AECL-8844
ATOMIC ENERGY »jWQ L'ENERGIEATOMIQUE OF CANADA LIMITED V^&jF DU CANADA LIMITEE
MEASURED DEPENDENCE OF SOME EFFECTIVE CROSS SECTIONS ON THERMAL NEUTRON TEMPERATURES IN THE RANGE -195°C TO 20°C
Mesure de la dependance de certaines sections efficaces a I'egard des temperatures de neutrons thermiques aliant de -195°C a 20°C
R.T. JONES and A. OKAZAKI
Chalk River Nuclear Laboratories Laboratoires nucleates de Chalk River
Chalk River, Ontario
August 1985 aout ATOMIC ENERGY OF CANADA LIMITED
Measured Dependence of Some Effective Cross Sections on Thermal Neutron Temperatures in the Range -195'C to 20°C
by
R.T. Jones and A. Okazaki
Reactor Physics Branch Chalk River Nuclear Laboratories Chalk River, Ontario KOJ 1J0
1985 August
AECL-8844 Mesure de la dépendance de certaines sections efficaces à l'égard des températures de neutrons thermiques allant de -195°C à 20°C
par
R.T. Jones et A. Okazaki
Résumé
On a mesuré la variation des sections efficaces, dans la répartition neutronique maxwellienne, en fonction de températures allant de - 195°C à n ?71 ?V> 93Q 20°C et, ce, pour la fission de U , U , Pu"3 et pour la capture de U238, Th232, Cu63, In115, Lu176 et Au197. On s'est servi de méthodes d'activation à feuille. Comme référence, on a employé Mn dont la dépendance 1/v est connue. Les résultats ainsi obtenus et quelques résultats provenant de mesures faites antérieurement en fonction de températures allant de 20°C à 300°C, sont comparés à des intégrations appropriées de données ENDF/B-V. A l'exception de Lu176 et Au197, les résultats sont en accord, dans les limites des incertitudes estimées des données ENDF/B-V.
L'Energie Atomique du Canada, Limitée Laboratoires nucléaires de Chalk River Chalk River, Ontario, Canada KOJ 1J0 Août 1985
AECL-8844 Measured Dependence of Some Effective Cross Sections on Thermal Neutron Temperatures in the Range -195°C to 20°C
by
R.T. Jones and A. Okazaki
ABSTRACT
The variation of effective cross section in Maxwellian neutron distributions with temperatures in the range -195°C to 20°C have been measured for U233, U235 and Pu239 fission, and for U238, Th232, Cu63,
InH5} Lul76, an(j Au*97 capture. Foil activation methods were used. Mn55, which has a known 1/v dependence, was used as the reference. The results, with some from previous measurements covering temperatures from 20°C to 300°C, are compared with suitable integrations of ENDF/B-V data. Except for Lu17^ and Au*97 the results agree within the estimated uncertainties with the ENDF/B-V data.
Atomic Energy of Canada Limited Chalk River Nuclear Laboratories Chalk River, Ontario KOJ 1J0 Canada
1985 August
AECL-8844 TABLE OF CONTENTS
Page
1. Introduction 1
2. Method 1
3. Experimental Arrangement 4
3.1 The Reactor Core 4 3.2 The Reference Irradiation Site 4
3.3 The Cold Neutron Irradiation Site 5
4. The Experimental Measurements 7
4.1 Activation Foils 7 4.2 Foil Irradiation 7 4.3 Foil Counting 8 4.3.1 Non-Fissile Foils 8 4.3.2 Fissile Foils (U233, U235, Pu239) 10 4.3.3 Fertile Foils (U238 and Th232) 11 5. Results and Comparison with Evaluated Differential Data 12
5.1 Results 12 5.2 Comparison of Results with ENDF/B-V Data and other Measurements 13
6. Summary 16
7. Acknowledgements 17
8. References 17
Tables 19
Figures 30
Appendix 44 Measured Dependence of Some Effective Cross Sections on Thermal Neutron Temperatures in the Range -195°C to 20°C
by
R.T. Jones and A. Okazaki
1. INTRODUCTION
In an earlier report(l) we described measurements of the variation of effective neutron interaction cross sections with the temperature of a Maxwellian distribution of neutrons. The temperature range covered was from 20°C to 300°C and the interactions included neutron induced fission of U233, U235 and Pu239, and neutron capture by Th232, U238,
