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 UNITED STATES ATOMIC ENERGY COMMISSION 
 
 ANGULAR DISTRIBUTION OF NEUTRONS FROM 
 TARGETS BOMBARDED BY 190 MEV DEUTERONS 
 
 by 
 
 A. C. Helmholz 
 Edwin M. McMillan 
 Duane E. Sewell 
 
 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 author(s). 
 
 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 
 
 ABSTRACT 
 
 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 + ae^)"'/^, and the measured widths in 
 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. 
 
 INTRODUCTION 
 
 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 l/5 radian. 
 
 For the more detailed measurements reported here, another method was used. Small samples 
 of materials capable of being activated by fast neutrons were placed in an array across the beam, 
 and their activities measured by a Geiger counter after bombardment. This method has the following 
 advantages: (1) all samples get exactly the same exposure time, obviating the need of a monitor and 
 the consequent added chance of error; (2) since the samples could be placed immediately in contact 
 with the 1 3/4 inch thick steel wall of the cyclotron vacuum chamber, any effect of scattering by this 
 wall is minimized; and (3) by suitable choice of samples with high activation thresholds, neutrons 
 degraded below a certain energy by inelastic scattering from surrounding matter are not detected. 
 
 EXPERIMENTAL ARRANGEMENT 
 
 Figure 1 is a plan view 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 
 
MDDC - 1081 
 
 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 l/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 Cu"(n,2n)Cu°^ (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. 
 
 VACUUM CHAMBER 
 
 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 
 the beam. 
 
 FIRST SERIES OF MEASURlEMENTS 
 
 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 l/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. 
 
MDDC - 1081 
 
 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 e^)"^A, where B is the distance from the center in radians, 
 and a is a constant characteristic of the target material. 
 
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 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. 
 
 H orizontal 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 to 6 = -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 
 
4 ] MDDC - 1081 
 
 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 width, 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 1 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 in 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 orbit 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 deuterons 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 show that radial oscillations certainly exist, and 
 
MDDC - 1081 
 
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 ATOMIC NUMBER OF TARGET 
 
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 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. 
 
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6 ] MDDC - 1081 
 
 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. Berber has computed the energy losses and the RMS scattering angles for a single pas- 
 sage through l/l6 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, cind 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 
 halt-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 
 
 [■^ 
 
 DISCUSSION 
 
 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. 
 Berber. 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. 
 
 ACKNOWLEDGMENTS 
 
 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. 
 
UNIVERSITY OF FLORIDA 
 
 3 1262 08908 0005