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r
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e*
'table" OrlJans of the E N U C ,
e .
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Certain preliminary explorations of t h e statistical-digital method aould
be and
6'
sheu1.d be earried out manually.
Iquantly
.
I w i l l say somewhat more 8ubae-
It L not quits i~possiblet h a t a manual-graphical approaah (with a CILDBU
lamount of law-pmciaion digital work interspersed) is feasible. It w o d d
require a not inounsiderab:le number of computer8 f o r eeveml daya per
c r i t i c a l i t y problem, but iit may be podiible, and It may perhsps doserve
eonsideration until and un:leks the EMIAC become8 available.
Thin manual-graphical procedure has actually some similarity with a
;etatistical-grap~rical prockdure with which solutions of a bombing problm
were obtained during the war, by a group worklng under s. Wd.lk# (Prlnoo-
-ton University arid Applied %thematics Panel, NDFtC,).
I ell look into
Ithis matter further, and possibly g e t Wilks' opinion on t h e lpsthrsrrtiorrl
aspects
.
:Cf and when the p~obZctnof (1)dl1 have been ratisfactorily badled in
$1
reasonable number of spec:ial cases, i t d l 1 be t h e t o hV98tigate t h e
more general case, where bydmdynamioia 8180 oome
ht0
oiency calculatiorie, aa augtgerstsd a t &he end of (1).
lctIOW
how t;o set up this problmi, too:
pw; &.e., effl-
I think that I
h e hrs t o follm, ray 1 W neutronr
4d- ; get t h e i r momentum and energy tram-
l;hrough a short time h t e m l
Per and generation i n t h e ambient mattcar; ealoulats f r o m tMm the dirplacement of matter3 r e c a l a d a t e t h e h i s t o r y of t h e 100 neutron8 by
srssuming that matter i s i n th@ middle position blbtweert
it8
original (unpar-
tarbed) state and the abovel djlsplaoed (perturbed) ntatsj recalauhtr t h e
displaaement of matter due t o %hi8 (oameotad) neutron hilltorg;
8 .
. e m
.e.
...e
..e
9.
.e
.. . . .
.e.
m e .e
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0
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Page Four
Improper, then t h e photons, too, may have to be t r e a t e d % x l l v t d u a l l ~
and s t a t i s t i c a l l y ,
on the lawe footing as the neutrons.
cowre, is non=tl.iviul complbatiion, but; it
CM
Thla is, of
hardly consume much more
t h e and instructIon8 then the oorrsrponding neutronic part.
It seem t o me, therefore, that t h i s apploach w l l l gradually lead t o a
oompletely satiafactory theory of effioienay, and u l t i a a t e l y p e d t pro-
diotlon of the behavior of a l l possible arrangeaentrr, t h e siargle oner a8
e.
e . .
e . .
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e . .
e.
e.
8
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Page Five
**e
t o h t l e ky.
e*#
bra
*e
e
e
e e a .e*
It ~ e e m98 if thsi l a t e Maya clr&etriw*
.
. e
I w i l l inquire more i n t o t h l e btter, and
of getA5ing tome of i t e time subsequently,
ia$Rer safe.
*
a *
0180
into the p o s s i b i l i t y
The indioations that I have had
80
r)
far on t h e latter score are enoourmglng,
In what follows, I w i l l give a more precise d e s c r i p t i o n of t h e rpproaoh
outlined in
of t h e 8hp:Leat way 1 can now
(1)j i . 8 . )
of ljxrrroblatrns.
Consider
from %he origin.
B
s p h e r i c a l b symmetric geometry.
888
t o handle this group
Let /-r be the dietanue
cen'tric, homogeneous ( s p h e r i c a l s h e l l ) sones, enumerated & an index
Zone No.
.
1-
I/-
i
is defined by
'A,/
1
I
L, .
con-
Describe t h e inhomogeneity of t h i s system by assuming
,.f
,, I^.
1-1
being givens
To
-
r-,
c
f2
-
c
/-r.
L
-.
1
, )'-
A'
1
where R is the o u t e r r*adhu of t h e e n t i r e syatem.
, the
1
-
i --- 1, ";.M ,
KO, 5,
5I
*..
,
K,
f>
Let the sys.t;m con8isi; of t h e three components discuaaed i n (l), (b),
to be denoted A, T, S, respectively. Describe t h e composition of each zone i n
terms of i t s content of each of A, T, S .
%ivsvolume fractions,,
plied by
Let t h e m be i n zone N o ,
Introduce the cross sections per
IO
'
[tT{
I
t*
L
Specify these f o r each lone I n rela-
. d j 3 ...
Ckba
$f;,
2 L'
, reepectively.
d
A;,
3
of pure n a t s r i a l , multi-
, and as functions of t h e
neutron velocity
;Fission i n A, w i t h production of
Scattering
AS
w e l l as fission me assumed t o produce i s o t r o p i c a l l y
*a
Page six
*
Eve-
iiseion neutmn has the velocity W0
.
I rupparo that tihi8 piatwe s;tther'givas a model or at leaet provides
a gmtotppe for ermntiul3.y all tholse phenombna about which we h v e relevant
o b s e m a t i s d infospation at prerenb, and attually for romewhat more.
be axpsicted t o provide
1~
It-may
rmsoaabls vehiole for tho additional rslevmt
obsez.oritlmdl mraterial %ha%
i s Pfbkely t o arirs i n the near future.
