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UNITED STATES ATOMIC ENERGY COMMISSION
ANGULAR DISTRIBUTION OF NEUTRONS FROM
TARGETS BOMBARDED BY 190 MEV DEUTERONS
A. C. Helmholz
Edwin M. McMillan
Duane E. Sewell
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University of California
This document consists of 7 pages.
Date of Manuscript: June 4, 1947
Date Declassified: July 10, 1947
This document is issued for official use.
Its issuance does not constitute authority
to declassify copies or versions of the
same or similar content and title
and by the same authorss.
Technical Information Division, Oak Ridge Directed Operations
Oak Ridge, Tennessee
ANGULAR DISTRIBUTION OF NEUTRONS FROM
TARGETS BOMBARDED BY 190 MEV DEUTERONS
By A. C. Helmholz, Edwin M. McMillan, and Duane C. Sewell
It is found that 190 Mev deuterons striking a thin target produce a beam of neutrons concentrated
about the forward direction of the deuterons. The angular distribution of intensity in this beam has
been studied, using as target materials Be, Al, Cu, Mo, Sn, Ta, Pb, and U. The shape of the dis-
tributions is represented approximately by the function (1 + at) ': ', and the measured widths m
radians between points of half intensity can be given approximately as 0.155 0.00060 Z, where Z is
the atomic number of the target material. It is pointed out that these data fit within a few per cent
a simple theory of neutron production, according to which the proton is "stripped" from the deuteron
by striking a target nucleus, leaving the neutron free.
When the 184 inch synchro-cyclotron of the Radiation Laboratory at the University of California
was first put into operation,' one of the earliest observations made was a rough survey of the angu-
lar distribution of the neutrons emitted from an internal target. This was done with a portable ion-
ization chamber; it was found that the neutrons came out as a rather sharp beam, whose axis was
along the direction of the incident deuterons. More accurate measurements seemed worth-while,
and a track was set up so that the chamber could be set at known positions across the beam, while
the ratios of the readings to those of a fixed monitor chamber were obtained. In this way it was found
that the beam had a half-width (width between points of half maximum intensity)of about 1 5 radian.
For the more detailed measur-ments reported here, another method was used. Small samples
of materials capable of being activated by fast neutrons were pl'iced in an array across the beam.
and their activities measured by a Geiger counter alter bombaronjent Thi: method has the following
advantages: (1) all samples get exactly the same exposure time. obviating the reed of a monitor and
the consequent added change of error; 1t2 since ine samples cjuld be placed immediately in contact
with the 13/4 inch thick steel wall of the cyclotron vacuum chamber, any effect of scattering by this
wall is minimized; and (31 by suitable choice of samples with high activation thresholds, neutrons
degraded below a certain energy by inelastic scattering from surrounding matter are not detected.
Figure 1 is plan veuL of the cyclotron, showing the location of the internal target on the end of
the probe, the final orbit of the deuterons, and the direction of the neutron beam. The targets placed
on the end of the probe were all of the same shape, being in the form of truncated wedges with a width
at the edge of 1/16 inch. The target materials used were Be, Al, Cu, Mo, Sn, Ta, Pb, and U. The sam-
ples to be activated were fastened to the surface of the vacuum tank, along horizontal and vertical
'Brobeck, W.M., E.O. Lawrence, et al. Phys. Rev. 71: 449 (1947).
MDDC 1081 [1
lines intersecting at the center of the neutron beam. All of the data given in this paper were taken
using as detectors disks of pure graphite, 1 11 '16 inch in diameter and 1,8 inch thick. The only
activity observed was the 20.5 minute C" formed by the reaction C"(n,2n)C", with a threshold at
21 Mev. Some other runs were made with copper samples, using the reaction Cu6'(n,2n)Cum (thresh-
old about 10 Mev): these agreed well with the carbon results. However, copper is a less satisfactory
material than carbon because the presence of decay periods other than the desired 10-minute period
complicates the decay correction.
