LA-UR-02-5253

MCNPX, Version 2.4.0

by

the MCNPX Team

Los Alamos National Laboratory

August 2002

# Introduction

The MCNPX 2.4.0 radiation transport code transports all particles at all
energies. It is a superset of MCNP4C3 and MCNPX2.3.0 plus a number of
new capabilities.

## Guarantee

MCNPX 2.4.0 is guaranteed. We are so confident of the quality of MCNPX
2.4.0 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. We
also will pay a brand new \$2 bill for any error in MCNPX 2.4.0 that has
been inherited from its constituent codes.[^1]

## Contents

1.  Introduction

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1.  MCNPX 2.3.0 features new to MCNP users

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1.  MCNP4C3 features new to MCNPX users

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1.  New MCNPX 2.4.0 features

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1.  User interface for new MCNPX 2.4.0 features

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1.  Future work

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1.  Acknowledgments

2.  References

# MCNPX 2.3.0 features new to MCNP users

MCNPX 2.4.0 includes all of the features and capabilities of MCNPX 2.3.0
(based on MCNP4B), which was recently released to RSICC. MCNPX features
that will be new to MCNP users include:

-   Physics for 34 particle types;

-   High-energy physics above the tabular data range;

-   Photonuclear physics (already in MCNP4C2);

-   Neutron, proton, and photonuclear 150-MeV libraries and utilization;

-   Mesh tallies (tally fluxes, heating, sources, etc., in a
    superimposed mesh);

-   Radiography tallies;

-   Secondary-particle production biasing; and

-   Autoconfiguration build system for compilation.

In particular, the mesh tallies enable users to plot source particle
locations, fluxes, energy deposition, particle tracks, DXTRAN
contributions, and other useful quantities on a superimposed tally grid.
This capability is useful for all transport problems, not just
high-energy problems.

# MCNP4C3 features new to MCNPX users

MCNPX 2.4.0 includes all the features and capabilities of MCNP4C3. Many
of these features have not been in MCNPX before because, until now,
MCNPX has been built on MCNP4B. Principal among these features not
previously available in MCNPX are

-   PC enhancements: MCNPX 2.4.0 is fully Linux and Windows capable;

-   Easier geometry specification with macrobodies;

-   Interactive geometry plotting;

-   Improved variance reduction with the superimposed mesh weight window
    generator;

-   Superimposed mesh plotting;

-   Delayed neutrons;

-   Unresolved resonance range probability tables;

-   Perturbations for material-dependent tallies;

-   ENDF/B-VI extensions;

-   Electron physics enhancements (upgrade to ITS3.0);

-   Weight window enhancements; and

-   Distributed memory multiprocessing.

# New MCNPX 2.4.0 features

## Summary

MCNPX 2.4.0 has several new capabilities not found in either MCNP4C or
MCNPX 2.3.0 (initials of principal developers are shown in
parentheses[^2]). Details of these features are described in additional
subsections below.

-   FORTRAN 90 modularity and dynamic memory allocation (GWM);

-   Distributed memory multiprocessing for the entire energy range of
    all particles (GWM);

-   Repeated structures source path improvement (LLC/JSH);

-   Default dose functions (LSW/JSH);

-   Light-ion recoil (JSH);

-   Enhanced color geometry plots (GWM/JSH);

-   Photonuclear cross section plots (JSH);

-   Proton cross section plots (JSH);

-   Proton reaction multipliers with FM cards (JSH);

-   Photonuclear reaction multipliers with FM cards (JSH/GWM);

-   Some speedups (GWM/JSH);

-   Logarithmic interpolation on input cards (JSH);

-   Cosine bins that may be specified in degrees (JSH);

-   Cosine bins may be specified for F2 flux tallies (JSH);

-   Source particles that may be specified by descriptors (JSH);

-   Pause command for tally and cross section plots (JSH); and

-   Correction of all known MCNPX and MCNP4C bugs/problems.

## Description

### FORTRAN 90 Modularity and Dynamic Memory Allocation

The F90 conversion provides improvements in code modularity,
standardization of functions such as timing across platforms, and
compiler reliability. F90 will run more slowly on some systems.
Specifically, we have eliminated equivalences as a means of dynamic
storage allocation by using F90 pointers and allocable arrays. We have
replaced most common calls with F90 modules. The code will compile in
both free and fixed F90 formats.

