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MICROCOPY RESOLUTION TEST CHART
NATIONAL BUREAU OF STANDARDS -1963
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ORNCP-2310
MASTER

- Pensar sovence ASTROS
LH NUCLEAR SCIENCE ABSTRACTS
AUG 10 1966
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that is minder dan
SURVEY OF THE V. S. SHIELDING CALCULATIONAL METHODS AND PROGRAMS*
S. K. Penny CONF-660143-
HC: /.001
Carex siis
meminta maailmamei
The foremost changes which the field of shielding calculations
is experiencing today are being brought about by the rapidly changing
field of computer technology. It has long been recognized that the
use of a computer is essential in order to perform shielding calcula-
tions which harbor any degree of sophistication or complexity. This
is strikingly evident when the geometry is complex. It is natural,
then, that our field should follow the field of computer technology.
e
under
historia de
The rapid access memories and mass-storage devices which are "just
around the corner" have brought about a revolution in the design
and implementation of calculational methods for radiation shielding.
Instead of a computer code and its input, we now think of such
notions as "coding systems" and "prototypes," "cross-section systems"
and "modules," and even "compilable systems."
In order to better understand some of these notions, Let us go
back a few years to the time when the IBM-7090 started to replace the
IBM-704. At this time the concept of a general purpose code was in
vogue. The Monte Carlo technique was becoming increasingly popular
and consequently a few general purpose Monte Carlo codes appeared
on the scene. -- There were also a few general purpose kernel-
integration codes evolving.4-6 The Carlson Sn codes? had not been
DANI -"'
*Research sponsored by the U. S. Atomic Energy Commission under
contract with the Union Carbide Corporation.
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developed to the extent of embodying a disciete-ordinate quadrature
and they employed a differential cross-section which was expanded
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Cica psicos
only to R. The Carlson Scodes were therefore not seriously con-
sidered for shielding calculations at this time. However, the United
Nuclear Corporation produced a discrete-ordinate code for spherical
geometry called NIOBEⓇ which seemed to be an excellent tool for shield-
ing calculations. United Nuclear Corporatior. also produced a moments-
waethod code for the attenuation of neutrcns in an infinite homogeneous
medium called RENUPAKand certainly the National Bureau of Standards
rinkiniai
had a gamma-ray code for a similar calculation. There were other
concepts evolving among which were the method of spherical harmonics"
and a United States version of the Spinney-Method (removel-diffusion)
which became a code called MAC. .
After the onset of this period an interesting change in philosophy
began to develop in the design of computer cries for shielding calcu-
lations. The concept of the "coding system" was starting to replace
the concept of a general purpose code. (I must hasten to apologize
at this point for any oversight of U. S. code development during this
time period.) Nctable examples among those working in this direction
berbandinavia
were the General Electric Company at Cincinnati, Ohio, the United
Nuclear Corporation, and the Technical Research Group. The General
Electric Corporation was in fact ahead of its time in implementing
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the coding system by automating cross-section input and other input
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data as well as for efficiently using the output data. Loc. It was
evident that the codes produced by the United Nuclear Corporationº,9,22,23
and the Technical Research Group24-26 utilized a "cross-section system"
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and that the structure of these codes smacked of the "modular" nature.
That is to say, the codes were manufactured by including certain
simple-purpose subroutines which obviated the chores of "housekeeping"
and by writing subroutines which fixed the character and purpose of
the code. Of course these subroutines were often commanded by an
executive program which did not, vary appreciably from code to code.
To give proper credit, I believe that the shielding community probably
learned from the reactor community, who employed the notions of
cross-section systems and subroutine modules at an earlier date. In
short, the general purpose code was in fact limited by computer
memory and systems as well as the fixed number of options. Hence
the coding system with its cross-section system and subroutine mouules
evolved to the present day situation where we see on display the
manufactured-product-codes dubbed here as "prototypes."
