywordVF=and just enter the valuevf. The default value of the volume fraction is 1.0. The volume fraction can be interpreted asa. the volume fraction of this standard composition component in the mixture,

b. the density of the standard composition component in this application divided by the theoretical or default density given in the Standard Composition Library, or

the product of (a) and (b).

Appendix A discusses the interaction between

rothandvf. For example, assume a homogenized mixture representing the water moderator and Zircaloy cladding around a fuel pin is to be described. If the volume of the clad is 5.32 cc and the volume of the water moderator is 44.68 cc, the mixture can be described using H_{2}O with a volume fraction of 0.8936 [i.e., 44.68/(44.68+5.32)] and ZIRCALOY with a volume fraction of 0.1064 [i.e., 5.32/(44.68+5.32)].

A5. *aden*

NUMBER DENSITY (not used for syntax 1, but required for 2). The number density is entered ONLY if 3

^{rd}entry on the standard composition specification is entered as zero. The number density is entered in units of atoms per barn-cm.

A6. *temp*

TEMPERATURE. The default value of the temperature is 300 K. The temperature can be omitted if entries A7 and A8 are also omitted.

A7. *iza*

ISOTOPE ZA NUMBER. Enter a value for each isotope in the standard composition component, entry 1. Do not enter a value if the volume fraction,

VF, is zero (A4 above).The ZA number of the isotope is entered if the user wishes to specify the isotopic distribution. This is done by entering

izaandwtpfor each isotope until all the desired isotopes have been described. In most cases the “ZA” ID number is (A+1000*Z), where A is the atomic mass or weight of the isotope, and Z is the atomic number. For example, the ZA number for^{235}U is 92235.Entries A7 and A8 can be skipped if the default values listed in Table 7.1.2 are acceptable.

A8. *wtp*

WEIGHT PERCENT OF THE ISOTOPE. If entry A7 is entered, a value must also be entered for A8. The weight percent of the isotope is the percent of this isotope in the element. The weight percent of all specified isotopes of the element must sum to 100 (± 0.01).

A9. **END**

The word

ENDis entered to terminate the input data for a standard composition component. ThisENDcan have a label associated with it that can be as long as 12 characters. The label is optional, and if entered must be preceded from theENDby a single blank. At least two blanks or a new line must separate this item from the next data entry.

STANDARD COMPOSITION INPUT FOR FISSILE SOLUTIONS (see Table 7.1.4).

Syntax:

```
SOLUTION {MIX=}mx RHO[fuelsalt]=fd (iza_i wtp_i) MOLAR[acid]=aml
MASSFRAC[name]=mfrac MOLEFRAC[name] =molfrac
MOLALITY[name]=molal DENSITY=roth
TEMPERATURE=temp VOL_FRAC=vf
END SOLUTION
```

where

mxis the mixture number,

fuelsaltis the Standard Composition Library component name of one of the fissile compounds

fdis the fuel density in grams of uranium or plutonium per liter of solution

acidis one of the Standard Composition Library acid compounds (e.g., HNO3 or HFACID)

nameis one of the Standard Composition Library solution components

amlis the acid molarity of theacidcomponent (moles ofacid/liter of solution)

mfracis the mass fraction ofnamein the solution (grams of metal inname/gram solution)

molfracis the mole fraction ofnamein the solution (moles ofname/mole solution)

molalis the mass fraction ofnamein the solution (moles ofname/kg water)

rothis the density of the solution,

vfis the density multiplier (ratio of actual to theoretical density of the solution),

tempis the temperature in Kelvin,

izais the isotope ID number from tableAvailable fissile solution components, and

wtpis the weight percent of the isotope in the material.

Below are the input data for fissile solutions.

**SOLUTION**

Keyword starting a solution specification. Solutions require the specification of the mixture and at least one component. Current possible components are given in the Standard Composition Library table,

Available fissile solution components. Only the mixture number and one component are required. Appendix A contains examples of the input data for solutions.

*mx*

MIXTURE ID NUMBER. A mixture number is required on every standard composition specification. It defines the mixture that contains the material defined by the standard composition specification data. The mixture numbers are utilized in the Unit Cell Specification for INFHOMMEDIUM, LATTICECELL, or MULTIREGION.

**RHO**[

*fuelsalt*]=

*fd*

**MOLAR**[

*acid*]=

*aml*

**MASSFRAC**[

*name*]=

*mfrac*

**MOLEFRAC**[

*name*]=

*molfrac*

**MOLALITY**[

*name*]=

*molal*

KEYWORD PARAMETERS TO DEFINE CONCENTRATIONS OF SOLUTION COMPONENTS. Each keyword specifies the unit, the component name from the Standard Composition Library and the component value, as shown Table 7.1.4. Up to three components can be specified for a solution if one is an acid. After the value, the isotopic enrichments of the nuclides can be given as pairs of isotope IDs and weight percent.

NOTE: the square brackets [ ] containing the component name are required.

**DENSITY=***roth*

Keyword specifying the overall solution density as grams per cubic centimeter or as a “?”, meaning it is to be solved for. Solving for the density is the default behavior, but the density can be given, and a component value can be solved for instead.

**TEMPERATURE=***temp*

Keyword defining temperature of the solution. The default value is 300 K.

**VOLFRAC=***vf*

Keyword defining volume fraction - the default volume fraction is 1.0. This value must be greater than 0.0. The volume fraction can be interpreted as: a. the volume fraction of this solution specification in the mixture, b. the density of the solution in this application divided by the calculated density of the solution, or c. the product of (a) and (b).

**END SOLUTION**

STANDARD COMPOSITION INPUT FOR CHEMICAL COMPOUNDS (see Table 7.1.5)

**Syntax:**

**ATOMnn** *mx* *roth* *nel* *ncza*_{1} *atpm*_{1} … *ncza*_{nel} *atpm*_{nel}
{*vf* {*temp* {*iza*_{1} *wtp*_{1} …} } } **END**

Below are the data for user-defined chemical compounds.

C1. **ATOMnn**

COMPOUND NAME. User-specified compounds (also defined as “arbitrary” in older versions of SCALE) require the user to provide all the information normally found in the Standard Composition Library. This option allows specifying a compound not available in the Standard Composition Library by utilizing nuclides and elements available in the library. An user-specified compound name must start with the four characters “

ATOM.” A maximum of twelve characters is allowed for the compound name, and imbedded blanks are not allowed.

C2. *mx*

MIXTURE ID NUMBER. A mixture number is required on every standard composition specification. It defines the mixture that contains the material defined by the compound specification data. The mixture numbers are utilized in the Unit Cell Specification for

INFHOMMEDIUM,LATTICECELL, orMULTIREGIONproblems and the KENO V.a or KENO-VI geometry data.

C3. *roth*

MIXTURE DENSITY. The density of the arbitrary material is entered in units of g/cm

^{3}.rothandvfinteract to produce the density of the mixture used in the problem. Note that this is a required entry and does not use “DEN=” keyword.

C4. *nel*

NUMBER OF ELEMENTS IN THE MATERIAL. Enter the number of components from the Standard Composition Library that are to be used to define this material.

C5. *ncza*

ID NUMBER. This is the “ZA” ID number for the element or isotope. Usually,

ncza=A+1000*Z, where A is the atomic mass or weight of the nuclide, and Z is the atomic number.

C6. *atpm*

ATOMIC or ELEMENT ABUNDANCE. Enter the number of atoms of this element per molecule of compound. Repeat the sequence

nczaandatpm(C5 and C6) for every element in the compound before going to entry C7.

C7. *vf*

VOLUME FRACTION. The default value of the volume fraction is 1.0. This value must be greater than 0.0. The volume fraction can be interpreted as

the volume fraction of this compound in the mixture,

the density of the compound in this application divided by the input density of the compound, or

the product of (a) and (b).

C8. *temp*

TEMPERATURE. The default value of the temperature is 300 K. The temperature can be omitted if entries C9 and C10 are also omitted.

C9. *iza*

ISOTOPE ZA NUMBER. Enter a value for each isotope in the element in the compound. The ZA number of the isotope is entered if the user wishes to specify the isotopic distribution. This is done by entering

izaandwtpfor each isotope until all the desired isotopes have been described. In most cases the “ZA” ID number is (A+1000*Z), where A is the atomic mass or weight of the isotope, and Z is the atomic number.Entries C9 and C10 can be skipped if the default values listed in Table 7.1.2 of Sect. 7.1 are acceptable.

C10. *wtp* WEIGHT PERCENT OF THE ISOTOPE. If entry C9 is entered, a
value must also be entered for C10. The weight percent of the isotope is
the percent of this isotope in the element. The weight percents of all
specified isotopes of the element must sum to 100 (± 0.01).

Repeat the sequence

izawtpuntil the sum of thewtps sum to 100. The sequenceizawtpis repeated until all of the desired isotopes have been specified.

C11. **END**

The word

ENDis entered to terminate the input data for compound. ThisENDcan have a label associated with it that can be as long as 12 characters. The label is optional, and if entered must be preceded from theENDby a single blank. At least two blanks or a new line must separate item C11 from the next data entry.

