MCNPX, Version 26D

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

Los Alamos National Laboratory

Franz X. Gallmeier

Oak Ridge National Laboratory

June 20, 2007

**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. Guarantee 3](#guarantee)

[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 Predictor Corrector Methodology
7](#the-predictor-corrector-methodology)

[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 11](#burn-materials)

[2.1.9. Automatic Fission Yield Selection Process
13](#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 14](#isotope-reactivity-options)

[2.1.12. Models Option 14](#models-option)

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

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

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

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

[2.1.17. Example 18](#example)

[2.2. CEM03 Upgrade 19](#cem03-upgrade)

[2.2.1. Intra Nuclear Cascade (INC) 20](#intra-nuclear-cascade-inc)

[2.2.2. Preequilibrium (PREC) 20](#preequilibrium-prec)

[2.2.3. Evaporation and/or Fission 20](#evaporation-andor-fission)

[2.2.4. Coalescence 21](#coalescence)

[2.2.5. Fermi Breakup 21](#fermi-breakup)

[2.2.6. Additional Notes 21](#additional-notes)

[2.3. Long File Names 21](#long-file-names)

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

[2.5. Spherical Mesh Weight Windows 23](#spherical-mesh-weight-windows)

[2.5.1. User Interface 23](#user-interface)

[2.5.2. Plotting 24](#plotting)

[2.6. Energy-Time Weight Windows 27](#energy-time-weight-windows)

[2.6.1. Cell-Based Example 28](#cell-based-example)

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

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

[2.7.1. User Interface 29](#user-interface-1)

[2.7.2. Diagnostics 30](#diagnostics)

[2.7.3. Important Considerations 30](#important-considerations)

[2.8. Delayed-Gamma Emission. 31](#delayed-gamma-emission.)

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

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

[2.8.3. Simple Multi-Particle Reactions
34](#simple-multi-particle-reactions)

[2.8.4. User Interface 35](#user-interface-2)

[2.8.5. Sampling and Execution 36](#sampling-and-execution)

[2.9. Criticality Source Convergence Acceleration
37](#criticality-source-convergence-acceleration)

[2.9.1. Example 37](#example-1)

[2.9.2. User Interface 38](#user-interface-3)

[3.0. MCNPX 26D Feature EXTENSIONS and Enhancements
39](#mcnpx-26d-feature-extensions-and-enhancements)

[3.1. Proton Step-Size Control 40](#proton-step-size-control)

[3.2. New Photon Emission Data 40](#new-photon-emission-data)

[3.3. New S(α,β) Scattering Law 41](#new-sαβ-scattering-law)

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

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

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

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

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

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

[3.10. Extended ZAID Identifiers 43](#extended-zaid-identifiers)

[3.11. LINLIN Contour Plot Default 43](#linlin-contour-plot-default)

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

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

[3.14. Improved Windows Installation 43](#improved-windows-installation)

[3.15. Spherical GRIDCONV 44](#spherical-gridconv)

[4.0. MCNPX 26D Corrections 45](#mcnpx-26d-corrections)

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

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

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

[4.1.3. KCODE/PRDMP 5th Entry 46](#kcodeprdmp-5th-entry)

[4.1.4. CEM03 Corrections 46](#cem03-corrections)

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

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

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

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

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

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

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

[4.1.12. Parallel burnup/depletion calculations with model cross
sections
47](#parallel-burnupdepletion-calculations-with-model-cross-sections)

[4.2. Minor Problem Corrections 47](#minor-problem-corrections)

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

[4.2.2. I8 Mesh Tally Plots 47](#i8-mesh-tally-plots)

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

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

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

[4.2.6. Incorrect LCS Error Message 48](#incorrect-lcs-error-message)

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

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

[4.2.9. PTRAC and Event Log Omission 48](#ptrac-and-event-log-omission)

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

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

[4.2.12. Zero Electron Mesh Tallies 49](#zero-electron-mesh-tallies)

[4.2.13. Universe Map 49](#universe-map)

[4.2.14. Tally Storages 49](#tally-storages)

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

[4.2.16. GRIDCONV Compiler Bug 49](#gridconv-compiler-bug)

[4.2.17. Geometry Plot Basis Vectors 49](#geometry-plot-basis-vectors)