Aul97} Lul76, in115 an Here we extend the measurements into the temperature range from 20°C to -195°C by means of a block of hydrogenous moderator cooled with liquid nitrogen. An extra interaction, neutron capture by Cu^3, is added to those studied, and comparison is made with integrated values from the ENDF/B-V library. 2. METHOD The reaction rate per unit mass in a well thermalized neutron spectrum of effective Maxwellian neutron temperature, T, is given by R(T) - N /c/cr(vr ) IL,(V) v dv •^o where N = number of atoms per unit mass a = neutron cross section n = neutron density distribution of temperature T and v = neutron velocity* - 2 - In the thermal energy region most nuclides have absorption cross sections which vary as or close to 1/v. The reaction rate for a nuclide with a 1/v dependence is independent of neutron energy distribution and hence neutron temperature and depends on the total neutron density. A convenient parameter to describe the deviation from 1/v dependence is the Westcott (2) g-factor, which is defined by «(T) = •Cg(v) "T(V) V dV (1) o -p 1 where v0 = 2200 m.s" and c0 = cross section at vQ For a 1/v cross section, g = 1 whereas for a non-l/v cross section, g is a function of the neutron temperature. The reaction rate can be expressed as R(T) = g(T) , v N/"°Y(v) dv The reaction rate is not measured directly in this experiment. Foils containing the nuclides of interest are irradiated in well thermalized neutron spectra. After the irradiation the gamma ray activity of the fission products in the case of the fissile nuclides, or of the capture products is measured. The measured activity per unit mass, Ai(T), for nuclide i is related to the reaction rate by A1(T) - R1(T) F E1 where F is a time dependent factor which takes into account irradiation time and decay, and e. relates the measured gamma activity to disintegration rate in the foil and hence includes counter efficiency, which can vary from day-to-day. - 3 - In the present experiment foils were irradiated simultaneously in two thermal spectra of different neutron temperatures. The ratio of the activities of the foils of nuclide i in the two spectra is i(Tl)/o"nTi(v) dv A±(T2) R.(T2)FE. gi(T2)/;nT(v) dv The factors F and £t are the same since the foils are irradiated and then counted at the same times. A similar ratio is obtained for nuclide j and dividing the two ratios gives rvvi vv LW. Thus if the energy dependence and hence [gj(Ti)/gj(T2>] of one of the nuclides is known, the ratio [gi(Ti)/gi(T2)] of the other nuclide can be obtained from measured activity ratios. Mn^5 has a 1/v (3) dependence so that g(Ti) = g(T2) = 1 and VV . WV = W (2) VV VV W It should be noted that the simultaneous irradiation in two different neutron spectra of both the test nuclide and Mn55> whose energy dependence of cross section is known, has the advantages that: - counter efficiencies - time dependence other than decay during counting - neutron density need not be known. - 4 - 3. Experimental Arrangement 3.1 The Reactor Core The irradiations were performed in the heavy water moderated ZED-2 reactor. To provide two regions in which a well thermalized neutron flux was available the core illustrated in Fig. 1 was installed. This consisted of 84 "ZEEP rods", in a hexagonal array of 200 mm pitch, arranged to give large rod free region of heavy water at the centre and on the perimeter of the reactor. "ZEEP rods" are natural uranium metal cylinders, 32.5 mm diameter, 150 mm long stacked in aluminum alloy tubes 1 mm thick with an outside diameter of 34.9 mm. The total length of uranium in each rod is 2.85 m. A typical depth of heavy water required to achieve criticality was 2.3 m. 3.2 The Reference Irradiation Site This was chosen to be close to the calandria wall on the west side of the reactor, as shown in Fig. 1. Foils to be irradiated were attached by polyethylene tape to an aluminum disk, of diameter 178 mm, suspended on a shaft close to the axial flux maximum. Placing the foils at a fixed radius on the disk, which was rotated at 30 rpm, ensured that they all received the same irradiation. The neutron temperature of the reference spectrum was taken to be the same as the physical temperature of the heavy water moderator. Since the minimum distance between a fuel rod and the foils was 0.43 m epithermal contamination of the spectrum is expected to be small. This has been confirmed by cadmium ratio measurements(l) that indicated a Westcott r-value of 2 x 10~4. - 5 - 3.3 The Cold Neutron Irradiation Site This was a small block of hydrogenous moderator in a cryostat cooled by liquid nitrogen at the centre of the reactor. The cryostat is illus- trated in Fig 2. It consisted of three concentric cylindrical containers made from 1.6 mm thick aluminum. The innermost was 230 mm high by 111 mm inner diameter. It contained the cold moderator and prevented the liquid nitrogen from coming into contact with it. Containment for the liquid nitrogen was provided by the second cylinder which was 355 mm high by 152 mm inner diameter. This was