LAMS-2537

( .

c% ●

1.

,.

CIC-14 REPORT COLLECTION

REPRODUCTION

COPY

LOS ALAMOS SCIENTIFIC LABORATORY

OF THE UNIVERSITYOF CALIFORNIAo LOSALAMOS NEW MEXICO

CORRELATIONS OF EXPERIMENTAL AND

THEORETICAL CRITICAL DATA

COMPARATIVE RELIABILITY, SAFETY FACTORS

FOR CRITICALITY CONTROL

....’ ;—’ .“.’:
LEGAL NOTICE

,’

This report was prepared as an account of Government sponsored work. Neither the United States, nor the

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A’. Makes any warranty or representation, e~ressed

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that such employee or contractor of the Commission, or

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Printed in USA. Price $ 1.25. Available

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from the
LAMS-253’7

CRITICALITY STUDIES

(TID-4500, 16th Ed.)

.

LOS ALAMOS SCIENTIFIC LABORATORY

OF THE UNIVERSITYOF CALIFORNIA LOS ALAMOS NEW MEXICO

REPORT WRITTEN: March 1961

REPORT DISTRIBUTED: May 15, 1961

CORRELATIONS OF EXPERIMENTAL AND

THEORETICAL CRITICAL DATA*

COMPARATIVE RELIABILITY, SAFETY FACTORS

FOR CRITICAL~Y CONTROL

by

Hugh C. Paxton

drawing freely from theoretical work of

Bengt G. Carlson William H. Roach

Aurel Goodwin, Jr.? George Safonov$

Gordon E. Hansen William R. Stratton

Carroll B. IWIS

J--

w

I

•~b; *This report supplements LAMS-2415

===% ~The DOW chemical Company, Rocky Flats Plant, Denver, Colorado Z===

‘The Rand Corporation, Santa Monica, California

Contract W-7405 -ENG. 36 with the U. S. Atomic Energy Commission

All LAMS reports are informal documents, usually prepared for a special pur-

.— pose. This report has not been edited, reviewed, or verified for accuracy.

o~.— All LAMS reports express the views of the authors as of the time they were

~~: written and do not necessarily reflect the opinions of the Los Alamos Sci-

.1 ———. 1 entific Laboratory or the final opinion of the authors on the subject.

1
.

..”
PREFACE

This report is a somewhat updated version of a paper

that was prepared for the ENEA Symposium on Criticality

Control (Karlsruhe, May 2-5, 1961)0 It may be fortunate

that the topic was assigned -- otherwise, it is probable

that all with appropriate interest, like the hapless author,

would have continued waiting for a more venturesome individual to take the required liberties with work of others.

As it iS, the resulting intercomparisons of computed and

experimental critical data form a logical extension of the

purely experimental compilation of LAMS-2415, CRITICAL DATA

FOR NUCLEAR SAFETY GUIDANCE.

3
4,. .
CORRELATIONS OF EXPERIMENTAL AND

THEORETICAL CRITICAL DATA

...... \

For the experimental part, this discussion will concentrate on data that are susceptible to generalization.

Practically, the scope will be limited to fissile systems

that may be approximated by simple descriptions - -

elementary geometry and generally homogeneous fuel regions.

This type of information has been termed “basic” nuclear

safety data. Thus , we ignore the specialized experiment

such as that intended to demonstrate safe operating conditions for a specific processing unit.

Similarly, we will not consider specialized calculations such as those designed to give effects of minor

changes in a given type of heterogeneous fissile assembly.

Rather, most attention will be given to computation which

hopefully may substitute for basic experimental data.

Before considering this class of calculation, however, let

us discuss a somewhat less demanding application of theory.