Figure 1. Experimental arrangement, showing the path of the deuteron inside the
cyclotron, the position of the internal target, and the direction of the deuteron beam.
The carbon samples were placed on the outer surface of the vacuum chamber wall;
the 105 inch dimension is the distance from the target to the sample in the center of
FIRST SERIES OF MEASUREMENTS
In this series, carbon samples were placed on 2 or 3 inch centers covering a horizontal range
of 56 inches or a vertical range of 20 inches from the center of the neutron beam. Greater ver-
tical heights come into the shadow of the magnet poles. The samples were exposed for a time suffi-
cient to give an initial activity on the center sample of about 5000 to 10,000 counts per minute; the
exposure times required were of the order of 5 to 15 minutes, depending on the deuteron current, the
maximum current being estimated at about 1 '2 microampere. The activities were then measured
with a Geiger counter, taking at least 1000 counts for each reading. All of the measurements were
corrected for decay and for lack of counting resolution at the higher rates. In the case of the hori-
zontal distributions, it was also necessary to correct for the variation of distance with angle.
Vertical distributions were taken with targets of Be, Cu, Sn, Pb, and U. These curves are very
similar to one another in shape, but have slightly different widths. The curve with a Cu target is
shown by the circle and solid line in Figure 2; the curves with Be and U targets are given in a
paper b' Dr. Serber. The shape of these curves can be represented with considerable accuracy by
the empirical relation; intensity (1 + a H)" ', where a is the distance from the center in radians,
and a is a constant characteristic of the target material.
t 4 -
s 6 -- -- \ -
2 / ^
-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
RADIANS FROM CENTER OF BEAM
Figure 2. Curves for angular distribution of fast neutrons from a copper target struck
by 190 Mev deuterons. Circles and solid line: vertical distribution. Dashed lines: outer
parts of horizontal distribution. Central part coincides with vertical distribution. The
horizontal curve on the right contains some neutrons caused by deuterons striking the dee.
Horizontal distributions were taken with targets of Be, Cu, Sn, and U. The central portions of
these are nearly identical to the corresponding vertical distributions. The outer portions on the left
side correspond to extensions of the vertical curves to greater angles; on the right side away from
the center of the cyclotron, they deviated appreciably from the vertical curves. For the case of a
copper target, the outer parts are shown as dashed lines in Figure 2. The extra intensity on the right
is certainly caused by deuterons striking the dee, which was confirmed by the fact that the dee ac-
quired an appreciable induced activity. Because of this distortion of the horizontal curves, only the
vertical curves were used in the half-width measurements. The empirical equation given above, when
extended tof = -0.4, falls below the dashed line by about a factor of two. The shape of the extreme
wings of the curve is not to be taken too seriously because of the probable presence of a weak back-
ground arising from nuclear processes in the target other than that responsible for the sharp neutron
beam. No attempt was made to evaluate this background or to correct for it, since it can have only
a small effect on the shape of the main part of the beam.
SECOND SERIES OF MEASUREMENTS
Since the results of the first series showed that the distributions all have the same form, but
have apparently significant variations in uidth, a second series of measurements aimed particularly
at determining the half-widths was made. Only vertical distributions were measured, and for each
exposure only nine samples were used, in groups of three with I 11,'16 inch spacing bracketing the
peak of the curve and the two half-intensity points. With the smaller number of samples it was pos-
sible to get three or four readings on each one, and to plot for each a decay curve, minimizing the
possibility of error in the activity determinations. All the target elements used in the first series
were repeated in this way, and in addition, Al, Mo, and Ta were used. Also, in order to obtain some
idea of the precision of the measurements from internal consistency, several independent runs were
made for each of the target materials; these were done in random order among the various targets.
All of the half-width measurements are given in Table 1.
Table 1. Half-widths of neutron beams in radians.