MCNPX 2.4.0 can be modified by patches, and as much of the MCNP4C coding
as possible has been preserved so that MCNP4C patches can be applied
directly to MCNPX 2.4.0.

Continuing improvements in the F90 structure are ongoing, especially
where they concern physics modules that have been brought into the code.

### Distributed Memory Multiprocessing for the Entire Energy Range of All Particles

Parallel Virtual Machine (PVM) software can be used to run the entire
MCNPX code in parallel. Fault tolerance and load balancing are
available, and multiprocessing can be done across a network of
heterogeneous platforms. Threading may be used for problems run in the
table data region only.

### Repeated Structures Source Path Improvement

Sources in repeated structures and lattices now may be specified with
the same notation as tallies, and the paths are printed correctly in the
output (see Section 5.2).

### Default Dose Functions

Fourteen standard dose functions in United States (US) or international
units may be applied to any tally without entering the tables on DE/DF
cards (see Section 5.1).

### Light-Ion Recoil 

Neutrons and protons undergoing elastic scatter can cause light-ion
targets (H, D, T, ^3^He, and ^4^He) to create particles (h, d, t, s, and
a) that are banked for subsequent transport with the proper two-body
kinematics (see Section 5.6.2).

### Enhanced Color Geometry Plots

Sixty-four colors are now available. Cells may be colored by any
cell-based quantity, not just material. Logarithmic shading of
importances, weight windows, and summary information is automatic.
Color-coded shading of mesh-based weight windows is available (see
Section 5.7).

### Photonuclear Cross Section Plots

Photonuclear interaction cross sections and their secondary particle
yields may now be plotted with the MCNPX cross section plotter (see
Section 5.8).

### Proton Cross Section Plots

Photonuclear interaction cross sections and their secondary particle
yields may now be plotted with the MCNPX cross section plotter (see
Section 5.9).

### Photonuclear Reaction Multipliers 

Photonuclear cross sections and yields may be used to multiply fluxes
and other tally quantities on FM tally cards. Now the production of
various secondary particles and reactions such as photofission may be
tallied (see Section 5.10).

### Proton Reaction Multipliers 

Proton cross sections and yields may be used to multiply fluxes and
other tally quantities on FM tally cards (see Section 5.10).

### Speedup

The increased generality and FORTRAN 90 conversion of MCNPX 2.4.k slow
the code down by \~15%. However, in certain cases, some speedups have
been added to make it faster than either MCNP4C3 or MCNPX 2.3.0,
particularly for repeated structures/lattice plotting and few-particle
MCNPX problems.

### Logarithmic Interpolation

E4 1.e-5 10log 1.e5

is equivalent to

> E4 1.e-5 .0001 .001 .01 .1 1 10 100 1000 10000 .

### Cosine Specification in Degrees

Cosine bins may be specified in degrees for F1 current tallies. Cosine
bins may now also be specified for F2 flux tallies (see Section 5.4).

### Source Particles May Be Specified by Descriptors

Previously,

SDEF par = n,

where

> n = 1,2,\...,9,\... (numbers).

Now,

SDEF par = n,

where

> n = n,p,\...,h,\... (character particle designators)

is optionally allowed (see Section 5.5).

### Pause Command for Tally and Cross Section Plots

The MCNPX geometry plot *PAUSE* command is now extended to tally and
cross section plots. When the word *PAUSE N* is put in a tally plotting
COM input file, the picture will display for *N* seconds. If the command
*PAUSE* (without the *N*) is in the COM file, then the display will hold
until a key is struck.

# User interface for new MCNPX 2.4.0 features

Section 4 provided a summary description of the new MCNPX 2.4.0
features. This section now describes the user interface changes for the
following subset of those features.

-   default dose functions: DFn;

-   repeated structures source specification: SDEF, SI;

-   logarithmic interpolation: Nlog;

-   expanded cosine specification: Cn;

-   SDEF particle specification: SDEF par h;

-   energy straggling: PHYS:N 4j I;

-   light ion recoil: PHYS: N 6j R;

-   enhanced color geometry plots: COLOR;

-   photonuclear cross section plots;

-   proton cross section plots; and

-   photonuclear and proton reaction multipliers: FM.

These features are described below and in the forthcoming new MCNPX
2.4.0 manual.

