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uNCLA 2 2 SSI uNCLASSIFIED UNCLASSIFIED BNL2022 Subject Category: PHYSICS UNITED STATES ATOMIC ENERGY COMMISSION THE TRANSMISSION OF NEUTRONS AND GAMMARAYS THROUGH AIR SLOTS. PART IV. THE EFFECT OF AN OFFSET ON THE TRANSMISSION OF NEUTRONS THROUGH AN AIR SLOT IN WATER By Robert D. Schamberger Ferdinand J. Shore Harvey P. Sleeper, Jr. ICA56 *,. . "=. / September 1, 1954 Brookhaven National Laboratory Upton, New York Technical Information Service, Oak Ridge, Tennessee Date Declassified: November 21, 1955. This report has been reproduced directly from the best available copy. Issuance of this document does not constitute authority for declassification of classified material of the same or similar content and title by the same authors. Printed in USA, Price 20 cents. Available from the Office of Technical Services, Department of Commerce, Wash ington 25, D. C. GPO 9880 This report was prepared asa scientific account of Govern mentsponsored work. Neither the United States, nor the Com mission, nor any person acting on behalf of the Commission makes any warranty or representation, express or implied, with respect to the accuracy, completeness, or usefulness of the in formation contained in this report, or that the use of any infor mation, apparatus, method, or process disclosed in this report maynot infringe privatelyowned rights. The Commission assumes no liability with respect to the use of,or from damages resulting from the use of, any information, apparatus, method, or process disclosed in this report. BNL2022 THE TRANSMISSION OF NEUTRONS AND GAMMARAYS THROUGH AIR SLOTS Part IV The Effect of an Offset on the Transmission of Neutrons Through an Air Slot in Water Robert D. Schamberger Ferdinand J. Shore Harvey P. Sleeper, Jr. 1 September 1954 REACTOR DEPARTMENT BROOKHAVEN NATIONAL LABORATORY Associated Universities, Inc. under contract with the United States Atomic Energy Commission Work performed under Contract No. AT302Gen16 Part IV The Effect of an Offset on the Transmission of Neutrons Through an Air Slot in Water As an aid in shielding against the passage of neutrons in air slots, the expedient often employed is to put a step or offset in the slot to impede the direct travel of radiation. As part of our investigation of neutron transmission through slots we studied the effect of a single such offset for slots of thickness 0.5 and 1.5 inches with an overall length of 48 inches. Both sections of the slot were 24 inches long by 34 inches wide and the offset distance, D, was varied from zero to a few inches. This variation was small compared with the 40inch source plate, so that the source remained effectively infinite in size. Fig. 1 is a sketch in dicating the essentials of the experiment. An infinite offset was ac complished approximately by having the bottom section filled with water. An experiment, to be discussed later, included a horizontal gap connecting the two vertical air slots. Thermal neutron data were taken in the water above the upper slot with both fission and BF3 counters. The usual procedure was to make a vertical traverse along the upper slot centerline. For small values of offset, when the transmission was large, the fission counter was employed. For larger offsets, the 1 x 6 inch BF3 counter was used. Horizontal tra verses were also taken in the thickness direction at vertical positions corresponding to about 1.5 and 7.5 inch water separations between the top of the aluminum box and the detection center of the counter. The vertical traverses for the 0.5 inch thick slot are presented in the semilog plot of Fig. 2. Ordinates are thermal flux per unit pile power and abcissae repre sent the height of the detector above the bottom of the water tank. The top of the slot holder assembly was at Z = 52.5 inches. Nomenclature ap pearing in the figure is described in Part I of this series of reports. Qualitative features of the traverses which bear comment are the following: For large Z, the l/e length is approximately 7 cm; characteristic of fastneutrons. For small Z; i.e., 54 inches, the 1/e length varies with offset and is larger for smaller offset. The be havior is consistent with the assumption that with large offsets the emergent spectrum of neutrons is softer than with small offsets. The peaks of horizontal traverses made in the neighborhood of Z = 54 inches have been normalized to the flux measured in the vertical traverses at 54 inches. The assumption is made that the shapes of hori zontal traverses taken with Z differing by fractions of an inch are closely the same. These normalized data are presented in Fig. 3. From the peak flux measured at 54 inches, using different values of offset, D, one obtains curve A given in Fig. 4. Curve B results from peak fluxes corresponding to Z = 60 inches. The characteristic to note is