MCNPX, Version 26C

by

John S. Hendricks

Gregg W. McKinney

Joe W. Durkee

Joshua P. Finch

Michael L. Fensin

Michael R. James

Russell C. Johns

Denise B. Pelowitz

Laurie S. Waters

Los Alamos National Laboratory

Franz X. Gallmeier

Oak Ridge National Laboratory

December 7, 2006

**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 2](#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. Collision Density Generation 5](#collision-density-generation)

[2.1.3. The Predictor Corrector Methodology
6](#the-predictor-corrector-methodology)

[2.1.4. BURN Card Setup 7](#burn-card-setup)

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

[2.1.6. Flux Normalization Parameters 9](#flux-normalization-parameters)

[2.1.7. Burn Materials 10](#burn-materials)

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

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

[2.1.10. Isotope Reactivity Options 13](#isotope-reactivity-options)

[2.1.11. Models Option 13](#models-option)

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

[2.1.13. The Isotope Generator Algorithm
15](#the-isotope-generator-algorithm)

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

[2.1.15. Example INPUT 16](#example-input)

[2.2. CEM03 Upgrade 17](#cem03-upgrade)

[2.2.1. Intra Nuclear Cascade (INC) 18](#intra-nuclear-cascade-inc)

[2.2.2. Preequilibrium (PREC) 18](#preequilibrium-prec)

[2.2.3. Evaporation and/or Fission 19](#evaporation-andor-fission)

[2.2.4. Coalescence 19](#coalescence)

[2.2.5. Fermi Breakup 19](#fermi-breakup)

[2.2.6. Additional Notes 19](#additional-notes)

[2.3. Long File Names 20](#long-file-names)

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

[2.5. Spherical Mesh Weight Windows 21](#spherical-mesh-weight-windows)

[2.5.1. User Interface 21](#user-interface)

[2.5.2. Plotting 22](#plotting)

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

[2.6.1. User Interface 26](#user-interface-1)

[2.6.2. Diagnostics 26](#diagnostics)

[2.6.3. Important Considerations 27](#important-considerations)

[2.7. Delayed-Gamma Emission. 27](#delayed-gamma-emission.)

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

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

[2.7.3. Simple Multi-Particle Reactions
30](#simple-multi-particle-reactions)

[2.7.4. User Interface 31](#user-interface-2)

[2.7.5. Sampling and Execution 32](#sampling-and-execution)

[2.8. Criticality Source Convergence Acceleration
33](#criticality-source-convergence-acceleration)

[2.8.1 Example 33](#example)

[2.8.2 User Interface 35](#user-interface-3)

[3.0. MCNPX 26C Feature EXTENSIONS and Enhancements
36](#mcnpx-26c-feature-extensions-and-enhancements)

[3.1. Proton Step-Size Control 36](#proton-step-size-control)

[3.2. New Photon Emission Data 37](#new-photon-emission-data)

[3.3. New S(α,β) Scattering Law 37](#new-sαβ-scattering-law)

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

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

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

[3.8. Interrupts in Electron Tracking
38](#interrupts-in-electron-tracking)

[3.9. Extended ZAID Identifiers 38](#extended-zaid-identifiers)

[3.10. LINLIN Contour Plot Default 39](#linlin-contour-plot-default)

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

[3.12. Allow Deleted Segmenting Surfaces
39](#allow-deleted-segmenting-surfaces)

[3.13. Improved Windows Installation 39](#improved-windows-installation)

[3.14. Spherical GRIDCONV 40](#spherical-gridconv)

[4.0. MCNPX 26C Corrections 41](#mcnpx-26c-corrections)

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

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

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

[4.1.3. KCODE/PRDMP 5^th^ Entry 42](#kcodeprdmp-5th-entry)

[4.1.5. CEM03 Corrections 42](#cem03-corrections)

[4.2. Minor Problem Corrections 42](#minor-problem-corrections)

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

[4.2.2. I8 Mesh Tally Plots 42](#i8-mesh-tally-plots)