## Default Dose Functions

The MCNPX DFACT mesh tally capability has been expanded to provide
standard dose conversions with the DE/DF cards.

Users may input a table as in MCNP/MCNPX (although the interpolation int
= log or int = lin may now be placed anywhere). n = tally number, which
implies particle type.

> DEn E1 E2 int E3 \...
>
> DFn F1 int F2 F3 \...

Or, the following DF card is accepted:

DFn iu=j fac=F int ic=I ,

where the following entries are all optional.

> iu = 1 = US units (rem/h)
>
> iu = 2 = international units (sieverts/h)
>
> Default: iu = 2 international units (sieverts/h)

fac = normalization factor for dose (acr is also accepted instead of
fac).

> fac = -1 = normalize results to Q = 20 by dividing the parametric form
> of Q \[5.0+17.0\*exp(-(ln(2E))\*2/6)\] from ICRP60 (1990), paragraph
> A12.
>
> fac = -2 = apply LANSCE albatross response function.

Default: fac = 1.0.

> int = "log" or "lin" results in "log" or "lin" interpolation of
> energy; the dose function is always linear. That is, "lin" results in
> "linlin" interpolation, and "log" results in "loglin" interpolation.

Default: for ic = 10, 40: log

> for ic = 20,31-39: recommended analytic parameterization.

ic = i = standard dose function.

> [i neutron dose function]{.underline}
>
> 10 = ICRP-21 1971
>
> 20 = NCRP-38 1971, ANSI/ANS-6.1.1-1977
>
> 31 = ANSI/ANS-6.1.1-1991 (AP anterior-posterior)
>
> 32 = (PA posterior-anterior)
>
> 33 = (LAT side exposure)
>
> 34 = (ROT normal to length and rotationally symmetric)
>
> 40 = ICRP-74 1996 ambient dose equivalent

[i photon dose function]{.underline}

10 = ICRP-21 1971

> 20 = Claiborne & Trubey, ANSI/ANS 6.1.1-1977
>
> 31 = ANSI/ANS-6.1.1-1991 \[AP (anterior-posterior)\]
>
> 32 = PA (posterior-anterior)
>
> 33 = (LAT side exposure)
>
> 34 = (ROT normal to length and rotationally symmetric)
>
> 35 = (ISO isotropic)
>
> Default: ic = 10

### Examples

> DF4
>
> DF0 ic 40 iu 1 lin fac 123.4
>
> DF1 iu=2 acr=-2 log ic=34

## Repeated Structures Source Specifications

The CEL source specification for repeated structures geometries is now
consistent with the tally specification. The old MCNP4C specification
still works, but the new one is

> sdef cel=d3 pos=0 6 0 ext d1 rad d2 axs 0 1 0
>
> si3 L (1\<10\[0 0 0\]\<11) (1\<10\[1 0 0\]\<11) (1\<10\[2 0 0\]\<11)
>
> (1\<10\[0 1 0\]\<11) (1\<10\[1 1 0\]\<11) (1\<10\[2 1 0\]\<11)

All of the output prints now also are consistent.

## Logarithmic Interpolation

Logarithmic interpolation is now allowed on input cards. It is similar
to the IJMR interpolation of MCNP. For example,

e0 1.e-3 6log 1.e4

is interpreted as

e0 .001 .01 .1 1 10 100 1000 10000 .

## Expanded Cosine Specification

Cosines may now be specified in degrees. They may also now be specified
with flux tallies:

\*C2 150 120 90 60 30 0 .

The \* on the C2 card interprets cosines as in degrees. Entries must be
such that the cosine is monotonically increasing.

## SDEF Particle Specification

The source particle type now may be specified on the SDEF card by its
symbol:

SDEF par=h

## PHYS:n Changes

For neutrons, the fifth entry is the model/table energy cutoff (see new
Print Table 41). In previous MCNPX versions, this was the third PHYS:N
entry.

For particle types n \> 2 (e,..., h,...), the fifth entry is the energy
straggling (see Section 5.6.1).

For neutrons or protons, the seventh entry is the light-ion recoil
control (see Section 5.6.2).

### Energy Straggling (Particle Types n \> 2)

Dick Prael's and Grady Hughes's energy-straggling model in MCNPX 2.2.6
and later is specified as follows.

