LA-UR-08-1808

*Approved for public release;*

*distribution is unlimited.*

*Title:*

*Authors:*

*Intended for:*

MCNPX 26F Extensions

John S. Hendricks

Gregg W. McKinney

Michael L. Fensin

Michael R. James

Russell C. Johns

Joe W. Durkee

Joshua P. Finch

Denise B. Pelowitz

Laurie S. Waters

M. William Johnson

Los Alamos National Laboratory

Franz X. Gallmeier

Oak Ridge National Laboratory

[http://mcnpx.lanl.gov](http://mcnpx.lanl.gov/)

![](media/image1.png){width="2.4069444444444446in" height="0.975in"}

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MCNPX 26F Extensions

by

John S. Hendricks

Gregg W. McKinney

Michael L. Fensin

Michael R. James

Russell C. Johns

Joe W. Durkee

Joshua P. Finch

Denise B. Pelowitz

Laurie S. Waters

M. William Johnson

Los Alamos National Laboratory

Franz X. Gallmeier

Oak Ridge National Laboratory

March 24, 2008

Copyright 2008. Los Alamos National Security, LLC. All rights reserved.

This material was produced under U.S. Government contract
DE-AC52-06NA25396 for Los Alamos National Laboratory, which is operated
by Los Alamos National Security, LLC for the U.S. Department of Energy.
The Government is granted for itself and others acting on its behalf a
paid-up, nonexclusive, irrevocable worldwide license in this material to
reproduce, prepare derivative works, and perform publicly and display
publicly. Beginning five (5) years after (insert date permission to
assert copyright was obtained), subject to additional five-year
worldwide renewals, the Government is granted for itself and others
acting on its behalf a paid-up, nonexclusive, irrevocable worldwide
license in this material to reproduce, prepare derivative works,
distribute copies to the public, perform publicly and display publicly,
and to permit others to do so.\
\
NEITHER THE UNITED STATES NOR THE UNITED STATES DEPARTMENT OF ENERGY,
NOR LOS ALAMOS NATIONAL SECURITY, LLC, NOR ANY OF THEIR EMPLOYEES, MAKES
ANY WARRANTY, EXPRESS OR IMPLIED, OR ASSUMES ANY LEGAL LIABILITY OR
RESPONSIBILITY FOR THE ACCURACY, COMPLETENESS, OR USEFULNESS OF ANY
INFORMATION, APPARATUS, PRODUCT, OR PROCESS DISCLOSED, OR REPRESENTS
THAT ITS USE WOULD NOT INFRINGE PRIVATELY OWNED RIGHTS.

**CONTENTS**

[1.0. Introduction 1](#introduction)

[1.1. Summary of New MCNPX Features 1](#summary-of-new-mcnpx-features)

[1.2. Availability 2](#availability)

[1.3. Documentation 3](#documentation)

[1.4. Cash Awards Quality Assurance Program
3](#cash-awards-quality-assurance-program)

[2.0. Description of new MCNPX Features
4](#description-of-new-mcnpx-features)

[2.1. Depletion/Burnup 4](#depletionburnup)

[2.1.1. Depletion Process 5](#depletion-process)

[2.1.2. CINDER90 approach to temporal nuclide inventory calculations
5](#cinder90-approach-to-temporal-nuclide-inventory-calculations)

[2.1.3. Collision Density Generation 6](#collision-density-generation)

[2.1.4. The Cross-Section Averaging for Depletion Acceleration Method
(CSADA)
7](#the-cross-section-averaging-for-depletion-acceleration-method-csada)

[2.1.5. BURN Card Setup 8](#burn-card-setup)

[2.1.6. Burn Time, Total System Power, and Power Fraction
10](#burn-time-total-system-power-and-power-fraction)

[2.1.7. Flux Normalization Parameters
11](#flux-normalization-parameters)

[2.1.8. Burn Materials 12](#burn-materials)

[2.1.9. Automatic Fission Yield Selection Process
14](#automatic-fission-yield-selection-process)

[2.1.10. Metric Tonnes of Uranium (MTU)
14](#metric-tonnes-of-uranium-mtu)

[2.1.11. Isotope Reactivity Options 15](#isotope-reactivity-options)

[2.1.12. Models Option 15](#models-option)

[2.1.13. Fission Product Tracking/Output Frequency
15](#fission-product-trackingoutput-frequency)

[2.1.14. The Isotope Generator Algorithm
17](#the-isotope-generator-algorithm)

[2.1.15. Proper Tracking of Entire Decay Chains
18](#proper-tracking-of-entire-decay-chains)

[2.1.16. Burnup/depletion with repeated structures
19](#burnupdepletion-with-repeated-structures)

[2.1.17. Time Dependent Concentration Changes: MATMOD keyword
19](#time-dependent-concentration-changes-matmod-keyword)

[2.1.18. Metastable Isotope Representation
20](#metastable-isotope-representation)

[2.1.19. Examples 21](#examples)

[2.2. Heavy Ion Transport 23](#heavy-ion-transport)

[2.2.1. Input 23](#input)

[2.2.2. Tallies 24](#tallies)

[2.2.3. Other Input 24](#other-input)

[2.2.4. Variance Reduction. 25](#variance-reduction.)

[2.2.5. Changes to PRINT Tables. 25](#changes-to-print-tables.)

[2.2.6. Limitations 26](#limitations)

[2.3. LAQGSM Physics. 26](#laqgsm-physics.)

[2.4. CEM03 Upgrade 27](#cem03-upgrade)

[2.4.1. Intra Nuclear Cascade (INC) 28](#intra-nuclear-cascade-inc)

[2.4.2. Preequilibrium (PREC) 28](#preequilibrium-prec)

[2.4.3. Evaporation and/or Fission 29](#evaporation-andor-fission)

[2.4.4. Coalescence 29](#coalescence)

[2.4.5. Fermi Breakup 29](#fermi-breakup)

[2.4.6. Additional Notes 29](#additional-notes)

[2.5. Long File Names 29](#long-file-names)

[2.6. Terminate Tallies at Desired Precision
30](#terminate-tallies-at-desired-precision)

[2.7. Spherical Mesh Weight Windows 31](#spherical-mesh-weight-windows)

[2.7.1. User Interface 31](#user-interface)

[2.7.2. Plotting 32](#plotting)

[2.8. Energy-Time Weight Windows 35](#energy-time-weight-windows)

[2.8.1. Cell-Based Example 36](#cell-based-example)

[2.8.2. Mesh-Based Example and WWOUT File Changes
36](#mesh-based-example-and-wwout-file-changes)

[2.9. Charged Ions from Neutron Capture in Table Range
37](#charged-ions-from-neutron-capture-in-table-range)

[2.9.1. User Interface 37](#user-interface-1)

[2.9.2. Diagnostics 38](#diagnostics)

[2.9.3. Important Considerations 38](#important-considerations)

[2.10. Delayed-Gamma Emission. 39](#delayed-gamma-emission.)

[2.10.1. The Products of Fission: Residual Nuclides and Radiation
40](#the-products-of-fission-residual-nuclides-and-radiation)

[2.10.2. Decay Chains and Emission Sampling
41](#decay-chains-and-emission-sampling)

[2.10.3. Simple Multi-Particle Reactions
42](#simple-multi-particle-reactions)

[2.10.4. User Interface 43](#user-interface-2)

[2.10.5. Sampling and Execution 44](#sampling-and-execution)

[2.10.6. Fission Yield Data 45](#fission-yield-data)

[2.11. Criticality Source Convergence Acceleration
45](#criticality-source-convergence-acceleration)

[2.11.1. Example 45](#example)

[2.11.2. User Interface 47](#user-interface-3)

[3.0. MCNPX Feature EXTENSIONS and Enhancements
48](#mcnpx-feature-extensions-and-enhancements)

[3.1. Proton Step-Size Control 48](#proton-step-size-control)

[3.2. New Photon Emission Data 49](#new-photon-emission-data)

[3.3. New S(α,β) Scattering Law 49](#new-sαβ-scattering-law)

[3.4. Differential Data Tallies Extended to Table Physics
49](#differential-data-tallies-extended-to-table-physics)

[3.5. Neutron models produce light (A\<4) nuclei \< 100 MeV
50](#neutron-models-produce-light-a4-nuclei-100-mev)

[3.6. Weight-Window Upper Bounds Limiter
50](#weight-window-upper-bounds-limiter)

[3.7. Separate Printout of Induced Fission Multiplicity
50](#separate-printout-of-induced-fission-multiplicity)

[3.8. Weight-Window MESH Angles in Radians and Degrees
51](#weight-window-mesh-angles-in-radians-and-degrees)

[3.9. Interrupts in Electron Tracking
51](#interrupts-in-electron-tracking)

[3.10. Extended ZAID Identifiers 51](#extended-zaid-identifiers)

[3.11. LINLIN Contour Plot Default 51](#linlin-contour-plot-default)

[3.12. Weight-Window Contour Plot Improvement
52](#weight-window-contour-plot-improvement)

[3.13. Allow Deleted Segmenting Surfaces
52](#allow-deleted-segmenting-surfaces)

[3.14. Improved Windows Installation 52](#improved-windows-installation)

[3.15. Spherical GRIDCONV 53](#spherical-gridconv)

[3.16. Spherical Mesh Tally Plots 54](#spherical-mesh-tally-plots)

[3.17. Delayed-Gamma Enhancements 54](#delayed-gamma-enhancements)

[3.18. Photofission Yield Data 55](#photofission-yield-data)

[3.19. Decay Omitted from LCA NOACT=-2 Option
55](#decay-omitted-from-lca-noact-2-option)

[3.20. Piping PTRAC Results 55](#piping-ptrac-results)

[3.21. Muon Capture Secondary Particle Production
55](#muon-capture-secondary-particle-production)

[3.22. Additional Enhancements 56](#additional-enhancements)

[3.22.1. ILOG interpolation 56](#ilog-interpolation)

[3.22.2. MODE J R 57](#mode-j-r)

[3.22.3. Photofission prompt gamma warning
57](#photofission-prompt-gamma-warning)

[3.22.4. NNDC Delayed-Neutron Emission Probabilities
57](#nndc-delayed-neutron-emission-probabilities)

[4.0. MCNPX Corrections 57](#mcnpx-corrections)

[4.1. Significant Problem Corrections
57](#significant-problem-corrections)

[4.1.1. Auger Electrons Below Energy Cutoff
57](#auger-electrons-below-energy-cutoff)

[4.1.2. Detectors in Lattice Geometries
57](#detectors-in-lattice-geometries)

[4.1.3. KCODE/PRDMP 5th Entry 57](#kcodeprdmp-5th-entry)

[4.1.4. CEM03 Corrections 58](#cem03-corrections)

[4.1.5. SDEF Fails with SP -31 x for Equiprobable Bins Sampling
58](#sdef-fails-with-sp--31-x-for-equiprobable-bins-sampling)

[4.1.6. Surface Sources in Repeated Structures
58](#surface-sources-in-repeated-structures)

[4.1.7. Periodic Boundary Conditions in Repeated Structures
58](#periodic-boundary-conditions-in-repeated-structures)

[4.1.8. Delayed Neutrons/Gammas with Biased Photonuclear
58](#delayed-neutronsgammas-with-biased-photonuclear)

[4.1.9. Delayed Neutrons/Gammas Inelastic Scatter
58](#delayed-neutronsgammas-inelastic-scatter)

[4.1.10. Delayed Neutrons/Gammas from (n,p) Reactions
58](#delayed-neutronsgammas-from-np-reactions)

[4.1.11. Delayed Neutrons/Gammas with Biased Photonuclear
59](#delayed-neutronsgammas-with-biased-photonuclear-1)

[4.1.12. Parallel Burnup/Depletion Calculations with Model Cross
Sections
59](#parallel-burnupdepletion-calculations-with-model-cross-sections)

[4.1.13. Surface Sources in Repeated Structures
59](#surface-sources-in-repeated-structures-1)

[4.1.14. No Fatal Error for LAT without FILL
59](#no-fatal-error-for-lat-without-fill)

[4.1.15. Double Fluorescence with Pulse Height Tallies and WWP or ESPLT
59](#double-fluorescence-with-pulse-height-tallies-and-wwp-or-esplt)

[4.1.16. Burnup of 1000 or More Materials without MAT Keyword
59](#burnup-of-1000-or-more-materials-without-mat-keyword)

[4.1.17. Power Fraction Calculation for Burnup
59](#power-fraction-calculation-for-burnup)

[4.1.18. DATAPATH Sometimes Chosen Incorrectly
59](#datapath-sometimes-chosen-incorrectly)

[4.1.19. SSW s(-c) Can Fail with Repeated Structures
60](#ssw-s-c-can-fail-with-repeated-structures)

[4.1.20. F6 Heating Tallies Wrong for Photonuclear
61](#f6-heating-tallies-wrong-for-photonuclear)

[4.1.21. Heavy Ion Directions 61](#heavy-ion-directions)

[4.1.22. Photonuclear Mix and Match 61](#photonuclear-mix-and-match)

[4.1.23. Mesh Tally Gaps 61](#mesh-tally-gaps)

[4.2. Minor Problem Corrections 62](#minor-problem-corrections)

[4.2.1. Cylindrical Weight-Window Mesh
62](#cylindrical-weight-window-mesh)

[4.2.2. I8 Mesh Tally Plots 62](#i8-mesh-tally-plots)

[4.2.3. Continue Cards for Input with FATAL Errors
62](#continue-cards-for-input-with-fatal-errors)

[4.2.4. Sometimes Can Plot Only First Mesh Tally
62](#sometimes-can-plot-only-first-mesh-tally)

[4.2.5. Incorrect KCODE/Message Passing Interface (MPI) Error Message
62](#incorrect-kcodemessage-passing-interface-mpi-error-message)

[4.2.6. Incorrect LCS Error Message 62](#incorrect-lcs-error-message)

[4.2.7. Mesh Tally Writing to Backup RUNTPE
62](#mesh-tally-writing-to-backup-runtpe)

[4.2.8. Pulse-Height-Tally Variance Reduction Techniques with MPI
63](#pulse-height-tally-variance-reduction-techniques-with-mpi)

[4.2.9. PTRAC and Event Log Omission 63](#ptrac-and-event-log-omission)

[4.2.10. FM Tally Multiplier in Model Physics Regime
63](#fm-tally-multiplier-in-model-physics-regime)

[4.2.11. Make Clean Enabled for PC Build
63](#make-clean-enabled-for-pc-build)

[4.2.12. Zero Electron Mesh Tallies 63](#zero-electron-mesh-tallies)

[4.2.13. Universe Map 63](#universe-map)

[4.2.14. Tally Storages 63](#tally-storages)

[4.2.15. Lost Particles with Coincident REC Surfaces
64](#lost-particles-with-coincident-rec-surfaces)

[4.2.16. GRIDCONV Compiler Bug 64](#gridconv-compiler-bug)

[4.2.17. Geometry Plot Basis Vectors 64](#geometry-plot-basis-vectors)

[4.2.18. WWN Label Error 64](#wwn-label-error)

[4.2.19. READ Card Placements 64](#read-card-placements)

[4.2.20. Residual Nucleus Warning 64](#residual-nucleus-warning)

[4.2.21. S(α,β) Ultra-Low Energies 64](#sαβ-ultra-low-energies)

[4.2.22. Large Problem Sizes for Parallel Execution
65](#large-problem-sizes-for-parallel-execution)

[4.2.23. Mesh Tally TR Option 65](#mesh-tally-tr-option)

[4.2.24. Crash for non-orthogonal spherical mesh direction cosines
65](#crash-for-non-orthogonal-spherical-mesh-direction-cosines)

[4.2.25. Mesh Tallies Keyword Capitalization
65](#mesh-tallies-keyword-capitalization)

[4.2.26. Mesh Tallies Data Interpolation
65](#mesh-tallies-data-interpolation)

[4.2.27. Power Fraction Calculation for Individual Burn Materials
66](#power-fraction-calculation-for-individual-burn-materials)

[4.2.28. Negative MAT Numbers on the BURN card
66](#negative-mat-numbers-on-the-burn-card)

[4.2.29. Print LAQGSM Flag 66](#print-laqgsm-flag)

[4.2.30. Internal Corrections 66](#internal-corrections)

[5.0. Future work 67](#future-work)

**MCNPX 26F Extensions**

**ABSTRACT**

> MCNPX is a Fortran90 Monte Carlo radiation transport computer code
> that transports nearly all particles at nearly all energies for nearly
> all applications. The new capabilities of the latest version, MCNPX
> 26F, beyond those in MCNPX 2.5.0, are described.

# Introduction

MCNPX (MCNP eXtended) is a Fortran90 (F90) Monte Carlo radiation
transport computer code that transports nearly all particles at nearly
all energies. It is a superset of MCNP4C3 and has many capabilities
beyond MCNP4C3. MCNPX is a production computer code that models the
interaction of radiation with matter. Its quality is highly regarded and
cash awards (described in Section 1.4) are offered for bugs.

## **Summary of New MCNPX Features**

The new capabilities and enhancements of MCNPX 26F beyond MCNPX 2.5.0
are listed below. (Where applicable, the initials of the principal
developers are shown in parentheses.[^1]) Note that the delayed-gamma
emission and criticality source convergence acceleration capabilities
are developmental. They are not backed by the MCNPX cash awards quality
assurance program and must be used cautiously. However, these
capabilities are considered of such significance that they are included.
Note also that total (not prompt ) is the default for fission neutrons.
The new MCNPX 26F beyond MCNPX 2.5.0 capabilities include the following:

-   Depletion/burnup[^2](MLF);

-   Heavy-ion (Z\>2) transport (MRJ + LSW/GWM/JSH);

-   LAQGSM physics model (MRJ);

-   CEM03 physics;[^3]

-   Long file names (JSH);

-   Delayed-gamma emission (JWD);[^4]

-   Criticality source convergence acceleration (JPF);

-   Energy-time weight windows (JSH);

-   Spherical mesh weight windows (JSH);

-   Charged ions from neutron capture in table range (MRJ);

-   Tallies terminated at desired precision: STOP card (JSH);

-   Corrections/enhancements/extensions:

    -   Weight-window MESH angles in radians and degrees (JSH);

    -   Piping PTRAK results (RCJ);

    -   Photofission yield data (JWD);

    -   Decay omitted from LCA NOACT=-2 option (GWM);

    -   Pulse-height tally variance reduction fix for double
        fluorescence (JSH);

    -   Weight-window contour plot improvement (GWM);

    -   Improved windows installation (MRJ/GWM);

    -   Spherical GRIDCONV (MRJ);

    -   Spherical mesh tally plots (GWM);

    -   Proton step size control: HSTEP on M card (GWM);

    -   New photon emission data: PHTLIB (REP/GWM);

    -   New S(α,β) scattering law (REM/GWM/JSH);

    -   Muon capture secondary particle production (GWM/RCJ/MRJ/MWJ);

    -   Differential data tallies extended to table physics (GWM);

    -   Separate printout/calculation of induced fission multiplicity
        (JSH);

    -   Interrupts in electron tracking (GWM);

    -   Extend ZAID identifiers (GWM);

    -   LINLIN contour plot defaults (GWM);

    -   Allow deleted segmenting surfaces (FXG);

    -   Weight-window upper bounds limiter (GWM/JSH);

    -   F6 heating fix for photonuclear problems (JSH);

    -   Neutron models produce light (A\<4) nuclei \<100 MeV (REP/GWM);

    -   Additional enhancements and corrections.

## Availability

The latest general-release version of MCNPX is MCNPX 2.5.0, which is
available from the Radiation Safety Information Computational Center
(RSICC)[^5] and the Office of Economic Cooperation and
Development/Nuclear Energy Agency (OECD/NEA) in Paris, France.[^6]

For approved users, beta test program versions, including MCNPX 26E, may
be downloaded from the MCNPX website.[^7] Approximately 1800 MCNPX beta
test users are an essential part of the MCNPX software quality assurance
program. To become a new beta test user usually requires being an MCNPX
sponsor, collaborator, or participant in an MCNPX workshop training
course. For more information, contact us at the following email address:
mcnpx@lanl.gov.

MCNPX is U.S. export controlled. Generally, MCNPX is easy to obtain for
legitimate purposes, but restrictions protect the code, data, and
documentation once it is acquired.

## Documentation

*Restricted Documentation:*

Complete MCNPX documentation is available in the **"**MCNPX™ User's
Manual,"[^8] which comes with MCNPX from RSICC or OECD/NEA and is
available to MCNPX beta testers from the Worldwide Web (WWW).[^9]

*Unrestricted Documentation:*

Documentation of MCNPX features in MCNPX 2.5.0---that is, all MCNPX
features beyond MCNPX 2.3.0 and MCNP4C---is provided in "MCNPX
Extensions, Version 2.5.0."[^10]

MCNPX capabilities developed since the previous RSICC or OECD/NEA
international release version, MCNPX 2.5.0 (namely, the additional
capabilities of MCNPX 26F), are documented in this report.

All of the extended MCNPX capabilities are summarized in the one-page
MCNPX features list.[^11]

## Cash Awards Quality Assurance Program

We are so confident in the quality of MCNPX that John Hendricks offers
cash awards to the first person who finds any bug in the code. He will
pay \$20 to the first person finding anything that does not meet or
exceed the capabilities of MCNPX 2.3.0 and MCNP4C3. European users will
be awarded €20. He also will pay a brand new \$2 bill for any error in
MCNPX that has been inherited from its constituent codes.[^12] A list of
all winners since June 2001 can be found on the MCNPX WWW site.[^13]

# **Description of new MCNPX Features**

Total (not prompt ) is now the default for fission neutrons. To track
previous problems with the prompt default, turn off total with the TOTNU
NO card and command.

Note that the new delayed-gamma emission and criticality source
convergence acceleration capabilities are developmental. These
capabilities are not backed by the MCNPX cash awards program and must be
used cautiously. Nevertheless, they are considered of such significance
that they are included.

The principal new capabilities of MCNPX beyond MCNPX 2.5.0 described in
detail in this section are

-   Depletion/burnup,

-   Heavy-ion transport,

-   LAQGSM physics model,

-   CEM03 physics,

-   Long file names,

-   Tallies terminated at desired precision: STOP card,

-   Spherical mesh weight windows,

-   Energy-time weight windows,

-   Charged ions from neutron capture in table range,

-   Delayed-gamma emission, and

-   Criticality source convergence acceleration.