The Adjustment of Empirical Data

As experimental data seldom apply to ideal systems

which may be described in similar terms, empirical

5
correlation of the data generally requires conversion to

uniform conditions. This process, in turn, makes use of

data correlations which may be strictly empirical or

guided by theoretical models. (It is apparent that

successive approximations may be involved if there is a

relationship between input and output correlations.) As

for example, corrections on critical mass are frequently

within 10%, the ultimate in precision is often not required of the model used for correction. Figures 1 and 2

are examples of two empirical representations of the same

data, the first without regard to a theoretical model, and

the other in a form suggested by such a model (l). In each —

case the data are critical volumes of families of cylinders

‘f ‘02F2 - H20 solutions in which the uranium is enriched

to about 93 w/o U235 [we shall symbolize this uranium

U(93) ].

Figure 1 shows, for cylinders of various height/

diameter values, ratios of critical volumes to the

spherical value for the same solution. It may be noted

that there is no obvious distinction between curves for

solutions at two widely different uranium concentrations.

In Fig. 2 are represented effective extrapolation distances

of critical cylinders, 5C, which satisfy the buckling

relationship
.
‘N
where d and h are diameter and height of the critical cylinder and r~ is the radius of the corresponding sphere.

The sphere extrapolation distance 5~ is the sum of an

experimental reflector savings and an assumed or computed

bare-sphere extrapolation distance. (The latter value, of

course, remains an inherent part of the correlation.) If

simple theory applied precisely, 6C would be independent of

h/d . As it is, deviations from a constant value are

sufficiently small that there may be some confidence in

extrapolations to extreme values of h/d. Such extrapolations are impossible with the more direct representation of

Fig. 1.

Another example of a simple calculation that is useful

for adjusting or extending experimental data gives critical

masses of modestly diluted metal systems in terms of

effective absorption and transport cross sections of the

diluent. These cross sections, in turn, are obtainable

from reactivity coefficients of diluent and undiluted

fissile material. Figure 3 compares directly-observed

critical masses of diluted enriched-uranium metal with

results from integrated reactivity coefficients that were

9

measured in an undiluted sphere. The primary critical data

are from measurements by Jarvis (unpublished). The computed relationships are expected to hold through a range in

which fixed one-group cross sections apply - - up to about

50 v/o dilution for graphite and perhaps to 70 v/o for most

medium-Z and high-Z elements. This sort of correlation

provides the bases for corrections of critical data to

standard densities and concentrations.

A step further from detailed theory is a scheme for

correlating cubic lattices of air-spaced fissile units,

which is suggested by the power relationships of Fig. 3.

In Fig. 4, data from Oak Ridge National Laboratory (~),

the best presently available for cubic arrays, follows the

form, critical number of given units = (lattice density)-s,

where s is constant over the range of measurement.

Figure 5, which shows the way in which s depends upon type

of unit and effectiveness of reflector about the array (3), —

is then a basis for generalization to unmeasured systems.

The picture of relationship between the critical mass

of a plane array of discrete units and that of a uniform

slab of the same material leads to the correlations of

Fig. 6. Here, ORNL data on arrays of solution cylinders

(~) are represented in terms of thicknesses of critical

solution if spread over the base area of the array. It is

11
1000

300

G’

L

&

E 100‘ \

u.—-+-

.—

~

0‘rL

c1) I

I I I I

I I I I I I I I

AA 24.5 kg U(93) slabs(l”x 8“X 10”)-

1 no internal moderation

II ~

o 24.5 kg U (93) slabs (l”x 8“X 10”)

plexiglas moderator

between units

FIG.4

from ORNL C

non linear 1

F-59-7-87

[

CRITICAL CUBIC ARR

OF METAL SLABS

3– WITH AND WITHOUT

BETWEEN UNITS

re extrapolation

of multiplication data1

\

AYS

o

PLEXIGLAS+

0.01 ,W0.03

F-fraction of Iatti :e occupied by umts

o.I 0.3

12
2.0

1.8

1.6

[.4

1,2

s

1.0

0.8

0.6

c).4

0.2

0

I I I I

‘o concrete-reflected lattice

O partially- reflected lattice

❑ unreflected lattice

l: equivalent 20kg U(93) spheres

2: equivalent 32kg U(93) spheres

3: 24.5 kg U (93) slabs, I“x8”X 10”

