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MDDC 880 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., 122048 850A4648 Printed in U.S.A. PRICE 5 CENTS THE NUMBER OF NEUTRONS EMITTED BY A RABE 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 radiumberyllium 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 MDDC 880 MDDC 880 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 boroncarbide 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 + T3cos2 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. MDDC 880 [3 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 MDDC 880 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 A21, Formula 15 gives the density n of thermal neutrons as a function of z. For a (RaBe) 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 ez/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 106 at Zo = 40 inches Q " = 3.432 x 10' at Zo = 44 inches Q . 70.78 142 x neutrons 4.954 x 10 sec MDDC 880 [5 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 END OF DOCUMENT UNHIVERSITV OF FLORIDA I111111III 11111 III II 111111 111111 l ii II hi!lill!l111l1ll 3 1262 08910 5364 I i' it i I J I 
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