A most popular technique that is employed in the United States
today is the Monte Carlo technique. Its popularity stems from the
fact that in principie one may incorporate complicated geometric and
source configurations into calculations of radiation transport. The
energy and angular distributions of radiation which penetrates
relatively large thicknesses of material can also be calculated in
principle. Moreover, with the advent of simplified programming systems,
such as FORTRAN, and fast computers, the Monte Carlo technique is
available to many more people today than it was a few years ago. In
fact the sterotipe of the Monte Carlo expert, who labors over a sub-
routine written in symbolic language to make it extremely efficient,
is disappearing. He is still essential, but he works closely with
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other members of a programming team which is concerned with the con-
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struction of a coding system alluded to earlier.
The importance of the coding system is seen by observing that
a physicist or engineer may be relieved of the burden of the large
programming effort in the complete construction of a Monte Carlo
code and may restrict his efforts to the writing of a few suvroutine
modules to perform the random sampling and scoring techniques peculiar
to his purpose. The Monte Carin technique lends itself well to the
notion of a coding system. An executive program can easily be con-
structed to generally control the inpuc and output land to command
the algorithms necessary for generating the life histories of the
radiation and for tabulating the score or expected values of these
histories. Subroutine modules can be constructed to handle fairly
general geometry and to easily implement cross section input.
The
algorithms governing the generation and scoring of the life histories
can be easily arranged in a modular form.
Among the Monte Carlo coding systems extant in the United States
are the 05Ra nd OGRE<° systems of Oak Ridge National Laboratory,
UNC-SAM?9 of United Nuclear Corporation, and 1-0550 of General Dynamics,
USAF Nuclear Aerospace Research Facility. There is evidence that
others are probably using coding systems a few of which are Technical
Operations Research, 32 Atomics International, Radiation Research
Associates, 52 and Lockheed-Georgia Company at Marietta.
The future course of the evolution of Monte Carlo s ystems is
interesting to contemplate. A movement is already afoot to inter-
connect the many cross-section systems for both reactor and shielding
calculations via ‘a national "hookup." Many installations, which have
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cross-section data arranged neatly in an automated system, have
expressed an interest and a desire to aid in compiling a national
cross-section system which many of you may linow as the Evaluated
Nuclear Data File or ENDF."
The possibilities of sharing data
swiftly and automatically have obvious advantages, not the least of
which may be economic. Moreover there is the possibility of an inter-
national "hookup" with which many of you inay also be familiar. One
of the most interesting ideas on the horizon is the "compilable
system." The idea is simply that a computer facility may have, as
a subsystem, the aforementioned code system ensconsed in mass storage
along with subroutine modules which ar likely to be used and perhaps
even a special compiler which will more than likely be FORTRAN. This
compilable system could then be approached by the physicist or enſineer,
who would have a special purpose task to perform, with the minimum of
effort and programmang skill so that he could concentrate on the
special subroutines he would need for random sampling and scoring.
I have said very little about the Munte Carlo techniques them-
selves and the reason is that the techniques have not ciianged a great
deal, although there are some old notions which are being resurrected.
The techniques of survival biassing, Russian Roulette and splitting
(based on weight standards), and expected values are commonly used
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today. There has been little imagination incorporated into scoring
techniques and perhaps too much imagination has been brought to bear
on sampling techniques. Practically nothing has been done about
assessing the statistical errors inherent in the Monte Carlo processes.
This situation is rather sad since for larg attenuations it seems
intuitive that the distributions will differ appreciably from normal.
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LEGAL NOTICE
The report nus prepared un secowi of Governou opousond work. Neidy che limited
Melos, nor the coamustoa, nor way around uting car wil of the wirebon:
. Wakus may warruty or reprcinala uon, expressed or implied, mth respect to the accu-
racy, dwa pleteness, or we felness of the information contained in this report, or the owe
of may lalormethan, apparatu, ai , ar mani daclound this report my har tatring
pinkaly owned redus; or
1. Ammus ny liabides with respect to the w ol, or lar d'nayo watter from the
Nowy alurudhon, wanatus, method, or mascus decloond to the report.
As wood to the abovo, "perHU scting a hotell nad the cominstea" Lozlu y
Moyna a contractar a un cumleaton, or mployees are connector, W ed that
much wpisyo a contractor of the Counselling a wwwploynd met minister meenee,
decolmalar, or por den sena to, any commation present to beli plement or connet
vith the countsabou, w komplement mal mah cairan.