4: 30kg assemblages of U (93) pieces

(peff-40%)—

I I-& 5, 6“-cJiam. solution cyls., H/U-235=44

\, 9

6:8” diam. solution cyls., HIU-235 =44

\

i’: 8“diam. solution cyls,, H/ U-235 =309–

8:9~2’’diam. solution cyls., H W-235=297

\ k

9: 3-3’’ thick solution slabs

LATTICE-DENSITY EXPONENT

vs “FRACTION CRITICAL” OF

\ AN ISOLATED UNIT FOR

1

& rl VARIOUS DEGREES OF EXTERNAL

\ 1-. \ REFLECTION

u. c U.* U.o u. u I.u

“fraction critical” of unit

13
14
obvious that this representation breaks down at a finite

height if the cylinder diameter is such that an individual

unit can be made critical. Limited data on plane arrays of

massive metal spheres appear to fall into a similar

pattern, which suggests the possibility of useful generalization.

One feels less comfortable about the generalization of

purely empirical forms for which the reason is not clear.

An example is the relatively close clustering of ratios of

water-reflected to bare critical volumes for a considerable

variety of systems with similar moderation, as represented

in Fig. 7 (~). Though this correlation is highly suggestive

and establishes reasonable limits, we do not expect it to be

reliable in detail. In this case, there happens to be hope

for a simple guiding model, because a reasonable trend is

from the observed minimum volume ratio of ~ 0.4 (for small,

efficient systems) toward unity as neutron leakage becomes

successively less important in fission economy (or as km

decreases). Thus , the greatest problem might not be how

to improve the correlation, but, rather, how to find a

better representation in practical engineering terms.

Though volume ratios at standardized densities may form a

nearly unique function of km, the latter is not a convenient process parameter.

15
2

184s6

7—8 579

w

(n I Q .Q

Q*

?

yJ\
These illustrations, intended primarily to show the

utility of crude theoretical models for data adjustment,

will serve a second purpose. They give some basis for

judging the uncertainties added to primary data when prepared for correlations.

Computation as a Substitute for Experiment

Attention now will be turned to a realm in which we

contend that highly-refined calculation is required. This

is where computed values are intended to substitute for

experimental data in nuclear safety guidance. Just as

experimental values require some index of reliability,

computations which replace them should leave the user with

a feel for probable error. Practically, there may be even

more stringent requirements on computation than on experiment because of doubters who remember the days when a

factor-of-two error in calculated critical mass was customary unless nearby experimental data were available for

normalization. In spite of vastly improved input data,

computational facilities, and techniques, some of the

stigma remains; hence our opinion that calculation for the

purpose under discussion should be so good as to sell

itself to the more skeptical. (After reasonably-complete

high-quality computational surveys exist, there may be a

17
place for short cuts “which seem to work”.)

The requirements implied above are: realistic input,

convincing method, and a wide enough range of checks

against experiment to establish error patterns. The most

useful form in which data might emerge is a computational

survey. The classic of this type is the series of surveys

of bare, spherical critical systems undertaken by Safonov

a number of years ago (~). For U233, U235 or PU239,

diluted by H20, D20, Be, BeO or C, he presented critical

sizes and certain spectral indices as functions of

moderator-fuel ratio. Other series cover the ternary systems of U235-U238-C, U235-Be-C, and, at elevated temperature, U235-U238-H20 . Parameters for his multigroup diffusion method were chosen carefully, and reasonably represent

processes including inelastic scattering and resonance

region effects. As the diffusion approximation cannot

apply precisely to a small system for which radius and

mean-free-path for fission are of the same order, it was

necessary to adjust high-energy transport cross sections

for agreement with critical data from fast-neutron

assemblies.