STANDARD COMPOSITION INPUT FOR MIXTURES AND ALLOYS (see Table 7.1.6)

**Syntax:**

**WTPTnn** *mx* *roth* *nel* *ncza*_{1} *wpct*_{1} … *ncza*_{nel} *wpct*_{nel}
{*vf* {*temp* {*iza*_{1} *wtp*_{1} …} }} **END**

Below are the input data for arbitrary (i.e., user-defined) physical mixture or alloy.

D1. **WTPTnn**

ARBITRARY MIXTURE/ALLOY NAME. The arbitrary user-specified mixture/alloy option allows specifying a mixture or an alloy not available in the Standard Composition Library by utilizing the nuclides and elements available in the library. An arbitrary mixture/alloy name must start with the four characters “

WTPT.” A maximum of 12 characters is allowed for the arbitrary mixture/alloy name. Imbedded blanks are not allowed in an arbitrary mixture/alloy name. Appendix A contains input data for arbitrary mixture/alloys.

D2. *mx*

MIXTURE ID NUMBER. A mixture number is required on every standard composition specification. It defines the mixture that contains the material defined by the arbitrary compound specification data. The mixture numbers are utilized in the Unit Cell Specification for

INFHOMMEDIUM,LATTICECELL,MULTIREGION, orDOUBLEHETproblems and the KENO V.a or KENO-VI geometry data.

D3. *roth*

MIXTURE DENSITY. The density of the arbitrary material is entered in units of g/cm

^{3}.rothandvfinteract to produce the density of the mixture used in the problem. Note that this is a required entry and does not use “DEN=” keyword.

D4. *nel*

NUMBER OF ELEMENTS IN THE MATERIAL. Enter the number of components from the Standard Composition Library that are to be used to define this arbitrary material.

D5. *ncza*

ID NUMBER. This is the “ZA” ID number for the element or isotope. Usually,

ncza=A+1000*Z, where A is the atomic mass or weight of the nuclide, and Z is the atomic number.

D6. *wpct*

ATOMIC or ELEMENT ABUNDANCE. Enter the weight percent of this element in the arbitrary alloy. The sum of all the weight percents for each specified element in the arbitrary alloy MUST be 100.0. Repeat the sequence

nczaandwpct(D5 and D6) for every element in the arbitrary mixture/alloy before going to entry D7.

D7. *vf*

VOLUME FRACTION. The default value of the volume fraction is 1.0. This value must be greater than 0.0. The volume fraction can be interpreted as:

the volume fraction of this mixture or alloy in the mixture,

b. the density of the mixture or alloy in this application divided by the input density (

roth) of the mixture or alloy, or

the product of (a) and (b).

D8. *temp*

TEMPERATURE. The default value of the temperature is 300 K. The temperature can be omitted if entries D9 and D10 are also omitted.

D9. *iza*

ISOTOPE ZA NUMBER. Enter a value for each isotope in the element in the arbitrary alloy. The ZA number of the isotope is entered if the user wishes to specify the isotopic distribution. This is done by entering

izaandwtpfor each isotope until all the desired isotopes have been described. In most cases the “ZA” ID number is (A+1000*Z), where A is the atomic mass or weight of the isotope, and Z is the atomic number.Entries D9 and D10 can be skipped if the default values listed in Table 7.1.2 are acceptable.

D10. *wtp*

WEIGHT PERCENT OF THE ISOTOPE. If entry D9 is entered, a value must also be entered for D10. The weight percent of the isotope is the percent of this isotope in the element. Weight percents of all specified isotopes of the element must sum to 100 (±0.01).

D11. **END**

The word

ENDis entered to terminate the input data for an arbitrary compound. ThisENDcan have a label associated with it that can be as long as 12 characters. The label is optional and if entered must be preceded from theENDby a single blank. At least two blanks or a new line must separate this item from the next data entry.

### 7.1.3.4. Unit cell specification for infinite homogeneous problems

This section describes the unit cell data that can be entered for an
**INFHOMMEDIUM** problem. Additional information is available in
Appendix B.

Syntax:

**INFHOMMEDIUM** *mx* {**CELLMIX**{=}*mix*} **END**

The data required to specify the unit cell for an **INFHOMMEDIUM** unit
cell are given in Table 7.1.7. The individual entries are explained in
the following text.

**celltype**

INFHOMMEDIUM. The keywordINFHOMMEDIUMis entered to indicate this unit cell contains one mixture with no geometry corrections. This data must be entered. The keyword may be truncated to any number of characters as long as the characters present are identical from the beginning of the keyword (i.e., INF is acceptable). All mixtures not in a defined unit cell are by default processed as infhommedium.

*mx*

MIXTURE NUMBER. The mixture number defines the mixture to be used in the cell. This data must be entered. Be sure the mixture number entered is defined in the standard composition data.

**CELLMIX**=*mix*

CELL-WEIGHTED MIXTURE NUMBER. (the = sign can be replaced by a space if desired). Enter ONLY if a cell-weighted mixture is to be generated. Enter a unique mixture number to be used by XSDRN to create the cell-weighted mixture (Sect. 7.1.2.4). For

INFHOMMEDIUMcells, cross sections for the cell mixture are equal to the shielded values of the original mixture.

**END**

The word

ENDis entered to terminate theINFHOMMEDIUMdata. An optional label can be associated with thisEND. The label can be as many as 12 characters long and is separated from theENDby a single blank. At least two blanks must follow this entry.

### 7.1.3.5. Unit cell specification for LATTICECELL problems

This section describes the unit cell input data for a **LATTICECELL**
problem. The **LATTICECELL** description is especially suited to
self-shield arrays of repeated cells such as a fuel assembly lattice.
The unit cell specification plays a major role in providing accurate
problem-dependent cross sections using the computational procedures
described in Sect. 7.1.2.3. Unit cells are limited to (a) infinitely
long cylindrical rods in a square or triangular lattice, (b) spheres in
a cubic or triangular lattice, (c) a symmetric array of slabs, or (d) an
asymmetric array of slabs. Both “regular” and “annular” fuel geometries
can be used in **LATTICECELL** problems. “Regular” cells allow a
concentric spherical, cylindrical, or symmetric slab configuration,
where the central region is fuel, surrounded by an optional gap, an
optional clad, and an external moderator. “Annular” cells also allow
concentric spherical, cylindrical, or asymmetric slab configurations,
but the central region corresponds to an inner moderator region which is
surrounded by a fuel region having an optional gap and optional clad on
each side of the fuel. An inner gap may be specified inside the fuel
region, and an outer gap may be specified outside the fuel region.
Similarly an inner clad may be specified inside the fuel region, and an
outer clad may be specified outside the fuel region. For both regular
and annular fuel cells, the outer boundary of the unit cell is
determined from the square or triangular pitch of the array.

Regular cells are **SQUAREPITCH**, **TRIANGPITCH**, **SPHSQUAREP**,
**SPHTRIANGP**, and **SYMMSLABCELL**.

Annular cells are **ASQUAREPITCH** (or **ASQP**), **ATRIANGPITCH** (or
**ATRP**), **ASPHSQUAREP** (or **ASSP**), **ASPHTRIANGP** (or **ASTP**),
and **ASYMSLABCELL**

Syntax:

celltypectp PITCH(orHPITCH)pitchmmFUELD (or FUELR)fuel mf

GAPD (or GAPR)gap mgCLADD (or CLADR)clad mc

IMODD (or IMODR)imod mimIGAPD(or IGAPR)igap mig

ICLADD(orICLADR)iclad mic{CELLMIX=mix}END

The unit cell geometry data required to specify a LATTICECELL problem are given in Table 7.1.8. The individual entries are explained in the text below.

**celltype**

LATTICECELL.The keywordLATTICECELLis entered to indicate this unit cell contains mixtures that are positioned in a regular array. This data must be entered. The keyword may be truncated to any number of characters as long as the characters present are identical from the beginning of the keyword (e.g.,LATis acceptable). This unit cell is normally used for regular arrays of materials such as fuel pins in an assembly.

**ctp**

TYPE OF LATTICE. This defines the type of lattice or array configuration. Any one of the following alphanumeric descriptions may be used. Note that the alphanumeric description must be separated from subsequent data entries by one or more blanks. Fig. 7.1.1 Mixture and position data are entered using keywords. Mixture number 0 may be entered for void and may be used multiple times in each and all unit cells. For regular cells, the minimum requirement is that a fuel region and a moderator region are specified and no other inner components are specified. For annular cells, the minimum requirement is the fuel and outer moderator and inner moderator regions are specified. Regular and annular cell configurations are specified as shown below.

Regular Cells

SQUAREPITCHis used for an array of cylinders arranged in a square lattice, as shown in Fig. 7.1.1. The clad and/or gap can be omitted.

TRIANGPITCHis used for an array of cylinders arranged in a triangular-pitch lattice as shown in Fig. 7.1.2. The clad and/or gap can be omitted.