## Depletion/Burnup

The depletion/burnup capability is based on CINDER90, which was written
by William B. Wilson, and MonteBurns, which was written by Holly R.
Trellue. The initial patch to MCNPX was developed by Joe W. Durkee and
Gregg W. McKinney. Most of the corrections and enhancements to
MCNPX 26A, 26B, 26C, 26D, and 26E were developed by Michael L. Fensin
and integrated by John S. Hendricks.[^14]^,^[^15]^,^[^16] Currently, the
depletion/burnup/transmutation capability is limited to criticality
(KCODE) problems.

The new MCNPX 2.6.F capabilities are

-   The second entry on the AFMIN keyword is now used to set decay chain
    tracking criteria in CINDER90. Note that "AFMIN 1.E-10 1.E-4 " on
    the BURN card will restore tracking and run CINDER much faster than
    the current default value:

> AFMIN 1.E-10 1.E-10
>
> However, transport of histories, not CINDER, is what slows most
> problems and the new default value of 1.E-10 is much more accurate.

-   Atom and mass fractions specified in the output are now the atom and
    mass fractions of each isotope for the entire burn material instead
    of the atom and mass fraction contributions to the actinide and
    nonactinide portions of the material.

### Depletion Process {#depletion-process .Style-Heading-3h3-+-Times-New-Roman}

MCNPX depletion is a linked process involving steady-state flux
calculations in MCNPX and nuclide depletion calculations in CINDER90.
MCNPX runs a steady-state calculation to determine the system
eigenvalue, 63-group fluxes, energy-integrated reaction rates, fission
multiplicity (ν), and recoverable energy per fission (Q values).
CINDER90 then takes those MCNPX-generated values and performs the
depletion calculation to generate new number densities for the next time
step. MCNPX takes these new number densities and generates another set
of fluxes and reaction rates. The process repeats itself until after the
final time step specified by the user.

MCNPX calculates parameters only for those materials listed on the MCNPX
material cards, produced by the isotope generator algorithm, or selected
by the specified fission-product tier. When the information is not
specified from MCNPX, CINDER90 tracks the time-dependent reactions of
3400 isotopes using intrinsic cross-section and decay data inherent in
the CINDER90 code. MCNPX is only capable of tracking energy-integrated
reaction-rate information for those isotopes containing transport cross
sections. For those isotopes not containing transport cross-section
information, MCNPX calculates a 63-group flux that is sent to CINDER90
and matched with a 63-group cross-section set inherent in CINDER90 to
generate 63-group reaction rates. Those reaction rates are then energy
integrated to determine the total reactions occurring.

For MCNPX to burn materials properly, the user must point to the
CINDER.dat library file. This file contains decay, fission yield, and
63-group cross-section data not calculated by MCNPX. The CINDER.dat
library file will be accessed properly by the code if the file is placed
in the working directory in which the user is executing MCNPX or in a
directory in which the command window PATH is set to the directory where
CINDER.dat resides. If MCNPX cannot find the CINDER.dat, a fatal-error
message will be printed and the case will cease calculation.

### CINDER90 approach to temporal nuclide inventory calculations {#cinder90-approach-to-temporal-nuclide-inventory-calculations .Style-Heading-3h3-+-Times-New-Roman}

CINDER90 utilizes decay and energy integrated reaction-rate
probabilities along with fission yield information to calculate the
temporal nuclide buildup and depletion. The library of data in CINDER90,
residing in the CINDER.dat library file, includes isotope decay and
interaction probability data for 3400 isotopes including, \~30 fission
yield sets, and yield data for 1325 fission products.

The depletion equation for a specified isotope is

$\frac{\text{dN}_{m}}{\text{dt}} = - N_{m}(t)\beta_{m} + {\overline{Y}}_{m} + \sum_{k \neq m}^{}{N_{k}(t)\gamma_{k \rightarrow m}}$
, where

$\beta_{m}$ = the total transmutation probability of isotope *m*

$\gamma_{k \rightarrow m}$ = the probability of isotope *k* transmuting,
by either decay or absorption, into isotope *m*,

${\overline{Y}}_{m}$ = the production rate, and

$N_{m}(t)$ = the time-dependent atom density of isotope *m*.

This equation is nonlinear because the transmutation probabilities rely
on the time-integrated flux, which is also dependent upon time-dependent
number densities. To linearize the process, the transmutation
probabilities are set to a constant value over the time step. The set of
differential equations utilized to solve for temporal nuclide
buildup/depletion of a system of isotopes is coupled since each equation
contains time-dependent isotope density information from other nuclides.
Instead of trying to solve the large sparse matrix of equations using
the matrix exponential method, the set of coupled equations in CINDER90
is reduced to a set of linear differential equations using the Markov
method. Linear chains are created for each isotope transmutation path,
starting from initial specified isotope concentrations, generating the
following equations:

$\frac{{dΝ}_{i}}{\text{dt}} = {\overline{Y}}_{i} + Ν_{i - 1}(t)\gamma_{i - 1} - Ν_{i}(t)\beta_{i}$
,

where quantities are now indexed by the order in which they appear
within a given sequence and $\gamma_{i - 1}$ is the transmutation
probability of forming nuclide element $Ν_{i}$. The solutions of each
linear chain determines a partial nuclide density, $Ν_{i}$, and is
computed by the following equation

$Ν_{n}(t) = \prod_{k = 1}^{n - 1}{\gamma_{k}\left\{ {\overline{Y}}_{m}\left\lbrack \frac{1}{\prod_{l = 1}^{n}\beta_{l}} - \sum_{j = 1}^{n}\frac{e^{- \beta_{\text{jt}}}}{\prod_{i = 1, \neq j}^{n}\left( \beta_{i} - \beta_{j} \right)} \right\rbrack + Ν_{1}^{0}\sum_{j = 1}^{n}\frac{e^{- \beta_{\text{jt}}}}{\prod_{i = 1, \neq j}^{n}\left( \beta_{i} - \beta_{j} \right)} \right\}}$
.

Each calculated partial nuclide density, $Ν_{i}$, computed from a linear
chain, is then summed to obtain the total nuclide inventory of nuclide
$N_{m}$. The differential equation governing the computation of $Ν(t)$
is therefore only coupled to any preceding elements in the sequence
leading to the *i*^th^ element.

The test for significance in CINDER90 involves calculating the passby
quantity, $P_{n}(t)$. The passby of a nuclide is the time-integrated
transmutation of that nuclide for a specified time interval:

$P_{n}(t) = \int_{0}^{t}{Ν_{n}(t)}\beta_{n}\text{dt}$ .

The passby therefore may be thought of as possible progeny of nuclides
generated from a specific isotope.

###  {#section .Style-Heading-3h3-+-Times-New-Roman .unnumbered}

### Collision Density Generation  {#collision-density-generation .Style-Heading-3h3-+-Times-New-Roman}

MCNPX calculates continuous energy-integrated reaction rates for all
isotopes containing transport cross-section information, for the
following reaction rates: (n,gamma), (n,f), (n,2n), (n,3n), (n,alpha)
and (n,proton). CINDER90 must use the MCNPX-calculated 63-group fluxes
to determine the rest of the interaction rates that accumulate in the
transmutation process, as well as determine reaction-rate information
for isotopes not containing cross-section information.

For example, MCNPX currently does not calculate the continuous (n,beta)
reaction rates. CINDER90 must take the 63-group flux calculated by MCNPX
and multiply its inherent 63‑group (n,beta) cross section to determine
the amount of (n,beta) reactions in the system. Furthermore, many
nuclides may be created during the transmutation process that do not
possess transport information in MCNPX for particle tracking. For these
isotopes, a 63-group flux calculated in MCNPX will be matched to a
63-group cross-section set in CINDER90 to determine reaction-rate
information. The energy group structure used for the 63-group set may be
found at the top of the CINDER.dat file. The 63-group cross sections in
CINDER90 were collapsed over a generic spectrum that may or may not be
representative of the system to be analyzed and thus may lead to large
discrepancies in the isotope inventory of daughter products from these
reactions.

The energy integrated total collision rates calculated in MCNPX for use
in the CINDER90 code for depletion are printed at the end of each KCODE
cycle. The units of these reaction rates in MCNPX 2.6.D are
\[collisions/second\] (in MCNPX 2.6.C the units of these reactions were
collisions/(atom-second)\]). Reaction rates are printed only for those
isotopes also used in the transport calculation. The calculated relative
errors of these reaction rates correspond only to the current cycle
calculation and are not the propagated errors of the reaction rates over
the entire depletion calculation.

### The Cross-Section Averaging for Depletion Acceleration Method (CSADA) {#the-cross-section-averaging-for-depletion-acceleration-method-csada .Style-Heading-3h3-+-Times-New-Roman}

The depletion equations use fluxes, nuclide number densities, and cross
sections to determine the time-dependent nuclide inventory. The
simplified one-group consumption equation, without decay, is

> $\frac{\text{dN}(r,t)}{\text{dt}} = - \Phi(r,t) \ast \sigma(r) \ast N(r,t)$
> .

The corresponding solution for nuclide density is

> $N(r,t) = N_{0}(r)e^{- \sigma(r)\int_{t_{1}}^{t_{2}}{\Phi(r,t)\text{dt}}}$
> .

Therefore, the change in nuclide concentration is dependent on the
time-integrated flux. Unfortunately, the time-dependent flux (integrated
to get the time-integrated flux) also is dependent on the nuclide
density, which makes the above equation nonlinear. To make the above
equation linear, an assumption must be made about the time-dependent
flux. MCNPX currently assumes that the flux is constant throughout the
burn step:

> $N(r,t) = N_{0}(r)e^{- \sigma(r)\Phi(r)_{t,\ \text{average}}}$ .

This approximation is true only if the average flux used in the
calculation is the "true average" flux over the burn step, and the
spectral change over the time step is linear.

MCNPX makes an approximation of the average flux behavior by using the
CSADA technique.[^17] This technique involves the following multistep
process:

1.  A burnup calculation is completed in CINDER90 to the half time step
    \[*t*(*i*)*t*(*i*+1/2)\] (Predictor Step).

2.  Fluxes and collision densities are recalculated in a steady-state
    MCNPX calculation at the half-time step.

3.  The recalculated fluxes and collision densities then are used to
    burn over the full time step \[*t*(*i*)*t*(*i*+1)\] (Corrector
    Step).

The fluxes and collision densities recalculated at the half time step
are assumed to be the average fluxes and collision densities encountered
during the entire time step. This approximation is true only if the flux
shape change between the two time steps varies linearly; this technique
is usually an acceptable approximation. Implementing this technique
allows the user to burn a system using fewer burn steps than if no
approximation were made on the average flux behavior.

However, even with this approximation, burning with large time steps
that encounter large flux-shape changes during the time step will lead
to inaccurate calculations. Therefore, the user must use time steps that
are small enough to capture the flux-shape change accurately over time.

### BURN Card Setup {#burn-card-setup .Style-Heading-3h3-+-Times-New-Roman}

The following example explains the setup for a BURN card.

BURN TIME=T~1~,T~2~,T~3~,\...

PFRAC=F~1~,F~2~,F~3~,\...

POWER=P

MAT=M~1~,M~2~,M~3~,\...

OMIT=J~1~,N~1~,I~11~,I~12~,\...,J~2~,N~2~,I~21~,I~22~,\...

AFMIN=A1 A2

MATVOL= V~1~, V~2~, V~3~, \..., V~n~

MATMOD= \...

BOPT=B1,B2,B3,B4 ,

where

> T*~i~* = duration of burn step *i* (days). Default is one time step of
> one day.
>
> F*~i~* = power fraction of each time step. The default for this
> parameter is to assume F*~i~* = 1.0 for each time step if a PFRAC
> keyword is not specified at all.
>
> P = power level (MW). Default is 1.0 MW.
>
> M*~i~* = list of material numbers to include in the burn. The default
> for this parameter is to burn all materials. If a MAT number is
> negative, recoverable energy per fission and neutrons per fission
> (flux normalization parameters) are tallied, however, the material is
> not burned. A fatal error results if every MAT number is negative.
>
> J*~i~* = *i*^th^ material for which to omit nuclides I~*i*1~, I~*i*2~,
> etc. Currently, there is no default for this parameter.
>
> N*~i~*= number of omitted nuclides listed for the *i*^th^ material.
> Currently, there is no default for this parameter.
>
> I~*i*1~, I~*i*2~, \... = 1^st^, 2^nd^, etc. omitted nuclides for the
> *i*^th^ material. Currently, there is no default for this parameter.
>
> A1 = atom fraction minimum below which the atom fraction is set to
> zero. Default is 1.0e-10.
>
> A2 = Depletion chain convergence criteria in CINDER90.Default value is
> 1e-10. Setting this value to a higher number (i.e. 1e-4 instead of
> 1e-10) causes CINDER90 to run faster with poorer accuracy in decay
> chain tracking.
>
> V~i~ = Total volume of all cells \[cm^3^\] containing burn material,
> M*~i~*, on the MAT keyword of the BURN card
>
> B1 = Q value multiplier. Default is 1.0.
>
> B2 = burn table output frequency, ordering, and content flag.
>
> Input Value Output Inventory Ordering

1 High to low, based on mass (Default)

2 High to low, based on activity

3 High to low, based on specific activity

4 Increasing zaid

Positive input values cause output to be printed only at the end of the
entire job. Negative input values cause output to be printed at the end
of each burn step. Three tiers of fission-product content are available.
To specify the content, add zero (default), 10, or 20 to the magnitude
of the B2 input value.

> TIER Fission-product content.
>
> 1 Zr-93, Mo-95, Tc-99m, Ru-101, Xe-131, Xe-134,
>
> Cs-133, Cs-137, Ba-138, Pr-141, Nd-143, Nd-145. (Default)
>
> 2 All incident neutron cross sections contained in the Fp array
> included in
>
> the current (v. 2.5.0) XSDIR.
>
> 3 All isotopes contained in the Fp array.
>
> B3 = Models option
>
> -1 Fatal error if models are used in the problem.
>
> 0 Zeros out the atom fraction of any data using a model. It is
> preferable to determine which isotopes are needed to be zeroed out and
> place them on the omit keyword for the burned material; however, this
> option exists as a simpler alternative to the omit keyword.
>
> 1 Runs with models.

A blank BURN card will run a case for 1 day, at 1 MW, with a
corresponding PFRAC=1.0, burning all materials, using the TIER 1 fission
products, and listing the nuclide output in high-to-low mass (as long as
the isotope generator algorithm does not generate a nuclide in which
there exists no transport cross sections in the XSDIR, which ultimately
would lead to a fatal error).

### Burn Time, Total System Power, and Power Fraction {#burn-time-total-system-power-and-power-fraction .Style-Heading-3h3-+-Times-New-Roman}

The TIME keyword corresponds to the incremental time duration for each
depletion step. Each "T*~i~*" listed in this keyword corresponds to a
time duration (days) in which the system is burned.

For example:

> TIME = 10, 100, 15 .

The system is first burned for 10 days, followed by a 100-day burn,
followed by a 15-day burn, for a total burn of 125 days.

The POWER keyword is the total system power level (in megawatts).
Because this value corresponds to the total recoverable energy from the
system, the value entered on this keyword should correspond to the total
recoverable thermal system power.

For example:

> POWER = 100 .

In this case, the total recoverable thermal system power is assumed to
be 100 MW.

The PFRAC keyword corresponds to the fractional value of total system
power (POWER) in which to burn the system for the equivalent time
duration. The PFRAC option only changes the total magnitude of power
used to normalize the flux, and does not account for possible
temperature changes in an actual power change. For each T*~i~* value
listed on the TIME keyword, a corresponding F*~i~* value listed on the
PFRAC keyword must exist. For each T*~i~* value that does not contain a
corresponding F*~i~* value, F*~i~*=0 for that time step. The exception
is when the PFRAC keyword is not specified at all, and then each
F*~i~*=1 for every time step.

If F*~i~*=0 for a time step, then the following will occur:

1.  A reaction-rate calculation is completed at the beginning of the
    step

2.  A decay from T*~i~* to T~*i*+1~ is completed without a CSADA
    calculation

3.  If it is determined that both T*~i~* to T~*i*+1~ have both F*~i~*=0
    to F~*i*+1~=0 then a reaction-rate calculation is only competed at
    T*~i~*, and at T~*i*+1~ an eigenvalue calculation is completed
    without tallies

For example:

> TIME = 11, 33, 22, 44, 45
>
> PFRAC = 1.0, 0, 0, 0.9, 1.2
>
> POWER = 10

For the first 11 days of system life, the system is burned at 1.0\*10
MWth of the total system power at 10 MWth. For the next 33 days, the
system is only decayed and the power is set to 0 MWth. A reaction-rate
calculation is completed for the 11^th^ day; however, these reaction
rates do not affect the burnup and are used to determine system
parameters at the 11^th^ day. An eigenvalue calculation without
reaction-rate tallying is completed at the 44^th^ day. For the next 22
days, the system is only decayed and the power is set to 0 MWth. For the
next 44 days of system life, the system is burned at 0.9\*10 MWth of the
total system power at 9 MWth. For the final 45 days of system life, the
system is burned at 1.2\*10 MWth of total system power at 12 MWth.

### Flux Normalization Parameters {#flux-normalization-parameters .Style-Heading-3h3-+-Times-New-Roman}

MCNPX generates collision densities for the CINDER90 depletion
calculation. These generated collision densities are normalized per
source neutron. CINDER90 requires a total flux to deplete the system
properly The following flux multiplier transforms the MCNPX normalized
flux into a total flux for the CINDER90 depletion calculation:

> $\varphi_{\text{total}} = \varphi_{\text{MCNPX}} \times \text{Flux}\ \text{Multiplier} \Rightarrow \text{Flux}\ \text{Multiplier} = \frac{\text{Power}\ \text{Level} \times \nu}{Q_{\text{value}} \ast k_{\text{eff}}}$
> .

MCNPX calculates the system-averaged ν and Q value. The power level used
for the flux multiplier calculation is the power entered on the POWER
keyword. The Q value used in the calculation is an estimate of the
recoverable energy per fission event. Currently, MCNPX takes the prompt
recoverable energy per fission (Q-prompt) and multiplies that value by
the constant normalization factor 1.111 that was calculated by dividing
200 MeV by the prompt fission energy release of U-235. The constant
normalization factor 1.111 is an estimate of the delayed fission energy
contribution and capture-gamma energy contribution.

The capture-gamma energy contribution is highly dependent upon system
geometry and therefore the normalization constant may or may not
estimate the actual Q value properly. Underestimating the Q value leads
to an overestimation of the system fluxes and thus, an overestimation of
the system collision densities. Because the equation for nuclide
depletion,

> $\frac{\text{dN}(r,t)}{\text{dt}} \approx - \sum_{i}^{E}{\varphi_{i}(r,t)}\Sigma_{i}(r,t)N_{i}(r,t)$
> ,

is highly dependent on the collision densities, increasing the collision
density leads to an overestimation of the material burnup. In the
current depletion capability, three methods are used to correct this
overestimation:

> 1\. Adjusting the Q value multiplier (B1 value on the BOPT keyword;
> default = 1.0),
>
> 2\. Modifying the total thermal system recoverable energy by adjusting
> the power level entered on the POWER keyword, and
>
> 3\. Altering the system power on the PFRAC keyword.

### Burn Materials {#burn-materials .Style-Heading-3h3-+-Times-New-Roman}

The materials to be burned must be listed on the MAT keyword. Each
"M*~i~*" entry corresponds to the material number listed in data cards
section of the input deck.

For example:

> BURN TIME=100,70
>
> MAT=1,3,4
>
> POWER=1.0
>
> PFRAC=1.0,1.0
>
> BOPT=1.0 -12 1.0
>
> C Material Cards
>
> m1
>
> 8016.60c 4.5854e-2
>
> 92235.60c 1.4456e-4
>
> 92238.60c 1.9939e-2
>
> 94238.60c 1.1467e-4
>
> 94239.60c 1.0285e-3
>
> 94240.60c 7.9657e-4
>
> 94241.60c 3.3997e-4
>
> 94242.60c 5.6388e-4
>
> m2 2004 -1.0
>
> m3 40000.60c -1.0
>
> m4 1001.60c 4.7716e-2
>
> 8016.60c 2.3858e-2
>
> 5010.60c 3.6346e-6
>
> 5011.60c 1.6226e-5
>
> mt4 lwtr.01t

In this example, materials m1, m3, and m4 will be burned.

Burnup is calculated for the entire system of materials listed on the
MAT keyword, as well as for each individual material listed on the MAT
keyword containing a fissile actinide.

NOTE: For negative material numbers, the recoverable energy per fission
and neutrons per fission tallied are then utilized in the power
normalization and the calculation of fission power fractions. Actinide
and non-actinide buildup/depletion information for negative MAT numbers
is not displayed in the output file because the negative MAT numbered
materials are not burned. The global system burnup displayed in print
table 210 is nonphysical when using negative MAT numbers, however, the
individual material burnup listed in the INDIVDUAL MATERIAL BURNUP
section is the expected burnup of the rest of the materials in the
system.

The total system burnup, as well as other important time-dependent
parameters, is listed on the burn table.

For example:

neutronics and burnup data

step duration time power keff flux ave. nu ave. q burnup Source

(days) (days) (MW) (GWd/MTU) (nts/sec)

0 0.000E+00 0.000E+00 1.000E+00 1.15793 4.428E+15 2.878 209.106
0.000E+00 8.591E+00

1 1.000E+02 1.000E+02 1.000E+00 1.00865 5.157E+15 2.900 209.094
5.892E+01 8.658E+00

2 7.000E+01 1.700E+02 1.000E+00 0.98152 5.465E+15 2.920 208.965
1.002E+02 8.722E+00

For each individual material, another burn table is created that lists
the fraction of fission power created by that specific material, as well
as the individual burnup of that material. The power fraction is
calculated for an individual material using the following methodology:

1.  Determine if the material contains an actinide.

2.  If yes, sum the continuous energy fission energy created to obtain
    individual burn material fission energy.

3.  Sum all of the total material fission energy contributions for each
    material that contains an actinide.

4.  Calculate the power fraction as

> $\text{power}\ \text{fraction} = \frac{\left( \text{ΦΣ}_{f}\text{VQ} \right)_{i}}{\sum_{i}^{}\left( \text{ΦΣ}_{f}\text{VQ} \right)_{i}}$
> .