Recently, Mills (7) has applied more modern techniques —

to the binary systems that Safonov surveyed, and, for H20-

moderated U233, U235 or PU23’, he included, with spheres,

18
critical cylinders of infinite length and slabs of infinite

extent, and added H20 reflection. Also covered, is a portion of the U235-U238 -H20 series for bare spheres. The DSN

method that Mills employed (~) has the advantage of applying

realistically to fast-neutron systems, and input data presumably have been improved since the time of Safonov~s work

-- particularly a specific coded

eraging cross sections throughout

The high energy cross section set

scheme of Bell’s for avresonance regions (9_).

is that of Hansen and

Roach (10), in which parameters have been adjusted within

their ranges of uncertainty to fit a wide variety of integral fast-neutron data.

Other DSN surveys of interest to us were conducted by

Roach for water-reflected U(93)-H20 and Pu239-Pu240-H20

spheres at normal and reduced densities, and by Stratton for

bare and water-reflected U(93)-H20-C spheres (both sets unpublished, but cross sections appear in Ref. 10), A difference with Mills’ procedure, expected to be of minor influ.

ence, is an alternative hand method of averaging resonance

cross sections. Anisotropic scattering cross sections for

hydrogen are used in each case (except Millst points of

Fig. 21).

It is appropriate to mention that detailed computation,

like good experiment, is expensive. The DSN method

a modern, high-capacity computer, and the necessary

requires

time

19
increases with degree of moderation - - where advantages

over the less-demanding multigroup diffusion method largely

disappear. For this reason, Goodwin uses multigroup

diffusion calculations for extensive nuclear-safety surveys, supplemented by fewer DSN results to provide check

points and to cover neutronic complexities that are beyond

the simpler

sion to use

on those of

Comparisons

method (for example, 11). We shall have occasome of Goodwints results, while concentrating

Safonov, Mills and Roach.

of Experiment and Commutation

Experimental data for bare spheres of highly-enriched

uranium metal diluted in various degrees by D20, Be, BeO

and C (graphite) are represented in Fig. 8. Watermoderated systems, which will be considered in more detail,

are included only for comparison of form. Errors in data

interpretation (shape conversion unspecified impurities,

inhomogeneities, and incidental reflection) should be

generally within 10%, with limits for H O and D O solutions 2 2

appreciably smaller. Exceptions are the lower point that

applies to undiluted metal (the shape was extreme and

density uncertain), and possibly the point for z 90 v/o

H20, where there was a compositional correction. Density

corrections, according to critical mass = const (density)~2
1

>

=i

n0

3

(n

>

0

n

w

m

a

l--

o

(3Z

u)

l--
are quantitative. Calculations by both Safonov and Mills

agree reasonably with experiment, maximum deviations being

about 20%. In Safonov*s case, this is particularly significant because most of the critical experiments followed his

work. As expected, Mills* results show improvement.

Experimental critical masses for water-moderated

highly-enriched uranium spheres, both bare and waterreflected, are presented in Fig. 9. The importance of

changes in U235 density at constant H/U235 atomic ratio is

illustrated by the dual representation of data for concentrated solutions, first at normal densities then at the

larger densities corresponding to idealized homogeneous

metal-water mixtures. Even though such mixtures cannot be

attained in practice, they represent an upper limit to

density at a given value of H/U235, hence, a lower limit to

critical size. From the corresponding critical volume

curves, Fig. 10, we see that the minima for solutions disappear for metal-water mixtures.

As has been noted, corrections, for example, to

densities of mixtures of uranium compounds and water are

straightforward for unreflected systems. When water

reflection is added, however, the influence of a coredensity change is reducedt as indicated by Fig. 11 for

water-moderated water-reflected spheres. The core-density

22
23
24
c)0

CEhnwzZ

i->

Idxn0zwz+

(/)

Ll- oK3zw

.