SPHSQUAREPis used for an array of spheres arranged in a square-pitch lattice. A cross section view through a cell is represented by Fig. 7.1.1. The clad and/or gap can be omitted.

SPHTRIANGPis used for an array of spheres arranged in a triangular-pitch (dodecahedral) lattice. A cross section view through a cell is represented by Fig. 7.1.2. The clad and/or gap can be omitted.

SYMMSLABCELLis used for an infinite array of symmetric slab cells, as shown in Fig. 7.1.3. The clad and/or gap can be omitted.

Annular Cells

ASQUAREPITCHorASQPis used for annular cylindrical rods in a square-pitch lattice as shown in Fig. 7.1.4. The inner and outer clad and gap are independently entered so they must be different materials and dimensions. Note that each mixture in the problem can be used only once and in only one zone of a cell.

ATRIANGPITCHorATRPis used for annular cylindrical rods in a triangular-pitch lattice as shown in Fig. 7.1.5. The inner and outer clad and gap are independently entered, so they must be different materials and dimensions.

ASPHSQUAREPorASSPis used for spherical shells in a square-pitch lattice as shown in Fig. 7.1.4. The inner and outer clad and gap are independently entered, so they must be different materials and dimensions.

ASPHTRIANGPorASTPis used for spherical shells in a triangular-pitch (dodecahedral) lattice as shown in Fig. 7.1.5. The inner and outer clad and gap are independently entered, so they must be different materials and dimensions.

ASYMSLABCELLis used for a periodic, but asymmetric, array of slabs as shown in Fig. 7.1.6. The inner and outer clad and gap are independently entered, so they may be different materials and dimensions.

**PITCH**or**HPITCH**

ARRAY PITCH. This is the center-to-center spacing or half-spacing between the fuel lumps (rods, pellets, or slabs),

pitch, in cm followed by the outer moderator material number, mm, as shown in Fig. 7.1.1 through Fig. 7.1.6.

**FUELD**or**FUELR**

OUTSIDE DIMENSION OF FUEL. This is the outside diameter or radius of the fuel, fuel, in cm followed by the fuel mixture number,

mf, as shown in Fig. 7.1.1 through Fig. 7.1.6.

**GAPD**or**GAPR**

OUTSIDE DIMENSION OF OUTER GAP. Enter only if outer gap is present. This is the outside diameter or radius of the outer gap,

gap, in cm followed by the gap mixture number, mg, as shown in Fig. 7.1.1 through Fig. 7.1.6.

**CLADD**or**CLADR**

OUTSIDE DIMENSION OF OUTER CLAD. Enter ONLY if a clad is present. This is the outside diameter or radius of the outer clad,

clad, in cm followed by the clad mixture number, mc, as shown in Fig. 7.1.1 through Fig. 7.1.6.

**IMODD**or**IMODR**

DIMENSION OF INNER MODERATOR. Enter ONLY if an annular cell is specified. This is the outside diameter or radius of the inner moderator,

imod, in cm followed by the inner moderator mixture number,mim, as shown in Fig. 7.1.4 through Fig. 7.1.6.

**IGAPD**or**IGAPR**

OUTSIDE DIMENSION OF INNER GAP. Enter ONLY if an annular cell is specified and inner gap is present. This is the outside diame*ter or radius of the inner gap,

igap, in cm followed by the inner gap mixture number,mig, as shown in Fig. 7.1.4 through Fig. 7.1.6.

**ICLADD**or**ICLADR**

OUTSIDE DIMENSION OF INNER CLAD. Enter ONLY if an annular cell is specified and inner clad is present. This is the outside diameter or radius of the inner clad,

iclad, in cm followed by the inner clad mixture number,mic, as shown in Fig. 7.1.4 through Fig. 7.1.6.

{

**CELLMIX=}mix**

CELL-WEIGHTED MIXTURE NUMBER. [the = sign can be replaced by a space if desired). Enter ONLY if a cell-weighted mixture is to be generated. Enter a unique mixture number to be used by XSDRN to create the cell-weighted mixture (Sect. 7.1.2.4).

**END**

The word

ENDis entered to terminate theLATTICECELLdata. An optional label can be associated with thisEND. The label can be as many as 12 characters long and is separated from theENDby a single blank. At least two blanks must follow this entry. Must not start in column 1.

### 7.1.3.6. Unit cell specification for MULTIREGION cells

A **MULTIREGION** cell can be used to define a 1-D geometric arrangement
that is more general than allowed by a **LATTICECELL**. It can also be
used for large geometric regions where the geometry effects for the
cross sections are small. For CENTRM/PMC self-shielding, lattice effects
can be approximated by applying reflected, periodic, or white external
boundary conditions to a MULTIREGION cell. HOWEVER, MULTIREGION CELLS
SHOULD NOT BE USED FOR BONAMI-ONLY SELF-SHIELDING OF AN ARRAY UNIT CELL.
In this case a LATTICECELL should always be used for BONAMI
self-shielding in order to incorporate the proper Dancoff effects.

The data required for a MULTIREGION cell are given in Table 7.1.9 and explained in the following text.

**celltype**

MULTIREGION. The keywordMULTIREGIONis used to represent arbitrary 1-D geometries, with no restrictions the on number or placement of mixtures in the cell. The keyword may be truncated to any number of characters as long as the characters presented are identical from the beginning of the keyword (i.e., M is acceptable).

**cs**

TYPE OF GEOMETRY. The type of geometry must always be specified for a

MULTIREGIONcell. The available geometry options are listed below.

SLAB. This is used to describe a slab geometry.

CYLINDRICAL. This is used to describe cylindrical geometry.

SPHERICAL. This is used to describe spherical geometry.

BUCKLEDSLAB. This is used for slab geometry with a buckling correction for the two transverse directions. Inactive in SCALE 6.2 and later.

BUCKLEDCYL. This is used for cylindrical geometry with a buckling correction in the axial direction. Inactive in SCALE 6.2 and later.

**RIGHT_BDY**

RIGHT BOUNDARY CONDITION. This is defaulted to

VACUUM. The available options and their qualifications are listed below.

VACUUM. This imposes a vacuum at the boundary of the system.

REFLECTED. This imposes mirror image reflection at the boundary. Do not use forCYLINDRICALorSPHERICAL.

PERIODIC. This imposes periodic reflection at the boundary. Do not use forCYLINDRICALorSPHERICAL.

WHITE. This imposes isotropic return at the boundary.

**LEFT_BDY**

LEFT BOUNDARY CONDITION. This is defaulted to

REFLECTED. The available options and their qualifications are listed below.

VACUUM. This imposes a vacuum at the boundary of the system.

REFLECTED. This imposes mirror image reflection at the boundary. ForCYLINDRICALorSPHERICAL, this is the only valid boundary condition because the left boundary corresponds to the centerline of the cylinder or the center of the sphere.

PERIODIC. This imposes periodic reflection at the boundary.

WHITE. This imposes isotropic return at the boundary.

**ORIGIN**

LOCATION OF LEFT BOUNDARY ON THE ORIGIN. The default value of

ORIGINis 0.0. This is the only value allowed forCYLINDRICALorSPHERICALgeometry. ForSLABs, enter the location of the left boundary on the X-axis perpendicular to the slab (in cm).

**DY**

BUCKLING HEIGHT. This is the buckling height in cm. It corresponds to one of the transverse dimensions of an actual 3-D slab assembly or the length of a finite cylinder. Inactive in SCALE 6.2 and later.

**DZ**

BUCKLING DEPTH. This is the buckling width in cm. It corresponds to the second transverse dimension of an actual 3-D slab assembly. Inactive in SCALE 6.2 and later.

**CELLMIX**

CELL-WEIGHTED MIXTURE NUMBER. Enter ONLY if a cell-weighted mixture is required. Enter a unique mixture number used to create a cell-weighted homogeneous mixture (Sect. 7.1.2.4).

**END**

The word

ENDis entered to terminate these data before entering the zone description data. It must not be entered in columns 1 through 3, and at least two blanks must separate it from the zone description. A label can be associated with thisEND. The label can be a maximum of 12 characters and is separated from theENDby a single blank. At least two blanks must follow this entry.The zone description data are entered at this point. Entries 10 and 11 are entered for each zone, and the sequence is repeated until all the desired zones have been described. To terminate the data, enter the words END ZONE. Zone dimensions must be in increasing order.

**mxz**

MIXTURE NUMBER IN THE ZONE. Enter the mixture number of the material that is present in the zone. Enter a zero for a void. Repeat the sequence of entries 10 and 11 for each zone. Mixtures other than zero must not be used more than once in a cell and may be used in no more than one cell.

**rz**

OUTSIDE RADIUS OF THE ZONE. Enter the outside dimension of the zone in cm.

In

SLABgeometry,rzis the location of the zone’s right boundary on the X-axis. Repeat the sequence of entries 10 and 11 for each zone.

**END ZONE**

Is used to terminate the

MULTIREGIONzone data. Enter the wordsENDZONEwhen all the zones have been described. Note thatZONEis a label associated with thisEND. This label can be as long as 12 characters, but the first four characters must beZONE. At least two blanks must follow this entry.