6.
There are some clean-cut notions regarding the use of importance
sampling which are being resurrected today. One should not approach
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the technique of importance sampling blindly. All too often reliance
on intuition may be a case of "the blind leading the blind." Clearly
the use of the exponential transformation as a guide to importance
sampling has merit and is used to some cxtent today. The use of a
more genera.l transformation, of which the exponential transformation
is a special case, is another guide which is being considered. The
latter can be associated with the adjoint of the transport equation
end there are several groups investigating this concept among which
are Coveyou, et al., at Oak Ridge, Kalos now of the MAGI (Mathematical
Applications Group, Inc.), and Gelbard et al. at the Westinghouse
Bettis Laboratory. It is difficult to give proper credit for these
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ideas. Herman Kahn's exposition4 on Monte Carlo techniques contains
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in some form almost all, if not all, the techniques that have been
used. Goertzelwrote about some of these notions quite early and
later Goertzel and Kalos elucidated."Probably the first practical
use of the exponential transforzation was by Beach et al. This was
followed by the work of Perkins and Burrell." Several others have
incorporated the exponential transformation and the most recent appli-
cations, and perhaps the most elegant, have been reported by Leimdörfer?9
(if I may intrude upon the European scene), Clark, 4' and Chilton. 41
As I mentioned before, the scoring techniques have not evolved
a great deal. It is common practice to use an uncollided flux estimator
ilton. 42
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at each collision to calculate a current, & flux in a volume, or a flux.
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at a point. Kalos*
has pointed out that these estimators lead to
an infinite variance and he proponed an alternate scheme. It is
not clear why his suggestion has not come irito common usage, but it
is now seriously being considered by some groups. A novel estimator
was used by Amster et al." and again by Trubey** for enother appli-
cation. This estimator was based on the first flight from the source.
Turning to another fubject, the discrete-ordinate Carlson Sn codes
are now being considered as research tools in shielding. The turning
point was when Lethrop at Los Alamos applied the technique to gamma-
ray shielding problems. Others working concurrently in this area
were the groups at General Atomi. 's at Ia Jolla, Atonics Inter-
national, Westinghouse Bettis Laboratory, and Oak Ridge National
Laboratory. The principal change was the expansion of the differential
cross-sections to higher orders of Legendre polynonials.
It is clear
that the one-dimensional codes may readily be used, but there are
some unsolved difficulties with the two dimensional versions. One of
the problems, namely that of computer storage required, will certainly
be resolved with the next generation computers.
It is fairly certain
that this technique will come into common usage particularly for
parametric studies and for the estimation of heating. The advantage
of handling multilayered configurations in a fairly ex&ct way makes
the technique seem more attractive than that of the point kernel inte-
gration. The Carlson S, technique lends itself to the fancy notions
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of modularity only to the extent of employing a cross-section system
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The last major topic is that of the point kernel-integration
technique. This technique depends on having a goodly supply of
attenuation data in infinite homogeneous media or else experimental
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data in a thick bulk medium. Consequently it is helpful to have at
one's disposal codes which are fairly exact in simple geometry namely
those empioying the moinenčs-method, the Carlson Sn technique, spherical
harmonics, etc. The kernel-integration technique is only an approxi-
mation and probably is only applicable to situations where the source
is embedded in a bulk shieid. The technique has enjoyed longevity
and there are many prescriptions for utilizing the infinite medium
data for the case of a multilayered shield.*oger Basically the tech-
nique is simply that of ray-tracing in that one compute the distances
in each portion of the shield along the ray from a source point to
a rield point, uses some formula to arrive at an attenuation rinction,
and ultimate.ly integrates over the source volume. There are embellish-
ments of this basic technique such as attaching an angular distri-
bution as the rays cross the outer surface of the shield and as in
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the two-component method *' where one not only attaches an angular
distribution, but integrates over the surface. By and large the in-
plementation of this technique is an art, but is not to be discounted
when one is fairly familiar with the shield configuration and when
time is of the essence as in parametric studies. This technique
lends itself to modularity in the employment of geometry, input-output
and perhaps integration modules.