insulated from the outermost container by 25 mm of expanded polystyrene insulation at the sides and bottom and by a 100 mm thick plug at the top. The outer container was 420 mm high by 210 mm outer diameter. To prevent ingress of reactor heavy water it was sealed at the top by a 6.4 mm thick aluminum lid and '0' ring through which passed a tube to allow venting of nitrogen gas. To make the cryostat sink in the reactor heavy water an 11 kg lead weight at the end of a 790 mm long by 9.5 mm diameter aluminum rod was attached to its base. The entire assembly was suspended from the beams at the top of the reactor by a 13 mm diameter aluminum tube. The elevation of the centre of the cold moderator above the reactor calandria floor was 1.1 m. A plastic tube was used to extend the nitrogen vent tube to above the heavy water surface. Polyethylene [(CH2)n], Nylon [CO(CH2>4 CON H(CH2)6 NH] and paraffin wax [C25 H52] were all tested for suitability as the cold moderator. The first two were found to crack and distort too severely when cooled by liquid nitrogen so paraffin was selected. This too suffered extensive micro-cracking but could be easily recast when required. The first design for the cold moderator consisted of a solid cylinder of paraffin wax 225 mm high by 111 mm diameter. It was actually cast in five pieces, four of them 50 mm high and one of them 25 mm high. This was used for tests of the cryostat and the cold moderator. - 6 - Temperatures in the cryostat were monitored by two chromel-alumel thermocouples which passed through the vent tube. One was placed In the liquid nitrogen space and one in the centre of the cold moderator. The output voltages of the thermocouples were read and converted to temperature by a data-logging system based on a Hewlett-Packard 9825 computer. A thermocouple in an ice-water mixture at 0°C was used as a reference. Fig. 3 shows the variation of temperature in the centre of the paraffin wax as it was cooled and then sealed in the cryostat before being allowed to warm. After it was sealed the cryostat was immersed in a large water bath for this test. The results showed that after the last filling with liquid nitrogen the centre of the cold moderator remained at about liquid nitrogen temperature for 2\ hours. This was more than enough for the envisaged irradiations in the reactor. The results also indicated that it should be possible to make measurements at intermediate temperatures during the warming phase. Measurements were next made of the radial neutron distribution in the paraffin wax at ambient (24°C) and low (-195°C) temperatures. Foils of Lu-Mn-Al alloy were used for this, since the activity ratio, Lu^^^/Mn^6 was the most neutron temperature sensitive available. This ratio normalized to that obtained at an ambient temperature reference position, is plotted in Pig. 4. At 24°C the ratio shows a slight rise from 1.0 at the outer surface as the centre of the wax is approached; absorption hardening of the neutron spectrum in the hydrogenous moderator may account for this. The variation in the ratio is equivalent to a 3 or 4°C change in neutron temperature. At -195°C the ratio is 0.59 at the wax surface and sinks to a constant value of 0.475 after a penetration of about 20 mm into the moderator. This is inter- preted to mean that rethermalization is complete at that point. Also shown in Fig. 4 are the Mn56 activity distributions arbitrarily normalized at the wax surface. These may be taken to have the same shape as the neutron density distribution. They show a considerable density depression due to neutron absorption by the hydrogen in the moderator that, as expected, is larger for the cooled case. - 7 - On the basis of these measurements the design of the cold moderator was modified to provide a central cylindrical cavity of 50 mm diameter by 150 mm long. The resulting thickness of at least 30 mm of paraffin wax on all sides of the cavity was judged to be enough to rethermalize the neutrons. At the same time, a reasonably large volume of fairly constant flux in which to irradiate foils was made available. To support foils in the cavity an expanded polystyrene plug with slots cut in it was made. The moderator assembly is illustrated in Fig. 5 where the locations of thermocouples are also shown. Previous measurements(l) indicate that the epithermal neutron flux at the cryostat irradiation site is negligible. 