### 7.1.3.7. Unit cell specification for doubly heterogeneous (DOUBLEHET) cells

The data required for a **DOUBLEHET** cell are given in Table 7.1.10 and
explained in the following text.

Details about the computation procedures for **DOUBLEHET** cells can be
found in Sect. 7.1.2.3.

“Grain” refers to a spherical fuel particle surrounded by one or more
coating zones and does not include the matrix material the grains are
in. “Grain type” refers to a grain that has specified dimensions and
mixtures such as a 0.025-cm-radius UO_{2} fuel kernel with a
0.01-cm-thick carbon coating. Another grain type could be a
0.012-cm-radius PuO_{2} fuel kernel with a 0.01-cm-thick carbon
coating. The user must first define all grain types in a fuel element.
Next, all fuel element–related data must be entered.

Since all grains and the matrix material are homogenized into a single
uniform mixture for the fuel element, there are restrictions on how each
grain type must be defined so that the volume fraction of each grain
type within the homogenized fuel mixture can be determined. Related
entries are **PITCH**, **NUMPAR** (number of particles), and **VF**
(volume fraction). If there is only one grain type for a fuel element,
the code needs the pitch and will directly use the input value if
entered. If **PITCH** is not given, then the **VF** (if given) is used
to calculate the pitch. If neither **PITCH** nor **VF** is given, then
**NUMPAR** is used to calculate the pitch and the volume fraction. The
user should only enter one of these items.

If more than one grain type is present, additional information is needed
since all grain types are homogenized into a single mixture. Similar to
the one grain type case, the pitch is needed to perform the CENTRM
spherical cell calculations. However, the pitch by itself is not
sufficient to perform the homogenization. Therefore, the user needs to
input **VF** or **NUMPAR** for each grain type. Since each grain’s
volume is known (grain dimensions must always be entered), entering
**NUMPAR** or **VF** for each grain type essentially provides the total
volume of each grain type and therefore enables the calculation of the
other unknowns (**VF** or **NUMPAR**, and **PITCH**). In this case,
since pitch is not given, the available matrix material is distributed
around the grains of each grain type proportional to the grain volume to
calculate the corresponding pitch.

Syntax:

**DOUBLEHET** *fuelmix* **END**

**GF**(**D**|**R**)=*fuel mg*
(**COAT**(**D**|**R**)=*coat mc*)|(**COATT**=*coat mc*)
{**H**}**PITCH**=*mod* **MATRIX**=*mm* **NUMPAR**=*npar*
**VF**=*vf* **END GRAIN**

**mct** **ctp** **FUEL**(**D**|**R**)=*mfuel*
{**FUELH**=*hfuel*} {**FUELW**=wfuel}
{**GAP**(**D**|**R**)=*mgap mmg*}
{**CLAD**(**D**|**R**)=*mclad* *mmc*}
{**H**}**PITCH**=*mpitch* *mmm* {**CELLMIX**=*mcmx*} **END**

**celltype**

DOUBLEHET. The keyword DOUBLEHET is used to represent a doubly heterogeneous problem such as fuel units that are composed of grains of fuel.

*fuelmix*

HOMOGENIZED MIXTURE NUMBER. Enter a unique mixture number to be used for the homogenized grains and matrix material.

**END**

The word

ENDis entered to terminate these data before entering the grain and fuel element description data. It must not be entered in columns 1 through 3, and at least two blanks must separate it from the zone description. A label can be associated with thisEND. The label can be a maximum of 12 characters and is separated from theENDby a single blank. At least two blanks must follow this entry.

The grain description data are entered at this point. Entries 5 through
12 are entered for each grain, and the sequence is repeated until all
the grains have been described. To terminate the data, enter the words
**END GRAIN**. Data may be entered in any order.

**PITCH**or**HPITCH**

EQUIVALENT CELL DIMENSION. This is the equivalent spherical diameter (or radius), in cm, of the “average” unit cell for this grain, as shown in Fig. 7.1.7. Physically, the volume of the average unit cell is equal to the volume of the fuel element divided by the total number of all grain types.

**GFD**or**GFR**

OUTSIDE DIMENSION OF FUEL. This is the outside diameter or radius of the fuel zone in a grain,

fuel, in cm followed by the fuel mixture number,mg, as shown in Fig. 7.1.7.

**COATD**or**COATR**

OUTSIDE DIMENSION OF COATING. This is the outside diameter or radius of a coating zone,

coat, in cm followed by the coating mixture number,mc, as shown in Fig. 7.1.7. As many coating-mixture pairs as desired may be entered. If the coating dimensions are entered using COATD or COATR, then the COATT keyword should not be used.

**COATT**

THICKNESS OF COATING. This is the thickness of a coating zone,

coat, in cm followed by the coating mixture number,mc, as shown in :numref`fig7-1-7`. As many coating-mixture pairs as desired may be entered. If the coating dimensions are entered using COATT, then the COATD or COATR keyword should not be used.

**MATRIX**

MIXTURE NUMBER OF THE MATRIX MATERIAL. This is the mixture number,

mm, of the matrix material that encloses the grains.

**NUMPAR**

NUMBER OF PARTICLES. This is the number of grains,

npar, of this type in each fuel element.

**VF**

VOLUME FRACTION. This is the volume fraction,

vf, of grains of this type in each fuel element’s fuel zone. A fuel element’s fuel zone is entered using the entry number 16-FUELD(orFUELR).

**END GRAIN**

This is used to terminate the grain zone data for this grain type. At least two blanks must follow this entry.

REPEAT ENTRIES 4-11 FOR EACH GRAIN TYPE IN A FUEL ELEMENT.

**mct**

TYPE OF FUEL ELEMENT (macro cell type). One of the keywords

PEBBLEorRODor SLAB is entered to indicate the type of the fuel element, i.e., the second layer of heterogeneity. This data must be entered. The keyword may NOT be truncated.PEBBLEis used for spherical fuel elements;RODis used for cylindrical fuel elements; and SLAB for plate fuel elements.

**ctp**

TYPE OF LATTICE. This defines the type of lattice or array configuration. Any one of the following alphanumeric descriptions may be used. Note that the alphanumeric description must be separated from subsequent data entries by one or more blanks. Fig. 7.1.1 Mixture and position data are entered using keywords. Mixture number 0 may be entered for void and may be used multiple times in each and all unit cells. For regular cells, the minimum requirement is that a fuel region and a moderator region are specified and no inner components are specified. For annular cells, the minimum requirement is the fuel and outer moderator and inner moderator regions are specified. Regular and annular cell configurations are specified as shown below.

Regular Cells

SQUAREPITCHis used for an array of cylinders arranged in a square lattice, as shown in Fig. 7.1.1. The clad and/or gap can be omitted.

TRIANGPITCHis used for an array of cylinders arranged in a triangular-pitch lattice as shown in Fig. 7.1.2. The clad and/or gap can be omitted.

SPHSQUAREPis used for an array of spheres arranged in a square-pitch lattice. A cross section view through a cell is represented by Fig. 7.1.1. The clad and/or gap can be omitted.

SPHTRIANGPis used for an array of spheres arranged in a triangular-pitch (dodecahedral) lattice. A cross section view through a cell is represented by Fig. 7.1.2. The clad and/or gap can be omitted.

SYMMSLABCELLis used for an infinite array of symmetric slab cells, as shown in Fig. 7.1.3. The clad and/or gap can be omitted.

Annular Cells

ASQUAREPITCHorASQPis used for annular cylindrical rods in a square-pitch lattice as shown in Fig. 7.1.4. The inner and outer clad and gap are independently entered so they may be different materials and dimensions.

ATRIANGPITCHorATRPis used for annular cylindrical rods in a triangular-pitch lattice as shown in Fig. 7.1.5. The inner and outer clad and gap are independently entered, so they may be different materials and dimensions.

ASPHSQUAREPorASSPis used for spherical shells in a square-pitch lattice as shown in Fig. 7.1.4. The inner and outer clad and gap are independently entered, so they may be different materials and dimensions.

ASPHTRIANGPorASTPis used for spherical shells in a triangular-pitch (dodecahedral) lattice as shown in Fig. 7.1.5. The inner and outer clad and gap are independently entered, so they may be different materials and dimensions.

ASYMSLABCELLis used for a periodic, but asymmetric, array of slabs as shown in Fig. 7.1.6. The inner and outer clad and gap are independently entered, so they may be different materials and dimensions.

**PITCH**or**HPITCH**

ARRAY PITCH. This is the center-to-center spacing or half-spacing between the fuel lumps (pebbles or rods or slabs),

mpitch, in cm followed by the outer moderator material number,mmm, as shown in Fig. 7.1.1 and Fig. 7.1.2.

**FUELD**or**FUELR**

OUTSIDE DIMENSION OF FUEL. This is the outside dimension (diameter or radius for sphere/cylinder or x-thickness for slab) of the fuel region,

mfuel, in cm, as shown in Fig. 7.1.1 and Fig. 7.1.2.