There are other techniques which are not commonly used, but should
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be mentioned. The Spinney-method (removal-diffusion) is probably used
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only to any great extent by the group at Battelle-Northwest; the
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code 18 MAC. closely allied with the spinney-Method is the "trans-
fusion" technique reported by Trubey." This technique is aimed
toward the calculation of low energy neutron fluxes and in principle
one uses a transport code to calculate the spatially dependent
sources to be introduced into a multigroup diffusion code. The tech-
nique of invariant imbedding is being investigated by the Rand Corp.
and General Dynamics, USAF Nuclear Aerospace Research Facility.
closely related is the transmission matrix technique of Liedtka
et al. There are sther computer code applications to shielding
problems, but since the main interest is that of attemiation I will
not delve into the matter.
The future of the shielding calculational techniques in the
U. S. lies with the future of computer technology.
I expect to see
more, and hopefully more censible, Monte Carlo applications. It is
almost certain the compilable system will come into being.
The use
of the discrete-ordinate Carlson Sn technique will increase and
perhaps become commonplace. We will always have the kernel-integra-
tion technique for it is without doubt the tool of the engincer
who must make rapid calculations and who must perform parametric
studies. I believe that the Spinney-method will be used to a larger
extent especially when the European codes NRN and COMPRASII are
introduced into the United States. In any case the future is
exciting to contemplate and hopefully will be fruitful.
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REFERENCES
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1.
J. J. Locchler and J. E. MacDonald, Flexible Monte Carlo Programs
FMC-N and FMC-G, APEX-706 (April 1961).
2. R. R. Coveyou, et al., "The Oak Ridge Random Research Reactor
Routire (05R): A General Purpose Monte Carlo Code for the IBM-704,"
Neutron Physics Div. Ann. Progr. Rept. Sept. 1958, CRNL-2309,
p. 87; ani S. K. Penny, "A General Purpose Monte Carlo Gamma-
Ray Code," Neutron Phys. Viv. Ann. Progr. Rept. Sepćo 1961,
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3. E. J. Leshan, RBU, Caiculation of Reactor History Including the
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J. T. Martin, J. P. Yalch, and W. E. Edwards, Shielding Computer
4.
2
Pirograms 14-0 and 14-1, Reactor Shieid Analysis, GE-ANPD,
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6. D. M. Peterson, Shield Penetration Programs, NARF-61-39T, FZK-9-170
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.
7. B. Carlson, Numerical Solution of Transient and Steady-State
8.
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S. Prei
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".
"IT
Neutron Transport Problems, LA-2260 (Oct. 1959).
S. Preiser, et al.,A Program for the Numerical Integration of the
Boltzmann Transport Equation - NIOBE, ARL Tech. Rept. 60-3.14
(Dec. 1960)..
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9. J. Certaine, et al., RENUPAK - An IBM-704 Program for Neutron
Moment Calculations, UNC-NDA-2120-3 (Dec. 1959).
19. H. Bohl, Jr., et al., PIMG--A One-Dimensional Multigroup Pl Code
-
.
for the IBM-704, WAPD-TM-135 (July 1959); and R. C. Gast, A P-9
Multigroup Method for Solution of the Transport Equation in Slab
Geometry, WAPD-232 (itay 1950).
11. E. G. Peterson, MAC--A Bulk Shielding Code, HW-73381 (April 1962).
12. J. P. Yalch and J. E. MacDonald, Program 20-2, A Program for
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Approximating Cross Section Dependence on Energy, GEMP-3.13
(June 1962).
13. J. P. Yalch and J. E. MacDonald, Program 20-4, A Program for Aver-
aging Differential Scattering Cross Sections, GEMP-115 (June 1962).
14.
J. P. Yalch and J. E. MacDonald, Program 20-5, A Program for
Preparation of Spectrum Tables from Evaporation Model, GEMP-116
(June 1962).