PHYS:n 4j I (5th entry on PHYS:n card) ,

where

> I = 0: Prael's new straggling model---an energy correction addressing
> stopping powers of charged particles (default)
>
> = 1: continuous slowing down ionization model; and
>
> = -1: straggling model used in MCNPX 2.2.4 and previous releases.

n = particle type:

for

n = N, entry I is the library energy cutoff (formerly the third entry);

> n = P, entry I is unused; and
>
> n = E, the straggling model control is the same as MCNPX 2.3.0 and
> MCNP4C3.

### Light-Ion Recoil (Incident Neutrons and Protons only)

PHYS:n 6j R (seventh entry on PHYS:n card) ,

where

> n = N or H (neutrons and protons only);
>
> 0 \< R ≤ 1: number of light-ion particles (h, d, t, s, and a) to be
> created at each elastic scatter on light nuclei for H, D, T, ^3^He,
> and ^4^He. The ionization potential is accounted for, and the proper
> two-body kinematics is used (with neutron free-gas thermal treatment
> if appropriate) to bank the created particles with the proper energy
> and angle.

Auxiliary cards:

> mode n h d t s a ,
>
> where n and/or h is required to produce light-ion elastic recoil from
> either neutrons and/or protons, and
>
> h,d,t,s,a are required to produce any of these particles.

Note that protons colliding with hydrogen to produce more protons can
produce an overwhelming number of protons; caution is required.

> cut:N 2j 0 ,

where

> N = h,d,t,s,a may be needed to produce low-energy elastic recoil ions.
> The default alpha (a) energy cutoff is 4 MeV; however, dropping the
> alpha cutoff to zero will result in the minimum energy cutoff for an
> alpha of 1 keV, thus enabling the creation of E \> 1 keV alphas.

## Enhanced Color Geometry Plots (D-10:JSH-2002-09)

The new plotting capabilities are accessible via either the interactive
geometry plot capability or the command/prompt interface.

In the interactive capability, the "SCALES n" button has been moved up
two lines (after the cursor) to make room for a larger "COLOR name"
button. The default is "COLOR mat", which colors problem cells by the
program material number. This button must be clicked to get "COLOR off"
(black and white) and then clicked again to color by whatever parameter
is listed after the "Edit" button. For example, in the right margin,
"cel" must be clicked, which will make the "Edit" quantity "cel". Next,
"COLOR" must be clicked so that it says "COLOR cel"; on the next plot,
the color shades will be by program cell number.

In the command/prompt input mode, the label command must be set, such as

PLOT\> label 0 1 rho;

then the color command must be set such as

PLOT\> color on

and the coloring will now be by rho, the atom density.

## Photonuclear Cross Section Plots (D-10:JSH-02-98)

Until now the only photon cross sections that could be plotted in MCNPX.
Photoatomic reaction numbers are all negative: -1 = incoherent, -2 =
coherent, -3 = photoelectric, -4 = pair production, -5 = total, -6 =
heating. For the MCNPX photonuclear cross section plotting, the reaction
numbers are all positive. The principal photonuclear cross sections are:
1 = total, 2 = nonelastic, 3 = elastic, 4 = heating, \>4 = various
reactions such as 18 = (γ,f). The photonuclear yields (multiplicities)
for various secondary particles are specified by adding 1000 x the
secondary particle number to the reaction number. For example, 31001 is
the total yield of deuterons (particle type d = 31); 34001 is the total
yield of alphas (particle type α = 34); 1018 is the total number of
neutrons (particle type n = 1) from fission. To find out which reactions
are available for a particular nuclide or material, enter an invalid
reaction number, such as mt = 99, and MCNPX will list the available
photonuclear reactions and the available yields such as 1018, 31018,
34018. Entering a bad nuclide, xs = 12345.67u, will cause MCNPX to list
the available nuclides.

The figures below illustrate photonuclear cross section plots for mt = 1
and mt = 2005.