Target Be Al Cu Mo Sn Ta Pb U
1st series .162 ---- .174 ---- .203 ---- .213 .205
2nd series .159 .155 .181 .178 .206 .200 .208 .201
164 .158 .170 .183 .197 .199 .197 .208
.155 .148 .169 .183 .191 .206 .198 .203
.150 .150 .180 .188 .206
These values are plotted against atomic number in Figure 3. The mean of the total spreads of values
for the different targets is 3 per cent, which can be taken as a rough measure of the degree of
precision of the measurements
PROPERTIES OF DEUTERON BEAM
In order to interpret these results, it is necessary to know certain things about the deuterons
striking the target, particularly their energy and their spatial and angular distribution. The dis-
cussion of these matters is closely tied in with the more general problem of understanding the oper-
ation of the synchro-cyclotron, and some of the material used m the following discussion comes
from observations made by members of the cyclotron group for the latter purpose.
First, some conclusion must be made about the energy of the deuterons. The nominal energy
given by the radius (81 inches) and magnetic field (14,250 oersteds) is 195 Mev. However, the
possibility must not be ignored that the radius of curvature of the oribt may differ from the geo-
metrical radius at the probe; this can be caused by a displacement of the magnetic center of the
field from the geometrical center of the tank, or by radial oscillations of the deilerons in their
orbit. The first effect mentioned is easily checked. From measurements of the azimuthal and radial
variations of the field, it is possible to compute the displacement of the magnetic center' at the 81
inch radius, this was found to be about 3 '4 inch, in a direction nearly perpendicular to the probe
radius. This displacement was verified by measurements of the current to the probe when two de-
fining vanes were'put in from the left and bottom of Figure 1; it makes a negligible change in the
energy. The other effect is harder to measure, and a detailed discussion would go beyond the limits
of the subject of this paper. The observations made snow that radial oscillations certainly exist, and
S/1 /z U
0 20 40 60 80 100
ATOMIC NUMBER OF TARGET
Figure 3. All measurements of neutron beam half-width (width between points of half maximum
intensity) plotted against atomic number of target. The ordinate scale is in radians; note that its
origin is below the bottom of the plot. The lines A and B give the theoretical half-widths computed
in the "opaque nucleus" and "transparent nucleus" approximations respectively. The best straight
line fit to the experimental points comes close to line A at uranium and close to B at beryllium.
that their amplitudes probably range from about zero to about two inches. Since the oscillating ions
always strike the target near the peak of the oscillation, the amplitude must be subtracted from the
probe radius to get the radius of curvature. We therefore estimate the effective radii to range from
79 to 81 inches, and the deuteron energies from 185 to 195 Mev, the mean energy being about 190 Mev.
We must next consider the question of what happens to the deuterons while passing through the
target. Dr. Serber has computed the energy losses and the RMS scattering angles for a single pas-
sage through 1/16 inch of the various materials, with the following results.
Table 2. Effect of target on deuteron beam.
Material Energy loss RMS scattering angle
Be 1.0 Mev .0024 radian
Al 1.6 .0056
Cu 4.9 .015
Mo 5.3 .019
Sn 3:7 .017
Ta 8.0 .029
Pb 5.4 .026
U 8.8 .035
Since the vertical angle of the deuteron orbit is limited to about 0.01 radian by the dee aperture,
it is apparent that for targets from Cu to U, most of the deuterons passing through the target once
will strike the dee before making a second passage through the target, and the contribution from
those that do go through again with reduced energy will not be important. In the cases of Be and Al,
it would take several passages for the RMS scattering angle to reach 0.01 radian, and, therefore,
there must be an appreciable number of deuterons going through the target several times. However,
the energy loss in these cases is small, and this effect does not make a serious error in the mean
energy. The energy loss in U would give, according to the theory, a change of about 2 per cent in
half-width, which is within the accuracy of the half width measurements. Therefore, the energy
losses in the targets will be neglected.
Next, we can examine sources of angular spread other than the intrinsic width of the neutron
beam. One such source is the multiple scattering in the target, as given in Table 2. This becomes
appreciable in the heavier targets, and is included in the calculated results of the accompanying
theoretical paper. Other sources of spread are the spatial and angular spread of the incident deu-
terons. The easiest to determine is spatial distribution of the deuteron beam striking the target.