15. J. P. Yalch and J. E. MacDonald, Program 20-6, A Program for Com-
puting Nuclear Excitation and Transition Probabilities from
Measured Gamma Ray Intensities, GEMP-117 (June 1962).
15.
J. J. Loechler, Flexible Mɔnte Carlo Source Generation, xDC 61-4-52
17./J. E. MacDona
(April 1961).
17./ J. E. MacDonald, J. T. Martin and J. P. Yalch, Specialized Reactor-
Shield Monte Carlo Program 18-0, GEMP-102 (October 1962).
18. J. E. MacDonald and J. T. Martin, Shielding Computer Program 20-0,
APEX-610 (August 1961).
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19. J. P. Yalch and J. E. MacDonald, Program 20-3, A Program for Com-
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putation of Total Macroscopic Cross Section and Collision Pro-
babilities for Specified Material Composition, GEMP-114 (June
1962).
20. J. M. Martin, Shield Region Data Converter Program 20-7, APEX-605
(August 1961).
22.
J. P. Yalch and J. E. MacDonald, Program 20-8, A Program for Inter-
preting Program 18-0 Source and Escape Particle Tapes, GEMP-123
(July 1962).
22. Burton Eisenman and Elinor Hennessy, ADONIS - An IBM 7090 Monte
Carlo Shielding Code which Solves for the Transport of Neutrons
or Gamma Rays in Three-Dimensional Rectangular Geometry, UNUCOR-
635 (March 1963).
Walter Guber and Martin Shapiro, Advanced Shield Calculational
23.
Techniques - Volume III: A Description of the Sane and Sage Pro-
grams, UNUCOR-633 (Marci 1963); and Morton R. Fleishman, Advanced
Shield Calculational Techniques - Volume IV: A Sane-Sage User's
Guide, UNUCOR-634 (March 1963).
24. R. A. Liedtke and H. A. Steinberg, A Monte Carlo Code for Gamma-
Ray Transmission through Laminated Slab Shields, WADC-TR-58-80
, (April 1958).
25. H. Steinberg, Monte Carlo Code for Penetration of Crew Compartments :
II, TRG-211-3-FR (Dec. 1959).
26. H. Steinberg, et al., Analytic and Monte Carlo Studies of Gamma
Ray Shadow Shielding, TRG-215-FR (May 1961.).
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27. R. R. Coveyou, v. G. Sullivan, H. P. Carter, D. C. Irving, R. M.
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Freestone, Jr., and F. B. K. Kam, O5R, A General-Purpose Monte
Carlo Neutron Transport Code, ORNL-3622 (February 1965); and
W. E. Kinney, Program STATEST, An Application of the Method of
Statistical Estimatior to the Calculation of Neutron Flux in
Anisotropically Scattering Media by Monte Carlo, ORNL-3715
(November 1964).
S. K. Penny, D. K. Trubey, and M. B. Emmett, OGRE--A Monte Carlo
28.
System for Gamma-Ray Transport Studies Including an Example
(OGRE-P1) for Transmission through Laminated Slabs, ORNL-3805
(April 1966); and D. K. Trubey and M. B. Emmett, OGRE-G, An
OGRE System Monte Carlo Code for the Calculation of Gamma-Ray
Dose Rate at Arbitrary Points in an Arbitrary Geometry, ORNL-TM-1212
(Ja!.. 1966).
29. B. Eisenman and F. t. Nakache, UNC-SAM, A FORTRÁN Monte Carlo
System for the Evaluation of Neutron or Gamma--Ray Transport in
Three-Dimensional Geometry, UNC-5093 (Aug. 1964).
30. D. G. Collins, A Monte Carlo Procedure for Calculating Penetra-
tion of Neutrons through Straight Cylindrical Ducts, NAKF-61-33T,
MR-N-286 (November 24, 1961); and D. G. Collins, A Monte Carlo
Multibend Duct Procedure, NARF-62-31T, MR-N-297 (Sept. 15, 1962).
31. Dominic J. Raso, Monte Carlo Codes to Investigate the Reflection
and Transmission of Gamma Rays and Neutrons in Homogeneous and
Heterogeneous Slabs, TO-B 63-82, Vols. I-III (Oct. 1963).