The burnup for each individual material then is calculated using

$\text{Burnup} = \text{Burnup}_{\text{previous}\ \text{step}} + \frac{\text{Power}\ \text{Level}\  \times \ \text{Power}\ \text{Fraction}\  \times \ \text{Time}\  \times \text{PFRAC}}{\text{MTU}}$
.

\[MTU = MTHM (metric tonnes of heavy metal) and is explained further in
the section on Metric Tonnes.\]

For example (corresponding to the BURN and material cards listed above):

Individual Material Burnup

Material #: 1

step duration time power fraction burnup

(days) (days) (GWd/MTU)

0 0.000E+00 0.000E+00 1.000E+00 0.000E+00

1 1.000E+02 1.000E+02 1.000E+00 5.892E+01

2 7.000E+01 1.700E+02 1.000E+00 1.002E+02

Material #: 3

step duration time power fraction burnup

(days) (days) (GWd/MTU)

0 0.000E+00 0.000E+00 0.000E+00 0.000E+00

1 1.000E+02 1.000E+02 0.000E+00 0.000E+00

2 7.000E+01 1.700E+02 0.000E+00 0.000E+00

Material #: 4

step duration time power fraction burnup

(days) (days) (GWd/MTU)

0 0.000E+00 0.000E+00 0.000E+00 0.000E+00

1 1.000E+02 1.000E+02 0.000E+00 0.000E+00

2 7.000E+01 1.700E+02 0.000E+00 0.000E+00

...

In this example, materials 1, 3, and 4 were burned, and only material 1
contained fissionable actinides. The stated power fraction for material
1 is 1.000E+00 because material 1 supplied all of the fission power to
the system.

### 

### Automatic Fission Yield Selection Process {#automatic-fission-yield-selection-process .Style-Heading-3h3-+-Times-New-Roman}

The CINDER90 code offers a thermal, fast, high-energy fission yield for
each fissile isotope contained in the CINDER.dat library file. The
proper fission yield to be used for a specified problem is dependent on
the impinging neutron energy at the interaction site. Because CINDER90
is a deterministic code that uses one-group constants and does not
account for multi-energy behavior, knowledge of the neutron spectrum
must be imported from the steady-state continuous energy calculation.

MCNPX determines which fission yield to use for a specified problem by
calculating the integral fission rate for the defined energy boundaries
(thermal, fast, and high energy), determining which energy range
contains the majority of fissions, and then selecting the appropriate
fission yield corresponding to the energy range containing the majority
of fissions at each time step.

This calculation is completed separately for each burn material.
Therefore, if a specific calculation warrants a thermal fission yield
for one burn material and a fast fission yield for another burn
material, MCNPX will be able to implement a thermal fission yield for
the burn material experiencing a thermal spectrum and a fast fission
yield for the burn material experiencing a fast spectrum. The process is
automatic; thus, users do not have to worry about selecting an
appropriate fission yield that best represents their system because
MCNPX will determine the correct fission yield automatically.

### Metric Tonnes of Uranium (MTU) {#metric-tonnes-of-uranium-mtu .Style-Heading-3h3-+-Times-New-Roman}

MCNPX lists burnup in units of GWD/MTU. The MTU term calculated in MCNPX
is actually the sum of the masses of isotopes containing \>90 protons.
Therefore, thorium and plutonium contribute to the MTU calculation. It
is possible for elements containing \>82 protons to fission; however,
the probability of fission is very low. If a fuel (82 \< Z \< 90) is
analyzed, the burnup must be adjusted to reflect appropriately the
nature of how the burnup calculation is completed.

### Isotope Reactivity Options {#isotope-reactivity-options .Style-Heading-3h3-+-Times-New-Roman}

The OMIT keyword allows the user to run a transport calculation without
including the transport data from a specified isotope. If an omit
keyword is used, then the isotope is omitted from the transport
calculation and omitted from the output file. Reaction rates are still
generated for the isotope by importing a 63-group flux into CINDER90,
matching the 63-group flux calculated from MCNPX to a 63-group
cross-section set inherent within CINDER90, energy integrating the
reaction rates, and then producing a total collision rate for each
collision type tracked.

The OMIT keyword has the following format:
OMIT=J~1~,N~1~,I~11~,I~12~,\...,J~2~,N~2~,I~21~,I~22~,\...

J*~i~* = *i*^th^ material for which to omit nuclides I~*i*1~, I~*i*2~,
etc.

> If J~1~=-1, then the omitted nuclide list is applied to all materials
> and J~2~, J~3~, etc., are not allowed. No default.

N*~i~* = number of omitted nuclides listed for the *i*^th^ material. No
default.

I~*i*1~, I~*i*2~, ...= 1st, 2nd, etc., omitted nuclide for the *i*^th^
material. No default.

The AFMIN keyword allows the user to determine below which mass fraction
an isotope will be excluded from the transport calculation. The A value
of AFMIN keyword signifies the minimum atom fraction for all isotopes in
which isotopes below that atom fraction will have their atom fraction
set to zero. The default is A = 1.0E-10. The B value of AFMIN signifies
the concentration below which CINDER will no longer follow a nuclide
chain. The default is B = 1.0E-10 for burnup (1.0e-4 for delayed
neutrons / gammas.) The B value greatly affrects the speed of CINDER and
should be set to 1.e-4 (less accurate) for short test problems when the
time required for CINDER is comparable to that required in MCNPX
transport.

### Models Option {#models-option .Style-Heading-3h3-+-Times-New-Roman}

The B3 section of the BOPT keyword invokes the models option.
Cross-section models are a heritage of the high energy physics
capabilities of MCNPX. The models are benchmarked for a variety of
problems for neutron energies \>150 MeV. The B3 section of the BOPT
keyword allows the user to disallow the use of models if the
cross-section energy of interest is below the benchmarked value.

For the B3 section of the BOPT keyword, the following options exist:

B3=-1 Fatal error if models are used in the problem.

B3=0 Zeros out the atom fraction of any isotope using a cross-section
model. It is preferable to determine which isotopes are needed to be
omitted and to place them on the OMIT keyword for the burned material.
This option zeroes out the atom fraction thereby sending a zeroed out
reaction rate for further calculation.

B3=1 Runs with models.

### Fission Product Tracking/Output Frequency {#fission-product-trackingoutput-frequency .Style-Heading-3h3-+-Times-New-Roman}

The B2 value on the BOPT keyword corresponds to the selected fission
products used in the MCNPX transport process, as well as the format for
the nuclide concentrations in the output file. MCNPX reports nuclide
concentrations only isotopes that are listed on the material cards,
generated by the isotope generator algorithm, and/or selected from a
fission product tier.

B2 = burn table output frequency, ordering, and content flag.

> Input Value Output Inventory Ordering
>
> 1 High to low, based on mass (default)
>
> 2 High to low, based on activity
>
> 3 High to low, based on specific activity
>
> 4 Increasing zaid

Positive input values cause the output to be printed to the output file
only at end of an entire job. Negative input values cause output at the
end of each burn step.

Three tiers of fission-product content are available. Each tier
corresponds only to those isotopes that are used for particle transport
in MCNPX and the nuclide densities, which are reported in the output
file. To select a specific tier, add zero (default), 10, or 20 to the
magnitude of the B2 input value.

> TIER Fission-Product Content
>
> 1 Zr-93,Mo-95,Tc-99m,Ru-101,Xe-131,Xe-134,
>
> Cs-133,Cs-137,Ba-138,Pr-141,Nd-143,Nd-145. (default)
>
> 2 All Incident Neutron Cross Sections contained in Fp Array included
> in
>
> current (v. 2.5.0) XSDIR

3.  All isotopes contained in Fp Array

The fission product array for MCNPX includes all fission products
available in ENDF VII.0 that have yield information in CINDER90:

31069,31071,32070,32072,32073,32074,32076,33074,33075,34074,34076,34077,34078,34079,

34080,34082,35079,35081,36078,36080,36082,36083,36084,36085,36086,37085,37086,37087,

38084,38086,38087,38088,38089,38090,39088,39089,39090,39091,40090,40091,40092,40093,

40094,40095,40096,41093,41094,41095,41097,42092,42094,42095,42096,42097,42098,42099,

42100,43099,44096,44098,44099,44100,44101,44102,44103,44104,44105,44106,45103,45105,

46102,46104,46105,46106,46107,46108,46110,47107,47109,47111,48106,48108,48110,48111,

48112,48113,48114,48116,49113,49115,50112,50113,50114,50115,50116,50117,50118,50119,

50120,50122,50123,50124,50125,50126,51121,51123,51124,51125,51126,52120,52122,52123,

52124,52125,52126,52128,52130,52132,53127,53129,53130,53131,53132,53133,53134,53135,

54123,54124,54126,54128,54129,54130,54131,54132,54133,54134,54135,54136,55133,55134,

55135,55136,55137,56130,56132,56133,56134,56135,56136,56137,56138,56140,57138,57139,

57140,58136,58138,58139,58140,58141,58142,58143,58144,59141,59142,59143,59145,60142,

60143,60144,60145,60146,60147,60148,60150,61147,61148,61149,61151,62144,62147,62148,

62149,62150,62151,62152,62153,62154,63151,63152,63153,63154,63155,63156,63157,64152,

64153,64154,64155,64156,64157,64158,64160,65159,65160,66156,66158,66160,66161,66162,

66163,66164,67165,68162,68164,68166,68167,68168,68170,69169,

For example:

> BOPT 1.0 -14 1.0 .

In this case, Tier-2 fission products were selected, and the fission
product and actinide concentrations, as well as the burn tables, are
listed at the end of each time step in increasing zaid order with
cross-section models being implemented for isotopes not containing
tabular cross-section data:

-   = list at the end of each time step,

4.  = list isotope concentrations in increasing zaid, and

> 4 + 10 = use Tier-2 fission products.
>
> B3 = 1.0, use cross-section models for isotopes no containing tabular
> data

### The Isotope Generator Algorithm {#the-isotope-generator-algorithm .Style-Heading-3h3-+-Times-New-Roman}

Capturing every decay chain product from every initial parent isotope
for transport in MCNPX would be a very memory intensive process. Also,
although CINDER90 tracks decay and depletion cross-section data for 3400
isotopes, many of these isotopes do not contain useful transport
information for MCNPX. To save computation time and reduce the influx of
unimportant information, if an isotope is specified on an MCNPX material
card, only the immediate daughter products are tracked in MCNPX for
particle transport. CINDER90 still tracks all of the
daughter/granddaughter/great-granddaughter/etc., decay reactions for
3400 isotopes; therefore, the total isotopic concentrations listed in
MCNPX are the true concentrations from the depletion process. However,
the steady-state particle transport model includes only those isotopes
listed on the material cards, selected from a fission product Tier,
and/or produced by the isotope generator algorithm.

The following chart displays the isotopes generated for an isotope that
has a Z \> 4. The location of each generated isotope corresponds to the
position of that isotope as it would appear in the Chart of the
Nuclides:

![](media/image2.png){width="3.2472222222222222in"
height="3.9694444444444446in"}

![](media/image3.png){width="3.3534722222222224in"
height="3.0701388888888888in"}

### Proper Tracking of Entire Decay Chains {#proper-tracking-of-entire-decay-chains .Style-Heading-3h3-+-Times-New-Roman}

Because the isotope generator algorithm captures only the daughter
reactions of the isotopes specified on the material card, the entire
isotope decay chain will not be implemented into the MCNPX transport
model and subsequently will not be tracked in the MCNPX output file.

For MCNPX to track a decay chain member, that isotope must be listed on
the material card at beginning of life (BOL). Because the decay chain
members will not be present at BOL, the decay chain member's zaid is
automatically put on the corresponding Mn material card, with an atom
density of 1E-36. Therefore, the buildup of that specific decay chain
member will be tracked in the MCNPX transport calculation and the
corresponding nuclide mass will be listed in the output file.

### Burnup/depletion with repeated structures {#burnupdepletion-with-repeated-structures .Style-Heading-3h3-+-Times-New-Roman}

Burnup/depletion requires that the volumes of the burn materials be
known in order to compute isotopic masses and fluxes. For burnup regions
without repeated structures, MCNPX will try to calculate a volume and,
if unsuccessful, a fatal error is generated and the user is required to
then specify the material volume using a VOL card. In the case of cells
in a lattice, MCNPX is only capable of successfully accounting for the
volumes of materials if each cell is used only once in the lattice.
Otherwise, if certain cells are repeated in a lattice, MCNPX is unable
to determine the total volume of everywhere the material is repeated.

The MATVOL keyword is used to account for the volume of materials listed
in a repeated structure.

MATVOL = V~1~, V~2~, V~3~, ..., V~n~

V*~i~* = Total volume of all cells \[cm^3^\] containing burn material,
M*~i~*, on the MAT keyword of the BURN card

If the MATVOL keyword is utilized on the BURN card then there must exist
a corresponding MATVOL entry for every entry on the MAT keyword of the
BURN card. If repeated structures are used without a MATVOL keyword,
MCNPX either will not be able to calculate a volume or will incorrectly
calculate the volume, assuming that the total volume for the entire burn
material is equal to the volume stated on the VOL card rather than the
cumulative volume for all repeated cells containing the material.

###  {#section-2 .Style-Heading-3h3-+-Times-New-Roman .unnumbered}

### Time Dependent Concentration Changes: MATMOD keyword {#time-dependent-concentration-changes-matmod-keyword .Style-Heading-3h3-+-Times-New-Roman}

To model real life depletion systems, isotopes may have to be added or
extracted in order to the conditions of the operating strategies. For
example, in a pressurized water reactor, boron must be diluted as fuel
is depleted in order to maintain criticality.

The MATMOD keyword is used to account for manual concentration changes
of particular isotopes of specific materials at certain time steps.

MATMOD= NT TS~1~ NM~1~ MT~1,1~ K~1,1~ $Z_{\text{1,1}}^{1}$
$C_{\text{1,1}}^{1}$ $Z_{\text{1,1}}^{2}$ $C_{\text{1,1}}^{2}$. .
.$Z_{\text{1,1}}^{K_{\text{1,1}}}$ $C_{\text{1,1}}^{K_{\text{1,1}}}$\
MT~1,NM1~ K~1,NM1~ $Z_{\text{1,NM}_{1}}^{1}$ $C_{\text{1,NM}_{1}}^{1}$
$Z_{\text{1,NM}_{1}}^{2}$ $C_{\text{1,NM}_{1}}^{2}$ . . .
$Z_{\text{1,NM}_{1}}^{K_{\text{1,NM}_{1}}}$
$C_{\text{1,NM}_{1}}^{K_{\text{1,NM}_{1}}}$

> TS~NT~ NM~NT~ MT~NT,1~ K~NT,1~ $Z_{\text{NT,1}}^{1}$
> $C_{\text{NT,1}}^{1}$ $Z_{\text{NT,1}}^{2}$ $C_{\text{NT,1}}^{2}$ . .
> . $Z_{\text{NT,1}}^{K_{\text{NT,1}}}$
> $C_{\text{NT,1}}^{K_{\text{NT,1}}}$
>
> MT~NT,NMNT~ K~NT,NMNT~ $Z_{\text{NT,NM}_{\text{NT}}}^{1}$
> $C_{\text{NT,NM}_{\text{NT}}}^{1}$ $Z_{\text{NT,NM}_{\text{NT}}}^{2}$
> $C_{\text{NT,NM}_{\text{NT}}}^{2}$ . . .
> $Z_{\text{NT,NM}_{\text{NT}}}^{K_{\text{NT,NM}_{\text{NT}}}}$
> $C_{\text{NT,NM}_{\text{NT}}}^{K_{\text{NT,NM}_{\text{NT}}}}$

###  {#section-3 .Style-Heading-3h3-+-Times-New-Roman .unnumbered}

> NT = Number of time steps (1 through NT)
>
> TS~NT~ = Time step (1..NT) for which to manually change nuclide
> concentrations of material MT~NT,NMNT\ .~ Enter "1" for 2nd, etc. (If
> positive, apply concentrations discretely at T~i~ and T~i+1/2~. If
> negative, apply at T~i~, and make linear interpolation between T~i~
> and T~i+1~ to determine the concentration at T~i+1/2~. If TS is
> negative at T~i~ and the concentrations of any of the altered isotopes
> at T~i+1~ is equal to the concentration set at T~i~, then the
> concentrations of the altered isotopes will be set to the value at
> T~i~ for T~i~, T~i+1/2~, T~i+1~. At T~i+3/2~ the isotopes will undergo
> a normal depletion and the concentrations will not be set to the value
> at T~i+1~.
>
> NM~NT~ = Number of materials at time step "NT" that incur nuclide
> concentration changes
>
> MT~NT,NMNT~ = NMth material number for which to manually change
> nuclides at time step "NT". Positive value indicates atom/wt. fraction
> and negative value indicates atom/gram densities.
>
> K~NT,NMNT~ = Number of nuclides to manually change for the NMth
> material
>
> $Z_{\text{NT,NM}_{\text{NT}}}^{K_{\text{NT,NM}_{\text{NT}}}}$ = 1st,
> 2nd,.. Kth nuclide of the MT~NT,NMNT~ th material at time step "NT"
> for which a concentration will be specified. List as a ZA value.
>
> $C_{\text{NT,NM}_{\text{NT}}}^{K_{\text{NT,NM}_{\text{NT}}}}$ =
> Concentration for the Kth isotope in material MT~NT,NMNT~ at time step
> "NT". Enter positive values for atom fractions or atom densities, and
> enter a negative value for wt. fractions or gram densities. See sign
> of MT~NT,NMNT~ to specify either fraction or density

NOTE: When using the MATMOD keyword, if a burn material is set to have a
concentration change at T~1~, the atom density of that isotope at T~1/2~
is set to the initial value specified at T~0~. This is only set for the
initial midpoint time step, the rest of the calculation will follow the
procedure mentioned above.

###  {#section-4 .Style-Heading-3h3-+-Times-New-Roman .unnumbered}

### Metastable Isotope Representation {#metastable-isotope-representation .Style-Heading-3h3-+-Times-New-Roman}

A convention for naming metastable isotopes in the XSDIR cross-section
library file for use in MCNPX has been determined. In the past, users
created their own naming convention for metastable isotopes to be used
in MCNPX, and as long as a tabular cross-section file was referenced in
the XSDIR for these types of isotopes, any naming convention could be
accepted \[That is, to represent Ag-110m, ZA=47210, Z=47 and
A=110+100\*(metastable state)\]. However, because MCNPX is linked to the
CINDER90 code which uses a different naming convention than MCNPX, an
MCNPX standard convention for naming metastable isotopes is required.
The identification of metastable isotopes, ZA, uses the following
equation:

A\' = (A+300) + (m\*100)

m=1,2,3,4

Example:

Ag-110m = 47510 47510 = 47110 + 1st metastable

MCNPX will convert the above naming convention to the naming convention
needed within CINDER90.

###  {#section-5 .Style-Heading-3h3-+-Times-New-Roman .unnumbered}

### Examples  {#examples .Style-Heading-3h3-+-Times-New-Roman}

The following example explains the input setup for the burn card:

> BURN TIME=15.0,30.0,30.0 MAT=3,4 POWER=2.0
>
> OMIT=3,3,8017,92234,92239,4,1,92234
>
> BOPT=1.0 -11

This card specifies a power level of 2 MW, with time steps of 15 days,
30 days, and 30 days, for a total of 75 days. Materials 3 and 4 are
included in the burn with isotopes 8017, 92234, and 92239 excluded from
material 3 and isotope 92234 excluded from material 4. Output will be
produced at the end of each burn step and ordered by decreasing mass,
and Tier-2 fission products will be treated.

Print Tables 40 and 50 are repeated in the output file for each time
step, giving the updated atom fractions and densities. Print Table 55
provides the burnup results at the end of each time step.

This next example explains the necessary keyword implementation for
burning a repeated structure while also utilizing manual concentration
changes at specific time steps. This example models a 4 X 4 fuel pin
array

...

1 1 6.87812e-2 -1 u=2 imp:n=1 vol=192.287 \$ fuel

3 2 4.5854e-2 1 -2 u=2 imp:n=1 vol=66.43 \$ clad

4 3 7.1594e-2 2 u=2 imp:n=1 vol=370.82 \$ water

6 4 6.87812e-2 -1 u=3 imp:n=1 vol=192.287 \$ fuel

7 5 4.5854e-2 1 -2 u=3 imp:n=1 vol=66.43 \$ clad

8 6 7.1594e-2 2 u=3 imp:n=1 vol=370.82 \$ water

10 0 -3 4 -5 6 u=1 imp:n=1 lat=1 fill=0:1 0:1 0:0

2 3

2 3

\...

\...

BURN TIME=50,10,500

MAT= 1 4

POWER= 1.0

PFRAC= 1.0 0 0.2

OMIT= 1,8,6014,7016,8018,9018,90234,91232,95240,95244

4,8,6014,7016,8018,9018,90234,91232,95240,95244

BOPT= 1.0, -4

AFMIN= 1e-32

MATVOL= 384.57 384.57

MATMOD= 2

1

1 -4 1 94238 1e-6

2

2 -1 2 94238 1e-6 94241 1e-6

-4 1 94238 1e-6

\...

The following example utilizes a lattice containing universes 2 and 3,
which are both repeated twice in the lattice. Universe 2 is comprised of
cells 1, 3, and 4, where cell 1 contains material 1, and universe 3 is
comprised of cells 6, 7, and 8, where cell 6 contains material 4. The
MAT keyword specifies that both materials 1 and 4 will be burned. The
combination of the TIME, POWER, and PFRAC keywords specify that these
materials will be burned first for 50 days at 100% of 1MW, then decayed
for 10 days, and then finally burned for 500 days at 20% of 1 MW.

The BOPT keyword specifies that the following options will be invoked:
Q-value multiplier = 1.0, tier 1 fission products, output ordered by
zaid, the output is printed at the end of each KCODE run and only
tabular transport cross sections are utilized. Because tabular transport
cross sections do not exist for every isotope generated, an OMIT keyword
is required in order to omit these isotopes from the transport process.
The transmutation of these isotopes is accounted for by sending a
63-group flux from MCNPX to be matched to a 63-group cross-section set
within CINDER90 which will be energy integrated to determine a total
collision rate. The OMIT keyword in the example omits 8 isotopes from
material 1 and 8 isotopes from material 4. The AFMIN keyword states that
only isotopes possessing an atom fraction below 1e-32 will be omitted
from the transport calculation.

Since repeated structures are utilized in the example, a MATVOL keyword
is required in order to calculate the track length estimated reaction
rates in each repeated structure. In this example, because material 1
and 4 are repeated twice and each material possesses a volume of
192.287, MATVOL keyword entries of 384.57 (192.287\*2) were required for
each material being burned.