25
exponents shown, which are from critical calculations by

Roach at two sets of densities differing by 20%, are used

here at face value.

With Fig. 12, we return to the U

235 critical-mass

curves with density-corrected computations superposed.

Only Mills has values for both bare and reflected spheres.

Though experimental points for solutions appear to be

accurate to within 5%, the two water-reflected points that

are derived from “hydride” assemblies should be discounted

because of serious uncertainties in composition and

reflector-savings corrections (recently-’’improved” corrections led to alarming shifts). Direct checks of computation against the undistorted hydride data would serve a

better purpose than inclusion on these curves. It should

be noted that experimental “unreflected” points are biased

downward, perhaps 2% for concentrated solutions, by the

nominal 1/16” stainless-steel container which was not included in calculations. Safonov~s values, which may be a

few percent high due to a thermal base of 500°F, have been

chosen as the latest and best of several sets. Generally,

the agreement between solutions data and calculation is

appreciably better than the maximum deviation of - 20%.

Empirical data for infinitely-long cylinders and slabs

of infinite extent (Figs. 13 and 14), of course are simply

26
o

IL

27
U)

i=za

1-wn0

Iz

1- —z

iIZ
1-

1-

0

Llz

lx

2

tw

m

u)

0

IL

c!)

Id

z

w

2

u)

s

Ld

n

w

(f)

1-
based on observation. For undiluted metals and solutions

near the critical minima, measurements on long cylinders

and broad slabs lead to reasonably convincing values for

the infinite systems. In other regions, estimates of slab

thicknesses are considerably more sensitive to conversion

errors than are the cylinder diameters. In spite of this,

it appears that Millst slab values are systematically high,

as contrasted with his calculations for cylinders.

Information about water-moderated plutonium assemblies

is not as clean as that for U235. Existing critical data,

for metal and for dilute solutions only, has recently been

supplemented by subcritical measurements of Schuske and his

coworkers at Rocky Flats on plutonium metal sheet with

Plexiglas as moderator and, in some cases, as reflector

(g) ● But data on the influence of ever-present Pu240

, and

on effects of variation in moderator composition are scanty.

For this reason, it is desirable to use detailed computation

for adjusting the Rocky Flats observations. Relative

critical masses of Plexiglas-moderated plutonium (bare or

Plexiglas reflected) and of water-moderated plutonium (bare

or water reflected) from such calculations appear in Fig.

15 ● Plutonium densities remain at normal values for the

mixtures. The curve for bare spheres was obtained by

Goodwin, and that for reflected spheres by Roach. Figure

30
31
16, also due to Goodwin and Roach, gives the percent increase in sphere critical mass of total Pu per percent

~240 content of the plutonium.

Making use of the last two sets of curves and density

exponents from Fig. 11$ critical masses from the Plexiglasmoderated assemblies were joined with the older data for

solutions and unmoderated metal as in Fig. 17. The

“idealized solutions” represented in addition to metalwater mixtures have a relationship between fuel density and

hydrogen-fuel ratio which is analogous to that of U02F2

solutions. Practical densities generally would be less

because of the excess acid required for stable Pu solutions.

In Fig. 18, where computed results are added to the experimental curves, the reasonable clustering is particularly

significant, as only

moderated assemblies

just dilute-solution

difficult to judge whether values from experiment or from

calculation are the more reliable. If consistence is a

valid criterion, it appears that critical masses are tied

down to within 20% over most of the range of moderation.