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32. D. G. Collins, Utilization Instructions for General Application
of the L-05 Monte Carlo Procedure, RRA-144 (May 29, 1964).
33. Henry C. Honeck, ENDF, Evaluated Nuclear Data File, Description
and Specifications, BNL-8381 (Aug. 1965).
34. H. Kahn, Applications of Monte Carlo, AECU-3259 (April 1954);
and H. Kahn, "Random Sampling (Monte Carlo) Techniques in Neutron
Attenuation Problems - I and II,"Nucleonics, 6, 27-37 and 60-65
(May 1950).
35. G. Goertzel, Quota Sampling and Importance Functions in Stochastic
Solutions of Particle Problems, AECD-2793 (June 1949).
36. G. Goertzel and M. H. Kalos, 'Monte Carlo in Transport Problems,"
Progress in. Nuclear Energy, Series I, Phys. and Math, Vol. 2
(Pergamon Press, New York, 1958), pp. 315-369.
37. L. A. Beach, et al., Stochastis Estimates of y-Ray Spectral
Intensities for Shallow and Deep Penetration, MRI-4412 (1954).
38. J. T. Perkins and M. O. Burrell, 'Efficiency of Some Biased Sam-
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pling Schemes in Monte Carlo Calculations," Nuclear Engineering
and Science Conference, April 6-9, 1969, published by Er.gineers
Joint Council.
39. M. Leimdörfer, "A Monte Carlo Method for the Analysis of Gamma
- Radiation Transport," Nukleonik, 6, 58-65 (March 1964); and
"On the Transtormation of the Transport Equation for Solving
Deep Penetration Problems by the Monte Carlo Method," Trans.
Chalmers Univ. Technol., Goethenburg, Sweden, No. 286 (1964).
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40. Francis H. Clark, The Exponential Transform as an Importance-
Sampling Device--A Review, ORNL-RSIC-14 (January 1966).
41.
A. B. Chilton, "A New Variant to the Exponential Transformation
Techniques in Monte Carlo Shielding Calculations," Nucl. Sci.
Eng., 24, 200-208 (Feb. 1966).
42. M. H. Kalos, "On the Estimation of Flux at a Point by Monte
Carlo," Nucl. Sci. Eng., 16, 111-117 (May 1963).
43. H. J. Amster, et al., Euripus-3 and Daedalus--Monte Corlo Density
Codes for the IBM-704, WAPD-TM-205 (February 1960).
44. D. K. Trubey and M. B. Emmett, A Comparison of First- and Last-
Flight Expectation Values Used in an OSR Monte Carlo Calculation
of Neutron Distributions in Water, ORNL-RSIC-3 (May 1965).
45. K. D. Lathrop, 'Use of Discrete-Ordinates Methods for Solution
of Photon Transport Problems," Nucl.. Sci. Eng., 24, 381-388 (April
1966); and D. K. Trubey, s. K. Penny, and K. D. Lathrop, A Compari-
son of Three Methods used to Calculate Gamma-Ray Transport in
Iron, ORNL-RSIC-9 (October 1965).
46. H. Bohl, Jr., et al., P3MG1--A One-Dimensional Multigroup P-3
Program for the Philco-2000 Computers, WAPD-TM-272 (Sept. 1963).
47. R. E. Malenfant, The Code QAD P-5, Los Alamos, Unpublished; and
'J. K. Witthaus, The Code QAD P-R, Aerojet, San Ramon, Unpublisha.
48. W. B. Green, Mortimer, A Modification of the Ratrap Code Which
Includes the Two Component Method of Shield Analysis, NAA-SR-9327
(December 1963).
ORNL - AEC - OFFICIAL
- 16-
ORNI - AEC - OFFICIAL
49. D. X. Trubey, Calculation of Fission-Source Therma l-Neutron
ORNI – AEC - CFFICIAL
Distrioution in water by the Transfusion Method, ORNL-3487
(Aug. 1964).
50. D. Yarmush, et al., The Transmission Matrix Method for Penetra-
tion Problems, WADC-TR-59-772 (Aug. 1960).
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