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ATOMIC ENERGY COMMISSION
A THERMAL NEUTRON VELOCITY SELECTOR AND ITS
APPLICATION TO THE MEASUREMENTS OF
THE CROSS SECTION OF BORON
E. Fermi, J. Marshall, and L. W. Marshall
University of Chicago
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A THERMAL NEUTRON VELOCITY SELECTOR AND ITS
APPLICATION TO THE MEASUREMENT OF
THE CROSS SECTION OF BORON
E. Fermi, J. Marshall, and L. W. Marshall
Argonne Laboratory, University of Chicago*
All three authors now at Institute for Nuclear Studies, University of
Slow neutrons emerging from various moderators with different
geometries usually have average velocities comparable, but by no means
equal to the thermal agitation velocity. Large differences, both positive
and negative, are observed depending on the nature and the geometry of
the moderating substance. This phenomenon has been observed by vari-
ous experimenters. (1) (2) (3) (4)
(1) J. Rainwater and W. W. Havens, Jr., Phys. Rev. 70, 136 (1946).
(2) W. W. Havens, Jr. and J. Rainwater, Phys. Rev. 70, 154 (1946).
(3) J. H. Manley, L. J. Haworth, and E: A. Luebke, Phys. Rev. 69, 405
(4) R. F. Bacher, C. P. Baker, and B. D. McDaniel, Phys. Rev. 69,443
In this paper we have collected some typical examples of the vari-
ations of average velocity of slow neutrons using different moderators
as indicated by changes in the apparent cross section of boron. Since
boron is often used as a standard substance in slow neutron measurements
its cross section has been determined also using monochromatic neutrons
obtained with a velocity selector of new design operated in connection
with the thermal column of the Argonne graphite pile.
The observed temperatures of the neutrons emitted from the vari-
ous moderators and arrangements of moderators appear to be in accord-
ance with the individual arrangements employed. Within the experimental
errors of the method the cross section of boron varies as the 1/v law and
the measured cross section is 703 x 10-24 cm2 per atom for neutrons of
velocity 2200 meters per second.
Temperatures of Neutrons from Various Sources
With the thermal purification column of the graphite pile at the
Argonne Laboratory as a primary neutron source, a number of measure-
ments were made of the cross section of boron. In all cases the detector
was a proportional counter filled with BF3 gas. By the use of cadmium
.diaphragms a neutron beam was obtained with small angular dispersion.
The absorber and detector in these experiments were both boron
and consequently both obeyed the 1/v law of neutron absorption. It was
possible, therefore, to use the corr section method given by Bethe(5) to
calculate the cross section of boron for monoenergic neutrons of energy
(5) H. A. Bethe, Rev. Mod. Phys. 9, No. 2, 134 (1937).
kT where T is the absolute temperature of the Maxwellian distribution
emitted from the source. Since the cross section of 2200 meters per
second neutrons (kT at 2930K) is known, one can then determine the ef-
fective temperature of the neutron beam. It must be understood that
these effective temperatures are bas d on the assumption that the neutron
beam is Maxwellian in velocity distribution. This is certainly not strictly
true for most sources employed.
The results of these experiments are given in Table I. It is quite
clear from an inspection of the table that the effective temperature of the
neutron beam depends strongly on the source of neutrons. During these
experiments the temperature of the thermal column was na the neighbor-
hood of 300C or 303K.
Source of Neutrons Absorber Cross Section for Effective
kT neutrons Tem' O
1. Beam from surface Gaseous BF3 oB = 855xi0-Z4cmZ Ig
of thermal column
2. Beam passed through 598 x 0-24 408
a 3.7 cm. slab of
3. Beam passed through "corrected to 20.40C 288
7.6 cm. of heavy water oB = 710 x0-24 cm2
at 33.70C in a container
Table I (continued)
Source of Neutrons
4. Beam passed through
a 22 cm. column of
graphite 10 cm.square
5. Beam from hole in
125 cm. deep, 10 cm.
Pyrex plate cal-
6. Beam from a "block
hole" in thermal column,
a hole 10 cm x 10 cm x 22
cm high connected to sur-
face of thermal column by
a 42 cm. tube of cadmium
of internal diam. 2.5 cm.
ross Section for
2800 x 10-24
701 x 10-24cm2 293
755 xl0-24 255
The source arrangement given opposite I produces low temperature
neutrons because of the filtering action of the graphite in the pile and
thermal column. (6) Very slow neutrons whose De Broglie wave lengths
(6) H. L. Anderson, E. Fermi, and L. Marshall, Phys. Rev. 70, 815 (1946).
are longer than periodicities encountered in the graphite crystals are
scattered very little and can penetrate to the surface of the column more
easily than the faster neutrons. In case 2 the slower neutrons are re-
moved preferentially because both the absorption and scattering cross
sections of hydrogen are larger and also scattering in the forward direc-
tion is preferred at higher energy. Heavy water (case 3) acts somewhat
in the same way because also for deuterium compounds the scattering
cross section and the coherence of successive free paths vary with the
energy in the same direction as for hydrogen compounds. Therefore the
effective temperature of the neutrons is raised from the initial 1980K to
2880K. The fact that this last temperature is quite close to the actual
temperature of the heavy water probably is coincidental. In case 4 the
filtering effect of the graphite is shown very strongly. Most neutrons
that are scattered are removed from the beam and the graphite column
is so long that almost none of the warm neutrons can travel the whole
distance without being scattered. Case 5 gives a rather good approxima-
tion of the temperature of the source. The neutrons in the beam from the
deep hole should be a fair sample of the neutrons present at the bottom
of the hole. Essentially it is a case of black body radiation from a hole
in the wall of a furnace. Case 6 was expected to give a good temperature
value, but failed to do so, probably because the hole was not deep enough.