4. The Experimental Measurements 4.1 Activation Foils The materials to be investigated were available as circular foils whose compositions and dimensions are given in Table 1. Also shown in the table are the reactions being studied with the half-life of the activity counted. For each foil type it is necessary to know the relative amount of the isotope of interest in every foil. In the case of elemental foils this is given by the foil mass. Alloy foils were intercalibrated by irradiating on a rotating wheel in the NRU reactor thermal column. The amount of isotope was then assumed to be proportional to the measured gamma-ray activity. 4.2 Foil Irradiation To form the ratios of Equation 2 it is necessary to irradiate foils containing Mn55 and the other isotopes of interest in the cryostat and on the reference wheel. Since Mn^5 is a 1/v absorber the induced activity is proportional to the neutron density. As this quantity varied - 8 - throughout the irradiation volume in the cold moderator it was necessary to place a Mn-Ni foil as close as possible to each of the other foils. To achieve this the foil pairs were wrapped together in 0.03 mm thick aluminum boxes. At the reference wheel this is not necessary since turning the wheel ensures that all the foils experience the same average neutron density. However, to simplify neutron self-shielding corrections, as discussed in the Appendix, co-wrapped pairs of foils were in fact used. An exception to the use of co-wrapped foils was, of course, the Lu-Mn-Al material where the Mn^5 Was included in the alloy. Two of each foil type were irradiated in both the reference spectrum and in the cryostat. For a cold neutron irradiation the cold moderator was cooled by addition of liquid nitrogen to the cryostat until the innermost thermocouple indicated the temperature of boiling liquid nitrogen (-195°C). Then, after a final charge of liquid nitrogen had been added, the assembly was sealed and installed in the reactor. Irradiations were for periods of from one half to one hour at a constant nominal reactor power of either 50 W or 100 W. The corresponding neutron flux level was approximately 8 1 10 cm-2s- . For some irradiations the moderator in the cryostat was at ambient temperature while for others an intermediate temperature was achieved by allowing the previously cooled moderator to warm up a little before the irradiation. Throughout all the irradiations the temperatures in the cryostat were monitored by the thermocouples. 4.3 Foil Counting 4.3.1 Non-Fissile Foils The gamma-ray activity of the foils was counted with a pair of Nal detectors having 63.5 mm diameter by 25.4 mm thick crystals. An automatic sample changer positioned the foils between the crystals and a computer controlled counting system recorded the following: the number of counts in - 9 - each channel above a fixed discriminator level, the time of day and the el;.psed time of each count. The foils were mounted in Lucite trays before be ng stacked in the sample changer. The stack, which included some empty tiays for background measurements, was counted many times in a "once through then restack" mode. Data analysis consisted of the following: correction for counter dead time and activity decay; subtraction of room background, rejection of counts more than three standard deviations from the mean for a foil, and normalization by foil mass or sensitivity. 4.3.1.1 Foils Containing Mn55 The activity counted was 2.582 h Mn56. ^ discriminator setting of 500 keV was used for all foils although it was only really necessary for those which also contained lutetium, where it prevented detection of quanta arising from the decay of 3.68 h Lu176m and 3.7 x 1010 y Lu176. In the case of the Mn-Ni foils the only interfering activity is that of 2.52 h Ni65 which can be calculated to contribute <0.3% to the measured counts. Since this can only affect the results of the experiment if the cross section for the Ni64(n,Y) Ni65 reaction differs very markedly from 1/v it was ignored. 