[4.2.18. WWN Label Error 50](#wwn-label-error)

[4.2.19. READ Card Placements 50](#read-card-placements)

[4.2.20. Residual Nucleus Warning 50](#residual-nucleus-warning)

[4.2.21. S(α,β) Ultra-Low Energies 50](#sαβ-ultra-low-energies)

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

[4.2.23. Mesh Tally TR Option 50](#mesh-tally-tr-option)

[4.2.24. Internal Corrections 50](#internal-corrections)

[5.0. Future work 51](#future-work)

**MCNPX, VERSION 26D**

**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
> 26D, are described along with the recent changes in MCNPX 26A, 26B,
> 26C.

# 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, and its quality is guaranteed; it
can be used with confidence. The MCNPX guarantee is described in Section
1.4.

## **Summary of New MCNPX Features**

The new capabilities and enhancements of MCNPX 26D beyond MCNPX 2.5.0
(that is, all changes in MCNPX 26A, 26B, 26C, and 26D) are listed as
follows (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. Although they are not fully guaranteed and must be used
cautiously, they are considered of such significance that they are
included. Note also that total nu (not prompt nu) is the default for
fission neutrons. The new MCNPX 26D capabilities are:

-   Depletion/Burnup Enhancements (MLF)

    -   Increased fission product array to account for new fission
        products listed in ENDF VII.0,

    -   MATVOL keyword for implementing repeated structures in burnup,

    -   Collision rates listed in units of (collisions/second).

-   Energy-time weight windows (JSH),

-   Corrections/enhancements/extensions

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

        MCNPX 26D also includes the following MCNPX 26A, 26B, and 26C
        capabilities beyond MCNPX 2.5.0:

-   depletion/burnup,[^2]

-   CEM03 physics,[^3]

-   long file names (JSH),

-   delayed-gamma emission (JWD),[^4]

-   criticality source convergence acceleration (JPF),

-   spherical mesh weight windows (JSH),

-   charged ions from neutron capture in table range (MRJ),

-   tallies terminated at desired precision: STOP card (JSH), and

-   corrections/enhancements/extensions, including

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

    -   weight window contour plot improvement (GWM),

    -   improved windows installation (MRJ/GWM),

    -   spherical GRIDCONV (MRJ),

    -   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),

    -   separate printout 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),

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

    -   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 26D, 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 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 RSICC's international release
version, MCNPX 2.5.0 (namely, the capabilities of MCNPX 26A, 26B, 26C,
and 26D), are documented herein.

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

## Guarantee

MCNPX is guaranteed. We are so confident of the quality of MCNPX that we
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. We 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 nu (not prompt nu) is now the default for fission neutrons. To
track previous problems with the prompt nu default, turn off total nu
with the TOTNU NO card and command.

Note that the new delayed gamma emission and criticality source
convergence acceleration capabilities are developmental. Although they
are not fully guaranteed and must be used cautiously, they are
considered of such significance that they are included.

The principal new capabilities of MCNPX beyond MCNPX 2.5.0 are

-   Depletion/burnup,

-   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, and , 26D 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 26D capabilities are

-   Increased fission product array to account for new fission products
    listed in ENDF VII.0,

-   MATVOL keyword for implementing repeated structures in burnup,

-   Collision rates listed in units of (collisions/second).

### 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 carries out the
depletion calculation to generate new number densities at the following
time step. MCNPX then takes those new number densities and generates
another set of fluxes and reaction rates; the process repeats itself
until after the final time step.

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. However, CINDER90 tracks the
time-dependent reactions of 3456 isotopes using intrinsic cross-section
and decay data inherent in the CINDER90 code when the information is not
specified from MCNPX. 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 which 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 3456 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$\beta_{m}$ is the total transmutation probability of isotope m:

$\gamma_{k \rightarrow m}$is the probability of isotope k transmuting,
by either decay or absorption, into isotope m, ${\overline{Y}}_{m}$ is
the production rate and $N_{m}(t)$is 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
posses transport information in MCNPX for particle tracking. For these
isotopes, a sixty three 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 Predictor Corrector Methodology {#the-predictor-corrector-methodology .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 a
predictor corrector 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; in most cases,
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~,~M3~,\...