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

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

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

[4.2.6. Incorrect LCS Error Message 43](#incorrect-lcs-error-message)

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

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

[4.2.9. PTRAC and Event Log Omission 43](#ptrac-and-event-log-omission)

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

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

[4.2.12. Zero Electron Mesh Tallies 43](#zero-electron-mesh-tallies)

[4.2.13. Universe Map Crash 44](#universe-map-crash)

[4.2.14. Insufficient Storage for Tallies
44](#insufficient-storage-for-tallies)

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

[4.2.16. GRIDCONV Compiler Bug 44](#gridconv-compiler-bug)

[4.2.17. Geometry Plot Basis Vectors 44](#geometry-plot-basis-vectors)

[4.2.18. WWN Label Error. 44](#wwn-label-error.)

[4.2.19. Crash for Some READ Card Placements
45](#crash-for-some-read-card-placements)

[4.2.20. Internal Corrections 45](#internal-corrections)

[5.0. Future work 45](#future-work)

**MCNPX, VERSION 26C**

**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
> 26C, are described.

# Introduction

MCNPX (MCNP eXtended) is a Fortran90 (F90) Monte Carlo radiation
transport computer code that transports nearly all particles at nearly
all energies. It is a superset of MCNP4C3 and has many capabilities
beyond MCNP4C3. MCNPX is a production computer code that models the
interaction of radiation with matter, and its quality is guaranteed; it
can be used with confidence. The MCNPX guarantee is described in Section
1.1.4.

## **1.1. Summary of New MCNPX Features**

The new capabilities and enhancements of MCNPX 26C beyond MCNPX 2.5.0
and MCNPX26B are listed as follows (where applicable, the initials of
the principal developers are shown in parentheses).[^1] Note that the
first two 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 MCNPX26C capabilities
are:

-   delayed-gamma emission (JWD),[^2]

-   criticality source convergence acceleration (JPF),

-   spherical mesh weight windows (JSH),

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

-   depletion/burnup enhancements (MLF),

-   corrections/enhancements/extensions

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

    -   weight window contour plot improvement (GWM),

    -   improved windows installation (MRJ/GWM),

    -   spherical GRIDCONV (MRJ), and

    -   additional enhancements and corrections.

        MCNPX 26C also includes the following MCNPX 26A and 26B
        capabilities beyond MCNPX_2.5.0:

-   depletion/burnup,[^3]

-   CEM03 physics,[^4]

-   long file names (JSH),

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

-   corrections/enhancements/extensions

    -   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),

    -   additional enhancements and corrections.

## 1.2. Availability

The latest general-release version of MCNPX is MCNPX 2.5.0, which is
available from the Radiation Safety Information and 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 MCNPX26C, may
be downloaded from the MCNPX website.[^7] Approximately 1600 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 <mcnpx@lanl.gov>.

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

## 1.3. 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 MCNPX2.3.0 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, and
26c), are documented herein.

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

## 1.4. 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, and

-   Charged ions from neutron capture in table range,

-   Delayed-gamma emission,

-   Criticality source convergence acceleration..

## 2.1. Depletion/Burnup

The depletion/burnup capability is based on CINDER 90, 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 and 26C 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 26C capabilities are

-   Variable dimensioning

-   Proper execution with cross section models

-   Proper tracking of short half-life isotopes

-   Continue Runs

Previous versions of MCNPX depletion confined the user to only 100 burn
materials per depletion calculation. Now users can burn as many
materials as user computer memory permits. Previous version of MCNPX
depletion also did not properly track atom fractions for isotopes
implementing model derived cross sections. MCNPX 26C now adequately
tracks the buildup of isotopes implementing a cross section model.

A CINDER90 bug caused the calculation to kick out short-half life
isomers, leading to an incorrect buildup of nuclides resulting from the
decay of short lived isomers. MCNPX 26C tracks all isomers regardless of
the length of half-life, thus properly accounting for nuclide buildup
from the decay of short lived isomers.

MCNPX 26C now also works with continue runs.