4.3.1.2 Foils Containing Cu63 Elemental copper foils were used and the 12.74 h activity of was counted. The potential interfering activity is that of Cu&6 arising from activation of the only other copper isotope, Cu^5. This has a half-life of 5.1 m and was eliminated by waiting at least two hours after the end of the irradi- ation before counting the foils. A 50 keV discriminator level was used. - 10 - 4.3.1-3 Foils Containing Au197 Gold is monoisotopic and elemental gold foils were used; there was, therefore, no problem with interfering activities. The discriminator was set at 50 keV. 4.3.1.4 Foils Containing Lu The 6.71 d Lu^^^ activity was measured two days after the irradiation when the Mn56 and 3.68 h Lu176m activities had died away. Before the irradiation the foils were counted to measure their natural background activity due to the 3.7 x 10^0 v Lu-^o activity. The measured Lul?7 activity was corrected for this background which was small (0.5%). 233 235 239 4.3.2 Fissile Foils (U , U , Pu ) A similar system to that described in Section 4.3.1 but with larger Nal crystals (101.6 mm diameter by 101.6 mm thick) was used to count the fission products in these foils. The main difference was that the foil stack after being counted in the normal way was immediately counted in reverse order instead of being restacked. This arrangement allowed a simple correction to be made for the complicated decay of the mixture of fission products. This was, after subtracting room background and previously measured natural activity, to add the counts obtained from each foil in successive forward and backward counting cycles. This is a sufficiently accurate correction if the decay can be approximated as linear throughout a forward and backward counting cycle. This was verified by the observed constancy from cycle to cycle of the ratio of count rates for foils of the same material in the cryostat and on the reference wheel. - 11 - 4.3.3 Fertile Foils (U and Th The capture of neutrons by U"° and the subsequent radioactive decays may be represented as follows: ,,238, _,. 239 23.5 m 239 2.35 d. 239 U (n,7) UTT —-- NMp —— Pu P P The decays counted were those of Np239 to Pu^39 starting some two days after ths irradiation. In about 6% of Np239 decays a 106 keV gamma ray is emitted followed by a 228 or 278 keV gamma transition which is heavily internally converted to 98 keV Pu X-rays. The same counter system was used as for the fissile foils but with the addition of a single-channel analyzer to each counting channel. The window of each analyzer was set around the peak at 100 keV and coincidences, between the 106 keV gamma rays and the X-rays, were counted. Since natural uranium foils were used there was a small contribution to the coincidence count rate due to residual fission product activity. This was corrected by including a U235_AI foil in the stack and also counting fission product activity above a 1.2 MeV discriminator setting. The ratio of fission product coincidence counts per fission product count above 1.2 MeV was derived from the U^^-Al foil counting. The processes occuring when Th232 ^s converted to U^33 by neutron capture are: 232 233 22 m 233 27 d 233 Th (n,7) Th -j . Pa _ • U - 12 - In this case the Pa2^3 decay gives rise to a gamma ray of energy 312 keV. This gamma ray was counted with a Ge(Li) spectrometer and was prominent and well separated from other gamma rays. The peak area was obtained by summing the contents of all channels in the region of the peak and subtracting the background estimated by averaging a few channels in the flat region on each side of the peak. 5. Results and Comparison with Evaluated Differential Data 5.1 Results The results are given in Tables 2 through 10 where each table refers to one of the interactions studied. Altogether seven irradiations were performed with the "cold" moderator, three of them at room temperature (~23°C), two at liquid nitrogen temperature (-195°C), and the remaining two at intermediate temperatures of -110°C and -77°C. The latter two were achieved by irradiating during the warming of the moderator and are the averages of the temperatures recorded at the inner surface of the moderator. This temperature actually varied by about 14°C during the irradiation. A complete set of data was not obtained for every irradiation. In the tables R$jn is the average of the measured activity ratios as defined in Equation 2. g(T)/g(20) is the same ratio corrected for the following three effects; (1) epithermal neutron interaction (2) deviation of the reference temperature from 20°C (3) neutron self-shielding effects. - 13 - Previous measurements^) showed that correction (1) was significant only for the In^5) JJ238f an(j Au^-97 capture reactions and that it was largest for U238 (0.6%). Correction (2) was only important for Lu176 capture and Pu^39 fission which have a high sensitivity to neutron temperature. It was largest for the former at 0.4% per °C. Neutron self-shielding in pairs of foils irradiated in close proximity is discussed in the Appendix. The corrections to Rj,jn were less than 0.5% and are given in the table in the Appendix. The method described in the appendix to Reference 1 was used to estimate the random errors associated with the results. This method allows measurements taken on different occasions and at different neutron temper- atures to be combined to give a better error estimate. The errors are given in Table 11 which shows they fall into the range +0.6% to +1.5% with an average value of +1%. 5.2 Comparison of Results with ENDF/B-V Data and Other Measurements The results are also shown in Fig. 6 to 14 where the ratio g(T)/g(20) is plotted against neutron temperature. The temperature range has been extended to 300°C so that the results of Reference 1 can also be displayed. The lines in the figures are derived by integration of the ENDF/B-V differential cross section data over the Maxwellian neutron distribution (5) (see Equation 1). In general the present low temperature and the earlier high temperature results agree within the estimated experimental uncertainties with the ENDF/B-V data. In the case of neutron capture by Lu*76 (Fig. 6) the measured g(T)/g(20) ratios are in better agreement with the solid line - 14 - than the ENDF/B-V based dotted line. The solid line was derived from our evaluation of the available differential data (6), which for reasons given in Reference 1, is believed to be batter than that in ENDF/B-V. At low temperatures there is little difference between the two lines. As the capture cross section depends sensitively on the neutron temperature the agreement of the measurements with the evaluated data indicates that the neutron temperature is within about +10°C of the physical temperature of the moderator. For u235 fission (Fig. 7) there is an appreciable variation (about 10%) in the g-factor over the temperature range. The measured values agree within the estimated uncertainties with the ENDF/B-V data. There had been reports C1^) that there was a 2% discrepancy between the average JJ235 fission cross section measured in a thermal Maxwellian spectrum and The U233 fission results (Fig. 8) agree with the ENDF/B-V data, which decrease slightly faster with neutron energy than 1/v. The Pu^39 fission cross section (Fig. 9) has a marked dependence on neutron temperature. The results agree with ENDF/B-V data. The present measurements confirm the reduced neutron temperature dependence at low temperatures. - 15 - The U238 capture results (Fig. 10) are consistent with the ENDF/B-V data in which the cross section does not drop as fast as for 1/v dependence. To reduce the difference between calculated and measured moderator temperature coefficients of light water reactors, Bouchard et al. (?) have proposed a capture cross section that decreases faster than 1/v. This dependence would give a g-factor at -195°C about 20% higher than at 20°C in marked disagreement with our measured ratio of 0.98. At temperatures above 20°C the difference between the proposed and 1/v dependence is smaller. At 300°C the estimated g-factor is about 0.93 whereas both the measured and ENDF/B-V values are 1.01. Thus, the present low temperature results rule out the proposed departure from 1/v below 0.025 eV. The earlier high temperature results also rule out, though to a lesser extent, the proposed behavior of the cross section above 0.025 eV. The Th232 capture results (Fig. 11) are in good agreement with the ENDF/B-V data. The cross section decreases slightly faster with neutron energy than 1/v. The average of the two measurements at -195°C is 1.014 + 0.015 and agrees with the 1.008 + 0.009 obtained by Green (9) using a method similar to that described here. The capture cross section has been measured by Little et al. (8) from 0.006 to 18 eV. These measurements agree well with ENDF/B-V data except below 0.06 ev where they begin to steadily deviate to lower values. Little et al. note that an extrapolation of their data would give a g-factor at liquid nitrogen temperature (-195°C) 10 to 12% lower than at room temperature, in significant disagreement with the present measurements and that of Green. The Cu63 results (Fig. 12) are