A MATMOD keyword is used in order to manually change the concentration
of certain isotopes at specified time steps. In this example, manual
isotope concentration changes are to be completed at 2 time steps. At
time step 1, material 4 will have the atom density of 1 isotope changed:
94238 will be set to 1e-6 atoms/b-cm. At time step 2, material 1 will
have the atom densities of 2 isotopes changed: material 1 will have
isotope 94238 changed to 1e-6 atoms/b-cm and isotope 94241 will be
changed to 1e-6 atoms/b-cm, material 4 will have the atom density of 1
isotope changed: 94238 will be set to 1e-6 atoms/b-cm.

## Heavy Ion Transport

MCNPX can transport heavy ions,[^18]^,^[^19] such as iron, lead, and
gold, above 5 MeV.

### Input {#input .Style-Heading-3h3-+-Times-New-Roman}

To transport heavy ions, add the particle type "#" on the MODE card. The
particle-type symbol "#" is used to represent heavy ions on nearly all
MCNPX input cards where particle types are designated. The "#"
represents all possible heavy ion types (basically any ion that is not
one of the light ion types in MCNPX which are deuterons, tritons, He-3
and alpha particles). Although the '#' is generic to all heavy ions, the
individual heavy ions are tracked by their appropriate Z (charge) and A
(mass number). The user cannot choose to transport any
[particular]{.underline} heavy ions (other than specific source
particles) although tallies can be made for specific ions.

MCNPX Particles

  ------- --------------- ----------- ------------ ------------ --------------
  IPT\*   Name of         Symbol      Mass\        Low Kinetic  Mean Lifetime\
          Particle                    (MeV)        Energy       (seconds)
                                                   Cutoff\      
                                                   (MeV)        

  35      heavy ion       \#          varies       5.0          Huge
  ------- --------------- ----------- ------------ ------------ --------------

The "#" may be used wherever a normal particle type is called for. If
placed on the MODE card with other particles types, heavy ion transport
is turned on. If placed in a tally such as *F4:#*, a track length tally
of the heavy ions will be printed in the output. The "#" may also be
used in mesh tallies.

To use a heavy ion as a source particle, the ZA identifier is put into
the PAR keyword field of the SDEF card such as SDEF PAR = 6012 which
will start a C-12 ion. Note that the energy is still input as total
energy and not energy/nucleon.

Heavy ions can also be used as a distribution of source particle types.
The specification:

*sdef par = d1*

*si1 L 1 9 3006 26056 92238*

*sp1 1 1 0.1 0.3 0.5*

samples five different source particles: neutron, proton, Li-6, Fe-56,
and U-238 in the relative frequencies given on the SP card. Dependent
distributions can be used to specify different energies for different
heavy ions.

The heavy ions use LAQGSM as the default nuclear cascade/evaporation
model. The LAQGSM model can be used for other particles by setting the
10^th^ entry on the LCA card to 1. There are no ENDF data tables for the
heavy ion reactions, so there is no transition energy between table and
model physics as there is for protons and neutrons.

When running with heavy ions turned on ('#' on the MODE card),
[any]{.underline} residuals that are produced from any model physics
(such as CEM, Bertini, etc.) will be transported even if the source
particle is not a heavy ion. For example, a proton source that is
directed into a target and uses CEM as the model physics will produce
residuals from the nuclear reactions. If the "#" sign is on the MODE
card, these residuals will be banked and transported. Note that the
table physics regime does not normally create residuals, so any
interaction using proton and neutron libraries will not produce
transportable heavy ions.

The MCNPX heavy ion algorithm requires that the list of possible heavy
ions that can be transported is pre-defined. However, the list is quite
large. Most isotopes in the Table of Isotopes (\~2205 isotopes) are
available to be tracked. On the rare occasion when an isotope is created
that is not on this list (e.g., something far from the line of
stability) the ion is stopped immediately and its energy is deposited at
the stopping point.

### Tallies {#tallies .Style-Heading-3h3-+-Times-New-Roman}

The FT RES special-treatments tally option enables creation of user bins
for tallying specific isotopes of heavy ions. The general form is
FT*n*:\<pl\> RES where *n* is the tally number and \<pl\> is the
particle type, #. Inputs to the FT RES option can be made in three ways:

1.  Specifying FT RES with no isotopes listed automatically creates a
    bin for each of the 2205 ion types.

2.  Specifying FT RES *z1 z2* will create user bins for all isotopes
    between the proton numbers z1 and z2.

3.  ZA identifiers can be explicitly listed after the RES keyword for
    each user bin.

For example:

> *F4:# 6\
> FT4 RES 8016 20040 26000 92238*

creates a track length tally in cell 6 and then separately tallies
isotopes 8016, 20040, 26000 and 92238. Specifying the elemental ZAID for
Fe (26000) will lump all Fe isotopes into one bin. The FT RES option
works with type 1, 2, 4 and 6 tallies for heavy ions. For F8 tallies,
the FT RES option still works as a residual tally.

For mesh tallies, type 1 (particle track) and type 3 (energy deposition)
work with heavy ions although there is no capability to separate out
contributions from specific heavy ion species.

### Other Input {#other-input .Style-Heading-3h3-+-Times-New-Roman}

PHYS:# has the input features for a generic charged particle. Note:
Light-ion recoil control still only applies to light ions. There is no
heavy ion recoil for proton elastic scattering events.

SSR, SSW: Surface source reading and writing. The charge and mass for
each heavy ion are stored in the surface source file, WSSA, and will be
read back to reconstruct the proper source distribution.

M: The HSTEP step size parameter applies to all charged particles
(except electrons which use ESTEP) including heavy ions.

### Variance Reduction. {#variance-reduction. .Style-Heading-3h3-+-Times-New-Roman}

Heavy ions, similar to light ions, are able to use any variance
reduction technique that is applicable to charged particles that use
physics models for interactions. Any variance reduction technique used
for heavy ions will apply equally to all heavy ion particles.

Weight windows, Cell importance, SPABI, ESPLT: All work with heavy ions

FCL, EXT: Only apply to neutral particles; not functional with charged
particles and heavy ions.

DD, PD, DXTRAN: Only apply to neutral particles; not functional with
charged particles and heavy ions.

### Changes to PRINT Tables. {#changes-to-print-tables. .Style-Heading-3h3-+-Times-New-Roman}

The stopping powers for the primary or default Heavy Ion are printed
with the normal stopping power tables in Print Table 85. An optional
table, Print Table 87, prints the stopping powers that are generated for
all of the secondary heavy ions. Stopping powers for secondary heavy
ions are only calculated on an elemental, not isotopic basis, so only
the proton number of the heavy ion will determine which table is
printed. Note that all heavy ions specified with a distributed source
will use the secondary stopping power tables. The Z and A identifier for
each table are shown in the particle identity field at the top of the
table.

Print Table 87 does *not* follow the standard default convention of most
other MCNPX print tables because stopping powers for all 100 elements
for each material would result in huge output files. To print table 87
it must be specified specifically on the PRINT card:

PRINT n n 87 n

Where the values of n are other tables desired for printing.

To print all output *including* Print Table 87 the PRINT card is:

PRINT -1 87

The -1 turns off print table 1 (which does not exist) and turn on all
other prints; then 87 turns on print table 87 as well. Thus all tables
and print table 87 will be printed.

PRINT as an execution-line option, PRINT in the Message Block, and a
blank PRINT card in the input will not result in the output of Print
Table 87.

MCNPX Output Tables

  --------------- -------------- ------------------------------------------
  **Table         **Type**       **Table Description**
  Number**                       

  **87**          **optional**   **Secondary heavy ion stopping powers and
                                 straggling**
  --------------- -------------- ------------------------------------------

Changes have also been made to the Print Table 110 (the first 50
particle histories) so that when a distributed source of heavy ions is
requested, the Z and A identifiers for the sampled source particle are
printed in the source particle field.

### Limitations {#limitations .Style-Heading-3h3-+-Times-New-Roman}

The heavy ion capability has some restrictions when used with other
features in MCNPX. No heavy ion transport information is written to the
HISTP file (aside from the usual recoils from which the heavy ions are
started). The PTRAC file contains the heavy ion particles and their
track information but the individual heavy ion identity (Z and A) are
**not** recorded.

The summary tables contain all the heavy ion information summed
together; there is no way to break out individual heavy ion
contributions for these tables.

## LAQGSM Physics.

The Los Alamos Quark-Gluon String Model v. 3.01 in MCNPX[^20] contains
elements of the CEM INC physics model (see following section) and GEM
evaporation model but is intended to handle a wider variety of particles
and energies. LAQGSM can simulate the interactions of A1+A2
interactions, and well as nucleons (protons and neutrons) and gammas. By
default, LAQGSM handles all the heavy-ion interactions as well as
light-ion interactions above 1 GeV/nucleon (below this, ISABEL is still
the default model). However, setting the 10^th^ entry (*ilaq*) on the
LCA card to 1, redirects all light ions to LAQGSM. Neutrons and protons
are also sent to LAQGSM (instead of FLUKA) when their energies are above
the transition energy.

LAQGSM physics is controlled by the 10^th^ LCA input parameter, *ilaq*.

+----------------+-----------------------------------------------------+
| **Input        | **Description**                                     |
| Parameter**    |                                                     |
+----------------+-----------------------------------------------------+
| ***ilaq***     | > **Choose light ion and nucleon physics modules.** |
|                | >                                                   |
|                | > **If ilaq=0, use LAQGSM for light-ion             |
|                | > interactions only above 940 MeV/nucleon. ISABEL   |
|                | > will handle light-ion interactions below this     |
|                | > energy. Use FLUKA for protons and neutron         |
|                | > interactions above the energy cutoff specified by |
|                | > flenb1 and flenb2 on LCB card. LAQGSM will be     |
|                | > used for heavy ion interactions at all energies   |
|                | > (DEFAULT)**                                       |
|                | >                                                   |
|                | > **if ilaq=1, use LAQGSM for all light-ion         |
|                | > interactions as well as all heavy-ion             |
|                | > interactions. LAQGSM also replaces FLUKA for      |
|                | > high-energy proton and neutron reactions.**       |
+----------------+-----------------------------------------------------+

LAQGSM requires two data files (atab.dat and channel1.tab) in addition
to 3 of the standard CEM data files (shell.tbl, gamman.tbl and
mass.tbl). Note that LAQGSM is used even when the *ilaq* variable is not
1 to transport light ions that otherwise would not be transported.

## CEM03 Upgrade

The CEM2K physics package has been replaced with the CEM03 physics
package.[^21] The MCNPX user interface is unchanged: if the 9^th^ entry
on the LCA card is 1, then CEM03 will be used.

CEM03.01[^22] is a version of the Cascade-Exciton Model (CEM). It is a
completely new, updated, and modified version, not just an incremental
improvement, in comparison to its predecessors, CEM2k+GEM2,[^23]^,^[^24]
CEM2k,[^25] CEM98,[^26] CEM97,[^27] and CEM95.[^28]

CEM03.01 describes reactions induced by nucleons, pions, and photons as
a three-stage process: IntraNuclear Cascade (INC), followed by
preequilibrium emission of particles during the deexcitation of the
excited residual nuclei formed during the INC, followed by evaporation
of particles from or fission of the compound nuclei. If the excited
residual nucleus produced after the INC has a mass number A \< 13,
CEM03.01 uses a recently updated and improved version of the Fermi
Breakup model to calculate its decay instead of considering a
preequilibrium stage followed by evaporation from compound nuclei.
CEM03.01 considers also coalescence of complex particles up to ^4^He
from energetic nucleons emitted during the INC.

The main improvements of CEM03.01 in comparison with its predecessors
are described in the following sections.

### Intra Nuclear Cascade (INC) {#intra-nuclear-cascade-inc .Style-Heading-3h3-+-Times-New-Roman}

We developed new approximations to describe more accurately experimental
elementary energy and angular distributions of secondary particles from
hadron-hadron and photon-hadron interactions using available data and
approximations published by other authors. We have normalized
photonuclear reactions to detailed systematics developed by
others.[^29]^,^[^30] The condition for transition from the INC stage of
a reaction to preequilibrium was changed; on the whole, the INC stage in
CEM03.01 is longer, whereas the preequilibrium stage is shorter in
comparison to previous versions. The algorithms of many INC routines
were changed and almost all INC routines were rewritten, speeding up the
MCNPX INCL algorithm significantly. Also, some preexisting bugs in the
INC were fixed.

### Preequilibrium (PREC) {#preequilibrium-prec .Style-Heading-3h3-+-Times-New-Roman}

The condition for transition from the preequilibrium stage of a reaction
to evaporation/fission was changed; on the whole, the preequilibrium
stage in CEM03.01 is shorter, whereas the evaporation stage is longer in
comparison to previous versions. The widths for complex-particle
emission were changed by fitting the probability of several excitons to
"coalesce" into a complex particle that may be emitted during the
preequilibrium stage to available experimental data on reactions induced
by protons and neutrons.[^31] Algorithms of many PREC routines were
changed and almost all PREC routines were rewritten, speeding up the
code significantly. Some bugs were discovered and fixed.

### Evaporation and/or Fission {#evaporation-andor-fission .Style-Heading-3h3-+-Times-New-Roman}

The evaporation and fission stages of reactions are calculated by
CEM03.01 with an updated and improved version of the Generalized
Evaporation Model code GEM2[^32] by Furihata, which considers
evaporation of up to 66 types of different particles and light fragments
(up to ^28^Mg). In comparison to GEM2, the calculation of fission widths
in CEM03.01 was changed by fitting the ratio of the level-density
parameters at the saddle point to that in the evaporation channel to the
systematics of proton-induced fission cross sections by
Prokofiev.[^33]^,^[^34] Several routines by Furihata from GEM2 were
slightly modified in CEM03.01 and some bugs found in GEM2 were fixed.

### Coalescence {#coalescence .Style-Heading-3h3-+-Times-New-Roman}

The coalescence model implemented in CEM is improved.[^35] In comparison
with its initial version, we have changed the coalescence momentum radii
p_0 for the various light composite particles up to ^4^He by fitting
them to measured data on nucleon-induced reactions at energies up to 1
GeV.

### Fermi Breakup {#fermi-breakup .Style-Heading-3h3-+-Times-New-Roman}

The Fermi Breakup model used in CEM is improved.[^36]^,^[^37] In
comparison to its initial version, we have modified the model to decay
some unstable light fragments that could be produced by the original
Fermi Breakup model. Several bugs observed in the original version
\[12\] were fixed.

### Additional Notes {#additional-notes .Style-Heading-3h3-+-Times-New-Roman}

Almost all routines of CEM03.01 were rewritten and many algorithms were
changed so that the code is much faster now than all of its
predecessors. In comparison to its predecessors, the output of CEM03.01
was significantly extended, allowing us to calculate with the standard
CEM03.01 many additional characteristics of nuclear reactions.

CEM03 is more accurate but somewhat slower than the CEM2K it replaces.
CEM problems no longer track -- that is, the results from CEM2K do not
match the results of CEM03 for the same input decks. Problems using
model physics and having photonuclear reactions also no longer track.

## Long File Names

MCNPX file names may now be 40 characters long. The execute line message
may now be 240 characters long. File names also may be paths.

For example:

> MCNPX *name = ..\\..\\destination_output_files. inp = ..\\input_file*

In this example, the input file is named *input_file* and is located in
the next directory up.

***MDATA Files***

Mesh tally MDATA files now use the *name* option. In the above example,
the MDATA file would be named *destination_output_files.d* and would be
put in the directory ..\\..\\ .

***Implementation Details***

The 40-character length is set by the parameter *lfilen = 40* in
*module_global_parameters, GLOBAL1_zc.F .* Thus, longer file names
should be possible but have not been tested.

In some cases, warnings and fatal-error messages will give only the
first eight characters of a file name because of format constraints. In
most cases, the rewriting of all formats containing file names result in
cleaner output. The full file name usually is allowed. Short file names
no longer are followed by blanks to achieve the old eight-character file
name length.

## Terminate Tallies at Desired Precision

A new input card, "STOP", has been added to enable stopping of
calculations when a desired tally precision is reached:

STOP NPS n CTME m Fk e .

This card will cause MCNPX to stop after n histories, after m minutes,
or when the tally fluctuation chart bin of tally k has a relative error
less than e.

MCNPX will stop at the first met criteria.

For radiography problems, the second NPS card entry, n, may be provided
to specify how many histories are used for direct radiography tally
contributions:

STOP NPS n m .

For multitasking calculations, CTME will be checked only at rendezvous
points, where all tasks rendezvous for tally fluctuations and other
activities.

The tally precision stop will be checked only at rendezvous points for
the tally bin of the tally fluctuation charts. Thus, the calculation
usually will proceed for a short time after the desired error is
achieved. Thus,

STOP F111 .05

will cause MCNPX to stop at the first rendezvous for which the relative
error is less than 0.05. That is, MCNPX may stop at error = 0.048 or
other value slightly less than 0.05.

## Spherical Mesh Weight Windows

The mesh-based weight window and the weight-window generator are now
available in spherical geometry (X-3:JSH-2006-68). The spherical mesh
geometry may be thought of as an orange where the theta (θ) azimuthal
angles are the bounds between slices. Or the spherical mesh geometry may
be thought of as a globe where the phi (φ) polar angles are latitude and
the theta (θ) azimuthal angles are longitude. The north pole is at φ = 0
degrees; the south pole is at φ = 180 degrees; London is at θ = 0
degrees and all the way around the globe at θ = 360 degrees.

For problems that are best described in the R-φ-θ spherical geometry
coordinate system, spherical mesh weight windows can offer variance
reduction speedups of orders of magnitude compared to less suitable
rectangular and cylindrical meshes. A speedup of six orders of magnitude
over analog has been observed by using spherical mesh weight windows.
Note that rectangular mesh windows are about 30% slower than cell-based
windows and cylindrical and spherical mesh windows run about 60% slower
than cell-based windows. Problems with spherical geometry that may
benefit from spherical mesh weight windows include spherical detectors,
unknown materials hidden in spherical geometries, distant sources and
detectors in air, spherical satellite geometries, modeling planets, and
more.

### User Interface {#user-interface .Style-Heading-3h3-+-Times-New-Roman}

*Mesh Specification*

The weight-window generator mesh is specified with the MESH card. The
"GEOM" keyword now has the following possible entries:

XYZ or REC Cartesian coordinate rectangular mesh (unchanged)

RZT or CYL R-Z-θ cylindrical mesh (unchanged)

RPT or SPH R-φ-θ spherical mesh (new)

The RPT and SPH entries are new. The phi (φ) polar mesh bounds are
specified with the JMESH keyword. As with the cylindrical mesh, the
theta (θ) azimuthal mesh bounds are specified with the KMESH keyword.
Also consistent with the cylindrical mesh, the lower radial and angular
mesh bounds (R-φ-θ) are all implicitly zero.

*Example:*

Mesh geom sph origin 7 -9 -12 ref -23 39 -10 axs .4 -.5 .2 vec .1 -.2
-.7

imesh 60. iints 3

jmesh .1 .35 .5 jints 1 1 1

kmesh .2 .85 1 kints 1 1 1

In this example a spherical mesh is located at origin=7 -9 -12. The
reference location in the XYZ coordinate system of the problem is at
ref=-23 39 -10. The weight-window generator lower weight-window bound
will be W for whatever mesh cell contains this location, where W is half
the source weight by default or whatever is the 3^rd^ entry on the WWG
weight-window generator card. The polar (φ) axis of the spherical mesh
(as in latitude on the globe) is axs=.4 ‑.5 .2, which MCNPX will
normalize to a unit vector. The azimuthal planes (as in longitude on a
globe, or orange slices, or cylindrical mesh theta bins) are measured
relative to the azimuthal vector, theta (θ), vec=.1 -.2 -.7. VEC will
also be renormalized by MCNPX and must be orthogonal to φ. The radial
mesh bins have 3 interpolates between 0 and 60---that is, the mesh
bounds are at 0, 20, 30, and 60 cm. The polar angles (φ) are at .1, .35,
and .5 revolutions from the axs vector. The azimuthal angles (θ) are at
.2, .85. and 1 revolutions from the vec vector. Note that 0 ≤ φ ≤ .5 and
0 ≤ θ ≤ 1 are always required.

The polar and azimuthal angles may also be specified in radians or
degrees. For example, the JMESH and KMESH entries for the above example
in degrees would be:

jmesh 36 126 180 jints 1 1 1

kmesh 72 306 360 kints 1 1 1

### Plotting {#plotting .Style-Heading-3h3-+-Times-New-Roman}

The interface for geometry plots of the spherical mesh window boundaries
is the same as for cylindrical mesh boundaries. Geometry plots are
colored by the input weight windows from the WWINP file by selecting WWN
as the color option. The weight window and weight-window generator mesh
boundaries are plotted by clicking "CellLine" to get to the WWG or WW
options. The command-prompt plot commands would be "LA 0 1 wwn COLOR on
LA 0 0" to color by input windows. The commands "MESH 2" and "MESH 4"
plot the generator mesh from the MESH card and weight-window mesh from
the WWINP file.

Figures 1--3 illustrate three views of a geometry divided into cells
coincident with the spherical mesh, so that each color represents a
specific geometry and mesh cell in each view. Figures 2 and 3, drawn
through the mesh sphere origin and normal and orthogonal to the polar
axis, give the intuitive polar (Figure 2) and azimuthal (Figure 3)
views. However, skewed, off-center plots of spherical meshes with skew
axes give very non-intuitive plots as illustrated in Figure 1.

The most challenging part of the spherical mesh weight-window capability
was the plotting because the spherical mesh may be in one skew
coordinate system and the plot frame in another skew coordinate system
which has an "s,t" auxiliary coordinate system. In the most complicated
case, equations with hyperbolic sinh and cosh functions must be
simultaneously solved with trigonometric equations with sin and cos
functions. Iterative solutions were used in these special cases out of
desperation. And even these iterative solutions fail to draw mesh
boundaries correctly in some instances when both the plot extents are
unequal and the geometries are skew creating hyperbolas and intersecting
ellipses. Further, polar mesh boundaries looking down into the polar
angle sometimes plot incorrect ellipses when the ellipse is partially
(but not mostly) out of bounding radial sphere. Note that cylindrical
geometries are considerably simpler to plot because they never have to
plot hyperbolas and the ellipses, if any, do not intersect each other.

![](media/image4.png){width="7.1in" height="7.1in"}

**Figure 1**. Plot view: basis .84514 -.0507093 .169031 .408248 .408248
-.816497, or = -3 -9 -20, ex 100. Spherical mesh orientation: origin 7
-9 -12, axs .4 -.5 .2, vec .1 -.2 -.7.

![](media/image5.png){width="7.1in" height="7.1in"}

**Figure 2.** Plot view orthogonal to polar axis showing polar bins
jmesh = 36 and 126 degrees. The polar axis (0 degrees) is to the right
and is not plotted.