**FUELH**

HEIGHT OF FUEL ROD OR SLAB. This is the height (z-dimension) of the fuel plate,

hfuel, in cm. (only used to compute volume of fuel plate).

**FUELW**

WIDTH OF FUEL ROD or slab. This is the width/depth (y-dimension) of the fuel plate,

wfuel, in cm. (only used to compute volume of fuel plate).

**GAPD**or**GAPR**

OUTSIDE DIMENSION OF GAP. Enter only if outer gap is present. This is the outside diameter or radius of the outer gap,

mgap, in cm followed by the gap mixture number,mmg, as shown in Fig. 7.1.1 and Fig. 7.1.2.

**CLADD**or**CLADR**

OUTSIDE DIMENSION OF CLAD. Enter ONLY if a clad is present. This is the outside diameter or radius of the outer clad,

mclad, in cm followed by the clad mixture number,mmc, as shown in Fig. 7.1.1 and Fig. 7.1.2.

**CELLMIX**

CELL-WEIGHTED MIXTURE NUMBER. Enter ONLY if cell-weighted mixture,

mcmx, is to be created.

**IMODD**or**IMODR**

DIMENSION OF INNER MODERATOR. Enter ONLY if an annular cell is specified. This is the outside diameter or radius of the inner moderator,

imod, in cm followed by the inner moderator mixture number,mim, as shown in Fig. 7.1.4 through Fig. 7.1.6.

**IGAPD**or**IGAPR**

OUTSIDE DIMENSION OF INNER GAP. Enter ONLY if an annular cell is specified and inner gap is present. This is the outside diameter or radius of the inner gap,

igap, in cm followed by the inner gap mixture number,mig, as shown in Fig. 7.1.4 through Fig. 7.1.6.

**ICLADD**or**ICLADR**

OUTSIDE DIMENSION OF INNER CLAD. Enter ONLY if an annular cell is specified and inner clad is present. This is the outside diameter or radius of the inner clad,

iclad, in cm followed by the inner clad mixture number,mic, as shown in Fig. 7.1.4 through Fig. 7.1.6.

**END**

The word

ENDis entered to terminate theDOUBLEHETdata. An optional label can be associated with thisEND. The label can be as many as 12 characters long and is separated from theENDby a single blank. At least two blanks must follow this entry.

### 7.1.3.8. Optional MORE DATA parameter data

**MORE DATA** is an optional sub-block of the **READ CELL** block.
**MORE DATA** parameters allow certain default options in BONAMI and
XSDRNPM to be modified for individual cell calculations. Each **MORE
DATA** sub-block applies only to the unit cell immediately preceding it.
However a **MORE DATA** sub-block placed prior to all unit cell
definitions applies to all mixtures not assigned to a unit cell, which
are treated as infinite homogeneous media. If the default parameters are
acceptable, this section of input data should be omitted in its
entirety. Non-default values for one or more of the parameters can be
specified by entering the words **MORE DATA** followed by the desired
keyword parameters and their associated values. One or more of the
parameters can be entered in any order. Default values are used for
parameters that are not entered. Each parameter is entered by spelling
its name, followed immediately by an equal sign and the value to be
entered. There should not be a blank between the parameter name and the
equal sign. Each parameter specification must be separated from the rest
by at least one blank. For example, if an XSDRNPM calculation is
performed for particular unit cell (e.g., *cellmix=* is specified),

**MORE DATA ISN**=16 **EPS**=0.00008 **END MORE**

would result in using an S16 angular quadrature set and tightening the convergence criteria to 0.00008 in the XSDRNPM calculation.

A description of each entry is given. (Also see sections on BONAMI and XSDRNPM input description.)

**MORE DATA**These words, followed by one or more blanks, are entered ONLY if optional parameter data are to be entered. Entries 2 through 42 can be entered in any order.**NSENSX**This is the XSDRNPM sensitivity output file for TSUNAMI sequences.**CROSSEDT**BONAMI CROSS SECTION EDIT. Cross section print option for BONAMI 0/1 –no/yes (default is 0).**FFACTEDT**BONDARENKO FACTOR EDIT. Bondarenko factor (f-factor) print option 0/1 –no/yes (default is 0).**ISSOPT**BONAMI BACKGROUND XSEC OPTIONS. BONAMI background cross section selection option if > 1000 potential; otherwise, total cross section is used (default is –1).**IROPT**BONAMI IR/NR CALCULATION OPTION. BONAMI uses intermediate resonance (IR) if iropt=1 and narrow resonance (NR) approximation for iropt=0 (default is 0).**BELLOPT**BELL FACTOR OPTION. Optional user-defined bell factor calculation option (default is -1).**BELLFACT**BELL FACTOR. Optional user-defined bell factor for BONAMI (default is 0.0).**ESCXSOPT**ESCAPE CROSS SECTION CALC OPTION. Escape cross section calculation for IR calculations. 0/1 =consistent/inconsis tent (default is 0).**BONAMIEPS**BONAMI CONVERGENCE CRITERIA. BONAMI Bondarenko iteration convergence criteria (default is 0.001).**LBARIN**INPUT MEAN CORD LENGTH. Mean cord length for each zone (default is 0.00).**ADJTHERM**ADJUST 1D THERMAL CROSS SECTIONS TO MATCH SUM OF 2D CROSS SECTIONS. Flag determining whether 1-D cross sections are scaled to match the 2-D cross sections or the 2-D cross sections are scaled to match the 1-D cross sections.**EXSIG**ESCAPE CROSS SECTION. External escape cross section for BONAMI (default is 0.00).**IEVT**XSDRNPM CALCULATION TYPE. The type of calculation to be performed- fixed source, eigenvalue, alpha, zone width search, outer radius search, buckling search, direct buckling search (default is 1).**ICLC**THEORY OPTION. Number of outer iterations to use an alternative theory (diffusion, infinite medium, or B_{N}) before using discrete ordinates. Negative values indicate alternative theory (default is 0).**IPVT**PARAMETRIC EIGENVALUE SEARCH. 0 – none; 1 – search for eigenvalue equal PV; 2 – alpha search (default is 0).**IPP**WEIGHTED CROSS SECTION PRINT. 2 -> No print; -1 -> 1-D edit; 0-N – edit through PN cross section arrays (default is 2).**IFLU**GENERALIZED ADJOINT CALCULATION. 0 is a standard calculation; 1 is a generalized adjoint calculation (default is 0).**IFSN**FISSION SOURCE SUPPRESSION. Non-zero suppresses the fission source in a fixed source calculation (default is 0).**IQM**VOLUMETRIC FIXED SOURCES. The number of volumetric sources in a fixed source problem (default is 0).**IPM**BOUNDARY FIXED SOURCES. The number of boundary sources in a fixed source problem (default is 0).**XNF**SOURCE NORMALIZATION FACTOR. The value used to normalize the problem source (default is 1.0).**VSC**VOID STREAMING CORRECTION. The height of a void streaming path in a cylinder or slab in centimeters (default is 0.0).**EV**EIGENVALUE GUESS. Starting eigenvalue guess for a search calculation (default is 0.0).**EQL**INITIAL SEARCH CONVERGENCE. Initial eigenvalue search convergence (default is 0.0001).**XNPM**DAMPING FACTOR. Damping factor used in search calculations (default is 0.75).**ISN**ORDER OF ANGULAR QUADRATURE FOR XSDRNPM. Quadrature sets are geometry-dependent quantities that are defaulted to order 8 by the XSProc for**LATTICECELL**and cylindrical**MULTIREGION**. The default is 32 for**MULTIREGION**slabs and spheres. See the automatic quadrature generator and Appendix B for a more detailed explanation.**SZF**SPATIAL MESH SIZE FACTOR FOR XSDRNPM. The size of the mesh intervals can be adjusted by entering a value for**SZF**, which is a multiplier of the mesh size. The default value is 1.0. A value between zero and 1.0 yields a finer mesh; a value greater than 1.0 yields a coarser mesh. If**SZF**\(\leq 0\), the user specifies the number of mesh intervals in each zone immediately following the**MORE DATA**block. If**SZF**= 0, the interval spacing is automatically generated, while if**SZF**< 0 the intervals are equally spaced intervals in each zone.**IIM**MAXIMUM NUMBER OF INNER ITERATIONS FOR XSDRNPM. This is the maximum number of inner iterations to be used in the XSDRNPM calculation. The default value is 20. See Appendix B for a more detailed explanation.**ICM**MAXIMUM NUMBER OF OUTER ITERATIONS FOR XSDRNPM. This is the maximum number of outer iterations to be used in the XSDRNPM calculation. The default value is 25. If the calculation reaches the outer iteration limit, a larger value should be used. See Appendix B for a more detailed explanation.**EPS**OVERALL CONVERGENCE CRITERIA FOR XSDRNPM. This is used by XSDRNPM after each outer iteration to determine if the problem has converged. The default value of**EPS**is 0.00001. A value less than 0.00001 tightens the convergence criteria; a larger value loosens the convergence criteria.**PTC**POINTWISE CONVERGENCE CRITERIA FOR XSDRNPM. This is the point flux convergence criteria used by XSDRNPM to determine if convergence has been achieved after an inner iteration. The default value for PTC is 0.000001. A smaller value tightens convergence; a larger value loosens it.**BKL**BUCKLING FACTOR FOR XSDRNPM. A buckling factor should be used ONLY for a**MULTIREGION****BUCKLEDSLAB**or**BUCKLEDCYL**problem. Because cylinders are assumed to be infinitely long and slabs are assumed to be infinite in both transverse directions, the analytic sequence may tend to overestimate the total flux for a finite system. A buckling correction can be used to approximate the leakage from the system in the transverse direction(s). The extrapolation distance factor,**BKL**, is defaulted to 1.420892.**IUS**UPSCATTER SCALING FLAG for XSDRNPM. This option allows the use of upscatter scaling to accelerate the solution or force convergence. The default value is zero, in which case upscatter scaling is not used.**IUS**=1 facilitates upscatter scaling. Guidelines are not available to indicate when upscatter scaling is needed. Some problems will not converge with it, and some will not converge without it. See Appendix B for a more detailed explanation.**DAN**(mm) DANCOFF FACTOR for the specified mixtures used in BONAMI and in the CENTRM 2REGION option. This value overrides the internally computed Dancoff factor used in the resonance correction for the specified mixture*mm*. The Dancoff data are entered in the form**DAN**(mm) = Dancoff factor. Note that the parentheses must be entered as part of the data, and the mixture number, mm, must be enclosed in the parentheses. See Appendix B for additional details. (Note: this is not to be confused with the DAN2PITCH parameter in CENTRMDATA)**BAL**BALANCE TABLE PRINT FLAG for XSDRNPM. This allows control of the balance table print from**XSDRNPM**. The default value is**FINE**.**BAL**=**NONE**suppresses the balance table print.**BAL**=**ALL**prints all of the balance tables.**BAL**=**FINE**prints only the fine-group balance tables. See Appendix B for additional details.**DY**FIRST TRANSVERSE DIMENSION for XSDRNPM. This is the first transverse dimension, in cm, used in a buckling correction to calculate the leakage normal to the principal calculation direction (the height of a slab or cylinder). It should only be entered if XSDRNPM is to create cell-weighted cross sections and/or calculate the eigenvalue of a cylinder or slab system of finite height for a**LATTICECELL**problem.**DY**= is defaulted to an infinite height, or is set to**DY**for a buckled**MULTIREGION**cell description. A value entered here overrides any buckling height value entered in the**MULTIREGION**data.**DZ**SECOND TRANSVERSE DIMENSION for XSDRNPM. This is the second transverse dimension, in cm, used for a buckling correction for a slab of finite width. It should only be entered if XSDRNPM is to create cell-weighted cross sections and/or calculate the eigenvalue of a**LATTICECELL**slab of finite width.**DZ**= is defaulted to an infinite width, or is set to**DZ**for a buckled**MULTIREGION**slab cell of finite width. A value entered here overrides any buckling depth value entered in the**MULTIREGION**data.**COF**DIFFUSION COEFFICIENT FOR TRANSVERSE LEAKAGE CORRECTIONS IN XSDRNPM. The default value is 3. The available options are as follows.**COF**=0 sets a transport-corrected cross section for each zone**COF**=1 use a spatially averaged diffusion coefficient for each zone**COF**=2 use a diffusion coefficient for all zones that is one-third of the diffusion coefficient determined from the spatially averaged transport cross section for all zones**COF**=3 use a flux and volume weighting across all zonesSee Appendix B or XSDRNPM Input/Output Assignments in the XSDRNPM chapter, 3$ array, variable

