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Technical Information Division, Oak Ridge Directed Operations
Oak Ridge, Tennessee
UNITED STATES ATOMIC ENERGY COMMISSION
(a,n) CROSS SECTIONS OF BERYLLIUM, MAGNESIUM, AND ALUMINUM
Los Alamos Scientific Laboratory
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*,:.. (ao,n) CROSS SECTIONS'OF BERYLLIUM, MAGNESIUM, AND ALUMItUM
SBy I. Halpern
The (a,n) cross sections for Be, Mgand Al were measured as a function of a energy up to the
full energy of polonium a's. The cross sections were determined by counting the neutrons released
in the reactions in a graphite block with a slow neutron counter. The energy response of the counting
apparatus was reasonably "flat" as it would have to be to give significant results.
A number of excitation curves for (a,n) reactions in light nuclei appear in the literature.',s,'4
The emphasis has usually been placed on the location of thresholds and resonances rather than on the
measurement of cross sections. This is due in part to the difficulty of measuring the necessary neu-
tron yields to determine the cross sections. In the present experiment an attempt has been made to
measure tlh nbutron yields. The method used was such that some sacrifices in energy resolution
had to be made (especially ip the cases of Mg and AI) and the identification of resonances was made
In some (a,n) reactions, it is true, the final nucleus is left radioactive and a measurement of the
intensity of decay allows the calculation .of a cross section.3,4 But, even in some of these cases, it
might be preferable (and for other nuclei, it would, of course, be necessary) to measure the neutron
yield directly'in order to determine the cross section. Such a measurement requires the ability to
count neutrons with a known efficiency and this efficiency must be independent of neutron energy.
In the present experiment, a fair degree of energy-independence of counting efficiency, or
"flatness" was obtained by placing boththe cross section chamber (i.e., the source of neutrons) and
a slow neutron counter at appropriate positions in a large graphite block. The degree of flatness of
any particular arrangement of source and counter..in a block can be calculated to a good approxima-
tion by means of, elementary pile theory. Throughout a block in which there is a small source of fast
neutrons of energy E, there will be a distribution of thermal neutrons which have originally come
from the source and have been slowed down. This distribution depends on the size and shape of the
block and upon E. For every distance? from the source, a value of E, Em can be found that renders
the thermal flux at? a maximum, This maximum arises from the combined effects of the slowing
down and absorption of neutrons in graphite. To count neutrons with a given energy spectrum, one
would place the thermal neutron counter at such a distance from the source that E falls somewhere
wld i-the spectrum. A detailed cdleulatioi for the size of graphite block used in tis experiment
(6'by 5 by 10 feet) *hcws thaktith a source at the middle of the block, and the counter 55 cm away
Along the long tuiis of the tl~hk,-E is .5 Mev and that the counting efficiency for 4 Mev neutrons
would still be over 90% of tanhxinam.
S.-. The cou.tingwas done by,a conventional BF,-filled counting-tube whose pulses were amplified
,and fedizjt a discriminatqr and scalar. A BF, counter is essentially a counter of slow neutrons and
the above .i cupsion applies. ,The overall counting efficiency of the apparatus was determined by
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means of a standardized RaBe neutron source whose total neutron yield had been carefully measured
to within 2%
The cross section chamber was spherical (Figure 1) and contained an a source in the form of a
thin layer of polonium plated onto a small nickel sphere. The source was accurately held at the cen-
ter of the chamber. Enclosing it were two hemispherical steel spinnings onto the inside surface of
which were evaporated the targets. The pressure of gas in the chamber was varied so that the cross
section could be determined as a function of a-energy. The stopping gas used was nitrogen for its
neutron yield from polonium a's is harmlessly small. A few remarks about the energy resolution of
such a spherical cross section chamber are included herein.
FLANGE AND GASKET
CHAMBER TARGET MATERIAL
SPUN STEEL SHELLS
STEEL HEM1- "!
NICKEL BALL SHELLS I .
/\DIAMETER 3/16 IN. 3 IN. THICKNESS
THIN COPPER TO SOURCE OF
WALL OF CHAMBER GAS AND MANO-
GASKET of SOURCE
SCREW-IN PLUG .
Figure 1. Exploded view of cross section chamber.