![](media/image6.png){width="7.1in" height="7.1in"}

**Figure 3.** View normal to polar axis at origin showing azimuthal
planes at kmesh = 72, 306, and 360 degrees. The azimuthal vector, vec,
is to the right (360 degree plane).

## Energy-Time Weight Windows

MCNPX can now generate and utilize weight windows that are both energy-
and time-dependent. Previously, MCNP/X could do energy-dependent or
time-dependent windows, but not together. The new capability is fully
backwards compatible, including the 8^th^ WWG entry and 6^th^ WWP entry,
which convert energy-dependent windows to time-dependent windows.
However, time-dependent windows may be specified directly by using the
new WWT and WWGT input cards. These new input cards are directly
analogous to the WWE and WWGE cards for energy-dependent weight windows
and are the following:

WWT:p t~1~ t~2~ t~3~ ...

WWGT:p t~1~ t~2~ t~3~ ...

Where p is the particle type, and the t~N~ values are times in shakes.

The WWNn:p cards are numbered as before, where n=1,NE for NE energy
groups or n=1,NT for NT time groups. Where there are both time and
energy groups, then n=1,NE for time group 1; n=NE+1,2\*NE for time group
2; n=2\*NE+1,3\*NE for time group 3; and so forth.

If a time or energy is above the upper time or energy bin range it will
be treated as if it were in the top time or energy bin. This has always
been the case in all MCNP/X versions.

### Cell-Based Example {#cell-based-example .Style-Heading-3h3-+-Times-New-Roman}

The following generates a 2-energy group, 3-time group weight window. In
particular, the WWG card would generate weight windows to optimize
tally 111. The lowest weight-window bound in any energy-time bin group
in cell 45 (the reference cell) would be .25. The WWGE and WWGT cards
would generate 2 energy bins and 3 time bins for photons.

> WWG 111 45 .25
>
> WWGE:p 1 100
>
> WWGT:p 1 100 1.e20

The cell-based windows generated from the above cards would look like:

> WWP:p 5 3 5
>
> WWE:p 1 100
>
> WWT:p 1 100 1.e20
>
> WWN1:p W W W \... \$ energy 1 time 1
>
> WWN2:p W W W \... \$ energy 2 time 1
>
> WWN3:p W W W \... \$ energy 1 time 2
>
> WWN4:p W W W \... \$ energy 2 time 2
>
> WWN5:p W W W \... \$ energy 1 time 3
>
> WWN6:p W W W \... \$ energy 2 time 3

### Mesh-Based Example and WWOUT File Changes {#mesh-based-example-and-wwout-file-changes .Style-Heading-3h3-+-Times-New-Roman}

Mesh-based weight windows are generated on the WWOUT file and input is
from the WWINP file. If there are energy or time dependent windows then
a WWONE file is also generated, but its format is unchanged. If the
*name* option is used on the execute line, the WWOUT and WWONE file
names end in *e* and *1*, respectively. The WWOUT file format is changed
if time or energy-time windows are used. But it is backwards compatible
with upgrades.

The changes are marked in boldface in the following example. The 2^nd^
entry on the header (iv in subroutine WWFILE), which formerly was always
1, can now be 2 if time-dependent windows are present. When
time-dependent windows are present (iv=2) then the next line of integers
is the number of time bins for each particle type. This is followed as
always by the line of integers which is the number of energy bins for
each particle type. This line of energy bins per particle has always
been present regardless of how many energy bins are used. Further, only
for particle types with time-dependent windows, there is a line
preceding the list of energy bin upper bounds that lists the time bin
upper bounds. In this example it is 0.10000E+07 0.10000E+13. This is
followed by the always present list of upper energy bounds, in this case
100.00. For example:

1 **2** 2 16

**2 1**

1 1

20.000 12.000 1.0000 0.0000 0.0000 0.0000

2.0000 2.0000 1.0000 101.00 0.0000 0.0000

0.0000 101.00 0.0000 3.0000

0.0000 4.0000 3.0100 1.0000 16.000 101.00

1.0000

0.0000 4.0000 0.25000 1.0000 8.0000 0.50000

1.0000

0.0000 1.0000 1.0000 1.0000

**0.10000E+07 0.10000E+13**

100.00

0.20290E-04 0.21675E-04 0.26245E-04 0.35285E-04 0.17419E-03 0.48374E-02

## Charged Ions from Neutron Capture in Table Range

MCNPX can now produce light ions from neutron capture reactions in
certain isotopes in the table energy range when such data are not
available in the libraries. The optional "neutron capture ion algorithm"
(NCIA) is called for neutron capture in He-3, Li-6, and B-10 producing
protons, tritons, deuterons, and alphas according to the following
table:

Table 1. Available Reactions

  ------------------------------- ---------------------------------------
  Isotope                         Reactions

  He-3 (2003)                     n(He-3,h)t\
                                  n(He-3,d)d

  Li-6 (3006)                     n(Li-6,t)a

  B-10 (5010)                     n(B-10,g)a
  ------------------------------- ---------------------------------------

The optional NCIA would not be needed if the nuclear data libraries were
complete and contained these data. If these data are in the data tables
then the library physics produces the secondary ions instead of the
NCIA.

### User Interface {#user-interface-1 .Style-Heading-3h3-+-Times-New-Roman}

The NCIA capability is controlled by the PHYS:N card 7^th^ entry which
also controls light-ion recoil:

PHYS:N 6J L

where:

L = 3 NCIA on: create charged ions from neutron capture in the table
energy range if the library does not have secondary particle production
data for these ions. No light-ion recoil.

0 \<L ≤1 Light ion recoil with biasing factor L (produced L elastic
scatter recoil

ions per incident neutron.)

1 \<L ≤2 Light ion recoil with biasing factor L-1 and NCIA on.

Light ion recoil will only occur for neutrons and protons colliding with
H, D, T, He-3 and He-4. Neutron capture ions (NCIA) will only occur for
neutrons colliding with He-3, Li-6, and B-10 and only if the ion
production cross sections are unavailable in the data tables.

The 7^th^ PHYS:N or PHYS:H entry is ignored for collisions in the
physics model energy range because the models produce the required
elastic and inelastic ions automatically.

The default is L = 0 : no light ion elastic recoil and no neutron
capture ions.

### Diagnostics {#diagnostics .Style-Heading-3h3-+-Times-New-Roman}

The diagnostic indicating the NCIA has been used is in Print Table 100
of the OUTP file.

For example, when using He-3 (2003) as a material and specifying h, d,
and t on the mode card with NCIA turned on, Print Table 100 will show:

particle-production data for ipt= 34 being used from 2003.66c

no particle-production data for ipt= 9 from 2003.66c

using aceion for particle production for ipt= 9 in zaid 2003

no particle-production data for ipt= 31 from 2003.66c

using aceion for particle production for ipt= 31 in zaid 2003

no particle-production data for ipt= 32 from 2003.66c

using aceion for particle production for ipt= 32 in zaid 2003

2003.66c 5535 2-he-3 at 293.6K from endf-vi.1 njoy99.50

In this example, ipt=34 (alpha) production data is found. No data is
found for ipts 9 (protons), 31 (deuterium) and 32 (tritium).

### Important Considerations {#important-considerations .Style-Heading-3h3-+-Times-New-Roman}

*Energy Cutoff:* The energies of the light ions are often very low,
especially for thermal neutron captures. To enable transport of these
secondaries, use the CUT card to reduce the low energy cutoff.

*Secondary Production Correlations:* Unlike most secondary particle
production in the table region, NCIA particles are coupled. Capture in
He-3 produces a triton and proton. If the data library already had
proton production, the library would be used for the proton but the
tritons would be produced by NCIA. The NCIA correlation between the
triton and proton would be lost. Note that if the triton and proton are
both produced by the library there is no correlation, either.

*Heating Tallies:* Because neutron energy deposition is physically
mediated in most cases by the secondary particle emission, NCIA may be
inconsistent for heating calculations. Neutron heating is done with
kerma factors (heating numbers) whereas heating from the charged
secondaries is done at collisions. For +f6 tallies and type 3 mesh
tallies the charged ion heating is subtracted from the neutron heating
and thus is counted only once but inconsistently. For F6:n and
F6:h,d,t,a tallies the heating is counted once for each particle type.
If heating tallies are done in cells where charged ions are produced,
either turn off NCIA or remove the light ions from the MODE card.

## Delayed-Gamma Emission.

*Warning! The new delayed-gamma emission capability and delayed-neutron
capability is preliminary and not covered by the MCNPX cash awards
program. It has been included in MCNPX because of user and sponsor
demand.*

The radioactive decay of fission products, or residual nuclides excited
by neutron or photonuclear interaction, frequently results in the
emission of gamma/x-rays at times appreciably later than the initiating
event. These photon emissions are referred to here as "delayed gammas."

MCNPX already treats delayed neutrons from fission with both
delayed-neutron model physics and delayed-neutron library physics from
data tables.

MCNPX enables the automated calculation of delayed-gamma signatures
emitted due to (1) the decay of radioactive fission products created by
neutron fission or photofission, or (2) residual nuclides created by
simple multi-particle interactions (SMRs).[^38] The delayed-gamma
capability uses CINDER90, which was written by William B. Wilson,
modified by Holly R. Trellue to disable flux-induced transmutation. The
initial multigroup patch for fission-induced delayed-gamma emission was
developed by Gregg W. McKinney, Holly R. Trellue, and Laurie S. Waters.
Joe W. Durkee developed the modifications to enable line emission for
fission and SMRs.

The delayed-gamma capability has been developed for pulsed or low-flux
modeling. Thus, CINDER90 nuclear transmutation is limited to decay
chains only---neutron-induced transmutation is inactive. In contrast to
the KCODE isotopic burn capability, the delayed-gamma emission modeling
does not include neutron- (or photon-) induced isotopic transmutation by
CINDER90. However, SMR treatment for selected reactions of nuclides
present on the MCNPX material cards is treated. Execution of the
delayed-gamma capability is limited to fixed sources (SDEF) and surface
sources (SSW, SSR).

Additional documentation may be found in LA-UR-07-6302.[^39]

### The Products of Fission: Residual Nuclides and Radiation {#the-products-of-fission-residual-nuclides-and-radiation .Style-Heading-3h3-+-Times-New-Roman}

The relative amounts of fission products vary with the fissioning
isotope and the particle (i.e., neutron, photon, etc.) inducing the
fission. To illustrate this behavior, Fig. 4 shows CINDER90 ^235^U
fission-yield data for thermal and high energy neutron-induced fission.

![](media/image7.wmf){width="4.304166666666666in"
height="2.782638888888889in"}

> **Figure 4.** Thermal and fission-spectrum yield curves for ^235^U.

For sub-20-MeV neutrons, fission-product sampling is done for thermal,
fission, and 14‑MeV neutrons and isotopes of uranium, plutonium,
thorium, americium, californium, curium, einsteinium, fermium, and
neptunium.[^40] At high energies (E**n**\>20 MeV), LAHET[^41] is used to
produce a list of residual nuclides.

Many fission products are unstable. As part of their decay process,
photons are emitted. The delayed-photon emissions occur with intensities
and at energies that are unique to each radionuclide. As examples, Fig.
5 shows the 25-group and line emission spectra for ^139^Xe and ^94^Sr.

![](media/image8.wmf){width="5.125in" height="3.439583333333333in"}

> **Figure 5.** 25-group and line emission photon spectra for ^139^Xe
> and ^94^Sr.

### Decay Chains and Emission Sampling {#decay-chains-and-emission-sampling .Style-Heading-3h3-+-Times-New-Roman}

Not only are the fission-products and residual nuclides radioactive
sources, but so too are their decay products. Each contributes to the
delayed signature. Thus, a fission event may have hundreds or thousands
of lines contributing to its signature.

CINDER90 has been integrated into MCNPX to calculate the radioactive
decay-chain nuclide densities as a function of time. The nuclide
densities, decay constants, and particle (neutron, photon) emission
probabilities are used to calculate distributions that are sampled for
particle emission energy and delay time (direction is sampled
isotropically).

Photon emission data are available for 979 nuclides. These data are
comprised of (1) line (discrete) data and (2) continuous data. The
continuous component of the line data was developed using computational
physics models to augment "missing" measured data so as to create an
evaluated dataset whose calculated decay heats agreed with measured
values.[^42] These data are stored in file cindergl.dat. The composition
of the line data is listed in Table 2

Table 2. Cindergl.dat Delayed-Gamma Data Composition

+-----------------------+----------------------+----------------------+
| Composition by Data   |                      |                      |
| Component             |                      |                      |
+-----------------------+----------------------+----------------------+
| Data component        | Quantity             |                      |
+-----------------------+----------------------+----------------------+
| Total                 | 282035               |                      |
+-----------------------+----------------------+----------------------+
| Discrete              | 24199                |                      |
+-----------------------+----------------------+----------------------+
| Continuous            | 257836               |                      |
+-----------------------+----------------------+----------------------+
| ASCII lines           | 747730               |                      |
+-----------------------+----------------------+----------------------+
| Composition by        |                      |                      |
| Nuclide               |                      |                      |
+-----------------------+----------------------+----------------------+
|                       | Nuclides             | Quantity             |
+-----------------------+----------------------+----------------------+
| Discrete Only         | 526 (54%)            | 19821                |
+-----------------------+----------------------+----------------------+
| Continuous Only       | 292 (30%)            | 214293               |
+-----------------------+----------------------+----------------------+
| Discrete and          | 161 (16%)            | 47921 total          |
| Continuous Mix        |                      |                      |
|                       |                      | 4378D,67742C         |
+-----------------------+----------------------+----------------------+

All remaining nuclides, of the 3400 treated by CINDER90, require
treatment using the CINDER.dat 25-group data.

### Simple Multi-Particle Reactions {#simple-multi-particle-reactions .Style-Heading-3h3-+-Times-New-Roman}

The delayed-gamma simulation capability includes the treatment of simple
multi-particle reactions (SMRs).[^43] These are reactions in which only
two to four particles, a residual nucleus, and photons are present in
the final state. The reactions are designated using the ENDF "MT"
identifier. Presently, MCNPX treats eight such reactions, which are
listed in Table 3. Not all SMR types are available for all nuclides in
the MCNPX data library.

Table 3. Available Reactions

  ----------------------------- -----------------------------------------
  ENDF/B-VI MT                  Reactions

  16                            (n,2n)

  17                            (n,3n)

  37                            (n,4n)

  102                           (n,g)

  103                           (n,p)

  104                           (n,d)

  105                           (n,t)

  106                           (n,^3^He)

  107                           (n,alpha)
  ----------------------------- -----------------------------------------

For nuclides (present in MCNPX problem input files) experiencing SMRs,
delayed emission is treated in the same manner as fission products.
However, there is presently no treatment of target-nuclide depletion
(mass is not conserved).

Figure 6 illustrates the results of an SMR calculation involving the
bombardment of a sphere of ^16^O by 15-MeV neutrons. The ^16^O (n,p)
^16^N (t~1/2~=7.1 s) reaction produces a set of prominent photon lines
due to the decay of ^16^N.

![](media/image10.png){width="4.870833333333334in"
height="3.658333333333333in"}

**Figure 6.** Delayed-gamma signature produced by ^16^N as a result of
the (n,p) reaction for a pulsed 15-MeV neutron source (500000 source
neutron histories) surrounding a 3.975-cm-radius sphere of ^16^O. Shown
is the MCNPX F1 tally on the surface of the ^16^O sphere using time bins
of 0.001--0.01 s, 0.01--0.1 s, 0.1--1.0 s, 1--10 s, and 10--100 s with
uncertainty suppressed (noerr mcplot option).

### User Interface {#user-interface-2 .Style-Heading-3h3-+-Times-New-Roman}

Total is now the default for neutron fission. Thus the TOTNU card is no
longer needed unless only prompt is desired. To have only prompt
fission, use:

TOTNU NO

Delayed-neutron physics is controlled with the 4^th^ entry, DNB, on the
PHYS:N card. DNB (delayed-neutron bias) has the following options, where
negative entries do analog sampling (simulate nature), and positive
entries bias delayed-neutron production:

-1001 Analog sampling, models when libraries missing

-101 Analog sampling, models only

-1 Analog sampling, libraries only (Default)

0 None \-- do not create any delayed neutrons

N Create N delayed neutrons (1-15), libraries only

100+N Create N delayed neutrons (1-15), models only

1000+N Create N delayed neutrons (1-15), models when lib missing

Delayed-gamma physics is controlled with the 6^th^ entry, DGB, on the
PHYS:P card. DGB (delayed-gamma bias), has the following options:

0 None \-- do not create any delayed gammas (Default)

-101 Analog sampling, models only, multigroup-only emission

-102 Analog sampling, models only, multigroup + line emission

-103 Analog sampling, models only, line-only emission (fragile/fatal)

Line-only emission (DGB = -103) is "fragile" (untested capability and is
a fatal error).

Multigroup + line emission (DGB = -102) is most useful because line data
exist for only 979 nuclides and the remaining nuclides are treated with
multigroup-emission data.

Multigroup-only emission (DGB = - 101) is good for many applications
where individual line signatures are not required and runs about 5 times
faster than the line emission options. In addition, the multigroup
emission spectra converge much faster---sometimes orders of magnitudes
faster---than the individual line spectra emission as discussed in the
following section.

All options produce delayed-emission spectra for all radioisotopes
tracked by CINDER90.

### Sampling and Execution {#sampling-and-execution .Style-Heading-3h3-+-Times-New-Roman}

Delayed-gamma simulation by MCNPX is memory and execution-time
intensive. Both demands stem from the calculation of the time-dependent
atom densities and the use of the photon line-emission data to create
energy and time cumulative distribution functions (CDFs). These CDFs are
sampled for the energy and time of emission of each delayed gamma
(directional emission is taken to be isotropic in the laboratory
system).

Measures are taken in MCNPX to eliminate redundant calculations so as to
reduce execution time. These measures include the one-time calculation
of time-dependent atom densities by CINDER90, and the one-time
calculation and array storage of some CDF values. This comes at the
expense of memory. Modern desktop PCs and clusters having 1--2 Gbyte of
memory lack the necessary memory to store all of the required CDF
information.

Despite the use of execution-time reduction measures, time consuming
tasks remain. For instance, the emission energies of each radioactive
decay-chain nuclide must be loaded (from the master array into which all
cindergl.dat line data is saved during initialization) and sorted (for
line-emission purposes) for each fission event. This is necessary
because mass conservation involving fission, inclusive of the number of
prompt neutrons emitted, means that any fission product may have several
other "siblings" for a series of fission events. There is insufficient
storage on modern computers to store the line data for the assortment of
combinations of fission-product pairs and their associated decay chains.

Another major time-intensive task involves the identification of the
line at which a delayed gamma is emitted. Once the energy CDF is sampled
for a proposed emission energy, that energy is forwarded to a routine
along with an array containing all line-emission energies for the
fission event. That array is searched for the nearest-neighbor emission
energy corresponding to the proposed emission energy. This search task
adds appreciable time to the calculation---this search is not done for
multigroup delayed-gamma emission.

Because MCNPX is a Monte Carlo code, applications needing high-fidelity
line signatures may require billions of source particles to achieve
relatively stable signatures. Even then, lines may fluctuate appreciably
when relatively rare emission paths are sampled. Tallies should be
examined carefully to ensure that they are statistically robust.

### Fission Yield Data {#fission-yield-data .Style-Heading-3h3-+-Times-New-Roman}

Fission-yield data are available for ^233^U, ^234^U, ^235^U, ^236^U,
^238^U, ^237^Np, ^238^Pu, ^239^Pu, ^240^Pu, ^241^Pu, ^241^Am, and
^243^Am. The data for both neutron and photon induced fission reside on
the cinder.dat file. These data are used to generate delayed neutrons
and gammas.

## Criticality Source Convergence Acceleration

*Warning! The new criticality source convergence capability is
preliminary and not covered by the MCNPX cash awards program. It has
been included in MCNPX because of its significance to criticality
calculations.*

In Monte Carlo criticality calculations the eigenvalue, *keff*, usually
converges much faster than the eigenfunction which is the source
distribution or neutron flux in the system. The problem is acute for
loosely-coupled systems such as power reactors. MCNPX includes the
"Vacation Matrix" capability[^44] to better converge source
distributions in criticality calculations. The method has been developed
by Joshua Finch (Purdue University/LANL) in collaboration with John
Hendricks and Chan Choi (Purdue University.)

### Example {#example .Style-Heading-3h3-+-Times-New-Roman}

Figures 7--9 show results for a 35×35 lattice of fuel pins: each pin is
330 cm long and has a 0.8‑cm radius region of UO~2~ fuel enriched
to\~3%. Although a "standard" Monte Carlo calculation with many millions
of histories gives a good answer (Figure 7), a shorter calculation
(Figure 8) does not correctly model the fission distribution. The
estimate using the Vacation Matrix method (Figure 9) is much better.

![](media/image11.png){width="3.0in" height="2.8819444444444446in"}

**Figure 7:** Standard Monte Carlo, "Converged" with 2 million
historie**s**

![](media/image12.png){width="3.0in" height="2.911111111111111in"}

**Figure 8:** Standard Monte Carlo, 50K histories (poor convergence)

![](media/image13.png){width="2.9583333333333335in"
height="2.935416666666667in"}

**Figure 9:** Vacation Matrix method, 50K histories (adequate
convergence)

### User Interface {#user-interface-3 .Style-Heading-3h3-+-Times-New-Roman}

The 24^th^ entry of the DBCN card is used to toggle between different
matrix implementations. The default value of DBCN(24) is zero, when no
matrix method is used. The IDUM card is used in conjunction with the
DBCN card to produce more options, as described.

+------------+---------------------+-----------------+----------------+
| **DBCN(24) |                     | **Geometry      |                |
| Table**    |                     | Specification** |                |
+------------+---------------------+-----------------+----------------+
|            |                     | cell            | mesh           |
+------------+---------------------+-----------------+----------------+
| **Fission  | collision           | **2**           | **3**          |
| Estimate** |                     |                 |                |
+------------+---------------------+-----------------+----------------+
|            | track-length        | **5**           | **4**          |
|            |                     |                 |                |
|            | \[IDUM(3)=0\]       |                 |                |
+------------+---------------------+-----------------+----------------+
|            | combined            | **5**           | **4**          |
|            | \[IDUM(3)≠0\]       |                 |                |
+------------+---------------------+-----------------+----------------+

(Special diagnostics to the screen terminal are also available. If
DBCN(24)=-1, the cell based collisional vacation matrix will be written
to the screen. If DBCN(24)=1, the cell based collisional vacation matrix
will be used and written to the screen.)