**IPN**for more details.**NT3**UNIT WHERE XSDRNPM WRITES THE WEIGHTED LIBRARY. If XSDRN does a weighting calculation, this is the unit number it uses to write the weighted library on (default is 3).**NT4**UNIT WHERE XSDRNPM WRITES THE ANGULAR FLUXES. XSDRN writes the angular fluxes on this unit if it is non-zero (default is 16).**ADJ**Adjoint mode flag for XSDRNPM. Set to 1 to cause XSDRNPM to solve the adjoint problem (default is 0).**NTA**UNIT WHERE XSDRNPM WRITES THE ACTIVITIES. XSDRN writes the calculated activities on this unit if it is non-zero (default is 75).**NBU**UNIT WHERE XSDRNPM WRITES BALANCE TABLES. If the balance tables file is to be saved, enter the unit number where it is to be written (default is 76).**NTC**UNIT WHERE XSDRNPM WRITES THE DERIVED DATA. XSDRN writes the derived input data on this unit if it is non-zero (default is 73).**NTD**UNIT WHERE XSDRNPM WRITES THE DATA FOR A SENSITIVITY ANALYSIS. XSDRN writes the data for a sensitivity analysis on this unit if it is non-zero (default is 0).**FRD**UNIT WHERE XSDRNPM READS INPUT FLUX GUESS. If greater than 0, a flux guess will be read from this unit.**FWR**UNIT WHERE XSDRNPM WRITES OUPUT FLUX. If greater than 0, the space-dependent multigroup scalar flux is written in binary format to this unit.**WGT**CROSS SECTION WEIGHTING FLAG for XSDRNPM. The default is 0, not to perform cross section weighting. To turn on cross section weighting, a positive value should be entered. A value of 1 will weight the cross sections by nuclide; 2 will weight by mixture.**ZMD**(iz) ZONE WIDTH MODIFIERs for an XSDRNPM search problem. This allows entering a zone width modifier for zone iz in the XSDRNPM problem description. The zone width data are entered in the following form:**ZMD(iz)=modifier**Note that the parentheses must be entered as part of the keyword. The zone number iz, to which the modifier is applied, must be enclosed in the parentheses. The modifier is entered after the equal sign. See the “Dimension Search Calculations” description in the XSDRNPM chapter for more information.

**INT**(iz) NUMBER OF MESH INTERVALS FOR ZONE IZ in XSDRNPM. The default is 0, which causes the number to be calculated. The data are entered in the following form:**INT(iz)=number**Note that the parentheses must be entered as part of the keyword. The zone number iz, for which the number of intervals is specified, must be enclosed in the parentheses. The number of intervals is entered after the equal sign.

**KEF**DESIRED VALUE OF*k*_{EFF}for an XSDRNPM zone width search. The default value is 1.0. If it is desired to search for some other value, such as 0.9, then input it here.**KFM**The first eigenvalue modifier used in an XSDRNPM search. This value is used to make the first change in the XSDRNPM search. The default value is -0.1. A user may sometimes need to change this to make the search converge.**ID1**SCALAR FLUX PRINT CONTROL. The default value is -1, which suppresses printing the scalar fluxes in XSDRNPM. See the XSDRNPM Input/Output Assignments section in the XSDRNPM chapter, 2$ array, variable**ID1**for allowed values and corresponding actions.**ISCT**ORDER OF SCATTERING for XSDRMPM. The default is 5 for all libraries.**ICON**TYPE OF WEIGHTING (see Cross-Section Weighting section in the XSDRNPM chapter).**INNERCELL**- followed by integer N (zones in the cell). Cell weighting is performed over the N innermost regions in the problem. Nuclides outside these regions are not weighted.**CELL**- cell weighting**ZONE**- zone weighting**REGION**- region weighting**IGMF**NUMBER OF GROUPS IN COLLAPSED LIBRARY. Enter number of groups after equal sign, followed by group lower energy boundaries (eV) in descending order.**ITP**COLLAPSED OUTPUT FORMAT. The default is 0.

0-19 - cross sections are written only in the AMPX weighted library formats on logical 3. A weighted library is always written when IFG=1.

The various values of ITP (modulo 10) are used to select the different transport cross section weighting options mentioned earlier. The options are as follows:

ITP = 0, 10, … \(\sqrt{(\psi^{g}_{1} + (DG\psi))^{2}}\)

ITP = 1 ,11, … absolute value of current

ITP = 2, 12, … \(DB^{2}\psi_{g}\) + outside leakage

ITP = 3, 13, … \(\frac{\psi}{\Sigma^{g}_{t}}\)

ITP = 4, 14, … \(DB\psi_{g}\)

ITP = Other values are reserved for future development and should not be used.