consistent with ENDF/B-V data, which assume 1/v dependence and hence g=l. At -195°C the ratio, g(T)/g(20), was 0.991 + 0.006. This is lower than the 1.014 + 0.008 obtained from Green's (9) data with his moderator at liquid nitrogen temperature. - 16 - The Au197 results (Fig. 13) would be fitted better by a more steeply sloped line than that derived from ENDF/B-V. However, only the results for the lowest and highest temperatures deviate significantly from the ENDF/B-V line. Nevertheless the good agreement of the present result of 0.972 - 0.004 at -195°C with 0.969 ± 0.004 obtained from the liquid nitrogen data of Green (9) indicates a departure from ENDF/B-V. For neutron capture by InH5 (Fig. 14) there is an appreciable variation of the g-factor with neutron temperature, about 10% over the temperature range shown. The measurements are consistent with ENDF/B-V. 6. Summary The effective cross sections for fission of U~--, i|235 and pu239 2 3 17 and for neutron capture in Ij238j Th 32, Cu** , Inll5, Lu ^ and Au*97 were measured in Maxwellian neutron spectra having temperatures of 20°, -77°, -110° and -195°C. These and previously reported measurements for temperatures up to 300°C were compared with the effective cross sections 17 97 based on ENDF/B-V data. Except for Lu ^ and possibly Au^ , the present measurements agree within the estimated uncertainties with the ENDF/B-V data. The Ij238 results differ appreciably from those based on the modified u238 cross sections that had been proposed to reduce the discrepancy between measured and calculated moderator temperature coefficients of light water reactors. The Th232 results also differ significantly from those based on an extrapolation of the differential cross section measurements made down to 0.006 eV. - 17 7. Acknowledgements The authors gratefully acknowledge the assistance of the following: - G.A. Doncaster and D.A. Kettner who loaded and counted the foils. - P.D.J- Ferrigan who supervised the building of some of the apparatus and the loading and running of the reactor. - E. Pleau and D.J. Roberts who loaded and ran the reactor. - M.S. Milgrara, S.L. Jurgilas and R. Paulson who performed the integrations of the ENDF/B-V data. - D.E. Goldberg who prepared the figures, and E. Burke and E. Harrington who typed the manuscript. 8. References 1) Jones, R.T. and A. Okazaki, Dependence of Effective Cross Sections on Thermal Neutron Temperatures, Atomic Energy of Canada Limited Report, AECL-6483 (1979). 2) Westcott, C.H., W.H. Walker and T.K. Alexander, Effective Cross Sections and Cadmium Ratios for the Neutron Spectra of Thermal Reactors, Proc. 2nd UN Intl. Conf. Peaceful Uses of Atomic Energy, Geneva, 2£, 70 (1958). 3) Garber, D.I. and C Brewster, ENDF/B Cross Sections, BNL-17100 (ENDF-200), Brookhaven National Laboratory (1975). - 18 - 4) Kinsey, R., ENDF-201 ENDF Summary Documentation, BNL-NCS-17541, (ENDF-201) 3rd Edition (ENDF/B-V), UC-80, July, 1979. 5) Milgram, M.S., Private Communication, 1983. 6) Milgram, K.s., Private Communication, 1983. 7) Bouchard J., C. Golinelli and H. Tellier, Besoins en Donnees Nucleaires pour les Reacteur a Neutrons Thermiques, Nuclear Data for Science and Technology, Proc Int Conf. Antwerp 1982, Ed. K.H. BSckhoff. 8) Little R.C. et al., Neutron Capture and Total Cross Section of Thorium-232 from 0.006 to 18 eV, Nuclear Science and Engineering 79, 175, (1981). 9) Green L., Thermal Westcott g-Factor Measurement for Thorium-232, Nuclear Science and Engineering, 66, 127 (1978). 10) Proceedings of the IAEA Consultants Meeting on Uranium and Plutonium Isotopic Resonance Parameters, 28 September - 02 October 1981, Vienna, INDC (NDS) - 129/GJ. 11) J.R. Stehn, M. Divadeenam, and N.E. Holden, Evaluation of the Thermal 233 235 239 2 Neutron Constants for U, U, Pu and 41pu, Nuclear Data for Science and Technology, Proc Int Conf Antwerp, 1982, Ed. K.H. Bockhoff. - 19- TMLE 1 GOMPOSmCK AM) DIMENSIONS OF FOILS Foil Reaction and Weight % of Diameter Thickness Material Half Life Active Element (ran) (ran) 55 56 Mn-Ni Mil (n>7 )Mci (2.58 h) 11.0 11.28 0.130 Lu-Mn-Al I*i55 (n^Mn56 (2.58 h) 5.0 12.01 0.254 176 , .. 177 LT u (n, 7 )Lu (6.71 d) 10.0 _ 115 , 116 In-Al In (n,7)I NTn (54.2 m) 1.0 11.73 0.127 . 197 , . 