De prnx agree with this?
c
suffers a c o l l i s i o n i n eone No.
path, and pass inLo zone8 Nos.
a
lniewl
, it w i l l
I
I
I' j
rr.
leave t h i s zone along i t s s t r a i g h t
.
I
d'
It is deairable t o s t a r t
neutron whenever t h e neubron under consideration hhs suffered a c o l l i -
- i n t h e last-mentioned
sion (absorbing, s c a t t e r i n g , o r ,fissioning,
case s e v e r a l
'new' neutrons w i l l , s:F course, 'have t o be started), orwhenever it passes
i n t o another zone (wlthout having collided)
Consider fbrst, whether t h e neutronls l i n e a r l y extzapolated path
i
goes forWard from zone No.
into zone No.
I,'
I /
or
two p o s s i b i l i t i e s by I tmd 11.
If t h e neutron moves outward3 i . e . , if
If t h e neutron moves inward;
t a i n l y I.
if 3
i.8.)
I '
s2
=
I
L'
. Denote these
then we have cer-
o , then
we have e i t h e r
I OF 11, t h e l a t t e r if,, and only if, t h e path penetrates a t all i n t o t h e
sphere
\.
L
A
f,-,
I - r -
,
L
.
It, is easily seen that t h e l a t t e r i s equivalent t o
e
So we
The exit from zone No.
/*
haver
-"i-
c
/ I
si
i
w i l l ikherefore ocuw at,
p-
A-
.
i o
11
.
y-I.
4L I
It is easy t o calculate that the d i s t a n c e from t h e neutron's o r i g i n a l p o s i t i o n
t o t h e e x i t position
k
-
itl
_-
3
* c
f
'
, where
5
-.
4
.*
5
. . e
L
e.
__
0
.
+
td
.
. * -
If# on t h e other b n d ,
I /
<.,&[,
then the neutron is ruled t o have
suffered a collision while S t i l l wlthln ion0 Nom
The ] m i i t i o n at LhSa s t a g s i s n m
, after a t r a v e l *d',
or 5, or 4 neutroni.
procedure Pike t h e preceding ones:
There me-
rlte
Provi.de t h e c a l c u l a t i o n w i t h a m1ue
F.
belonging t o a random variable, s t a t i s t i c a l l y equidistributad in the interval
-_
e
Val
/
/
:/
f l
POITR/L
/.
-/I( { , t M 8 i s then
e q u i d i s t r i b u t e d in the intsr-
Let tihe seven above cases correspond t o ' t h e seven b f s r v a l a
: JG) /. ; I--,
Rule, t h a t that one of
turns out t o l i e .
{, reapeotively,
+
;
,
A,
j A, is; 45,
d)
those amen
holds i n whose i n t c e r v d / u a o t u a l l y
J3j
dl
cases
Now the value of AY caxi be specified.
avaj 18.b3.e cases in auccsrssion.
Absorption8
The neutron has diSappeaI%d,
this s i t u a t i o n by replaCinl:,lJ
.by. 0.
..
a
Let
US
b
consider t h e
6etwm
It is 8impl@Btt o c h a r a c t e r h e
aaa
am
e a
Page Eleven
asswbly), may be sorted out.
The manner in which t M e material can then be used for all kinds of
neutiron statistic investigations is obvious.
"-
I append a tentative %omputing u h e W for the calculation above.
It :la,,
of courae, neither an actual ncompUi;ing sheet" for a (human) computer
group, nor a aet-up f o r the ENIAC, but I think t h a t it is w e l l suited t o
serve as
B
basis for either.
It slrlouXd give a reasonably immediate idea of
the aniount of work t h a t i e involved i n t h e procedure in question,
I cannot asssrk, t h i s u i t h certainty yet, but it ieem t o me very
l i k d y that t h e i n s t r u c t i o n s given on thls %ompuking
tlogioafr capacity of the ENIAC.
sheet* do not exceed t h e
I dmbt.%hat t h e pr0COS8ing of 100 tneutronrt
w i l : ~t,ake much longer than the reaclinlg, punching and (once) sorting time of
100 aavds;
i a 8 . j
about B mtnutea.
Hence, taking 100 tneutmnst through 100 of
thetie stages should take about 500 minute483
i.8.)
5 hours,
'
U
Please 1st m e huw what you and Stan think of these things,
Dosa the
appiaanh and t h e fomnahtion andl gmeralitp. of the, czribicality problem 8eem
reaironable t o you, or would you :wafer some other variant?
Would you covlaider coming East Borne time t o dircurrs matterr further?
'When could this be9
,
With brit relgnrdcli
Very truly yours,
J3
....
* *
-
..a
9
r . .
.
w
a
w
Page i
'4
10
12
-
1s
14
S
s
15
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4
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ma.
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ma.
a .
a m .
a.
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Page Lv
48
.--
17
-
-
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f'$
__ :
.
U
g
'
...
-
-
I
* * * *
_.
From here
Only for
a
Only for
C1nl;y
for
Only
for
72
*
59 x71,
u
5 "
Page v
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