**GAMMA_MT_LIST**LIST OF GAMMA 1D REACTIONS ASSOCIATED WITH INPUT. A list of 1-D gamma reactions to be included on a condensed library for later use gamma_mt_list= numberEntries mt1 mt2 … mt_numberEntries.**NEUTRON_MT_LIST**LIST OF NEUTRON 1D REACTIONS ASSOCIATED WITH INPUT. A list of 1-D neutron reactions to be included on a condensed library for later use neutron_mt_list= numberEntries mt1 mt2 … mt_numberEntries.**NEUTRON_2D_LIST**LIST OF NEUTRON 2D ARRAYS FOR THE MICRO LIBRARY. This list flags the finalizer to place 2-D arrays (currently MT 2, 4, 16) on the micro library for use in SAMS.**ACTIVITY**Enter:IAZ (number of activities)

IAI (calculate activities by zone or interval)

0 – zone

1 – interval

LACFX (unit number to which activities are written)

LAZ (IAZ sets of numbers consisting of the nuclide and process numbers for each activity)

**BAND**NUMBER OF REBALANCE BANDS for XSDRNPM (default is 1).**IPRT**CROSS SECTION PRINT CONTROL. The default value is -2, which suppresses printing the cross sections in XSDRNPM. See XSDRNPM chapter, 2$ array, variable IPRT for allowed value, and corresponding actions.**GRAIN_K**Flag to control execution of XSDRNPM after each grain calculation for a**DOUBLEHET**cell.**SOURCE**(iz) ZONE SOURCE for an XSDRNPM fixed source problem. This allows entering a source spectrum for zone iz in the XSDRNPM problem description. The source spectrum data are entered in the following form:**SOURCE(iz)= numEntries spectrum_grp_1 … spectrum_grp_numEntries**Note that the parentheses must be entered as part of the keyword. The zone number, iz, to which the spectrum is applied, must be enclosed by the parentheses. The numEntries follows the equal sign and must be less than or equal to the number of energy groups for the problem. It is followed by numEntries numbers defining the spectrum for the first numEntries groups for zone iz. Groups not defined are set to zero. The spectrum applies uniformly to zone iz. A different spectrum may be entered for different zones.

**END MORE**Terminate the optional parameter data.

### 7.1.3.9. Optional CENTRM DATA parameter data

The CENTRM DATA block defines input parameter values for the CENTRM, PMC
and CRAWDAD modules. XSProc defines default values for these parameters
which are adequate for most applications. If all default values are
acceptable, this section of input data can be omitted. The CENTRM DATA
block applies only to the unit cell immediately preceding it. CENTRM
DATA placed prior to all unit cell data applies to all materials not
listed in any unit cell. Parameter values are assigned by entering the
words **CENTRM DATA** followed by the desired keyword parameters and
their associated values. One or more parameters can be entered in any
order. There should not be a blank between the parameter name and the
equal sign. Each parameter specification must be separated from the rest
by at least one blank. For example,

CENTRM DATA ISN=16PTC=0.0008N1D=1END CENTRM DATA

A description of CENTRM DATA parameters is given below.

**CENTRM DATA**These words, followed by one or more blanks, are entered ONLY if optional parameter data are to be entered. They must precede all other optional parameter data. Entries 2 through 42 can be entered in any order.**ISN**ORDER OF SN ANGULAR QUADRATURE FOR CENTRM. SN Quadrature sets are geometry-dependent quantities. Default value for**ISN**is 6 (only used for**NFST**and**NTHR**=0; and**NPXS**=1).**ISCT**LEGENDRE POLYNOMIAL P_{N}ORDER OF SCATTERING. These are used to determine the number of moments calculated for the scattering cross sections. Default value is 0 for 2-D MoC option and 1 for 1-D S_{n}, which have been found adequate for nearly all cases.**IIM**MAXIMUM NUMBER OF INNER ITERATIONS. This is the maximum number of inner iterations for Sn transport calculations in CENTRM. Default value is 10.**IUP**MAXIMUM NUMBER OF OUTER ITERATIONS IN THERMAL RANGE. This is the maximum number of outer iterations used to converge PW flux changes caused by upscattering in the thermal range. Default value is 3. More iterations (~ 15) may be required for higher accuracy in some cases.**NFST**FAST RANGE MULTIGROUP CALCULATION OPTION, E >**DEMAX**. This determines what type of calculation is done above**DEMAX**. The options are (0) S:sub:N, (1) diffusion theory, (2) homogenized infinite medium, (3) zonewise infinite medium, or (6) 2D MoC lattice cell [NOTE: NFST=4,5 are deprecated]. Default value is 0 (S_{N}).**NTHR**THERMAL RANGE MULTIGROUP CALCULATION OPTION, E <**DEMIN**. This determines what type of calculation is done below**DEMIN**. The options include (0) S:sub:N, (1) diffusion, (2) homogenized infinite medium, (3) zonewise infinite medium, or (6) 2-D MoC lattice cell [NOTE: NTHR=4,5 are deprecated]. Default value is 0 (S_{N}).**NPXS**POINTWISE RANGE MULTIGROUP CALCULATION OPTION,**DEMIN**< E <**DEMAX**. This determines what type of calculation is done between**DEMIN**and**DEMAX**. The options include (0) MG calculation, (1) 1-D S_{N}, (2) collision probability, (3) homogenized infinite medium, (4) zonewise infinite medium, (5) two-region, or (6) 2-D MoC lattice cell. Default value is 1 (S_{N}), except for square-pitch LATTICECELL where the default is 6 (2D MoC).**ISVAR**LINEARIZATION OPTION. This determines if the MG source and/or the cross sections are linearized in CENTRM calculations. Options for linearizing are (0) neither, (1) source, (2) cross section, or (3) both. Default value is 3.**ISCTI**LEGENDRE POLYNOMIAL P_{N}ORDER OF SCATTERING IN THE INELASTIC RANGE. These are used to determine the number of moments calculated for the inelastic scattering cross sections. Default value is 0, isotropic.**NMF6**INELASTIC FLAG. This determines if inelastic data are used. The options are to include (-1) no inelastic data, (0) discrete inelastic data, and (1) discrete inelastic and continuum. Default value is -1. Use of**NMF6**=1 is not recommended due to long running times.**IPRT**MIXTURE CROSS-SECTION OUTPUT OPTION. This determines the output of cross section. The options include (-3) none, (-2) output macro PW cross sections to file “_centrm.pw.macroxs”, (-1) 1-D MG cross sections, (N) P_{0}to P_{N}MG 2-D matrices. Default value is -3, none.**ID1**FLUX EDIT OPTION. This option determines the output of flux energy spectra. The options are (-1) none, (0) print MG fluxes, (1) also print MG flux moments, (2) save CE fluxes on output file, “_centrm.pw_flux”. Default value is -1.**KERNEL**BOUND KERNELS. This indicates use of CENTRM PW thermal kernel data [S(\(\alpha\),:math:beta)] for bound nuclides if**KERNEL**=1. If**KERNEL**=0, all thermal kernels are treated as free gas; Default is 1, use bound scattering kernels if available.**IPBT**PRINT GROUP SUMMARY TABLES. Group summary tables for each zone are printed in CENTRM if greater than 0. Default is 0. Balance ratios are not computed in thermal groups or for MoC option.**IPN**GROUP DIFFUSION COEFFICENT. Used for DB^{2}loss term. See XSDRNPM chapter for more information. Default is 2.**IXPRT**PRINT OPTION FOR CENTRM. This value is >0 if more information is printed to output. Default value is 0, minimum output.**MLIM**MASS VALUE RESTRICTION ON ORDER OF SCATTERING. Nuclides with mass ratios greater than**MLIM**are limited to a**NLIM**order of scattering. Default value is 100.**NLIM**ORDER OF SCATTERING RESTRICTION. This is the limiting order of scattering for all nuclides with mass ratios greater than**MLIM**. Default value is 0.**EPS**INTEGRAL CONVERGENCE CRITERIA. This is used by CENTRM after each outer iteration to determine if the problem has converged. Default value is 0.001. A value less than 0.0001 tightens the convergence criteria; a larger value loosens the convergence criteria.**PTC**POINTWISE CONVERGENCE CRITERIA. This is the point flux convergence criteria used by CENTRM to determine if convergence has been achieved after an inner iteration. Default value is 0.0001. A smaller value tightens convergence; a larger value loosens it.**B2**MATERIAL BUCKLING FACTOR (cm^{-2}). This is used with a buckled system. If a buckled system is specified for a unit cell, the code will use this value. Default value is 0.0.**DEMIN**LOWEST ENERGY OF POINTWISE FLUX CALCULATION. This value is the lowest energy (eV) for which CENTRM calculates PW fluxes. Default is 0.001 eV.**DEMAX**HIGHEST ENERGY OF POINTWISE FLUX CALCULATION. This value is the highest energy (eV) for which CENTRM calculates PW fluxes. Default is 20,000.0 eV, which encompasses the resolved resonance range of all actinides. It is recommended that DEMAX be <500 keV.**TOLE**CENTRM PW THINNING TOLERANCE. This is the tolerance used to thin the PW material cross sections after they are mixed. Default value is 0.001.**FLET**FRACTIONAL LETHARGY CONSTRAINT. This is the maximum lethargy difference between points in the flux solution energy mesh. Smaller values increase the number of energy points. Default value is 0.1.**DAN2PITCH**CENTRM DANCOFF FACTOR SEARCH. Fuel Dancoff factor to search for a Dancoff-equivalent pitch used in the CENTRM cell calculation. Only applicable in LATTICECELL and DOUBLEHET cases with fuel in center region, with SN or MoC transport solvers. Default is 0, which indicates no pitch modification. NOTE! This option should not be used to enter Dancoff factors for the CENTRM*2REGION*transport option-use EDAN(m) array in**MOREDATA**for these values.**MRANGE**PMC GROUP CROSS-SECTION PROCESSING RANGE. This option determines the range over which the group cross sections will be processed. The options are (0) compute new group cross section over the PW range, (1) over the resolved resonance range of each nuclide, or (2) over the PW flux range (**DEMAX**to**DEMIN**). Default value is 2.**N2D**PMC ELASTIC MATRIX PROCESSING FLAG. This option determines how MG P_{N}elastic scattering matrices are obtained. Options are (-2) perform operations in both (-1) and (2); (-1) compute P0 self-scatter, then renormalize matrix to shielded 1-D elastic values; (0) normalize original scatter matrix to shielded 1-D elastic values; (1) compute new P_{N}moments of elastic matrix using scalar flux and S-wave kinematics for both thermal and epithermal energy ranges; or (2) use flux-moments to compute “consistent PN” correction for diagonal elements of elastic P_{N}components. Default value is -1. For unit cell calculations in reactor lattices, option -2 may improve results. NOTE: option 0 is always used in thermal range except for option 1.**IXTR3**PMC P_{N}ORDER FLAG. This option determines the maximum order of Legendre moments to be retained on output MG library. The default is 5; i.e., retain scattering moments up to P_{5}if available on the input MG library. If (-1) is entered, all elastic moments on the MG library are included.**NPRT**PMC PRINT FLAG. This option determines what is printed to output. The options include (-1) minimum output, (0) standard output, (1) print 1-D cross sections, (2) print both 1-D and 2-D cross sections. Default value is -1, minimum output.**NWT**PMC MULTIGROUP SPATIAL-WEIGHTING FLAG. This option determines if the MG data are (0) zone-weighted or (1) cell-weighted. Default value is 0.**MTT**PMC MT PROCESSING FLAG. This option determines if reaction MTs are processed individually or treat dependencies explicitly. If**MTT**=0 all MTs are processed independently; if**MTT**=1, all MTs are processed except 1, 27, and 101. These are then computed as follows: MT101 = sum MT102 - 114, MT27 = MT18 + MT101, MT1 = MT2 + MT4 + MT16 + MT17 + MT27. Default value is 1.**N1D**PMC WEIGHTING FUNCTION FLAG. This is used to determine if (0) flux weighting or (1) current weighting is used to collapse the cross sections. Default value is 0, flux weighting.**PMC_DILUTE**PMC DILUTE BACKGROUND CROSS SECTION. The background cross section \(\sigma_{0}\) value above which nuclide cross sections are not processed in PMC but the BONAMI cross sections are used instead. No resonance shielding corrections are performed for materials with background cross sections greater than*pmc_dilute*. Higher values of*pmc_dilute*result in more nuclides being processed. The default value is 1.0E10.**MTOUT**PW REACTION TYPES. Reactions included by CRAWDAD on PW library for MG processing in PMC: (0) all; (1) output only MTs 1, 2, 4, 102, 18, 452, 455, 456 (and 107 for^{10}B or^{7}Li); (2) all from option (1) and all inelastic MTs and 16. Default is**MTOUT**=1 for**NMF6**=-1 and**MTOUT**=2 for**NMF6**>-1.**IBR**CENTRM RIGHT BOUNDARY TYPE. Type of boundary condition on right boundary of unit cell for CENTRM**LATTICECELL**calculations. See allowable IBR values in CENTRM. Default is white (**IBR**= 3) for 1D SN; 2D MoC transport option always uses reflected.**IBL**CENTRM LEFT BOUNDARY TYPE. Same as**IBR**, but for left boundary. Default is reflected (**IBL**= 1).**ALUMP**MASS LUMPING FRACTION. A value in range [0.0, 1.0] indicates fractional mass lumping criterion for CENTRM. Value of 0 indicates no lumping applied. For example,**ALUMP**=0.3 means that materials are combined into one or more lumps such that their masses are within +/-30% of the effective lump mass, while preserving the slowing-down power. This approximation reduces execution time. Default value is 0.2.**PMC_OMIT**PMC NUCLIDES SKIPPED. PMC normally processes problem-dependent (e.g., self-shielded) MG cross sections for all materials. If**PMC_OMIT**=1, processing is only performed for materials contained in fuel mixtures. Default value is 0 (all materials processed).**PXSMEM**CENTRM PW DATA STORAGE. Option to store PW data in memory or in external file during centrm execution. If**PXSMEM**=1, PW cross section data are stored by group in external scratch file during CENTRM calculation; if**PXSMEM**=0 (default value), all PW cross sections are kept in memory.**MOCMESH**CENTRM MOC MESH OPTION. Pre-defined space mesh intervals for CENTRM MoC calculation: 0=>coarse mesh (1 interval per zone); 1=>regular mesh (4 intervals in fuel, 2 in moderator, 1 in others); 2=> fine mesh (8 in fuel, 4 in moderator, 1 in others). Default=0.**MOCRAY**CENTRM MOC RAY SPACING. Distance between characteristic rays in CENTRM MoC calculation. Default=0.02.**MOCPOL**CENTRM NUMBER OF MOC POLAR ANGLES. Allowable values are 2, 3, 4. Default=3 (only used for**NPXS**=6).**MOCAZI**CENTRM NUMBER OF MOC AZIMUTHAL ANGLES. Allowable values are 2–16. Default=8 (only used for**NPXS**=6).**MOCZONE_INT**CENTRM MOC MESH BY ZONE. User-defined mesh intervals by zone; e.g., moczone_int(1)=5 defines five intervals for zone 1; zero value means not used. This overrides the predefined meshs described by**MOCMESH****ISRC**CENTRM SOURCE TYPE. CENTRM can use a fission-spectrum source (isrc=1), an input source spectrum (isrc=0), or a combination(isrc=3) for transport. Default=1.**XNF**CENTRM SOURCE NORMALIZATION. The integrated source (fission-spectrum and/or fixed source spectrum) is normalized to this value. Default=1.0.**ITERP**CRAWDAD TEMPERATURE INTERPOLATION METHOD. Method to use for CE cross section interpolation 0=>combination of square-root(T) and finite-difference; 1=>only square-root(T); 2=> only finite-difference. Default is 0.**END CENTRM**The word**END**is entered to terminate the optional parameter data. A label can be associated with this**END**. The label can be as long as 12 characters but must be preceded by a single blank. If this**END**is entered without a label, it must not begin in column 1. At least two blanks must follow this entry.