The velocity selector makes use of a rotating shutter to interrupt
the beam of neutrons from the thermal column of the pile. The shutter
was constructed by inserting a multiple sandwich of .004" to .008" cad-
mium foils and 1/32" aluminum sheet tightly into a steel cylinder about
l"l in diameter with walls 1132" thick. The shutter was mounted in ball
bearings on a heavy steel base plate and was belt and pulley driven by a
Dumore grinder motor. Maximum rotational speeds of 15000 revolutions
per minute were possible. It was constructed in the shops of the Metal-
lurgical Laboratory under the direction of Mr. T. J. O'Donnell who is re-
sponsible for its mechanical design.
A cross section of the shutter is shown in figure 1. From the thick-
ness of the aluminum spacers between the cadmium foils, and from the
dimensions of the shutter, one would estimate that no neutrons from a
parallel beam would be able to get through when the shutter was more
than 1.20 from its full open position. On the experimental arrangement
used it was impossible to use a strictly parallel beam of neutrons. The
collimators actually used allowed a maximum divergence of neutron direc-
tion in the beam of approximately 30 Consequently one would expect the
shutter to be completely closed during each 1800 of rotation except for an
interval of 30 + 2 x 1.20 = 5.4o. Actually it was found that the counters
indicated background intensity except when the shutter was in a 60 inter-
Through one end of the shutter was inserted a steel rod with its
axis perpendicular to the axis of the shutter and with a minor surface
ground and polished perpendicular to its axis at each end. Light from a
projection lamp and lense system was reflected from these surfaces onto
two photocells so placed that each photocell was illuminated twice during
each revolution. One of the photocells was used with an amplifier and
scaling circuit as a revolution counter. The other, adjustable and cali-
brated as to angular position, was connected to an electronic switch cir-
cuit which allowed pulses from the proportional counter to be recorded
only when the photocell was illuminated.
BF3 filled proportional counters were used as-the neutron detector.
A nest of four was connected in parallel and mounted at a distance of 146
cm. from the shutter. A thick shield of wood, iron and paraffin was placed
between the counters and the pile to compensate somewhat for the fact
that the top shield of the graphite pile is not so thick as might be desired.
A hole in this shield allowed neutrons from the shutter to reach the count-
The neutron beam between the shutter and the counters was colli-
mated to make sure that no slow neutrons from sources other than the
shutter could enter the counters. Slow neutrons reflected from the walls
and roof of the building were eliminated by protecting the sides and back
of the counters with a :" thick layer of boron carbide.
The shutter and an improved velocity selector arrangement are
more fully described in the paper of Brill and Lichtenberger which ac-
companies this paper for publication.
Determination of Boron Cross Section for Neutrons of Known Velocity
The cross section of pure BF3 at several different pressures was
measured for neutrons from the thermal velocity selector for velocities
ranging from 1700 to 5000 meters per second. Within the experimental
accuracy of the method the cross section of boron varied according to
the I/v law. After corrections for scattering were made the average
cross section of boron for neutrons of 2200 meters per second velocity
was 699 x 10-24 cm2 per atom. 2200 meters per second is the velocity
of a neutron of energy kT where T is 2930K.
In order to verify this value a similar measurement was made with
a different boron compound as absorber. Na2B407 was ignited at about
4000 and dissolved in heavy water. The solution was enclosed in a thin
walled aluminum cell and a second cell of identical wall thickness was
prepared containing an amount of heavy water equal to that in the solution.
The transmissions of these two absorbers for neutrons from the velocity
selector were measured and the value of the boron cross section for
2200 meters/second neutrons was found to be 700 x 10-24 cm2 corrected
In good agreement with these values was the cross section as cal-
culated from measurements at the indium resonance energy. (7) Trans-
mission measurements were made using a collimated beam of neutrons
from the interior of the graphite pile of the Argonne Laboratory. The
(7) J. Marshall, Phys. Rev. 70, 107 (1946).
indium foil detectors were protected from thermal neutron activation by
thick cadmium covers. Background measurements were made using an
indium filter. Thus the measurements were limited in more than one
way to neutrons absorbed strongly by indium.
BF3 gas in a steel cylinder was interposed in the c6llimated beam.
The BF3 was highly purified (the same gas as used in the thermal neutron
transmission experiments described above). The transmission of the
steel container filled with BF3 at 44 and 68 lbs. per in.2 was compared
with the transmission of the empty container. The density of gas used
was determined by weighing the cylinder. The pressures used and the
length of the cylinder (30 cm.) were such that the transmissions were in
an accurately determinable range (approximately a 2/3 transmission for
the 68 lb. sample).
The total cross section of BF3 for indium resonance neutrons was
measured as 107.1 x 10-24 cm2/atom. Assuming
O scattering (F) = 3.7 x 10-24 cm2
G scattering (B) = 2 x 10-24 cm2
Indium resonance energy = 1.44 ev.,
the boron absorption cross section for neutrons at velocity 2200 meters/
second is 710 x 10-24 cm2/atom.
The results of the three measurements are given in Table I.
Measurement a kT B) at 293K
Na2B40~rD30 velocity selector 700 x 10-24 cm2
BF3 699 x 10-24 cm2
BF3 In resonance 710 x 10-24 cm2
Average 703 x 10-24 cm2
This report is based on work done at the Argonne Laboratory, The
University of Chicago under the auspices of the Manhattan District,
U. S. Corps of Engineers, War Department.
5 O qI
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