Except for water-reflected metal, observations on

critical cylinders and slabs containing Pu are so limited

that conversions to the infinite forms must be based on

Safonov used the points applying to

for cross section adjustment (he used

data for this purpose). Here it is

32
l—

2—

3—

4—

5_

~

~

3—

4_

5—

6—

7—

8—

9—

4—

5—

6—

7_

8—

9_

3

tw

n

—

c)

L

3

a

t-
wn3

c1wnwX

n- wE>

WI z~

-l

c-) E

1-

(Y

0

Ll-

(2

U)

n- 1w

(Ywm

477 &y

- Sseuf /@yf,fA3

34
.,... v0>

n- 3

1- wn6zn

IdX

n- w

CK——

m

n- rwmw

u)z

ml m

UJw

CL>00wma

tLd0

35
models which apply to U235 (Figs. 19 and 20). In spite of

this added uncertainty, differences between Points based on

experiment and those computed by Mills are similar to the

uranium cases.

Computation with Limited Experimental Confirmation

Fissile systems that are sensitive to more than two

constituents demand computational guidance to a greater

extent than the essentially two-component mixtures upon

which we have concentrated. The simple reason is that the

new dimension (or more) makes complete experimental cover235

age prohibitive. Examples of practical interest are U -

~238 -H20 combinations for partially-enriched fuel-element

materials, U235-C-H20 for impregnated graphite elements,

and U235 -Be-H20 for impregnated beryllium.

As the transportation and general handling of partially-enriched uranium compounds (which may become moist)

is a current problem which requires attention, let us see

what is known about critical masses of water-moderated

U235-U238 combinations. The principal family of curves in

Fig. 21 are from Safonov for a temperature of 260°C

(500°F), but corrected to normal metal-water densities. To

indicate the order of neutronic changes when the temperature is dropped to 20°C, Mills calculates a 25% decrease in

36
v

CE—

i=0a

--l 6a~

l-- w

(Y

(n0

Ll- —zE2

1-w5

(-) >iznw

(x

u)0

Ll-
1-

c)

6

-1

1-

z

v

Y

z

w

(n

u-l

w

(n

0

LlZ

lJZ

1-

w

u)

-1

iI

wN

0

0

Ll-
.sQ

“;

-’a

.:

“.

b

.

\)

●

%Q

.

a

*QQv

.Q

>.

-Q%. Q

*Q“

0.9

‘+

.C3

“,

N

.’3\

.,

.N.

“w- .

-w.

.%.

39
the minimum critical mass for U(2% U235) versus a decrease

of just 5% for U(93)0 The gas model which he used may

overestimate the influence of temperature change, and we do

not know what differences Safonov might have found. so it

is with apology that we have added to Fig. 21 roomtemperature points from experiment and from a preliminary

survey by Mills (for this survey, convergence requirements

were * 1% on radius instead of the customary factor of 10

less) . Though temperature corrections would bring data of

the three general types more or less together, limitations

on experiment , present uncertainties in Mills’ calculations, and the inappropriate temperature of Safonov seem to

combine to call for a thorough computational survey. Mills

has undertaken this, including the establishment of asymptotes on the low-moderation side of minimum.

The next illustration is a set of critical masses for

U(93)-C-H20 which was computed by Stratton specifically for

nuclear safety (Fig. 22). As method and cross section sets

are identical to those used by Roach, comparisons of

Roach~s results and experiment for straight water moderation (Fig. 9) are pertinent. Computed critical masses for

graphite-U 235 systems fall closely with those of Mills on

Fig. 8. The few experimental values are from subcritical

measurements and all but the left-hand point refer to

40
IL

w

N

N
systems with inhomogeneous hydrogen distribution. Errors

of interpretation could be as great as departures from

computed values. For our purposes, limits were established

by scaling down computed curves to pass through the lower

experimental points, then applying a factor of safety of at

least 2. From the apparent reliability of calculations

with each moderating component separately and by comparison

with the crude points for ternary assemblies, it is

expected that most of this safety factor will be preserved.

Comments on Reliability and Safety Factors

The correlations which we have seen should leave us

with a feeling as to the potential reliability of both

experimental and computed critical parameters. In general,

experimental data fall into two categories: precision

measurements (critical or near subcritical) which require

only well-defined corrections to standard conditions, and

information which, because of imprecise critical determination, unclean assembly, or a degree of inappropriateness,

serves only as a crude guide. Fortunately, there are

reasonably abundant (though

former class.