The optional IDUM card entries have the following functions:

> IDUM(1) = 0 : bias B range of 0.7 \< B \< 2.3 (default)
>
> ≠ 0 : bias B range of 0.1·idum(1) \< B \< 3.0 -- 0.1·idum(1)
>
> IDUM(2) = 0 or 6 : average vacation matrix (default)
>
> = 5 : raw (cycle) vacation matrix
>
> = 4 : average fission matrix
>
> IDUM(3) = 0 : no change to fission estimate (default)
>
> ≠ 0 : used with DBCN(24)= 4 or 5, combined fission estimate

If the cell based geometry is used, each fissionable cell defined in the
problem occupies one dimension of the solution matrix. If the mesh based
geometry is used, the MESH card must be used to define the superimposed
mesh, and the WWG card must be used with an arbitrary tally (1^st^ entry
equal to tally number, 2^nd^ entry zero). The mesh is defined exactly as
for the weight-window generator, and it must overlay all fissionable
material. When the mesh based geometry is used, the solution matrix is
dynamically accumulated according to whether each mesh zone through
which the tracked particles pass is fissionable.

# MCNPX Feature EXTENSIONS and Enhancements 

Several MCNPX features have been extended and have included changes or
additions to the user interface:

-   proton step-size control: HSTEP on M card (GWM),

-   new photon emission data: PHTLIB (REP/GWM),

-   new S(α,β) scattering law (REM/GWM/JSH),

-   differential data tallies extended to table physics (GWM),

-   neutron models produce light (A\<4) nuclei \< 100 MeV (REP/GWM),

-   weight-window upper bounds limiter (GWM/JSH),

-   separate printout of induced fission multiplicity (JSH),

-   weight-window MESH angles in radians and degrees (JSH),

-   interrupts in electron tracking (GWM),

-   extension of ZAID identifiers (GWM),

-   LINLIN contour plot defaults (GWM),

-   weight-window contour plot improvement (GWM),

-   allow deleted segment surfaces (FXG),

-   improved Windows installation (MRJ/GWM),

-   spherical GRIDCONV (MRJ),

-   spherical mesh tally plots (GWM),

-   delayed-gamma enhancements (JWD),

-   photofission yield data (JWD),

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```
-   decay omitted from NOACT=-2 LCA option (GWM);

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```
-   piping PTRAK results (RCJ);

-   muon capture secondary particle production (GWM/RCJ/MRJ/MWJ); and

-   additional enhancements.

## Proton Step-Size Control 

The proton step size can be controlled by a new keyword, hstep, on the
material Mn card:

Mn hstep = m .

For example,

M123 estep = 10 hstep = 15 .

The hstep keyword for protons works just like the estep keyword for
electrons. The hstep keyword causes the number of proton substeps per
energy step to be increased to m (15 in the above example) for the
material (123 in the above example). If n is smaller than the built-in
default found for this material, the entry is ignored. Both the default
value and the estep value actually used are printed in Print Table 85 in
the MCNPX output file.

The estep keyword is used only for electrons, and hstep is used for all
other charged particles. If estep is specified and hstep is not, then
the estep value is used for hstep to preserve backward compatibility.

## New Photon Emission Data

The "new" Nov 2001 BCDLIB gamma emission data---which becomes PHTLIB in
binary form---are now the default. The BCDLIB library contains a better
description of the gamma decay process and produces a better gamma decay
spectrum. Gamma emission from metastable states is blocked for
half-lives \>1 ms. Thus, MCNPX consistently provides the prompt emission
spectra. The BCDLIB data contain the nuclear structure data needed to
generate deexcitation photons.

The BCDLIB file is found in the MCNPX source directory under Data/LCS.
When MCNPX is compiled, the PHTLIB (binary version) is created. The
PHTLIB creation also has been corrected to eliminate several long-lived
decay gammas that were \>1 ms.

Users of executable MCNPX versions should use the latest PHTLIB file.
After unzipping Win32.zip or Linux.tar.gz, etc., the files PHTLIB and
BERTIN in the data directory should be used and put in with the other
cross sections from ENDF, etc.

Users who compile MCNPX should get the latest PHTLIB from their build
directory,

*Build_directory*/src/phtlib/phtlib .

## New S(α,β) Scattering Law 

A new S(α,β) tabular data scattering law from NJOY (REM, T-16) was added
for compatibility with forthcoming ENDF/B-VII data libraries.

## Differential Data Tallies Extended to Table Physics

Differential cross-section data now may be calculated and tallied in the
table physics region. When noact=-2 (8^th^ entry on the LCA card), the
sourced particle immediately collides in the source material. All
subsequent daughter particles then are transported without further
collision, as if in a vacuum. Differential cross sections (secondary
energy and/or angle distributions, residual nuclei and light ions, and
other information) then can be calculated and tallied with an F1 or F8
tally. The tallied data then can be plotted.

The noact=-2 option no longer automatically sets all physics to model
physics. Now, table physics is used whenever possible to get the
differential data actually used in a given problem. To get the
differential data with models only, the use of table data can be turned
off with the PHYS:pl card, 5^th^ entry.

## Neutron models produce light (A\<4) nuclei \< 100 MeV

It has been a long-standing issue that the MCNPX physics models will not
produce a neutron interaction for some light nuclides (e.g., A=3) below
\~100 MeV. Now such production is the default. Although the cross
sections are not the best, one can now use models for things like n+He-3
which will then produce correlated secondaries.

## Weight-Window Upper Bounds Limiter

An 9^th^ entry has been added to the weight-window parameter card to
limit the *maximum* lower weight-window bound. The WWP card is as
follows, with the changes in boldface:

WWP:p Wup Wsurv MXSpl Mwhere Switch Mtime Wnorm ETsplt **WU**

where

Wup = upper bound is Wup times lower bound from WWN or MESH (default =
5)

Wsurv = Russian roulette survivors get this weight times lower bound
(default = 3)

> MXSpl = never split or roulette more than MXSpl for 1 (default = 5)
>
> Mwhere = -1/0/1 = check windows at surfaces/surfaces and collisions
> (default)/collisions
>
> Switch =-1/0/S = get windows from file/WWN (default)/S divided by IMP
> value
>
> Mtime = 0/1 interpret WWE energies as time bins (obsolete -- use
> WWT)(default = 0)
>
> Wnorm = multiply all window bounds by Wnorm (0 default = 1.0)
>
> ETsplt = MCNP5 only

**WU = lower window lower bounds will never exceed WU (0 default = no
limit).**

In many problems tracks passing through a cell will only rarely score or
will score very low, resulting in a very large generated weight-window
bound. Also adjoint Monte Carlo generation of weight-windows results in
unreasonably high weight-window bounds. When these windows are used (WWP
card) in a subsequent run the ultra-high windows roulette nearly all
particles in those phase space regions resulting in no future estimate
for the WWG and potentially biasing results. The 9^th^ entry on the WWP
card limits the maximum lower weight-window bound for any particle,
energy, or time, to WU. If WU is zero or unspecified, then there is no
limit.

## Separate Printout of Induced Fission Multiplicity

Induced fission multiplicity now is printed separately instead of being
combined with spontaneous fission in Print Table 117.

## Weight-Window MESH Angles in Radians and Degrees

The mesh-based weight-window generator required that azimuthal angles
for cylindrical meshes be specified in revolutions. Now these angles and
the polar and azimuthal angles of spherical meshes may be specified in
revolutions, radians, or degrees. For example, consider the following
spherical geometry MESH card on which the polar (JMESH) and azimuthal
(KMESH) angles are specified in revolutions.

> MESH geom SPH origin 7 -9 -12 ref -23 39 -10 axs .4 -.5 .2 vec .1 -.2
> -.7
>
> imesh 60. iints 3
>
> JMESH .1 .35 .5 jints 1 1 1
>
> KMESH .2 .85 1 kints 1 1 1

These angles may now be specified in degrees or radians as well as
revolutions. Thus the jmesh and kmesh entries for the above mesh card
specified in degrees would be:

> jmesh 36 126 180 jints 1 1 1
>
> kmesh 72 306 360 kints 1 1 1

The jmesh and kmesh entries for the above mesh card specified in radians
would be:

> jmesh .6283185 2.199114 3.141592 jints 1 1 1
>
> kmesh 1.256637 5.340707 6.283185 kints 1 1 1

MCNPX recognizes the appropriate units by looking for .5, 3.14, or 180
for the last spherical geometry jmesh entry and for 1, 6.28, or 360 for
the last spherical or cylindrical kmesh entry.

## Interrupts in Electron Tracking

The \<ctrl-c\> interrupts now work during electron tracking. Normally,
at the start of each \<ctrl-c\> particle track, or trajectory, MCNPX
checks to see if the interrupt flag has been set. However, for electrons
that may have many substeps, another tracking algorithm, DBMIN, has
interrupts that previously were not checked. DBMIN finds the minimum
distance to a boundary from a point, and then all tracking (substeps)
within that distance of the point does not have to check bounding
surfaces. By checking for \<ctrl-c\> interrupts in DBMIN, these
interrupts now work better for electron problems (GWM, 4/19/06).

## Extended ZAID Identifiers

The ZAID identifier may now be alphanumeric to allow more nuclides.
Examples would be 1001.abc or 1001.xyc or 1001.a9c, all of which are
continuous-energy neutron libraries.

## LINLIN Contour Plot Default

The default interpolation scheme for tally contour plots (FREE SC) is
now LINLIN to avoid carrying over a default of LINLOG, LOGLIN, or
LOGLOG, which then truncates out all the values less than zero. This
extension was suggested by Róbert Kákonyi at the University of Szeged,
Hungary.

## Weight-Window Contour Plot Improvement

The weight-window contour plots now plot white instead of blue for zero
(no window game played) and negative (zero importance) windows instead
of blue for zero windows (GWM 4/3/06).

## Allow Deleted Segmenting Surfaces

The tally segmenting capability (FSn tally card) was extended to work
for segmenting surfaces that are deleted duplicate surfaces. The
undeleted duplicate surface then is used automatically. This enhancement
was suggested by Jeff Bull. (Franz X. Gallmeier/GWM, 4/24/06).

## Improved Windows Installation

The windows configuration and installation has been improved (MRJ, GWM
6/2/06.)

A new version of GNU Make is included in the MCNPX source files. The
upgrade from 3.79 to 3.81 fixes the problem of having a PATH
environmental variable that exceeds 255 characters. This eliminates the
need for running \"Makepath\" before building the MCNPX executable on
Windows; however, this assumes that the person who installed your MSVC
and Intel compilers requested the installer to update your environment
variables. If you use this new version of Make and get a compile/link
error during the build (e.g., can\'t find some library), most likely
your environment variables are not permanently set. You have 3 options:

1\) Permanently update your environment variables using the My Computer
(right click) =\> Properties =\> Advanced =\> Environment Variables. The
important variables are: INTEL_COMPILER8.0 (or perhaps INTEL_FORTRAN80),
INTEL_SHARED, INTEL_LICENSE_FILE, PATH, LIB, and INCLUDE. You should see
these set in your MAKEPATH.BAT file as well. Simply create or edit these
environment variables and set them to the values listed in your
MAKEPATH.BAT file. The one I found missing from my LIB variable was the
following (note you do not have to worry about the length of these paths
anymore):

D:\\Program Files\\Microsoft Visual Studio .NET
2003\\Vc7\\PlatformSDK\\Lib

2\) Run the MSVC and Intel batch files to set your environment variables
before building MCNPX (vcvars32.bat for MSVC and ifortvars.bat for
Intel). Of course this is just as much of a hassle as running
MAKEPATH.BAT each time.

3\) Continue executing MAKEPATH.BAT before you compile.

Also, execution of the test problems in parallel has been improved by
forcing problems 18 and 36 to run sequentially.

## Spherical GRIDCONV

The GRIDCONV auxiliary code, which takes MCNPX mesh tallies from the
MDATA files and processes them into a usable form for Tecplot and other
graphics packages, has been extended to plot spherical mesh tallies. The
GRIDCONV modification is to provide all three coordinates in spherical
meshes to Tecplot.

To plot the spherical mesh in Tecplot do the following:

use the Data-\>Alter-\>Transform Coordinates menu option.

In the menu box, set Transformation to \"Spherical to Rectangular\"

Set the Theta variable to \"A\"

Set the Radius variable to \"R\"

Set the Psi variable to P

Leave the default to Create New Variables

Set Angles to \"Degrees\"

Hit \"Compute\" button.

Once the transformation is complete, hit \"Close\" and go to the upper
left hand corner and change the pull down menu from 2-D Cartesian to 3-D
Cartesian. From there, under Plot-\>Assign XYZ, set the X, Y and Z
variables to the variables you just created and you should get a nice
global style plot. Make sure when you specify a Contour plot that you're
plotting the \"flux\" variable (or whatever variable is of interest).

An example is illustrated below. (MRJ, 7/20/06)

[![](media/image14.png){width="6.208333333333333in"
height="5.520833333333333in"}[\
]{.underline}p_1MeV.png](../../../../../../../../e:%5Cdocuments%20and%20settings%5C079017%5Ceudora%5Cattach%5Cp_1MeV.png)

## Spherical Mesh Tally Plots

Spherical mesh tally grids may now be plotted just like cylindrical mesh
tallies. (GWM, 10/31/07)

## Delayed-Gamma Enhancements

Delayed-gamma emission now works with nuclides having delayed-neutron
table data as in the .66c data libraries. Further, analog capture no
longer needs to be forced with the 3^rd^ entry of the CUT:N card for
delayed-gamma emission. Thus MCNPX will now execute when the user uses
default delayed-neutron gamma settings. (JWD, 7/02/07)

## Photofission Yield Data

New photofission-yield data have been calculated using CEM for 12-MeV
photons. These data are available for ^233^U, ^234^U, ^235^U, ^236^U,
^238^U, ^237^Np, ^238^Pu, ^239^Pu, ^240^Pu, ^241^Pu, ^241^Am, and
^243^Am. These data reside after the neutron-fission-yield data on the
cinder.dat file. (JWD, 10/17/07)

## Decay Omitted from LCA NOACT=-2 Option

The LCA 8^th^ entry is *noact*. If *noact* = -2, source particles
immediately collide; all secondary particles produced are then
transported with no interactions and, as of MCNPX26E, no decay. The
*noact* = -2 option is used to compute, tally, and plot
double-differential cross sections and residual nuclei with an F1 or F8
tally in conjunction with the FT RES option. (GWM, 10/2/07)

**26F**

## Piping PTRAC Results

PTRAC results may be piped to a second code receiving periodic updates
of Monte Carlo histories while MCNPX is generating them. Unix Named
pipes are considered more reliable than attempting to have two processes
writing and reading from a potentially huge file. Pipes are also less
system dependent than MPI or PVM message passing.

PTRAC piping is controlled by two new options for the FILE keyword on
the PTRAC input card:

PTRAC file=AOV

PTRAC file=BOV

The FILE keyword options are ASC, BIN, AOV, and BOV. ASC and AOV write
ASCII PTRAC information; BIN and BOV write binary information. AOV or
BOV will overwrite an ASCII or binary file to a named pipe on unix
systems. AOV and BOV options are identical to the respective ASC and BIN
options, other than they require the PTRAC file to exist prior to
execution. The PTRAC file, if it is a regular file, will be overwritten.
(RCJ, 11/29/07)

## Muon Capture Secondary Particle Production

To simulate the production of muonic X-rays, MCNPX has been extended to
account for particle production from negative muon capture. This
includes not only the X-ray component, but secondary particle production
from the decay or fission of the nucleus, should an X-ray be absorbed in
the nucleus, or should the muon undergo capture on a proton in the
nucleus. Currently hyperfine-split K- and L-shell X-ray lines are
hardwired into the code for B-10, B-11, C-12, C-13, O-16, O-17, O-18,
Fe-54, Fe-56, Fe-57, Fe-58, I-127, Cs-133, Pb-204, Pb-206, Pb‑207,
Pb-208, U-235, and U-238. Please contact the MCNPX team if you would
like additional lines; we have an active program to calculate new lines.
A warning is given if the muon captures on a nuclide where no X-ray
lines are available. In these cases, no further muon-nucleus capture
will take place. (This will be changed in future versions of the code.)
In cases where the muon does capture on a nucleus, CEM physics is used
for the nuclear de-excitation or fission.

In previous versions of MCNPX, muons have undergone only slowing down
from ionization, and decay in flight with a half-life of 2.19703e-6
seconds. In decay, the electron, muon neutrino and anti-electron
neutrino are banked for transport if these particles appear on the MODE
card. The default lower energy cutoff for muon transport is 0.113 MeV; a
value that can be changed with the second entry on the cut:\| card. In
the current version of the code, once the muon reaches the energy
cutoff, it enters into the new muon capture physics routines. The
capture nuclide is sampled from all nuclides in the material using F\*Z
weighting, where F is the atomic fraction of all elements with atomic
number Z. One or more L-shell X-rays are sampled and banked for further
transport. Next, one or more K-shell X-rays are sampled. A K-shell X-ray
may be emitted, in which case it is banked for future transport, or the
X-ray may be absorbed by the nucleus with a probability of absorption
that varies by Z for Z\~\>82. Less than Z\~82, the energy of the X-ray
is too small to make a significant contribution to absorption. We do
intend to revisit the question of resonant absorption on light nuclei in
the future. If the X-ray is absorbed, CEM is called to calculate the
de-excitation (by neutron emission) or fission of the excited nucleus.
The excited nucleus has no change in Z or A from the original capture
nuclide, but it will have the muon attached. If fission occurs, the muon
attaches to the larger of the two fragments.

The negative muon attached to the nucleus may decay or may be captured
by a proton in the nucleus. A lookup table based on the Primakoff
relationship is used to calculate the lifetime of the muonic atom. A
bound muon disappears at a different rate than a free muon, since both
capture and annihilation channels are open. If it decays, the electron
and neutrinos are banked for further transport. If it is captured, the
residual is set to (Z-1, A), indicating the preferred channel of capture
on a proton. Currently a single excitation distribution is used for all
nuclides to assign a nuclear excitation, and CEM is used to determine
the subsequent decay or fission of the excited residual. Improvements in
the muon capture routines will be made in the future, especially for the
excitation function and for the fission barriers which are affected due
to the modified charge distribution induced by the presence of the muon
in the nucleus.

There is no change to the MCNPX user interface, this capability is
turned on at all times. (GWM/RCJ/MRJ/MWJ, 10/26/07)

## Additional Enhancements

### ILOG interpolation {#ilog-interpolation .Style-Heading-3h3-+-Times-New-Roman}

MCNPX now recognizes either log (MCNPX) or ilog (MCNP5) notation for
logrithmic interpolation on input cards. For example,

E99 1.e-6 4log .1 4ilog 1e4

Either log or ilog may be used interchangeably. (JSH, 11/30/07)

### MODE J R {#mode-j-r .Style-Heading-3h3-+-Times-New-Roman}

MCNPX now allows I J M R particle types on mode card instead of
interpreting these as special input characters for interpolate, jump,
multiply, and repeat. (JSH, 11/30/07)

### Photofission prompt gamma warning {#photofission-prompt-gamma-warning .Style-Heading-3h3-+-Times-New-Roman}

Use of photonuclear data libraries for Z \> 89 now causes the following
warning error message:

Warning. \"z\>90 has no photofission prompt gammas - use model.\"

Presently all photonuclear data tables do not include prompt gammas from
photofission. (JSH, 11/30/07)

### NNDC Delayed-Neutron Emission Probabilities {#nndc-delayed-neutron-emission-probabilities .Style-Heading-3h3-+-Times-New-Roman}

Delayed-neutron emission probabilities from the National Nuclear Data
Center (NNDC) at Brookhaven National Laboratory (BNL) have be added to
the CINDER database in file cinder.dat. The NNDC data covers all
nuclides with Z\<26. Of the \~80 nuclides on the NNDC list with nonzero
delayed-neutron emission values, only \~40 of these were included in the
CINDER database. The NNDC data make it possible to model neutron
activation of O-17 to produce delayed neutrons from O-17\[n,p\]N-17.
(GWM, 12/17/07)

# **MCNPX Corrections**

## Significant Problem Corrections

The following problems could cause incorrect answers. Fortunately, they
occur only in very special situations and affect only a few MCNPX users.

### Auger Electrons Below Energy Cutoff {#auger-electrons-below-energy-cutoff .Style-Heading-3h3-+-Times-New-Roman}

Auger electrons were not made from photoelectric fluorescence, and tally
heating from fluorescence was neglected when produced by photons below
the photon energy cutoff. The effect is small and has been found in all
previous MCNP and MCNPX versions. The affected tallies are the MCNPX +F6
and F6:e tallies. A \$2 award was made to Greg Cunningham (ISR‑1, LANL)
(D-5:JSH-2006-18) (GWM).

### Detectors in Lattice Geometries {#detectors-in-lattice-geometries .Style-Heading-3h3-+-Times-New-Roman}

Point detectors in lattice geometries could cause a crash. Possibly
answers could be wrong without a crash. The error results because the
*levp* variable could be changed erroneously in (and thus needed to be
restored after) the do 695 loop in subroutine *tallyd*. The possible
problem has occurred in all previous MCNP and MCNPX versions. A \$2
award was made to Kin Yip (Brookhaven National Laboratory)
(D-5:JSH-2006-111) (GWM, 3/7/06).

### KCODE/PRDMP 5th Entry  {#kcodeprdmp-5th-entry .Style-Heading-3h3-+-Times-New-Roman}

If the PRDMP 5^th^ entry is not one for KCODE problems, then RUNTPE
files can crash and other problems can occur because an array overflows.
The problem occurs only if the TFC update frequency, NPD, the 5^th^
entry, is larger than the current KCODE cycle, KCY, when adding to the
tally fluctuation charts. In most cases, this is not a problem because
the default value for NPD with KCODE is "1". A €20 award was made to
Sergey Belousov (INRNE-BAS, Sophia, Bulgaria) (D-5:JSH-2006-112) (GWM
4/19/06).

### CEM03 Corrections  {#cem03-corrections .Style-Heading-3h3-+-Times-New-Roman}

A number of small corrections were made to CEM03 by Dick Prael and Gregg
McKinney to correct for Z/A imbalances (REP/GWM 6/2/06).

