The number of neutrons emitted by Ra-Be source

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UNITED STATES ATOMIC ENERGY COMMISSION



I



THE NUMBER OF NEUTRONS EMITTED BY A RA- BE SOURCE (SOURCE I)



by
H. L. Anderson
E. Fermi
J. H. Roberts
M. D. Whitaker


Date of Manuscript:
Date Declassified:


March 21, 1942
January 28, 1947


Issuance of this document does not constitute
authority for declassification of classified
copies of the same or similar content and title
and by the same authors.






Technical Information Division, Oak Ridge Operations
AEC, Oak Ridge, Tenn., 12-20-48 --850-A4648


Printed in U.S.A.
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THE NUMBER OF NEUTRONS EMITTED BY A RA-BE SOURCE (SOURCE I)


By H. L. Anderson, E. Fermi, J. H. Roberts, and M. D. Whitaker


In order to simplify the design of experiments directed toward the production of a chain re-
action involving uranium, it is desirable to know the actual number of neutrons emitted by the
primary sources used. A series of experiments have been planned whose aim is to determine
this number. The measurements described are a part of this series. Here, the number of neutrons
per square cm emerging from the top of a carbon parallelepiped is measured and calculated, and
from a knowledge of the neutron distribution in the carbon, with a given placement of source, this
measurement is reduced to the neutron emission from the source.
A radium-beryllium neutron source containing about 1.16 grams of radium was placed 28
inches from the bottom of a carbon parallelepiped five feet on a side and of variable height. The
-ource was placed on the vertical axis of the pile, and the number of neutrons emerging from the
top surface at the center was determined for two different heights. These neutrons were detected
by a BF, proportional counter of 3.62 cm inside diameter, which was filled with BF, gas to a
pressure of 12.1 cm of mercury at 0C. A 10 cm section of the counter was exposed to the neutron
flux, the rest being shielded by a close fitting cadmium wrapper, in which a semicylindrical -.in-
dow 10 cm long had been cut. The glass walls of the counter tube and the metal cathode (a nickel
cylinder .010 inches thick) were found, experimentally, to have an absorption factor of 1.13. This
absorption factor was measured before the assembly of the counter by observing the decrease in
the counting rate of a smaller BF, counter placed near a graphite surface, when the glass tube
and nickel cylinder were slipped over it.


CARBON
SURFACE


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A boron carbide shield, containing a circular hole 13 cm in diameter, was used to define the
part of the upper carbon surface from which the counter could receive C neutrons. The counter
tube was mounted horizontally on a vertical cadmium sheet cylinder, in such a manner, that the
semicylindrical opening in the cadmium wrapper around the counter was symmetrically placed,
with respect to the circular opening in the boron-carbide shield. The axis of the counter was
26 cm above the carbon surface. Additional cadmium shields were arranged so that it was im-
possible for the counter tube to receive C neutrons, other than those originating in the carbon
surface defined by the boron carbide shield. The number of disintegrations produced in the tube
was counted with and without a cadmium shield over the 13 cm opening. The difference between
the number of counts per minute observed with and without cadmium was taken with the carbon
surface 40 inches above the source, and again with the surface 44 inches above the source as a
check. These numbers were found to be 90/min and 63/min. These numbers must be reduced to
the number of neutrons per second, Jo, emerging from unit area of the carbon surface at its center
by suitable geometrical considerations, and by making use of the known angular distribution of
the neutrons coming from the carbon surface. After Jo is known, the number of neutrons emitted
by the source can be calculated from a knowledge of the neutron distribution in the carbon pile.
An approximate calculation of the number of neutrons producing disintegrations in the counter
tube in terms of J1 will be done, and the accuracy will be improved by determining correction
factors to take care of the approximations made.
The angular distribution of the neutrons coming from the surface varies with the angle e,
which any neutron makes with the normal to the surface as cos 0 + T3-cos2 8. The fraction of the
neutrons which come off at any angle 0 is then

cos + V3cos2 0
v (1 + 2)

where the denominator is the definite integral of the numerator between the limits 0' and 90'. For
angles close to 900 this becomes


r (1+ 2)


and the number of disintegrations taking place per second in the counter is approximately

rR2 1oa (kT) 1 +_ i Ro J,(kT)
D "( 2-= 1.2679. D2


where 7rR is the area of the emitting carbon surface, D is the distance between surface and the
counter, and o(kT) is the cross section of the counter for absorption of a neutron of energy kT.
o(kT) will be calculated later.
H. W. Ibser has calculated this numerical factor accurately for the actual geometry used and
finds it equal to .9264 of the value. His calculation is on file with the secret library copy of this
report.
We have assumed in the approximation that the neutron current is the same for all parts of
the carbon surface from which neutrons were counted in the above experiment. Since the neutron
flux falls off as cos ix/a cos ry/a, it follows that the average neutron current would not be Jo,
which is the value at the center, but .9948 Jo for the surface of 13 cm diameter.