The ideas that we have

of detailed computation may

never sufficient) data of the

developed about the precision

be supplemented by what can be

42
judged from certain controlling input parameters and their

reliability. To illustrate this point, Fig. 23 shows

results of DSN computation (R. Aamodt-unpublished) which

extend the very limited experimental values of Fig. 3. The

answer to the question as to whether the calculations for

dilute ranges may be used for nuclear safety guidance is

not a clear “yes” or “no”. Within regions to the right of

upturns toward asymptotes, departures from the important

anchor-point for undiluted uranium are controlled by relatively straightforward scattering properties of the

diluent. Critical-mass values will not be a factor of two

high if capture by the diluent has less than 10% influence

on ~, the effective excess of neutrons produced per

absorption. This criterion will be satisfied over most of

the range that we are considering. Where curves break

away toward asymptotes, however, critical masses (and the

limiting critical compositions) become extremely sensitive

to capture cross sections, for which 50% errors have been

common. In view of this, I would not use,for nuclear

safety purposes, either critical masses above the scattering base or asymptote locations unless there were experimental confirmation. (Actually the need for such guidance

would imply the existence of enough material to make

possible some sort of experimental check.)

43
9

a

i

CRITICAL MASSES OF BARE SPHERES =

*

1111

OF U(93.5) DILUTED WITH OTHER METALS :

(AND GRAPH ITE)– AS COMPUTED BY AAMODT

111111 {“m-mwwww /

0.;03 4 = 6 7 ao:;l

2

0.s03 4 6 ‘ 7 8 9%’/

2

0.’3 466789)”

44
Before expressing an opinion about the general reliability of detailed computation, I wish to make a sideline

observation about non-input errors which are not uncommon.

Any detailed calculation such as DSN is similar to a

complex experiment that requires special procedures to

verify the proper functioning of equipment and guard

against extraneous effects. With the ever-present possibility of transcription error or machine malfunction, there

should be a careful consistency check of any isolated problem before the result is accepted. The advantage of a

parametric survey is that difficulties of this type are

likely to result in inconsistencies that are obvious. Provided calculations have been properly checked, I believe

that a probable error in critical mass of ~ 10% to 15% is

about right for existing DSN techniques with proven cross

section sets. This does not apply to regions in which

critical masses change precipitously with composition.

A complete discussion of factors that should be

applied to critical data for establishing nuclear safety

limits would require a full description of the operations

for which the limits are intended and of the nature of

controls. I do not know how to generalize past the

recommendations (and added precautions) which appear in the

NUCLEAR SAFETY GUIDE (13). When the necessarily arbitrary —

45
safety factors which appear there are translated to new

situations, it is obvious that there should be added allowance for uncertainties in data. The, importance of such an

allowance diminishes if the limit applies to an idealized

situation that is actually unapproachable in practice.

Examples would be the application to normal vessels of

limits for fully-reflected systems, and storage-shelf

limits that are based on a cubic array of maximum-size

units at the minimum allowed spacing. Hidden, but generally large, factors of safety in these cases greatly

relieve the demands on guiding data. Information specific

to a plant layout, in contrast to that which appears in our

surveys, of course would eliminate many of the hidden

safety factors that are now necessary.

Final Remarks

Any worker in the nuclear safety field, when faced by

gaps in critical data, feels that his efforts are tentative. In exactly this sense the present review is recognized as describing just the beginning of an effort that

should be carried on by many. A continuing, possibly

coordinated, computational program is needed - - and let

us hope that it will be of the best.

In representing detailed computational methods by the

46
DSN and multigroup diffusion techniques, it has not been

the intention to discriminate against alternatives such as

Monte Carlo. This method could make its appearance when

correlations are extended beyond the simple systems that

we have considered.