### SDEF Fails with SP -31 x for Equiprobable Bins Sampling {#sdef-fails-with-sp--31-x-for-equiprobable-bins-sampling .Style-Heading-3h3-+-Times-New-Roman}

Exponential sampling (SPn -31 x) failed for equiprobable bins (SIn a1 a2
a3 ...) if there were fewer than three entries on the SP card. The
problem has been in all previous MCNP/X versions and only affects AXS
and VEC keywords in the rare use of the equiprobable bin (partial range
on SI) treatment (GWM 2/27/07).

### Surface Sources in Repeated Structures {#surface-sources-in-repeated-structures .Style-Heading-3h3-+-Times-New-Roman}

Surface sources fail in repeated structures. When the surface source
particles are read for a history, the coordinates of the first one are
saved and then the subsequent particles from that history are put into
the bank. When the first particle of the history is retrieved for
transport the coordinates in all but the lowest level have been
forgotten. Instead, coordinates are used for other particles that were
banked. Eventually this causes the particle to get lost or have a "zero
lattice element hit error." The problem is in all MCNP4C and later MCNP
and MCNPX versions. A \$2 award was made to Steven Van Der Marck, NRG,
Netherlands, X-3-MCC:2007-057 (GWM 4/16/07)

### Periodic Boundary Conditions in Repeated Structures {#periodic-boundary-conditions-in-repeated-structures .Style-Heading-3h3-+-Times-New-Roman}

Periodic boundary conditions in repeated structures can lose particles
or have "zero lattice element hit" errors due to a bug in all MCNP and
MCNPX versions. A \$2 award was made to Phillipe Maes, Tractebel,
Brussels, Belgium, X-3-MCC:2007-055 (GWM 4/18/07)

### Delayed Neutrons/Gammas with Biased Photonuclear {#delayed-neutronsgammas-with-biased-photonuclear .Style-Heading-3h3-+-Times-New-Roman}

> The delayed-neutron/gamma treatment is wrong with biased photonuclear
> production turned on and with photonuclear libraries. This is because
> the particle weight is not properly reset after the photonuclear
> biasing. The problem only affects MCNPX 26C for this developmental
> feature. The correction has been made in MCNPX 26D to reset the
> particle weight to the incident photonuclear photon weight before
> calling the delayed-neutron gamma model (DNG_MODEL) (Ken Adams, SAIC,
> San Diego, GWM 1/6/07).

### Delayed Neutrons/Gammas Inelastic Scatter {#delayed-neutronsgammas-inelastic-scatter .Style-Heading-3h3-+-Times-New-Roman}

The delayed-neutron/gamma treatment (DNG_MODEL) was wastefully and
perhaps incorrectly called for center-of-mass inelastic scatter
collisions (one particle out) and elastic scatter collisions (GWM
4/6/07).

### Delayed Neutrons/Gammas from (n,p) Reactions {#delayed-neutronsgammas-from-np-reactions .Style-Heading-3h3-+-Times-New-Roman}

The delayed-neutron/gamma treatment (DNG_MODEL) did not generate delayed
neutrons and gammas from (n,p) (MT102) reactions (JWD 5/29/07).

### Delayed Neutrons/Gammas with Biased Photonuclear {#delayed-neutronsgammas-with-biased-photonuclear-1 .Style-Heading-3h3-+-Times-New-Roman}

The delayed-neutron/gamma treatment now selects the \"A-1\" fissioning
nuclide rather than the \"A\" nuclide sent by ACECOL for photonuclear
reactions, significantly affecting spectral output (JWD 06/13/07).

### Parallel Burnup/Depletion Calculations with Model Cross Sections {#parallel-burnupdepletion-calculations-with-model-cross-sections .Style-Heading-3h3-+-Times-New-Roman}

The atom fractions of isotopes using model cross sections in a parallel
burnup/depletion calculation were not updated at the end of each time
step due to a bug in Versions 26C and earlier. Versions 26D corrects
this bug and updates the atom fractions of isotopes using model cross
sections in a parallel burnup/depletion calculation at the end of each
time step (MLF 4/01/07).

### Surface Sources in Repeated Structures {#surface-sources-in-repeated-structures-1 .Style-Heading-3h3-+-Times-New-Roman}

Surface source particles in repeated structures geometries (using
universe U= and FILL=) could lose particles and/or with lattices have
"zero lattice element hit" bad trouble errors. \$2 awarded to Steven C.
van der Marck, NRG, Netherlands, X-3-MCC:2007-057. (GWM, 6/13/07)

### No Fatal Error for LAT without FILL {#no-fatal-error-for-lat-without-fill .Style-Heading-3h3-+-Times-New-Roman}

Specifying a lattice (LAT=) without a FILL generally makes no sense and
could cause wrong answers. It is now a fatal error for a cell card to
have LAT but not FILL. Previously, omitting the FILL parameter was
accepted and worked correctly for a "real world infinite lattice" (U=0),
in which case the lattice elements were filled with the material and
density of the lattice cell. But for an infinite lattice that filled a
cell (U≠0), trying to fill the lattice with its own universe or material
gave a fatal error if a FILL parameter was used and wrong answers if a
FILL parameter was omitted. \$2 awarded to Mathieu Agelou, CEA-Saclay,
France, X-3-MCC: 2007-061 (GWM, 7/9/07)

### Double Fluorescence with Pulse Height Tallies and WWP or ESPLT {#double-fluorescence-with-pulse-height-tallies-and-wwp-or-esplt .Style-Heading-3h3-+-Times-New-Roman}

Double florescent photons scored incorrectly to pulse height tallies
when either weight windows (WWP) or energy/time splitting (ESPLT) was
used in the problem. Reported by Jeff Bull, LANL X-3-MCC (JSH, 8/16/07)

### Burnup of 1000 or More Materials without MAT Keyword  {#burnup-of-1000-or-more-materials-without-mat-keyword .Style-Heading-3h3-+-Times-New-Roman}

The burnup was not capable of burning more than 1000 burn materials when
a MAT keyword was not specified on the BURN card due to a limit set in
MCNPX 2.6.D. MCNPX 2.6.E corrects this limit and allows the user to
examine as large a problem as computer memory permits (MLF 7/10/07).

### Power Fraction Calculation for Burnup  {#power-fraction-calculation-for-burnup .Style-Heading-3h3-+-Times-New-Roman}

The power fraction calculation in MCNPX26D was not properly volume
weighted. MCNPX 2.6.E properly volume weights the power fraction
calculation (MLF 08/17/07).

### DATAPATH Sometimes Chosen Incorrectly  {#datapath-sometimes-chosen-incorrectly .Style-Heading-3h3-+-Times-New-Roman}

The DATAPATH tells the code where to get cross-section information. The
hierarchy for locating the cross sections is the following:

1.  The current working directory;

2.  The directory specified by the DATAPATH variable on the MCNPX
    execution line;

3.  The directory specified by the DATAPATH variable in the Message
    Block in the input file;

4.  The DATAPATH environmental variable;

5.  The DATAPATH in the XSDIR file;

6.  The DATAPATH hardwired in the MCNPX source (/usr/local/lib for Unix,
    or C:\\MCNPX\\XS for Windows).

Both MCNP and MCNPX have always incorrectly set the DATAPATH in the case
where (a) no environmental variable is set, (b) no path is input in the
Message Block/execute line, and (c) the hardwired DATAPATH contains
data. In this case, the DATAPATH specified in the XSDIR file can be
overlooked. Note that as always, only the first two valid DATAPATHs will
be used by the code, so if XSDIR is not in the local directory and the
DATAPATH on the execution line, message block, or environmental variable
is set but incorrect, then the hardwired DATAPATH will not be checked.
\$2 awarded to David Dixon, LANL D-5, X-3:2008-001 (GWM, 10/3/07)

### SSW s(-c) Can Fail with Repeated Structures  {#ssw-s-c-can-fail-with-repeated-structures .Style-Heading-3h3-+-Times-New-Roman}

The SSW surface source write enables writing particles to a surface
source that cross a specified surface, s. The particles may be filtered
(omitted) if they do not enter or leave specified cells on the other
side of specified surfaces. A cell may specified, SSW s(c), where c is
the cell on the other side of surface s into which particles enter, or
SSW s(-c) where c is the cell on the other side of surface s from which
particles depart. In repeated structures, if c4 \< c3 \< c2 \< c1 \< c0
are cells at levels 4, 3, 2, 1, 0 from which a particle departs, suppose
a particle in lev = 4 in cell c4 crosses a surface at lev = 2, thus
exiting cell c2. In MCNPX25E and MCNP (all versions) c = c2 and
specification of c4 would only work if c4 and c2 shared the common
surface, s. In MCNPX25F -- MCNPX26D, c = c4. The change was
inadvertently introduced on January 27, 2005, when MCNPX was corrected
to enable pulse-height tallies in repeated structures. Generally, c = c2
would be the desired case, though specifying c = c4 is usually easier.

MCNPX is now extended to allow *either* c = c4 or c= c2 to be specified
to write particles crossing surface s in the lowest level cell (c4) but
crossing surface s at a higher level leaving higher level cell (c2).
User caution is advised because the code only knows which s(c) or s(‑c)
combinations are correct during particle transport; incorrect user
specification cannot be identified with an error message when reading
the input file. The user can either specify the lowest level cell which
may or may not bound surface s; or the user must know the departing cell
at a higher level where the surface crossing is made which is the level
of the cell into which the particle crossing surface s enters. This is
obvious only if surface s is specified only at one level.

Note that the change from c = c2 to c = c4 in MCNPX25F could be
considered an undocumented feature change rather than a bug. And the
MCNPX26E change to accept both constructs could be considered a feature
extension. Nonetheless, €20 was awarded to Steven van der Marck (NRG,
Petten, Netherlands) (X-3:JSH-2008-002) (JSH).

### F6 Heating Tallies Wrong for Photonuclear  {#f6-heating-tallies-wrong-for-photonuclear .Style-Heading-3h3-+-Times-New-Roman}

Heating tallies have always been wrong (all MCNP and MCNPX prior to
MCNPX 26E) for photonuclear events. The code sets a flag when electrons
are produced so that their progeny photons are not counted twice in F6
heating tallies. The flag is now reset for photonuclear events so that
neutrons, photons, and other photonuclear particles and their progeny
score to F6 heating tallies. Once photons produce electrons they and
their progeny photons no longer score to F6 heating tallies to avoid
being double counted.

The error is usually unnoticeable unless photonuclear production makes
significant contributions to F6 heating tallies. The error is most
pronounced in electron source problems with neutron heating tallies. \$2
awarded to Yousry Gohar, ANL, X-3-MCC:JSH-2008-003 (JSH) 10/5/07

**26F**

### Heavy Ion Directions {#heavy-ion-directions .Style-Heading-3h3-+-Times-New-Roman}

Heavy ion residual particle directions are now set correctly. In
MCNPX 26E they are wrong and usually led to lost particles or direction
cosines summing to zero. (MRJ) 12/04/07

### Photonuclear Mix and Match {#photonuclear-mix-and-match .Style-Heading-3h3-+-Times-New-Roman}

Photons at exactly the maximum photonuclear table energy or below the
model physics range erroneously had a zero photonuclear production cross
section. This is rare and so far has only happened when the source is
specified exactly at the maximum photonuclear data table energy.

Photonuclear library cross sections were always used below the maximum
table energy and photonuclear models were always used above. MCNPX has
been corrected so that when a photonuclear library is specified (M, MX
cards) the library data will be used at or below the maximum table
energy. Model cross sections are used above the model physics range. The
highest table value will be used at the maximum table value and if an
energy is ever between the maximum table value and the minimum model
physics range. (JSH, 12/05/07)

### Mesh Tally Gaps {#mesh-tally-gaps .Style-Heading-3h3-+-Times-New-Roman}

Mesh tally tracking in all code versions could prematurely stop and
return to particle tracking in some cases. This premature stopping would
underestimate fluxes, heating, and other quantities and show up as a gap
in the plot. Because the problem so clearly shows up in mesh tally
plots, it probably does not affect anyone who has had a reasonable plot
picture.

The problem arises when a particle enters a cell and begins checking for
intersections with mesh tallies along its track (this effects all
particles). The particle only looks for a crossing on the current plane
of the mesh. Once it finds that stepping the particle to that plane
means that the particle is still not in the mesh, it gives up and
returns to transporting of the particle history. Intersections with
other mesh planes are never checked. It is only when the particle has
another interaction or surface crossing that the track is rechecked and
it finds the mesh tally properly.

The solution in MCNPX26F is to force the particle to check all the outer
surfaces of a Cartesian mesh before returning.

\$2 awarded to Michal Mocko, LANCE-LC, LANL, X-3-MCC:JSH-2008-038 (MRJ)
2/22/08

## Minor Problem Corrections

The following problems do not cause wrong answers, but they may cause
crashes when encountered. In any case, they occur only in very special
situations and affect only a few MCNPX users.

### Cylindrical Weight-Window Mesh {#cylindrical-weight-window-mesh .Style-Heading-3h3-+-Times-New-Roman}

Neither the weight window nor the weight-window generator cylindrical
meshes properly used the theta bin. The improper use affected using,
generating, and plotting these weight-window meshes. Cylindrically
symmetric meshes (no theta bins) were unaffected. Answers also were not
affected because variance reduction affects only efficiency (GWM/JSH).

### I8 Mesh Tally Plots {#i8-mesh-tally-plots .Style-Heading-3h3-+-Times-New-Roman}

Improper initialization caused mesh tallies not to plot in MCNPX
versions compiled with the I8 configuration option, namely, 64-bit
integer code versions. A \$20 award was made to Bill Schmitt (Draper
Labs, Massachusetts) (D-5:JSH-2005-190) (GWM/JSH).

### Continue Cards for Input with FATAL Errors {#continue-cards-for-input-with-fatal-errors .Style-Heading-3h3-+-Times-New-Roman}

Continue cards failed for input with FATAL errors. A \$2 award was made
to Valery Taranenko (GSF, Germany) (D-5:JSH-2005-191).

### Sometimes Can Plot Only First Mesh Tally {#sometimes-can-plot-only-first-mesh-tally .Style-Heading-3h3-+-Times-New-Roman}

Geometry plots in the command mode (the mode with the PLOT\> prompt) for
mesh tallies failed in some cases:

> PLOT\> TALnn.m .

The above command would plot only the first mesh tally if there were
non-mesh tallies in the same problem (JSH).

### 

### Incorrect KCODE/Message Passing Interface (MPI) Error Message {#incorrect-kcodemessage-passing-interface-mpi-error-message .Style-Heading-3h3-+-Times-New-Roman}

The warning error message, "KCODE with load balancing is very
inefficient," had a bad format that caused a crash whenever criticality
problems were run in parallel with load balancing. A €20 award was made
to Steven van der Marck (NRG, Petten, Netherlands) (D‑5:JSH-2005-239)
(GWM).

### Incorrect LCS Error Message {#incorrect-lcs-error-message .Style-Heading-3h3-+-Times-New-Roman}

The LAHET (LCS) diagnostic message for "projectile negatives" and
"target negatives" incorrectly listed the atomic number twice rather
than the Z-number and then the atomic number. A \$2 award was made to
Igor Remec (ORNL) (D-5:JSH-2005-238) (GWM).

### Mesh Tally Writing to Backup RUNTPE {#mesh-tally-writing-to-backup-runtpe .Style-Heading-3h3-+-Times-New-Roman}

The mesh tallies could cause a crash when writing to backup *runtpe*
files. The backup *runtpe* files are those temporarily created for the
PRDMP 3J N option, which allows overwriting the *runtpe* file with only
the last N dumps to conserve space. A €20 award was made to Steven Van
der Marck (NRG, Netherlands) (D-5:JSH-2006-005), who also provided the
correction.

### Pulse-Height-Tally Variance Reduction Techniques with MPI {#pulse-height-tally-variance-reduction-techniques-with-mpi .Style-Heading-3h3-+-Times-New-Roman}

Pulse-height tallies (F8) with variance reduction techniques crashed
when run in parallel with MPI. A \$20 award was made to Ronald McConn
(PNL) (D-5:JSH-2006-019) (GWM).

### PTRAC and Event Log Omission {#ptrac-and-event-log-omission .Style-Heading-3h3-+-Times-New-Roman}

Both PTRAC (PTRAC card) and Event Logs (DBCN card) write the individual
events of a history. Neither wrote collisions using physics models
(rather than data tables) in the mix-and-match energy range. (GWM,
4/12/06)

### FM Tally Multiplier in Model Physics Regime {#fm-tally-multiplier-in-model-physics-regime .Style-Heading-3h3-+-Times-New-Roman}

The FM (tally multiplier) multiplies tallies by cross sections and other
quantities from the MCNPX data libraries. If the tally is at an energy
above the highest energy in the data tables, that is, in the model
physics energy region, then MCNPX (like MCNP) uses the cross section at
the highest energy of the table. However, when a model is used instead
of a data table, then no data table values are available at lower
energies and MCNPX may crash or get erroneous answers. In some cases,
this crash happens in the mix/match energy region between the lowest
data table energy and the highest data table energy. The new approach
(starting with MCNPX 26B) is to issue an error message at the first
occurrence of an FM multiplier above the energy range of a data table
and then to return a zero multiplier (MRJ, 4/18/06).

### Make Clean Enabled for PC Build {#make-clean-enabled-for-pc-build .Style-Heading-3h3-+-Times-New-Roman}

The Make Clean command now works at all levels of the build system on
PCs (GWM, 5/25/05).

### Zero Electron Mesh Tallies {#zero-electron-mesh-tallies .Style-Heading-3h3-+-Times-New-Roman}

> Electron mesh tallies gave all zeroes in void regions. Corrected by
> GWM, 2/23/06, and \$2 awarded to Carlo Petrovich (ENEA, Bologna,
> Italy) (D-5:JSH-2006-101, 4/24/06).
>
> Note that a low-density issue also exists in the workaround, namely
> adding materials of very low densities. For heavier-charged particles,
> a numerical problem occurs in the straggling routines with densities
> \<\~1e-9 g/cm^3^ and with densities \<\~1e-15 g/cm^3^ for electrons.
> For now, users should avoid such low densities.

### Universe Map {#universe-map .Style-Heading-3h3-+-Times-New-Roman}

The universe map for lattice/repeated structures geometries,
Print Table 128, could occasionally have an array overflow that caused a
crash in rare cases, thus affecting all previous code versions. A \$2
award was made to Benjamin Amiri, LANL, D-5 (D-5:JSH-2006-142) (GWM
5/26/06).

### Tally Storages {#tally-storages .Style-Heading-3h3-+-Times-New-Roman}

Some tallies with large numbers of cells and surfaces can cause a "bad
trouble" exit in MCNP with the message, "li\>lit+1   the trouble is in
the code, not in your problem." The problem is that insufficient space
is set aside for the TALLOC pointers to ITDS in OLDCD1 where there is a
"T" (totals bin) on the F card. A \$2 award was made to Benjamin Amiri,
LANL, D-5 (X-3:JSH-2006-053) (GWM 7/13/06).

### Lost Particles with Coincident REC Surfaces {#lost-particles-with-coincident-rec-surfaces .Style-Heading-3h3-+-Times-New-Roman}

> If the REC (rectangular surface) macrobody has coincident surfaces
> particles could get lost. A \$2 award was made to Richard Starr,
> NASA-Goddard (X-3:JSH-2006-069) (GWM 9/11/06)

### GRIDCONV Compiler Bug {#gridconv-compiler-bug .Style-Heading-3h3-+-Times-New-Roman}

The auxiliary program GRIDCONV (for plotting mesh tallies) would crash
for the Intel 9.1 complier because of the over-complexity of some write
statements. These have now been simplified. (GWM 7/13/06)

### Geometry Plot Basis Vectors {#geometry-plot-basis-vectors .Style-Heading-3h3-+-Times-New-Roman}

MCNPX now forces the geometry plot coordinate system always to be
right-handed. Previously, it was possible to specify left-handed
coordinate systems in some cases, which led to plotting errors or easily
misinterpreted plots. (GWM/JSH 5/6/05)

> The "Theta" command after the command prompt and the "Rotate" button
> in the interactive geometry plotter enable rotation of a geometry plot
> frame. The "PX", PY", and "PZ" commands after the command prompt and
> the "XY", "YZ", and "XZ" buttons in the interactive geometry plotter
> enable changing the view of a geometry plot frame. Because these
> commands only changed the first two basis vectors of the plot, and not
> necessarily the third, a left-handed geometry would sometimes result.
> This in turn sometimes caused improper drawing of cell or mesh
> boundaries. Now whenever the first two basis vectors are changed the
> third is always generated as the cross product ensuring a right-handed
> coordinate system only. (JSH 9/27/06)

### WWN Label Error {#wwn-label-error .Style-Heading-3h3-+-Times-New-Roman}

> If "WWN" is selected as the label quantity in the interactive geometry
> plotter, the values displayed would not be the weight windows. (JSH
> 8/1/06)

### READ Card Placements {#read-card-placements .Style-Heading-3h3-+-Times-New-Roman}

> If the READ card is part of a continued line in the cell cards an
> index was out of range which could cause a crash. (RCJ 10/5/06)

### Residual Nucleus Warning {#residual-nucleus-warning .Style-Heading-3h3-+-Times-New-Roman}

> Print only the first warning message instance of "residual nucleus out
> of ft8 res bin range" and then count the occurrences in the
> out-of-range user bin count. This prevents getting excessive warnings,
> particularly when only part of the residual nucleus range is being
> examined and for delayed-neutron/gamma problems (GWM 02/14/07).

### S(α,β) Ultra-Low Energies {#sαβ-ultra-low-energies .Style-Heading-3h3-+-Times-New-Roman}

The new ENDF/B-VII data enables neutrons to downscatter below 1.e-11 MeV
which causes the S(α,β) physics to crash. The reaction where this
occurred was a non- S(α,β) elastic scatter off oxygen. The following
possible fixes were ***not*** made:

1.  only call SABCOL S(α,β) for neutrons with E \> 1.e11 MeV ;

2.  return from SABCOL without doing S(α,β) physics if E \< 1.e11 MeV.

We chose to reset the energy to 1.e-11 MeV and then do the S(α,β)
physics. This is reflected in the summary table as an upscatter and with
this approach the molecular binding effect is not neglected. The problem
of such ultra-low energy neutrons must be very rare for this crash not
to have happened earlier (GWM 4/6/07).

### Large Problem Sizes for Parallel Execution {#large-problem-sizes-for-parallel-execution .Style-Heading-3h3-+-Times-New-Roman}

The maximum message size limit in the MPI implementation in MCNPX caused
problems to crash or hang when the arrays being passed exceeded it. In
particular, problems involving many tallies and/or burnup problems with
many materials would exceed the message size limit and fail. Now MCNPX
segments the cross-section array into manageable sizes (less than the
message size) when passing through an MPI call (MLF 05/20/07) times.