### 2.1.1. Depletion Process

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, fission rates, absorption rates, fission
multiplicity ν, and 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. Although MCNPX tracks only certain specified
isotopes that contain transport information, CINDER90 continues to track
the data of all 3456 isotopes using nuclide densities from the prior
time step to do the burnup calculation for the following time step.
Therefore, even though an isotope in a certain decay chain may not be
listed in an MCNPX calculation, the full decay process still is tracked
in the CINDER90 code exactly; therefore, the isotope concentrations
reported are still true isotope concentrations.

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 the code cannot find the CINDER.dat, a
fatal-error message will be printed and the case will cease calculation.

### 2.1.2. Collision Density Generation 

MCNPX calculates continuous energy reaction rates for (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.

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. 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. Reaction rates are printed only for those isotopes also used in
the transport calculation.

### 2.1.3. The Predictor Corrector Methodology

The depletion equations use fluxes, nuclide number densities, and cross
sections to determine the time-dependent nuclide inventory. The
simplified one-group depletion equation 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.

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.

### 2.1.4. BURN Card Setup

The following example explains the setup for a BURN card.

BURN TIME=T1,T2,T3,\...

PFRAC=F1,F2,F3,\...

POWER=P

MAT=M1,M2,M3,\...

OMIT=J1,N1,I11,I12,\...,J2,N2,I21,I22,\...

AFMIN=A

BOPT=B1,B2,B3 ,

where

> Ti = duration of burn step i (days). Default is one time step of one
> day.
>
> Fi = power fraction of each time step (0--1). The default for this
> parameter is to assume Fi = 1.0 for each time step if a *PFRAC* flag
> is not specified at all.
>
> P = power level (MW). Default is 1.0 MW.
>
> Mi = list of material numbers to include in the burn. The default for
> this parameter is to burn all materials.
>
> Ji = ith material for which to omit nuclides Ii1, Ii2, etc. Currently,
> there is no default for this parameter.
>
> Ni = number of omitted nuclides listed for the ith material.
> Currently, there is no default for this parameter.
>
> Ii1, Ii2, \... = 1st, 2nd, etc. omitted nuclides for the ith 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 (default) High to low, based on mass

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 (default) Zr-93,Mo-95,Tc-99m,Ru-101,Xe-131,Xe-134,

Cs-133,Cs-137,Ba-138,Pr-141,Nd-143,Nd-145.

2 All incident neutron cross sections contained in the Fp array included
in

> the current (v250) 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).

### 2.1.5. Burn Time, Total System Power, and Power Fraction

The *TIME* flag corresponds to the incremental time duration for each
depletion step. Each "Ti" listed in this flag 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* flag 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 flag 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* flag corresponds to the fractional value of total system
power (*POWER*) in which to burn the system for the equivalent time
duration. This flag 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 Ti value
listed on the *TIME* flag, a corresponding Fi value listed on the
*PFRAC* flag must exist.

For example:

> *TIME* = 11, 33, 22 ,
>
> *PFRAC* = 1.0, 0.9, 1.2 , and
>
> *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.

### 2.1.6. Flux Normalization Parameters

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:

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

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*
flag. 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* flag;
> default = 1.0),
>
> 2\. modifying the total thermal system recoverable energy by adjusting
> the power level entered on the *POWER* flag, and
>
> 3\. altering the system power on the *PFRAC* flag.

### 2.1.7. Burn Materials

The materials to be burned must be listed on the *MAT* flag. Each "Mi"
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 option, as well as for each individual material listed on the MAT
option 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 up the continuous energy fission energy created to
    obtain an individual burn material fission energy.

3.  Sum up 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

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

\[MTU = MTHM (metric tonnes of heavy metal) and is explained further in
Section 2.1.8.\]

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.

### 

### 2.1.8. Automatic Fission Yield Selection Process

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.

### 2.1.9. Metric Tonnes of Uranium (MTU)

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.