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

AFMIN=A

BOPT=B1,B2,B3 ,

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.
>
> J~i~ = i^th^ material for which to omit nuclides I~i1~, I~i2~, 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~i1~, I~i2~, \... = 1^st^, 2^nd^, etc. omitted nuclides for the i^th^
> material. Currently, there is no default for this parameter.
>
> A = atom fraction minimum below which the atom fraction is set to
> zero. Default is 1.0e-10.
>
> 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 card for the burned material; however, this
> option exists as a simpler alternative to the omit card.
>
> 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. This keyword was implemented to account for power level
changes occurring during system life as a result of the startup process
or the need to down-power the system for system maintenance. For each
T~i~ value listed on the TIME keyword, a corresponding F~i~ value listed
on the PFRAC keyword must exist. 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 example:

> TIME = 11, 33, 22
>
> PFRAC = 1.0, 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 of
system life, the system is burned at 0.9\*10 MWth of the total system
power at 9 MWth. For the final 22 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
appropriately. The following flux multiplier is calculated to transform
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. 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 is highly
dependent on the collision densities:

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

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. 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

(days) (days) (MW) (GWd/MTU)

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

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

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

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
    an 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. This keyword
presents the user with the ability to investigate the reactivity effects
that a certain isotope has on the analyzed system.

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~i1~, I~i2~, 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~i1~, I~i2~, ...= 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 dropped 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 1.0E-10.

### 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 data using a model. It is
preferable to determine which isotopes are needed to be zeroed out and
to place them on the omit card for the burned material; however, this
option exists as a simpler alternative to the omit card.

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 for actinides listed on the material cards or
generated by the isotope generator algorithm, as well as fission
products listed on the material cards or generated by the isotope
generator algorithm.

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 version 26D 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, 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; the Tier-2 fission products are used in MCNPX
transport and are listed in the output file as

-   = list at the end of each time step,

4.  = list isotope concentrations in increasing zaid, and

> 4 + 10 = use Tier-2 fission products.

### 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 3456
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, 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
3456 isotopes; therefore, the total isotopics 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 that are selected from the fission product
array and 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/image1.png){width="3.2472222222222222in"
height="3.9694444444444446in"}

![](media/image2.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 on the
corresponding burn material card, with an atom density of 1E-36, can be
input. 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

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

### Example  {#example .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.

## CEM03 Upgrade

The CEM2K physics package has been replaced with the new CEM03 physics
package[^18] which will soon also have the new LAQGSM physics package.
The MCNPX user interface has not changed: if the 9^th^ entry on the LCA
card is 1, then CEM03 will be used.

CEM03.01[^19] is the latest modification of the improved Cascade-Exciton
Model (CEM). It is a completely new, updated, and modified version, not
just an incremental improvement, in comparison with its predecessors,
CEM2k+GEM2,[^20]^,^[^21] CEM2k,[^22] CEM98,[^23] CEM97,[^24] and
CEM95.[^25]

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

### 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.[^26][^27] 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 with previous versions. The algorithms of many INC routines
were changed, and almost all INC routines were rewritten, which sped 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 with 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.[^28] Algorithms of many PREC routines were
changed, and almost all PREC routines were rewritten, which sped 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[^29] by Furihata, which considers
evaporation of up to 66 types of different particles and light fragments
(up to ^28^Mg). In comparison with 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.[^30]^,^[^31] Several routines by Furihata from GEM2 were
slightly modified in CEM03.01; some bugs found in GEM2 were fixed.

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

The coalescence model implemented in CEM is described is improved.[^32]
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.[^33]^,^[^34] In
comparison with 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 its predecessors.
The output of CEM03.01 was significantly extended, which allows us to
calculate with the standard CEM03.01 many more different characteristics
of nuclear reactions, in comparison with its predecessors.

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/image3.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/image4.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/image5.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 guaranteed. It has been included in
MCNPX 26D 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).[^35] 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).