47
REFERENCES

(~) H. C. Paxton, Critical data for nuclear safety

.widancej Los Alamos Scientific Laboratory Report

LAMS-2415 (1960). Most references to experiment

are contained in this report and Nuclear Safety

Guide (13).

(~) J. T. Mihalczo and J. J. Lynn, Multiplication

measurements with highly enriched uranium metal

slabs, Oak Ridge National Laboratory Report

CF 59-7-87 (1959).

(~) E. R. Woodcock and H. C. Paxton, The criticality

aspects of transportation of fissile materials,

to appear in Progress in Nuclear Energy Series IV,

Vol. 4, Pergamon Press, London (1961).

(~) D. Callihan, Review of criticality data obtained by

experimental methods, Proc. Symposium on Criticality

Control in Chemical and Metallurgical Plants,

O.E.E.C. European Nuclear Energy Agency, Karlsruhe

(1961) . Other references are in (~).

(5) D. F. Cronin, Critical mass studies, part X: uranium —

of intermediate enrichment, Oak Ridge National

Laboratory Report ORNL-2968 (1960) (classified).

J. G. Walford, et al, Criticality of 30% U

235

solutions in cylindrical geometry, DEG Memorandum

663 (1960); also private communication.

(6) G. Safonov, Notes on multi-group techniques for the —

investigation of neutron diffusion, The Rand

Corporation Report R-233 (1952).

.

48
G. Safonov, Survey of reacting mixtures employing

~235

, I%P39, and U233 for fuel and H20, D20, C,

Be, and BeO for moderator, The Rand C!orporatlon

Report R-259 (1954).

G. Safonov, Critical mixtures of uranium and 500°F

light water, The Rand Corporation Report R-279

(1955) .

(~) C. B. Mills,

solutions,

(1961) .

Minimum critical dimensions for water

to appear in Nuclear Sci. and Eng.

(g B. G. Carlson, The Sn method and the SNG and SNK

codes, Los Alamos Scientific Laboratory Report

AECU-3691 (1958).

B. G. Carlson, The DSN and TDC neutron transport

codes, Los Alamos Scientific Laboratory Report

JAMS-2346 (1959).

B. G. Carlson, The DSN code, Los Alamos Scientific

Laboratory

(~) George Bell,

Los Alamos

(1959) .

(lo) G. E. Hansen —

Report LAMS-2346, Appendix I (1959).

The theory of effective cross sections,

Scientific Laboratory Report LA-2322

and W. H. Roach, Sixteen group cross

sections, Los Alamos Scientific Laboratory Report

LAMS-2543. (To be issued).

W. H. Roach, Computational survey of idealized fast

breeder reactors, Nuclear Sci. and Engo 8, 621-651

(1960) .

49
(11) A. Goodwin, Jr., and C. L. Schuske, Plexiglas and

graphite moderated plutonium assemblies, to appear

in J. of Nuclear Energy (1961).

(12) C. L. Schuske, G. H. Bidinger, A. Goodwin, Jr., and

D. F. Smith, Plutonium Plexiglas assemblies,

USAEC Report RFP-178 (1960).

G. H. Bidinger, C. L. Schuske, and D. F. Smith,

Plutonium Plexiglas assemblies, part II, USAEC

Report RFP-190 (1960).

(13) Nuclear Safety Guide, American Standards Association

Subcommittee N6.8 and American Nuclear Society

Committee Project 8, document TID-7016, Rev. 1

(1961) .

50
APPENDIX

Data for U233

Though most nuclear safety problems center about

U235 and PU239, experimental and computed data for U

233

are added here for completeness. In Fig. 24, critical

masses of U233 solutions (and unmoderated metal), reduced

to apply to spheres, are compared with results of calculations by Mills and by Safonov. Figures 25 and 26 give

corresponding critical diameters of infinite cylinders

and thicknesses of infinite slabs, both as estimated from

experimental data and as computed by Mills.

51
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54