![](media/image1.png){width="5.698611111111111in"
height="4.278472222222222in"}

![](media/image2.png){width="5.579166666666667in"
height="4.188888888888889in"}

## Proton Cross Section Plots (D-10:JSH-02-98)

For proton cross section plotting, the reaction numbers are similar to
the neutron reaction numbers: all positive. The principal photonuclear
cross sections are: ±1 = total, ±2 = nonelastic, ±3 = elastic, ±4 =
heating, \>4 = various reactions. On the LA150H proton library, the only
available reaction is mt = 5 and its multiplicities, 1005, 9005, 31005,
etc. The multiplicity reaction numbers for interaction reaction mt = 5
are 1005 for neutrons, n = 1, 9005 for protons, h = 9, 31005 for
deuterons, d = 31, etc. To find out which reactions are available for a
particular nuclide or material, enter an invalid reaction number, such
as mt = 99, and MCNPX will list the available proton reactions and the
available yields such as 1005, 32001, 34002, etc. The proton
multiplicity, mt = 9001, 9004, 9005, etc., is generally available along
with the total cross section and heating number, mt = 1, mt = 4.
Entering a bad nuclide, xs = 12345.67h, will cause MCNPX to list the
available proton nuclides.

## Photonuclear and Proton Reaction Multipliers (D-10:JSH-02-98)

Photonuclear and proton cross sections may be used in tally multipliers
on the FM card. For example,

M102 92235 1 pnlib=27u

F2:P 1

FM2 (-1 102 18 1018)

It is always wise to plot the desired cross sections first to see if
they are available with the expected reaction numbers in the data
library. The tally multipliers treat the data the same way as the data
are treated in transport: the cross section at the lowest energy is
extended down to E = 0 for protons with mt \< 0; the cross section at
the highest energy of the table is extended to E = ∞ for proton
interaction cross sections with mt \< 0 and for photonuclear interaction
cross sections, mt \< 1000. These extrapolations can be seen in the
cross section plots.

# Future work

-   **Mix-and-match capability:** In the neutron (and other particle)
    energy range above the top energy of some data libraries but below
    the top energy of other libraries, MCNPX currently cannot mix both
    model and tabular data. Either the higher-energy data are ignored
    and models are used for all nuclides or the data are used where they
    exist and are extrapolated from the top of the energy table for
    nuclides where the data do not exist. A means of mixing and matching
    both tabular data and model data is being developed.

-   CEM 2K: The current CEM physics model is being updated.

-   Pulse height tallies with variance reduction.

-   Cugnon Intranuclear Cascade (INC) model and Schmidt evaporation
    model.

-   Special features for Space applications.

-   A capability to continue runs that write HTAPE files

-   Integration of HTAPE tallies directly into MCNPX.

-   Heavy ion tracking and interactions.

-   Improved high energy physics with the LAQGSM model.

# AcknowledgEments

The principal developers of MCNPX 2.4.0 are John Hendricks, Gregg
McKinney, Grady Hughes, Laurie Waters, Edward Snow, Skip Egdorf, Teresa
Roberts, and Franz Gallmeier (ORNL). MCNPX 2.4.0 is based on MCNPX
2.3.0, MCNP4C3, Dick Prael's LAHET code system, and Stepan Mashnik's CEM
code. MCNPX has benefited from many other developers over the years.

Dr. Grady Hughes has been instrumental in the development of MCNPX since
the program's inception in 1995. The code has also greatly benefited
from the work of the LANL nuclear data and physics teams (Mark Chadwick,
Robert C. Little, Stepan Mashnik, David Madland, Arnie Sierk, Morgan
White). John Hendricks and Gregg McKinney (now actively working on
MCNPX) were the principal developers and leaders of MCNP for the past
decade.

# References

Laurie S. Waters, Editor, \'MCNPX User\'s Manual - Version 2.1.5,\'

Los Alamos National Laboratory Report, TPO-E83-G-UG-X-00001

(November 14, 1999)

J. F. Briesmeister, Ed., \`\`MCNP - A General Monte Carlo N-Particle

Transport Code, Version 4C,\'\' LA-13709-M, Los Alamos National
Laboratory

(April 2000)

J. A. Halbleib, R. P. Kensek, T. A. Mehlhorn, G. D. Valdez, S. M.
Seltzer, M. J. Berger, \"ITS Version 3.0: The Integrated TIGER Series of
Coupled Electron/Photon Monte Carlo Transport Codes,\" Sandia National
Laboratories report SAND91-1634 (March 1992)

J. S. Hendricks, K. J. Adams, T. E. Booth, J. F. Briesmeister, L. L.
Carter, L. J. Cox, J. A. Favorite, R. A. Forster, G. W. McKinney, R. E.
Prael, \`\`Present and Future Capabilities of MCNP,\'\' *Applied
Radiation and Isotopes*, **53**, No. 4-5, 857-861, Elsevier Sciences,
Ltd. (Netherlands), Pergamon Press, NY (October - November 2000)