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The approximation used does not take into account the fact that the window, through which
neutrons pass through the cadmium shield around the counter tube, is in the form of a semicylinder.
This means that the cadmium boundaries which define the length of the counter tube are at a lower
level than the level at which the width is defined, by an amount that has a maximum value equal to
the radius of the tube. This results in the tube having an effective length that is 1.07 times as great
as the length of the semicylindrical opening in the cadmium surrounding the tube.
Even before we calculate the cross section of the counter, which has been designated as ar(T),
we will calculate the amount by which we must correct this cross section, in order to have it
apply to the Maxwellian neutron distribution which we actually have, instead of applying only to
the neutrons of energy kT. Since the cross section of the boron used varies as 1/V, in order to
get a factor relating the cross section for neutrons of energy kT to the average cross section for
the neutrons having a Maxwellian distribution about the energy kT, we must get the ratio of the
velocity of a neutron of energy kT to the average velocity of the neutron having the Maxwellian
distribution. Or, if C = %2/m, then the cross section will vary as the average of C/V.


Cf-- Vs e -V'/C' dV



0
f/ V /-YidV


Now, if we apply all these correction factors to the first numerical constant 1.2679, we find
that this becomes 1.1218 and the number of neutron captures per second in the counter becomes


1.108 R = .06925 J0o


where a(kT) has been changed to U by the inclusion of the last correction factor.
If we neglect the attenuation of the neutron current by absorption in the BF, of the counter,
which we can do in this case with an error of less than 1%, then we can say that the total cross
section of the counter is the number of boron atoms in the tube times the cross section of each,
or, the number of moles of the gas times the cross section per mole, which is 473 cm2 for boron
and neutrons of energy kT. Then
S number of moles x 473
a counter (kT) = 1
1.13

where 1.13 is the absorption factor of the wall material of the counter tube.

Volume of counter tube = x 10 = (362)2 x 10 =102.92 cc
4 4


12.1
Pressure = 76 atmospheres at 0C
76

102.92 12.1
Number of moles 22, x 7.311 x 10" moles
22,414 76

7.311 x 101 x 473
a counter (kT) = .306 cm2
1.13









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With the top of the carbon 40 inches above the source, the number of disintegrations per second
due to C neutrons was observed to be 1.5. Therefore

1.5 = .06925 Jo x .306


1 neutrons
J = 1.5 1 = 70.78 ne
S.06925 x .306 cme sec


and for the case where the top of the carbon pile is 44 inches above the source

63 1 neutrons
S60 .06925 x .306 = cm sec

In the report A-21, Formula 15 gives the density n of thermal neutrons as a function of z.
For a (Ra-Be) source, the neutrons may be represented as a super position of three groups
having ranges for slowing down to thermal energy and percentages as follows:


Per cent

15.0
69.3


Range in graphite

27.1 cm
39.8
58.9


For large z and a 5 ft column the formula reduces to


XNV .008565 e-z/27.61
Q


Near the top of the column an additional term must be added to represent the effect
boundary. We have then

.NV 008565 [=-Z/27.61 +Z/27.61 -2/27.61 (Z +/)


where Zo is the ordinate of the top. Since the diffusion coefficient is XV/3 we have


- XV aN \
Q 3Q aEZ = Zo


of the nearby


S.00856561 1 + -2 x 2.55/Vx 27.61] -Zo0.27.61
3 x 27.61 1 I


=1.9636 x 10-" Z-
27.61


-0 = 4.95 x 10-6 at Zo = 40 inches
Q

"-- = 3.432 x 10-' at Zo = 44 inches
Q

. 70.78 142 x neutrons
-4.954 x 10- sec










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from the data taken at Zo = 40 inches and

49.54 neutrons
Q x = 14.43 x 106 neutrons
3.432 x 10-'1 sec

from the data taken at Zo = 44 inches

.'. avg Q = 14.36 x 106 for source No. I

For the three sources I, I, and m, we have the results given in the following tabulation in which
we combine the value of Q and the comparisons given in the report C -10.

Source No. Q Grams radium Q/gram

I 1.44 x 107 1.16 1.24 x 107
H 1.28 x 107 1.0308 1.24 x 107
II 1.05 x 107 .84 1.25 x 107


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