The curve for beryllium (Flure 2) gives the (a,n) cross section as a function.of the average.
residual a range at the target. The counting rate was such that the statistical probable error coul
be kept below 2% for most of the points on the graph. The a source for this part of the:experimant
was 0.496 curies of polonium uniformly plated onto the nickel ball of Figure 1. The target, to, .was
fairly uniform in thickness (0.22 mg/cm'). Tungsten coils of several shapes and sizes were tested
for evaporating the targets and one with reasonably "point source" properties was chosen. The evap-
oration was done into one hemisphere at a time from this coil properly centered. The cu4e of pliure
2 can reasonably be regarded as a thin target excitation curve for the (a;n) reaction In Be, inasmech
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as the target was only 0.25 cm (air equivalent) thick. The shape of the curve resembles closely that
obtained by Bernardini' and by Bjerge.2 These two papers do not, however, locate the curves in the
same way with respect to the energy axis. In the first paper the first resonance peak, for example,
occurs at 2 cm a range, whereas in the second it appears at 1 cm. The present results tend to agree
with those of Bjerge and when integrated are in very close agreement with the recent thick target
results of Segre and Wiegand.s
The vertical lines through each point in the curve for magnesium (Figure 3) indicate the statisti-
cal probable error based on the number of counts taken to determine the particular point. The cross
section for the (a,n) reaction in Mg is considerably smaller than that in Be. To assure adequate
counting rates, a thicker target (.50 mg/cm2 = .38 cm air) and a thicker source (1.14 curies = .10 cm
air) had to be used. This thickening of source and target for heavier element targets (necessitated
largely by the Coulomb barrier reduction of cross sections) reduces the energy resolution of the
apparatus. This is rather unfortunate since, for heavier elements, resonance levels are closer together
and good energy resolution is very desirable. In the present experiment the extent of the smoothing
out of the curve is such as to make the location of resonance levels rather uncertain. There may be
resonances (Figure 3) at 3.0, 3.25, and 3.5 cm.
The target for aluminum (.63 mg/cm2 = .38 cm air) had to be made even thicker than for magne-
slum and no resonances are apparent. The cross section plotted in Figure 4 may be regarded as an
average cross section in the neighborhood of any point on the abscissa.
In this type of experiment there is a spread in energy of those a particles causing transformations
which is due to the varying fractions of their range spent by different a's in the source and target.
In addition, the finite size of the source ball makes it possible for varying path lengths through the
gas in the chamber. Difficulties may also arise from improper positioning of the source and target.
Superimposed on all these is the natural straggling of a particles when passing through matter. The
problem of positioning can be overcome and the inherent straggling amounts at most to about 2%of
the maximum range. But the other causes of decreased energy resolution are more serious. Under
normal circumstances, the required counting rate and the maximum size of the cross section chamber
would be given. From these it is possible to calculate the optimum size of the source ball and the
optimum thickness of polonium and target for best resolution. In the Be experiment, such a calcula-
tion showed that the narrowest distribution of a energies with the chamber filled to half an atmosphere
had a width at half-maximum of 5%of the a energy. (It should be mentioned that if the cross section
chamber were made reasonably larger, or if several counters were used simultaneously at proper
distances from the source, the resolution could be slightly improved.) It should also be pointed out
that the straggling in the present arrangement gets increasingly bad as the pressure is raised. As a
result, the resolution at low energy (high pressure) is much worse than at the high energy end.
I should like to thank Prof. H. H. Barschall for suggesting this experiment and R. L. Walker for
preparing most of its instrumentation. Prof. D. Lipkin kindly offered.several helpful suggestions for'
the evaporation of the targets. I should also like to thank L. Treiman for the very fine polonium
sources he prepared for this experiment.
1. Bernardini, Zeits. fur Phys. 85: 557 (1933). (Beryllium)
2. Bjerge, Proc. Roy. Soc. 164A: 243 (1938).(Beryllium)
3. Ellis and Henderson, Proc. Roy. Soc. 156: 358 (1936). (Magnesium)
4. Waring, I. R. S., and W. Y. Chang, Proc. Roy. Soc. 157: 652 (19J6). (Aluminum)
5. LA 136
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