### 2.1.10. Isotope Reactivity Options

The *OMIT* flag allows the user to run a transport calculation without
including the transport data from a specified isotope. This flag
presents the user with the ability to investigate the reactivity effects
that a certain isotope has on the analyzed system.

The *OMIT* flag has the following format:
OMIT=J1,N1,I11,I12,\...,J2,N2,I21,I22,\...

Ji = ith material for which to omit nuclides Ii1, Ii2, etc.

> If J1 = -1, then the omitted nuclide list is applied to all materials
> and J2, J3, etc., are not allowed. No default.

Ni = number of omitted nuclides listed for the ith material. No default.

Ii1, Ii2, ... = 1st, 2nd, etc., omitted nuclide for the ith material. No
default.

The *AFMIN* flag allows the user to determine below which mass fraction
an isotope will be dropped from the transport calculation. The *A* value
of *AFMIN* flag 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.

### 2.1.11. Models Option

The B3 section of the *BOPT* flag 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*
flag 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* flag, 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.

### 2.1.12. Fission Product Tracking/Output Frequency

The B2 value on the *BOPT* flag 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 (default) High to low, based on mass

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 (default) Zr-93,Mo-95,Tc-99m,Ru-101,Xe-131,Xe-134,

Cs-133,Cs-137,Ba-138,Pr-141,Nd-143,Nd-145.

2 All Incident Neutron Cross Sections contained in Fp Array included in

> current (v250) XSDIR

3 All isotopes contained in Fp Array

The fission product array:

> 01003,05010,05011,32072,32073,32074,32076,33075,34077,34079,34080,34082,35081,36082,36083,36084,36085,36086,37085,37086,37087,38086,38088,38089,38090,39089,39090,39091,40090,40091,40092,40093,40094,40095,40096,41095,41097,42095,42096,42097,42098,42099,42100,43099,44100,44101,44102,44103,44104,44105,44106,45103,45105,46104,46105,46106,46107,46108,46110,47109,47111,48110,48111,48112,48113,48114,48116,49115,50116,50117,50118,50119,50120,50122,50123,50124,50125,50126,51121,51123,51124,51125,51126,52122,52124,52125,52126,52128,52130,52132,53127,53129,53130,53131,53132,53133,53134,53135,54128,54129,54130,54131,54132,54133,54134,54135,54136,55133,55134,55135,55136,55137,56134,56136,56137,56138,56140,57139,57140,58140,58141,58142,58143,58144,59141,59142,59143,59145,60142,60143,60144,60145,60146,60147,60148,60150,61147,61148,61149,61151,62147,62148,62149,62150,62151,62152,62153,62154,63151,63152,63153,63154,63155,63156,63157,64152,64154,64155,64156,64157,64158,64160,65159,65160,66160,66161,66162

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.

### 2.1.13. The Isotope Generator Algorithm

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"}

### 2.1.14. Proper Tracking of Entire Decay Chains

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.
Understanding nuclide buildup and depletion is never a straightforward
process; therefore, receiving nuclide concentrations of members of an
isotopes decay chain may give insight into the variation in isotope
buildup and depletion. Further, decay chain members may have significant
cross sections that would lead to altered MCNPX flux and collision
density calculations.

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.

### 2.1.15. Example INPUT

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.

MCNPX requires that each cell to be burned contain a unique material
number. By giving each burn cell a unique material number, the user may
ensure that flux is normalized by the ratio of the fission rate in that
cell versus all other burn cells. Currently, if the user does not select
a unique material number for each individual burn cell, the flux will
not be normalized properly leading to incorrect results.

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.

## 2.2. 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

### 2.2.1. Intra Nuclear Cascade (INC)

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 code significantly; some preexisting bugs in the INC were fixed.

### 2.2.2. Preequilibrium (PREC)

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.

### 2.2.3. Evaporation and/or Fission

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.

### 2.2.4. Coalescence

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.

### 2.2.5. Fermi Breakup

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.

### 2.2.6. Additional Notes

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.

## 2.3. 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.

## 2.4. 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* F*k 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.