the slow decrease followed successively, as the offset is increased, by a rapid decrease, and then a slow decrease. Shown at the right hand side are fluxes obtained with the bottom slot filled with lucite; i.e., an infinite offset. For large offset curve B is much flatter than curve A. This is interpreted to mean that the higher energy component which is detected at the larger water separation of curve B is better collimated and that the interaction effect is smaller. A question of interest is whether the features observed for the 0.5 inch thick slots are the same for slots of different thickness. Data were obtained with 1.5 inch thick slots which allowed comparison with the 0.5 ibh data. Figs. 5 and 6 show vertical and horizontal traverses obtained when the upper half of the 1.5 inch thick slot was displaced. In Fig. 7, corresponding to Fig. 4, the qualitative behavior for the 1.5 inch thick gap is observed to be the same as with the 0.5 inch gap. The similarity of shape for the two thicknesses is demonstrated in Fig. 8. Ordinates for the 1.5 inch points were.determined by dividing the flux by the square of the ratio of slot thicknesses; i.e., factor of 32, or ninefold. Abcissae are in slot thickness units; i.e., offset divided by slot thickness. It is seen that the lower curve shape is essentially independent of slot thickness, whereas the unper curve, which included softer radiation, after transformation is not independent of slot thickness. It appears that for the more energetic neutrons, as a first approximation, the offset shape is independent of slot thickness. For displacements from zero to one slot unit, it is reasonable to assume that, as a first approximation, the transmitted flux will be due to unscattered neutrons. The response function can then be calculated over this range of displacements if one assumes that the problem is two dimen sional and that the detector integrates the emergent flux. This calculation, for those neutrons which do not penetrate water, is done in appendix A, and yields a T2 D2 dependence, where T is the slot thickness and D is the slot offset. In Fig. 9, curve B of Fig. 8 is replotted and a calculated curve is shown for which Phe flux is normalized at D = 0, and decreases with D according to T2 D . It is apparent, however, that when D approaches T substantial contributions to the transmitted flux must come from neutrons which have traversed some water in the region of the offset. In appendix B are out lined calculations which estimate the contribution coming through the corners. For this purpose, it is assumed that fast neutrons are attenuated with a 1/c length in water of 2.0 inches. The. calculation for D/T greater than unity was made at only two points; D = 1.625 and 2.0 inches for T = 1. inches. A summary of those calculations will be found in Table I in appendix B. It is seen that the simple assumption of lineofsight behavior, including exponential attenuation in the water medium at the corners, fits the data fairly well up to r/T = 1.1. This suggests that the first an.roximation theory is good so long as the offset is not much larger than the slot thickness. For larger separations, one may conjecture that the interacting neutrons are not all removed from the beam, and that some of them reach the detector. This would make the experimental points lie higher than the calculated ones, particularly for D greater than T. The difference between the experimental value and the sum of the infinite offset result and the calculated value would then represent the "inscat tered" component: at D/T = 1.33 something like 8 x 103 of that obtained at zero offset. The effect of a horizontal connecting air gap on the trans mission of a stepped slot is indicated in Fig. 10. Curve B is run No. 1828 reported in Fig. 2 for the 0.5 inch thick slot with 1.8 inch offset. Curve A was obtained with the same setup, except that there was a 3 inch high connecting air space at the offset. It is seen that with the air space an increase in flux is noted, and that curves A and B are almost parallel. At Z = 54 inches, the increase is a factor of 1.48 and at 60 inches it is 1.39. If the process of transmission at the offset involved a twofold large angle scattering, the low energy neutrons from the lower slot would scatter through the horizontal section with greater probability than the high energy neutrons because the cross sections are larger for the smaller energies. This would imply that curve A would initially be steeper than curve B. There is no evidence for this. In terms of curve B in Fig. 4, the effect of the air gap was to reduce the offset from 1.8 inches to about 1.2 inches. It is fair to state that for an offset a few times the slot thickness, inclusion of a horizontal connecting gap affects the neutron transmission of the slot in a minor way. APPENDIX A In order to approximate