References

- XSProc-IB64
Igor Ilich Bondarenko.

*Group constants for nuclear reactor calculations*. Consultants Bureau, 1964.- XSProc-RLL+15
Bradley T. Rearden, Robert A. Lefebvre, Jordan P. Lefebvre, Kevin T. Clarno, Mark A. Williams, Lester M. Petrie, and Ugur Mertyurek. Modernization enhancements in SCALE 6.2. In

*PHYSOR 2014*. Kyoto, Japan, 2015.- XSProc-Wil11(1,2)
Mark L. Williams. Resonance self-shielding methodologies in SCALE 6.

*Nuclear Technology*, 174(2):149–168, May 2011. URL: https://doi.org/10.13182/NT09-104, doi:10.13182/NT09-104.- XSProc-WA95
Mark L. Williams and Mehdi Asgari. Computation of continuous-energy neutron spectra with discrete ordinates transport theory.

*Nuclear Science and Engineering*, 121(2):173–201, 1995. Publisher: Taylor & Francis.

## 7.1.4. Appendices

- 7.1.4.1. XSProc: Standard Composition Examples
- 7.1.4.1.1. Standard composition fundamentals
- 7.1.4.1.2. Basic standard composition specifications
- 7.1.4.1.3. User-defined (arbitrary) chemical compound specifications
- 7.1.4.1.4. User-defined (arbitrary) mixture/alloy specifications
- 7.1.4.1.5. Fissile solution specifications
- 7.1.4.1.6. Combinations of standard composition materials to define a mixture
- 7.1.4.1.7. Combinations of user-defined compound and user-defined mixture/alloy to define a mixture
- 7.1.4.1.8. Combinations of solutions to define a mixture
- 7.1.4.1.9. Combinations of basic and user-defined standard compositions to define a mixture
- 7.1.4.1.10. Combinations of basic and solution standard compositions to define a mixture
- 7.1.4.1.11. Combinations of user-defined compound and solution to define a mixture

- 7.1.4.2. XSProc Standard Composition Examples
- 7.1.4.3. Examples of Complete XSProc Input Data
- 7.1.4.3.1. Infinite homogeneous medium input data
- 7.1.4.3.2. LATTICECELL input data
- 7.1.4.3.3. MULTIREGION input data
- 7.1.4.3.4. DOUBLEHET input data
- 7.1.4.3.5. Two methods of specifying a fissile solution
- 7.1.4.3.6. Multiple unit cells in a single problem
- 7.1.4.3.7. Multiple fissile mixtures in a single unit cell
- 7.1.4.3.8. Cell weighting an infinite homogeneous problem
- 7.1.4.3.9. Cell weighting a LATTICECELL problem
- 7.1.4.3.10. Cell weighting a MULTIREGION problem