## 2.5. 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.

### 2.5.1. User Interface

*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

### 2.5.2. Plotting

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).

## 2.6. 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.

### 2.6.1. User Interface

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.

### 2.6.2. Diagnostics

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).

### 2.6.3. Important Considerations

*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.

## 2.7. Delayed-Gamma Emission.

*Warning! The new delayed gamma emission capability and delayed neutron
capability is preliminary and not guaranteed. It has been included in
MCNPX26C 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 CINDER 90, 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 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

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) l[ine]{.underline} (discrete) data, and (2) c[ontinuous
data. The continuous component of the line data were developed using
computational physics models to]{.underline} 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]{.underline}

> 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

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

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

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.

## 2.8. Criticality Source Convergence Acceleration

*Warning! The new criticality source convergence capability is
preliminary and not guaranteed. It has been included in MCNPX26C 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

Figures 7 -- 9 show results for a 35 X 35 lattice of fuel pins : 330 cm
long, 0.8cm radius UO2 enriched \~3% . Although a "standard" Monte Carlo
calculation with many million histories gives a good answer (Figure 7) a
shorter calculation (Figure 8) does not correctly model the fission
distribution. The estimate with 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

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.

# 3.0. MCNPX 26C Feature EXTENSIONS and Enhancements  {#mcnpx-26c-feature-extensions-and-enhancements .Style-Heading-1h1-+-Times-New-Roman-Black-Underline .unnumbered}

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),

-   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.

## 3.1. 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.

## 3.2. 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 .

## 3.3. 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.

## 3.4. 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.

.

## 3.5. Separate Printout of Induced Fission Multiplicity

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

.

## 3.6. 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.

## 3.8. 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).

## 3.9. 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.

## 3.10. 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.

## 3.11. 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).

## 3.12. 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).

## 3.13. 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 env.
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 env. variables are not permanently set. You have 3 options:

1\) Permanently update your env. variables using the My Computer (right
click) =\> Properties =\> Advanced =\> Env. 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
env. 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 env. 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.

## 3.14. 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)

# **4.0. MCNPX 26C Corrections** {#mcnpx-26c-corrections .unnumbered}

## 4.1. 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.

### 4.1.1. Auger Electrons below Energy Cutoff

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).

### 4.1.2. Detectors in Lattice Geometries

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).

### 4.1.3. KCODE/PRDMP 5^th^ Entry 

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).

### 4.1.5. CEM03 Corrections 

(New 26C) 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).

## 4.2. 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.

### 4.2.1. Cylindrical Weight Window Mesh

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).

### 4.2.2. I8 Mesh Tally Plots

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).

### 4.2.3. Continue Cards for Input with FATAL Errors

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

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

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

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

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 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

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

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

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

### Zero Electron Mesh Tallies

> 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 Crash 

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).

### Insufficient Storage for Tallies

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

> 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-XXX) (GWM 9/11/06)

### GRIDCONV Compiler Bug

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

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.

> 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)

### Crash for Some READ Card Placements

> 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)

### Internal Corrections

The 20^th^ entry on the DBCN card now causes MCNPX26A to track
MCNPX2.5.0 instead of MCNP4C3 and MCNPX2.4.0. (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)

# 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}
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```
-   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

-   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}
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```
-   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 Durkee (LANL, D-5), Michael Fensin (LANL,
    X-3-MCC), Joshua Finch (LANL, P-23), Michael R. James (LANL, D-5),
    Russell C. Johns (LANL, D-5), Robert E. MacFarlane (REM, LANL,
    T-16), Denise B. Pelowitz (LANL, D-5), Laurie S. Waters (LANL, D-5),
    Franz X. Gallmeier (ORNL).

[^2]: 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. .

[^3]: 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 (LANL, X-1). The initial patch to MCNPX
    was developed by GWM and Joe W. Durkee (JWD, LANL, D-5). MCNPX26a,
    26b, and 26c were written mainly by Michael L. Fensin (MLF, D-5).

[^4]: 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.

[^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](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)