the flux trans mitted through offset slots, let us as sume that we have a two dimensional problem, that the detector integrates the emergent flux, and that we are dealing with only neutrons which travel straight line paths between source and i* detector. The calculation then can be broken into two parts depending upon whether the neutron path is entirely in air or whether it also includes some water. In part A, we consider that the complete path is in air, and in part B,  include the effect of water on the as sumption of exponential attenuation in the water. For a source point lying at x, one ap proach is to calculate the angle sub tended at x, Fig. 11, by that part of the top of the slot which is defined by the corners halfway up and at the top. The assumption is made that the emergent flux is proportional to the angle sub tended. The desired result is then ob  tained by integrating over x. For off sets, D, less than or equal to half the slot thickness, T, the desired function is: Fig. 11 o D oD+Tx TD. xD.I D+Txxj I = dxlarcot arcot 2L ) dx + arctanj arcet  02L 'D2L 2L 2L rT + Idxl + arctan(ll arcotI(Tx JTD L2 '1 L (1) For D greater than or equal to T/2, and less than i, the function is: ,TD I 'D x D O dxarcot 2 arcot + dx arcot ) arcrt T  + xi + arctan ? ) arcot&) "n { ' In all cases, the angles are very small since L = 24 inches, T = 1.5 inches. We can replace the arcot and arctan functions by the first term in their series expansions and obtain to a good approximation: TD JD 2L T dx + 2TDx dx JTD 2L T2D2 2L .D I0 TD+x d 0 4 2L 1 TD+x IoJo 2 ' T dx + a x JTPL +T 2TDx dx = TD D 2L 2L Equations 3 and 4 can be written directly on the assumption that the angles involved are given by the chord divided by the radius, rather than the arc by radius. APPENDIX B For those cases in which neutrons traverse water along part of the straight line path from the source to the top of the air slot, it is not always pos sible to get an algebraic expression to describe the process. "e shall con sider four cases: a. D less than T; b. D greater than T, neutrons do not traperse either of ends R or S; c. D greater than T, neutrons traverse end R; and, d. D greater than T, neutrons traverse end S. Case a: For the experiments under dis cussion, the fast neutrons are attenu ated in the water with a 1/e length of approximately 1/u = 2 inches**. Since the length L = 24 inches, then uL;1, and for significant contributions l. L. From the geometry shown in Fig. 12, we can write L+o T" xy x K ~( I' I I . X L2 X r x 2 . Fig. 12 The contribution to the flux at y due to to exp (ul). The contribution emergent passing through R is proportional to the D x u I dx. a 00 2L jrO 0 a source element through the slot angle dy/2L, henc SD x uL x)1 2L dx dy 2  2L 0 0o 2L dx is proportional top for rays uL D x ul 2 dx dy 2 x '0 '0 uL 2L D dx 0 uL 1 _uL 2 L2uL2 By~ ~~1L symer a siia2eulti bandfrryspsigtruhS 2u L 2 2u L By symmetry a similar result is obtained for rays passing through S. Therefore, the total contribution is: a D2 Case b: For simplicity consider the case where T D 3T/2; i.e., in Fig. 13 d e T/2. Then the path length in water is given by e = d 2LA+y+d, and one can write .d x+d yL Ib dx 5 d 0 2L Td +T dx +1 dx Td x+d uL xd 2L T dy uL 2L JxdUL = A + B + C. Each of the integration y is of the form 2uLd xdyc with respect to Fig. 13 which can be expressed in terms of the exponential integrals. one can substitute 2uLd = K; x+d = a; K CI 2a (dx dz a For example, Z = ; dy = 2 dz e2 Z2 K ,.d = d0 [E 2 M) Similarly the terms B and C may be expressed in terms of exponential integral of the second order giving I( di Ex +Td ( j b ^ x & EEA K(x+d j dJ E2(2) 2(x+d) + dx E2 ) E2 +x+d) Hence, A K 2L E2 L 2(7li K \l The integration with respect to x can be carried out graphically for parti cular values of d and K. Case c: For those rays which traverse end R of Fig. 13 one has / L x+dy x+d+y T xd I% )) dx f d Id 0O uL x+d x+d+y d 2L letting x+d = m; uL = c; z = 2 ; dy = 2mc d ; m+y z z2 cMy c 2mc Sm+y = c I (tL.M+y mc c T+d T z .T+d Ic mdm c dz = j mdm IE c 2L 2d 2c z2 L d 2 Case d: For those rays which traverse end S of Fig. 13, one has I' uL y^ y+d+x and analogous to case c, can write .T +dx T .yd uLy Tg II dx = T d }d 2L 0 c The following table contains a summary of computations for Fig. 9. The con stants involved are: u = 0.5; T = 1.5 inches; and L = 2? inches. TABLE I Surimary of Computat ions IJORi4AIIZED TO UNITTY AT D = O I!5ORALIZED TO 1.08x10O AT D=a3 D/T I I, Total Total O 10 0 1.0 1.08(3) 0.5 .75 .0O16 .792 8.56(2) 0.75 .438 .0936 .532 5.75(2) 0.90 .19 .135 .325 3.51(2) 1.00 0 .167 2) (2) (2) .167 1.8 (2) 1.083 2.81 1.47 1.47 5.75 ( 6,21(1) 1..3. j33 .17 d 17 3.723 4.01 a (n) means times 10n SIre wish to acknowledge the contribution of Bruce Knight to these calcu lations. 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