### 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/image6.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.[^36] At high energies (E**n**\>20 MeV), LAHET[^37] 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/image7.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 were 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. [^38] These data are stored in file cindergl.dat. The
composition of the line data are 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).[^39] 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)

  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-photon 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/image9.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 nu is now the default for neutron fission. Thus the TOTNU card is
no longer needed unless only prompt nu 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)

Line-only emission (DGB = -103) is "fragile" (untested capability).
Multigroup + line emission (DGB = -102) is most useful because for many
reactions line data do not exist and for low-probability events
multigroup emission is statistically better. 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.

### 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 are 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 that 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.

## Criticality Source Convergence Acceleration

*Warning! The new criticality source convergence capability is
preliminary and not guaranteed. It has been included in MCNPX 26D
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[^40] 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-1 .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 an 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/image10.png){width="3.0in" height="2.8819444444444446in"}

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

![](media/image11.png){width="3.0in" height="2.911111111111111in"}

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

![](media/image12.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 26D 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), 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:

WWGP: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 3 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/image13.png){width="6.208333333333333in"
height="5.520833333333333in"}[\
]{.underline}p_1MeV.png](../../../../../../../../e:%5Cdocuments%20and%20settings%5C079017%5Ceudora%5Cattach%5Cp_1MeV.png)

# **MCNPX 26D 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 a~1~
a~2~ a~3~ ...) if there were fewer than 3 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 non-guaranteed
> 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) (MR=102) 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).

## 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).

### 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)

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

The 20^th^ entry on the DBCN card now causes MCNPX 26A 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

# 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,

-   improved physics with the LAQGSM/CEM03 model,

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

-   heavy-ion tracking and interactions, and

-   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 Fensin
    (MLF, LANL, X-3-MCC), Joshua P. Finch (JPF, LANL, P-23), 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).

[^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 GWM and Joe W. Durkee (JWD, LANL, D-5). MCNPX
    26A, 26B, 26C, and 26D 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 GWM.

[^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_2.5.0_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. 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 guarantee.

[^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"
    (Abstract: Los Alamos National Laboratory report 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-GroupReaction 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]: 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.

[^19]: 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).

[^20]: 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.

[^21]: 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.

[^22]: 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.

[^23]: 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.

[^24]: 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.

[^25]: 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>.

[^26]: 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).

[^27]: 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).

[^28]: 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.

[^29]: 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).

[^30]: A. V. Prokofiev, "Compilation and Systematics of Proton-Induced
    Fission Cross-Section Data," NIM, A463 (2001) 557--575.

[^31]: 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.

[^32]: V.D. Toneev, K.K. Gudima, "Particle Emission in Light and
    Heavy-Ion Reactions," *Nucl. Phys.* A400 (1983) 173c--190c.

[^33]: 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).

[^34]: 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.

[^35]: Herman M., Editor (June, 2005), ENDF-6 Formats Manual, Document
    ENDF-102, Report BNL-NCS-44945-05-Rev.

[^36]: England T.R. and Rider B.F. (October, 1994), "Evaluation and
    Compilation of Fission Product Yields," Los Alamos National
    Laboratory report LA-UR-94-3106.

[^37]: Wilson W.B., England T.R., Arthur E.D., Beard C.A., Bowman C.D.,
    Engel L.N., Gavron A., George, D.C., Daemen L.L., Hughes, III H.G.,
    Kinnison W.W., LaBauve R.J., Lee D.M., Lichtenstein H., Lisowski
    P.W., Muir, D.W., Palounek A.P., Perry R.T., Pitcher E.J., Prael
    R.E., Russell G.J., Sanders G., Waters L.S., Young, P.G, and Ziock
    H.J. (January 11--15, 1993), "Accelerator Transmutation Studies at
    Los Alamos with LAHET, MCNP, and CINDER90," Proceedings of the
    Workshop on Simulating Accelerator Radiation Environments.

[^38]: Katakura J. and England T.R., (1991), "Augmentation of ENDF/B
    Fission Product Gamma-Ray Spectra by Calculated Spectra," Los Alamos
    National Laboratory report LA-12125-MS.

[^39]: Herman M., Editor (June, 2005), ENDF-6 Formats Manual, Document
    ENDF-102, Report BNL-NCS-44945-05-Rev.

[^40]: Joshua P. Finch, acation Matrix Method for Fission Source
    Convergence in Monte Carlo Criticality Calculations,"PhD
    Dissertation, Purdue University, West Lafayette, Indiana (December
    2006)