This is found by making a radioautograph of the target after bombardment. The activity is concen-
trated in a thin band not over 1 '8 inch wide along the edge, with a vertical distribution in the form of
a peaked curve having a half-width of 7,8 inch, corresponding to an angle of 0.01 radian at the sample
position. The vertical angular spread of the deuterons is limited by the dee aperture to 0.01 radian
and is actually less than that, since the vertical oscillations of the orbits are observed to be con-
siderably smaller than the available aperture; the half-width is certainly not greater than 0.01 radian.
These spreads are random, and, therefore, must be combined with the intrinsic widths according to
the rules for random errors,-that is, the total spread is of the order of the order of the square,
root of the sum of the squares of the separate spreads and the intrinsic width.. Thus the resultant
errors are of the order of 1 per cent, and can be neglected.
MDDC 1081 7
The fact that measurements with detectors having different thresholds, or with an ionization
chamber, lead to consistent results, can be interpreted in two ways. Either most of the neutrons in
the beam have energies above the highest threshold, or else if there is present a considerable frac-
tion of lower energy neutrons, these are also distributed in a beam of about the same width. The
theoretical interpretation of the mechanism of neutron production favors the former possibility.
This is also consistent with measurements of the transition effects observed when paraffin is placed
in front of an ionization chamber.
The theoretical interpretation of the angular distributions is given in detail in a paper by Dr.
Serber. It is shown there that the probable chief mechanism is a process in which the proton of the
deuteron strikes the nucleus, leaving the neutron free. The neutron velocity at this instant is com-
pounded of the deuteron velocity and the relative motion of the neutron with respect to the center of
mass of the deuteron. The transverse component of the relative motion gives the angular spread,
and the longitudinal component should give a spread of energy with a mean amplitude of about 20
Mev about the mean neutron energy, which should be about 95 Mev. It is easy to see from this pic-
ture that the magnitude of the angular spread should be of the order of the ratio of the relative in-
ternal momentum to the total momentum, or the square root of the ratio of the deuteron binding
energy to its kinetic energy. Thus the spread should be about (2.18/190) or 0.17 radian, which is
indeed of the correct order. There is also to be expected an additional spread caused by the deflec-
tion of the deuterons in the Coulomb fields of the nuclei responsible for their dissociation, and this
additional spread should increase with atomic number. The observed shapes of the curves obtained
in the first series of measurements agree with the computed shapes, as illustrated in the previously
mentioned paper by Dr. Serber. The theoretical half-widths as a function of atomic number are in-
dicated by the solid lines in Figure 3, which are computed using the two limiting forms of the theory,
the "opaque nucleus" approximation A being probably better for the heavier elements, and the
"transparent nucleus" approximation B for the lighter elements. It will be seen that either curve
fits the experimental data with reasonable accuracy; in only two cases, Al and Sn, are the means of
the experimental points more than 3 per cent from the nearest theoretical curve, and these devi-
ations we believe are probably not significant. Nothing has been said so far about the relative neutron
.yields from the different targets. These ratios were hard to determine, since no means were avail-
able for measuring the deuteron currents passing through the thin targets, and only very crude es-
timates were made. The theory indicates that there should be no great variation of yield with atomic
number, and the experimental estimates are not inconsistent with this.
To conclude, we can say that a simple theory involving no arbitrary parameters fits the observed
distribution curves with regard to shape, absolute width, and variation of width with atomic number
within a few per cent, and therefore, that the presumption is strong that the theory is a correct in-
.terpretation of the mechanism of neutron production responsible for the beam.
The authors wish to express their appreciation to Professor E. O. Lawrence for his interest and
encouragement in this work, to Dr. R. L. Thornton and the cyclotron operating crew for their help in
Making the exposures, and to Miss Alice Dodson for her aid in computing the data.
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