### Mesh Tally TR Option {#mesh-tally-tr-option .Style-Heading-3h3-+-Times-New-Roman}

Mesh tallies using the TR card translate properly, but sometimes do not
rotate properly. A \$2 award was made to Choonsik Lee, University of
Florida, X-3-MCC:2007-056 (GWM 5/14/07)

### Crash for non-orthogonal spherical mesh direction cosines {#crash-for-non-orthogonal-spherical-mesh-direction-cosines .Style-Heading-3h3-+-Times-New-Roman}

The error message for non-orthogonal direction cosines for the spherical
mesh weight-window generator had a typo causing MCNPX to crash whenever
the user incorrectly specified AXS and VEC on the MESH card. MCNPX26C
and 26D only. \$20 awarded to Dudley A. Raine, III, SAIC, McLean, VA,
X-3-MCC:2007-62. (GWM, 7/2/07)

**26F**

### Mesh Tallies Keyword Capitalization {#mesh-tallies-keyword-capitalization .Style-Heading-3h3-+-Times-New-Roman}

Mesh tallies may now use capitalized keywords. For example,

RMESH11:E PEDEP

Would result in

fatal error. illegal keyword: PEDEP

Now PEDEP, pedep, Pedep, etc., all work.

\$2 Awarded Vitaly Kovaltchouk, Bubble Technology Industries, Chalk
River, Ontario, Canada. X-3-MCC:JSH-2008-013 (GWM, 11/28/07)

### Mesh Tallies Data Interpolation {#mesh-tallies-data-interpolation .Style-Heading-3h3-+-Times-New-Roman}

The I notation for linear interpolation between entries in mesh tallies
now works. Note that J (jump) and M (multiply) do not make sense.
Further note that log and ilog interpolation and \$ comments still do
not work for MCNPX mesh tallies. \$2 awarded to Brad Micklich, ANL,
X-3-MCC:JSH-2008-019 (GWM, 12/04/07)

### Power Fraction Calculation for Individual Burn Materials  {#power-fraction-calculation-for-individual-burn-materials .Style-Heading-3h3-+-Times-New-Roman}

The power fraction calculation for versions 2.6.d and 2.6.e was
incorrectly referencing the xsec array causing all individual material
power fractions to be set to zero. This referencing issue has been
resolved and now the code properly calculates the power fraction of each
individual burn material.

### Negative MAT Numbers on the BURN card  {#negative-mat-numbers-on-the-burn-card .Style-Heading-3h3-+-Times-New-Roman}

Negative MAT numbers on the BURN card are used to allow a material to
contribute to the flux normalization parameters without being burned in
CINDER90.This feature was platform and compiler dependent for versions
2.6.d and 2.6.e. A fix has been implemented to make this feature
platform and compiler independent. \$20 awarded to Bruce Wilkin, Atomic
Energy of Canada Limited, Chalk River Laboratories, Ontario, Canada,
X-3-MCC:JSH-2008-029 (MLF, 2/8/08)

### Print LAQGSM Flag {#print-laqgsm-flag .Style-Heading-3h3-+-Times-New-Roman}

MCNPX26E gave no indication when LAQGSM is turned on. The LAQGSM flag,
ILAQ, is now shown in Print Table 41 of the MCNPX output file. \$20
awarded to Kin Yip, BNL, X-3-MCC:JSH-2008-044 (MRJ, 3/18/08)

### Internal Corrections {#internal-corrections .Style-Heading-3h3-+-Times-New-Roman}

-   The 20^th^ entry on the DBCN card now causes MCNPX 2.6.0 to track
    MCNPX 2.5.0 instead of MCNP4C3 and MCNPX 2.4.0. (JSH 4/7/05)

-   The algorithm to change the size of singly-dimensioned integer
    arrays during the course of particle transport was corrected so that
    it no longer could cause array overflows. (RCJ 9/6/06)

-   Out-of-bounds conditionals which fail on some compilers but have
    been in MCNPX forever were corrected. For example,

if (k.gt.0.and.t(k).eq.zero) ...

> will work on older compilers, but on new compilers if k=0 then t(k)
> will fail because both conditions are treated together. (RCJ 10/16/06)

-   All references to the UNICOS operating system were deleted. (JSH
    10/24/06)

-   HTAPE3X had the appropriate I4 formats changed to I6 so that HTAPE3X
    could accommodate 5-digit cell and surface numbers. (FXG 9/12/06)

-   Comments extending to column 80 were revised to prevent processing
    errors when updating (RCJ 5/15/07)

-   Several FORTRAN90 constructs were fixed so that an array would not
    appear in an IF statement if it had not been dimensioned due to a
    conditional dimension (RCJ 5/15/07). For example,

if (ntburn.gt.0.and.kc8.le.0.and.matburn(icl).ne.0) call burn_trk(d,mk)

fails when matburn is not dimensioned. So the new construct is:

if (ntburn.gt.0.and.kc8.le.0) then

if (matburn(icl).ne.0) call burn_trk(d,mk)

endif

-   The printout of CTM (computer time elapsed in a run) overflowed for
    very long. Now the printout has been expanded so the print will not
    overflow until after 19 years. (GWM, 7/2/07)

-   Some large arrays for delayed neutrons/gammas were dynamically
    allocated (JWD, 7/2/07). Other corrections were made to allow
    problems to continue with a warning rather than a "hard stop." (JWD,
    10/03/07)

-   Autoconfiguration was modified (config.guess) to enable compilation
    on 64-bit AMD linux systems or any system with x86_64 chips. (RCJ,
    10/10/07)

**26F**

-   G95 compiler optimization bug: a workaround to enable heavy ions
    transport was made by renaming function SIGMAD as function FSIGMAD
    to avoid a conflict with the LAQGSM variable SIGMAD. (GWM/JSH,
    12/04/07)

-   AIX compiler optimization bug: a workaround to an optimization error
    on AIX computers was added at the suggestion of Francisco Ogando
    (UNED, Spain): the IV variable in routine SOURCB is set with an IF
    rather than a mathematical expression (which has been used since
    MCNP4.) Thus specification of VEC on the SDEF card now works on his
    and possibly other systems at optimization level 3.

-   Some heavy ion problems hung when the old version of the CEM data
    file level.tbl was read by LAQGSM. MCNPX will now ignore comments at
    the end of the level.tbl file.

-   I8 compilation failed for LAQGSM because LAQGSM declared the
    variable *istop* to be integer\*4. \$2 awarded to William M.
    Schmitt, Draper Laboratory, Cambridge, MA, X-3-MCC:JSH-2008-028
    (GWM, 2/8/08)

Plotting hung on 64-bit Linux compilers because of an uninitialized
value of "\*error flag" in C‑routine gawk of MCNPC.C. \$2 awarded to
Rainer Wilcke, Scientific Software Support Group, ESRF, Grenoble,
France, X-3-MCC:JSH-2008-030 (GWM, 2/8/08)

# Future work

The following projects are at least partially funded and are actively
being developed. These capabilities should be available soon in a future
MCNPX version:

-   additional CINDER90 capabilities: fixed-source depletion,

```{=html}
<!-- -->
```
-   improved convergence of eigenfunctions in criticality problems,

-   integration of HTAPE tallies directly into MCNPX, including continue
    runs,

-   electric and magnetic field tracking.

    The following projects are on our wish list. Some have been
    partially developed but await further funding.

-   detectors and DXTRAN for all neutral particles at all energy ranges
    with anisotropic scattering (currently approximated as isotropic for
    models),

-   CAD link,

-   secondary particle angle biasing for isotropic distributions,

-   neutral particle perturbation techniques extended to physics model
    region,

```{=html}
<!-- -->
```
-   plotting of physics model total and absorption cross sections, and

```{=html}
<!-- -->
```
-   forced collisions for neutral particles extended to physics models.

[^1]: John S. Hendricks (JSH, LANL, X-3-MCC); Gregg W. McKinney (GWM,
    LANL, X-3-MCC), Joseph W. Durkee (JWD, LANL, D-5), Michael L. Fensin
    (MLF, LANL, X-3-MCC), Joshua P. Finch (JPF, LANL, P-23 -- now GE
    Nuclear Energy, Wilmington, NC), Michael R. James (MRJ, LANL, D-5),
    Russell C. Johns (RCJ, LANL, D-5), Robert E. MacFarlane (REM, LANL,
    T-16), Denise B. Pelowitz (DBP, LANL, D-5), Laurie S. Waters (LSW,
    LANL, D-5), Franz X. Gallmeier (FXG, ORNL), M. William Johnson (MWJ,
    LANL, D-5)

[^2]: The depletion/burnup capability is based on CINDER 90, which was
    written by William B. Wilson (LANL, T-16), and MonteBurns, which was
    written by Holly R. Trellue (HRT, LANL, X-1). The initial patch to
    MCNPX was developed by Gregg W. McKinney (GWM, LANL, X-3-MCC) and
    Joe W. Durkee (JWD, LANL, D-5). MCNPX 26A, 26B, 26C, 26D, and 26E
    were written mainly by Michael L. Fensin (MLF, LANL, X‑3‑MCC).

[^3]: CEM03 was developed mostly by Stepan G. Mashnik (LANL, X-3), with
    algorithms developed by Arnold J. Sierk (LANL, T‑16). LAHET was
    written by Richard E. Prael (REP, LANL, X-3) and adapted into
    MCNPX 26B by Gregg W. McKinney (GWM, LANL, X-3-MCC).

[^4]: The delayed-gamma capability utilizes CINDER 90, which was written
    by William B. Wilson (LANL, T-16), modified by Holly R. Trellue
    (HRT, LANL, X-1) and Joe W. Durkee (JWD, LANL, D-5). The multigroup
    patch to MCNPX was developed by LSW, HRT, and GWM; the line-emission
    upgrades were written primarily by JWD.

[^5]: <http://www-rsicc.ornl.gov/>

[^6]: [http://www.nea.fr](http://www.nea.fr/)/

[^7]: <http://mcnpx.lanl.gov/beta/>

[^8]: <http://mcnpx.lanl.gov/docs/MCNPX_2.6.0_Manual.pdf/>.

[^9]: <http://mcnpx.lanl.gov/>.

[^10]: <http://mcnpx.lanl.gov/opendocs/reports/Interface.pdf/>.

[^11]: <http://mcnpx.lanl.gov/opendocs/misc/FeaturesList.pdf/>

[^12]: Cash Award Fine Print: This offer is subject to cancellation or
    modification without notice. A bug is defined as an error we choose
    to correct in the source code. We make awards even for the most
    trivial or insignificant of problems, but not for proposed code
    enhancements or proposed extended capabilities. Awards are given
    only to the first MCNPX user reporting a problem. MCNP/X development
    team members are ineligible. Reported problems must be reproducible,
    and awards are paid when the correction is integrated into a
    forthcoming MCNPX version. We endeavor to make MCNPX the most
    error-free and robust Monte Carlo radiation-transport code possible,
    and we back this code with a cash award.

[^13]: <http://mcnpx.lanl.gov/opendocs/misc/Cashbugs.pdf/>.

[^14]: Michael L. Fensin, John S. Hendricks, and Samim Anghaie,
    "Enhanced Monte Carlo Linked Depletion Capabilities in MCNPX," Los
    Alamos National Laboratory report abstract LA-UR-05-9559, 2006
    International Congress on Advances in Nuclear Power Plants, Embedded
    International Topical Meeting at the 2006 ANS Annual Meeting, ICAPP
    \'06, Reno, Nevada (June 4--8, 2006).

[^15]: Michael L. Fensin, John S. Hendricks, Gregg W. McKinney, and
    Holly Trellue, "Advances in Monte Carlo Depletion Capabilities for
    MCNPX," Los Alamos National Laboratory report abstract,
    LA-UR-05-7895, full paper, LA-UR-06-0629. American Nuclear Society
    14th Biennial Topical Meeting of the Radiation Protection and
    Shielding Division, Carlsbad, New Mexico (April 3--6, 2006).

[^16]: Michael L. Fensin, John Hendricks, Holly Trellue, Gregg McKinney,
    "Advances in Monte Carlo Depletion Capabilities for MCNPX," Los
    Alamos National Laboratory Report LA-UR-06-3920, Transactions of the
    American Nuclear Society, 95, 497, 2006 Winter Meeting, Albuquerque,
    New Mexico (November 12--16, 2006).

[^17]: Michael L. Fensin, John Hendricks, Holly Trellue, Samim Anghaie,
    "Incorporation of a Predictor-Corrector Methodology and 1-Group
    Reaction Rate Reporting Scheme for the MCNPX Depletion Capability,"
    Los Alamos National Laboratory Report LA-UR-06-3925, Transactions of
    the American Nuclear Society, 95, 317, 2006 Winter Meeting,
    Albuquerque, New Mexico (November 12-16, 2006).

[^18]: James, MR; McKinney, GW; Hendricks, JS; Moyers, M, "Recent
    enhancements in MCNPX: Heavy-ion transport and the LAQGSM physics
    model," *Nuclear Instruments & Methods in Physics Research, Section
    A (Accelerators, Spectrometers, Detectors and Associated Equipment*
    vol.562, no.2, p.819-22 (23 June 2006)

[^19]: M. James, G. McKinney, J. Hendricks, and M. Moyers, 'Heavy-Ion
    Transport in MCNPX," *Los Alamos National Laboratory Report,
    LA-UR-05-8338,* American Nuclear Society 14th Biennial Topical
    Meeting of the Radiation Protection and Shielding Division,
    Carlsbad, New Mexico (April 3-6, 2006)

[^20]: Mashnik, S G, Sierk, A J; Gudima, K K; Baznat, M I, "CEM03 and
    LAQGSM03---new modeling tools for nuclear applications," *Journal of
    Physics - Conference Series, Institute of Physics,* vol:41 iss:1
    pg:340 -351 (2006)

[^21]: S. G. Mashnik, K. K. Gudima, M. I. Baznat, A. J. Sierk, R. E.
    Prael, and N. V. Mokhov, "CEM03.S1, CEM03.G1, LAQGSM03.S1, and
    LAQGSM03.G1 Versions of CEM03.01 and LAQGSM03.01 Event-Generators,"
    Los Alamos National Laboratory report LA-UR-06-1764 (March 6, 2006),
    also available at http://mcnpx.lanl.gov \> documents.

[^22]: Stepan G. Mashnik, Konstantin K. Gudima, Arnold J. Sierk, Mircea
    I. Baznat, and Nikolai V. Mokhov, "CEM03.01 User Manual," Los Alamos
    National Laboratory report LA-UR-05-7321 (2005); RSICC Code Package
    PSR-532, http://www-rsicc.ornl.gov/codes/psr/psr5/psr-532.html/
    (2006).

[^23]: S. G. Mashnik, K. K. Gudima, and A. J. Sierk, "Merging the CEM2k
    and LAQGSM Codes with GEM2 to Describe Fission and Light-Fragment
    Production," Los Alamos National Laboratory report LA-UR-03-2261
    (2003); E-print: nucl-th/0304012; Proc. 6th Int. Workshop on
    Shielding Aspects of Accelerators, Targets and Irradiation
    Facilities (SATIF-6), April 10--12, 2002, Stanford Linear
    Accelerator Center, CA 94025, USA, NEA/OECD, Paris, France, 2004,
    pp. 337--366.

[^24]: Stepan G. Mashnik, Arnold J. Sierk, and Konstantin K. Gudima,
    "Complex Particle and Light Fragment Emission in the Cascade-Exciton
    Model of Nuclear Reactions," Los Alamos National Laboratory report
    LA-UR-02-5185 (2002); E-print nucl-th/0208048.

[^25]: S. G. Mashnik and A. J. Sierk, "CEM2k---Recent Developments in
    CEM," Los Alamos National Laboratory report LA-UR-00-5437 (2000);
    Proc. of the 2000 ANS/ENS Int. Meeting, Embedded Topical Meeting
    Nuclear Applications of Accelerator Technology (AccApp00), November
    12--16, 2000, Washington, DC (USA), American Nuclear Society, La
    Grange Park, IL, 2001, pp. 328--341; E-print: nucl-th/0011064.

[^26]: A. V. Prokofiev, S. G. Mashnik, and A.J. Sierk. "Cascade-Exciton
    Model Analysis of Nucleon-Induced Fission Cross Sections of Lead and
    Bismuth at Energies from 45 to 500 MeV," Los Alamos National
    Laboratory report LA-UR-98-0418 (1998); E-print: nucl-th/9802027;
    *Nucl. Sci. Eng.* (1999), Vol. 131, No. 1, pp. 78--95.

[^27]: S. G. Mashnik and A. J. Sierk, "Improved Cascade-Exciton Model of
    Nuclear Reactions," Los Alamos National Laboratory report
    LA-UR-98-5999 (1998); E-print: nucl-th/9812069; Proc. Forth Int.
    Workshop on Simulating Accelerator Radiation Environments (SARE-4),
    Knoxville, TN, September 13--16, 1998, Oak Ridge National
    Laboratory, 1999, pp. 29--51.

[^28]: S. G. Mashnik, "User Manual for the Code CEM95," Bogoliubov
    Laboratory of Theoretical Physics, Joint Institute for Nuclear
    Research, Dubna, Russia (1995), CEM95 Code Package IAEA1247
    distributed by the OECD Nuclear Energy Agency, Paris, France, 1995,
    <http://www.nea.fr/abs/html/iaea1247.html>.

[^29]: S. G. Mashnik, K. K. Gudima, M. I. Baznat, A. J. Sierk, R. E.
    Prael, and N. V. Mokhov, "CEM03.01 and LAQGSM03.01 Versions of the
    Improved Cascade-Exciton Model (CEM) and Los Alamos Quark-Gluon
    String Model (LAQGSM) Codes," Los Alamos National Laboratory
    Research Note X-5-RN (U) 05-11; Los Alamos National Laboratory
    report LA-UR-05-2686 (2005).

[^30]: S. G. Mashnik, M. I. Baznat, K. K. Gudima, A. J. Sierk, and R. E.
    Prael, "CEM03 and LAQGSM03: Extension of the CEM2k+GEM2 and LAQGSM
    Codes to Describe Photo-Nuclear Reactions at Intermediate Energies
    (30 MeV to 1.5 GeV)," E-print: nucl-th/0503061, *J. Nucl. and
    Radiochem. Sci.*, Vol. 6, No. 2, pp. A1--A19 (2005).

[^31]: S. G. Mashnik, M. I. Baznat, K. K. Gudima, A. J. Sierk, "CEM03.01
    and LAQGSM03.01 Improvement for Gas-Production Cross Section
    Calculations," Los Alamos National Laboratory report LA-UR-05-8447
    (2005); Proc. 14th Biennial Meeting on the Radiation Protection and
    Shielding Division, Carlsbad, New Mexico, USA, April 3--6, 2006, CD
    with the RPSD2006 Procs., ANS, La Grange Park, IL, USA, 2006, ISBN:
    0-89448-693-4, pp. 169--172.

[^32]: S. Furihata, "Statistical Analysis of Light Fragment Production
    from Medium Energy Proton-Induced Reactions,\'" Nucl. Instrum.
    Methods B 171 (2000) 252--258; PhD thesis, Tohoku University, March,
    2003 (and references therein).

[^33]: A. V. Prokofiev, "Compilation and Systematics of Proton-Induced
    Fission Cross-Section Data," NIM, A463 (2001) 557--575.

[^34]: A. V. Prokofiev, S. G. Mashnik, and W. B. Wilson, "Systematics of
    Proton-Induced Fission Cross Sections for Intermediate Energy
    Applications," Los Alamos National Laboratory report LA-UR-02-5837
    (2002), E-print: nucl-th/0210071.

[^35]: V.D. Toneev, K.K. Gudima, "Particle Emission in Light and
    Heavy-Ion Reactions," *Nucl. Phys.* A400 (1983) 173c--190c.

[^36]: N. Amelin, "Physics and Algorithms of the Hadronic Monte-Carlo
    Event Generators. Notes for a Developer," CERN/IT/ASD Report
    CERN/IT/99/6, Geneva, Switzerland (1999).

[^37]: "GEANT4, Users\'s Documents, Physics Reference Manual,\" December
    8, 1998, [http://wwwinfo.cern.ch/asd/geant4/G4Users
    Documents/UsersGuides/](http://wwwinfo.cern.ch/asd/geant4/G4Users Documents/UsersGuides/)PhysicsReferenceManual/html/PhysicsReferenceManual.html.

[^38]: M. Herman, editor, *ENDF-6 Formats Manual*, Document ENDF-102,
    Report BNL-NCS-44945-05-Rev (June 2005).

[^39]: Joe W. Durkee, Jr., Gregg W. McKinney, Holly R. Trellue, Laurie
    S. Waters, and William B. Wilson, "Delayed-Gamma Signature
    Calculation for Neutron-Induced Fission Using MCNPX," Los Alamos
    National Laboratory report LA-UR-07-6302*,* in preparation for
    publication in *Progress in Nuclear Energy* (November, 2007*).*

[^40]: T. R. England and B. F. Rider, "Evaluation and Compilation of
    Fission Product Yields," Los Alamos National Laboratory report
    LA-UR-94-3106 (October, 1994).

[^41]: W. B. Wilson, T. R. England, E. D. Arthur, C. A. Beard, C. D.
    Bowman, L. N. Engel, A. Gavron, D. C. George, L. L. Daemen, H. G.
    Hughes, III, W. W. Kinnison, R. J. LaBauve, D. M. Lee, H.
    Lichtenstein, P. W. Lisowski, D. W. Muir, A. P. Palounek, R. T.
    Perry, E. J. Pitcher, R. E. Prael, G. J. Russell, G. Sanders, L. S.
    Waters, P. G. Young, and H. J. Ziock, "Accelerator Transmutation
    Studies at Los Alamos with LAHET, MCNP, and CINDER90," Proceedings
    of the Workshop on Simulating Accelerator Radiation Environments
    (January 11--15, 1993).

[^42]: J. Katakura and T. R. England, "Augmentation of ENDF/B Fission
    Product Gamma-Ray Spectra by Calculated Spectra," Los Alamos
    National Laboratory report LA-12125-MS (1991).

[^43]: M. Herman, editor, *ENDF-6 Formats Manual*, Document ENDF-102,
    Report BNL-NCS-44945-05-Rev (June 2005).

[^44]: Joshua P. Finch, acation Matrix Method for Fission Source
    Convergence in Monte Carlo Criticality Calculations,"PhD
    Dissertation, Purdue University, West Lafayette, Indiana (December
    2006)