J. S. Hendricks, G. W. McKinney, L. S. Waters, H. G. Hughes, E. C.
Snow,   \`\`New MCNPX Developments,\'\' LA-UR-02-2181, 12th Biennial
Radiation Protection and Shielding Division Topical Meeting, Santa Fe,
NM, American Nuclear Society, ISBN:8-89448-667-5,   ANS Order No. 700293
(April 14-18, 2002)

H. G. Hughes, K. J. Adams, M. B. Chadwick, J. C. Comly, L. J. Cox, H. W.
Egdorf, S. C. Frankle, F. X. Gallmeier, J. S. Hendricks, R. C. Little,
R. E. MacFarlane, R. E. Prael, E. C. Snow, L. S. Waters, M. C. White,
and P. G. Young, Jr., \"Recent Developments in MCNPX,\" Proceedings of
the Second International Topical Meeting On Nuclear Applications of
Accelerator Technology, 281, Gatlinburg, TN, September 20-23, 1998.

H. G. Hughes, K. J. Adams, M. B. Chadwick, J. C. Comly, L. J. Cox, H. W.
Egdorf, S. C. Frankle, J. S. Hendricks, R. C. Little, R. E. MacFarlane,
S. G. Mashnik, R. E. Prael, A. J. Sierk, L. S. Waters, M. C. White, P.
G. Young, Jr., F. Gallmeier, E. C. Snow, \`\`MCNPX for Neutron-Proton
Transport,\'\'  Proceedings of Mathematics and Computation, Reactor
Physics, and Environmental Analysis in Nuclear Applications, Madrid,
Spain, Vol. 2, p. 39-948 (September 1999)

E. C. Selcow, G. W. McKinney, T. E. Booth, J. F. Briesmeister, L. J.
Cox, R. A. Forster, J. S. Hendricks, R. D. Mosteller, R. E. Prael, A.
Sood, S. W. White, \"MCNP Capabilities at the Dawn of the 21st Century:
Neutron-Gamma Applications,\'\' MC2000: International Conference on
Advanced Monte Carlo for Radiation Physics, Particle Transport
Simulation and applications, Lisbon, Portugal (October 23-26, 2000)
LA-UR-00-5017

J. S. Hendricks, \"Advances in MCNP4C,\'\' Radiation Protection for Our
National Priorities, Spokane, Washington, September 17 - 21, 2000
(LA-UR-00-2643)

G. W. McKinney, T. E. Booth, J. F. Briesmeister, L. J. Cox, R. A.
Forster, J. S. Hendricks, R. D. Mosteller, R. E. Prael, A. Sood,
\`\`MCNP Applications for the 21st Century,\'\' Proceedings of the 4th
International Conference on Supercomputing in Nuclear Applications,
September 4-7, Tokyo, Japan (2000).

J. S. Hendricks, G. W. McKinney, L. J. Cox, \`\`Monte Carlo Advances for
the Eolus ASCI Project,\'\' PHYSOR2000 International Topical Meeting on
Advances in Reactor Physics and Mathematics and Computation, Pittsburgh,
PA (May 7-11, 2000)

K. J. Adams, T. E. Booth, J. F. Briesmeister, L. L. Carter, J. D. Court,
L. J. Cox, J. A. Favorite, R. A. Forster, J. S. Hendricks, G. W.
McKinney, R. E. Prael, \`\`Present and Future Capabilities of MCNP,\'\'
Fourth Topical Meeting on Industrial Radiation and Radioisotope
Measurement Applications (IRRMA 99), Raleigh, NC, page 38 (October 3-7,
1999)

[^1]: Cash Award Fine Print: Offer subject to cancellation or
    modification without notice. A bug is defined as an error in the
    source code that we choose to correct. We make awards even for the
    most trivial or insignificant problems, but not for proposed code
    enhancements or proposed extended capabilities. Awards 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 believe MCNPX and its
    predecessor codes are the most error-free and robust Monte Carlo
    radiation transport capabilities. We challenge you to find a bug!

[^2]: ^2^ Gregg W. McKinney (GWM), John S. Hendricks (JSH), Laurie S.
    Waters (LSW), Leland L. Carter (LLC).