198 Au Au (n, 7 )AN u (2.70 d) 100 11.28 0.051 Cu Cu63 (n,7 )Cu64 (12.74 h) 100 11.28 0.259 U^-Al U233 (n.fission) 2.47 11.53 0.254 IP-AI U235 (n.flssion) 5.0 11.53 0.254 „ 239 , 239 Pu -Al Pu (n.fisslon) 3.0 11.53 0.254 Th Th (n, 7 )Th * 100 11.53 0.138 U U (n, i )IT ** 99.3 11.73 0.064 * 31 d Pa/33 decays were measured. ** 23.5 d Np239 decays were measured. - 20 - TABLE 2 RESULTS FOR NEUTRON CAPTURE BY Lu176 Irradiation Location Temp LT u ! Mn RLu g(T) ° Activity Activity g(20) Cryostat 24.9 1.2583 1.0552 1.2821 1.0904 1.018 1.037 Reference 24.6 0.8493 0.7411 0.8566 0.7258 Cryostat 23.4 1.5411 2.7548 1.5472 7911 1.026 1.040 Reference 23.4 1.0143 8687 0.9923 8278 Cryostat 23.0 1.4417 9538 1.4710 9174 1.019 1.037 Reference 24.3 1.0037 3690 1.0121 3593 Cryostat -77 1.0423 1938 1.0418 1827 0.674 0.685 Reference 23.8 0.9509 9758 0.9708 9867 Cryostat -110 1.0163 3.3752 1.0280 .4299 0.616 0.620 Reference 21.5 0.9974 .0490 0.9998 .0459 Cryostat -195 0.4697 .0595 0.3782 0.8238 0.471 0.479 Reference 23.9 0.7887 0.8253 0.7886 0.8225 Cryostat -195 2.8494 2.0149 2.2592 1.6174 0.477 0.487 Reference 25.3 5.9791 2.0468 6.0192 2.0267 - 2.1 - TABLE 3 RESULTS TOR NEUTRON MEUCED KTSSION OF Ri239 239 Pu e(T) Irradiation Location Tanp Pu Mn R\~ &££-. # (°C) Activity Activity ^ g(20) 1 Cryostat 24.9 1.1482 1.9100 1.1505 1.8937 0.997 0.999 Reference 24.6 0.7927 1.3212 0.7938 1.2973 3 Cryostat 23.0 1.1589 3.3885 1.1553 3.3881 0.998 1.000 Reference 24.3 0.8152 2.3845 0.8192 2.3939 5 Cryostat -110 1.1665 5.1759 1.1615 5.1287 0.954 0.955 Reference 21.5 0.7389 3.1149 0.7334 3.0994 6 Cryostat -195 1.1701 2.2402 1.0000 1.8964 0.942 0.942 Reference 23.9 0.9545 1.7389 0.9725 1.7213 7 Cryostat -195 1.0046 3.1160 0.8290 2.5797 0.938 0.939 Reference 25.3 1.0654 3.1194 1.0652 3.0914 - 22 - TABUS 4 RESULTS FOR MJTRON CAPTURE Ei In115 1 g(T) Temp R " Irradiation Location In Mi g(20) Activity Activity Cryostat 24.9 2.3445 1.9016 2.3305 1.9063 0.989 0.989 Reference 24.6 1.6231 1.3028 1.6129 1.3042 Cryostat 23.4 2.7966 1.0941 2.7404 1.0638 0.999 0.999 Reference 23.4 1.8681 0.7209 1.8387 0.7228 Cryostat 23.0 1.1469 3.4100 1.1297 3.3613 0.997 0.997 Reference 24.3 0.8111 2.3870 0.8019 2.3955 Cryostat -77 2.3832 4.9057 2.3180 4.7459 0.976 0.977 Reference 23.8 1.4874 2.9589 1.4920 3.0092 Cryostat -110 2.8105 5.2572 2.7040 5.1028 0.973 0.973 Reference 21.5 1.68% 3.0647 1.6969 3.1243 Cryostat -135 3.4666 2.2785 3.0747 2.0049 0.962 0.961 Reference 23.9 2.7407 1.7189 2.7082 1.7119 Cryostat -195 1.0691 3.2596 0.9067 2.7512 0.978 0.977 Reference 25.3 1.0414 3.0846 1.0364 3.0972 - 23 - TABLE 5 RESULTS JDR NEUTRON INDUCED FISSION OF U235 235 Irradiation Location Temp u Mb g(T) # (°C) '.otivity Activity 1 Cryostat ?4.9 1.1485 1.9030 1.1489 1.9116 0.985 0.984 Reference 24.6 0.7931 1.2963 0.7943 1.2995 2 Cryostat 23.4 1.1628 1.0758 1.1568 1.0701 0.997 0.996 Reference 23.4 0.7877 0.7256 0.7815 0.7302 3 Cryostat 23.0 1.1389 3.3788 1.1351 3.4020 1.002 1.001 Reference 24.3 0.7986 2.3904 0.8086 2.4133 4 Cryostat -77 1.1930 4.8058 1.1954 4.7576 1.020 1.019 Reference 23.8 0.7365 2.9912 0.7329 3.0113 5 Cryostat -110 1.5095 5.0956 1.5152 5.1557 1.050 1.050 Reference 21.5 0.8787 3.1142 0.8731 3.1198 6 Cryostat -195 1.5829 2.0560 1.3630 1.7523 1.076 1.073 Reference 25.3 1.2376 1.7173 1.2452 1.7347 7 Cryostat -195 1.0043 2.8452 0.8764 2.4676 1.050 1.047 Reference 25.3 1.0474 3.1105 1.0419 3.0861 3 Cryostat 23.0 1.1376 3.3763 1.1456 3.4648 0.991 0.990 * Reference 24.3 0.8036 2.4082 0.8104 2.3820 5 Cryostat -110 1.1754 5.1177 1.1829 5.2372 1.036 1.036 * Reference 21.5 0.6783 3.1157 0.6897 3.1063 * These results were obtained fran natural uraniun raetal foils - 24 - TABLE 6 RESULTS FDR tEUTRQN CAPTURE Si Au197 A 198 g(T) Irradiation Location Temp g(20) ° Au Activity Activity Cryostat 24.9 1.0688 1.8264 1.0637 1.8145 0.990 0.990 Reference 24.6 0.7353 1.2345 0.7342 1.2503 Cryostat 23.4 1.5304 1.0422 1.5060 1.0211 1.003 1.003 Reference 23.4 1.0223 0.6988 1.0135 0.6890 Cryostat 23.0 1.4368 3.2992 1.4144 3.2509 0.994 0.994 Reference 24.3 1.0106 2.3071 0.9946 2.2725 Cryostat -77 1.6209 4.6206 1.5891 4.4702 0.993 0.993 Reference 23.8 1.0113 2.8393 1.0170 2.8653 Cryostat -DO 1.6370 4.9073 1.6151 4.8528 0.989 0.989 Reference 21.5 0.9977 2.9537 1.0034 2.9846 Cryostat -195 2.0844 2.0626 1.7904 1.7599 0.963 0.968 Reference 23.9 1.7227 1.6207 1.7141 1.6437 Cryostat -195 0.8114 2.9213 0.6861 2.4405 0.970 0.975 Reference 25.3 0.8486 2.9449 0.8508 2.9548 - 25 - TABLE 7 RESULTS FOR NEUTRON CAPTURE BY U238 239 Irradiation Location Temp w Mn RNp g(T) •Sin g(20) Np Activity Activity Cryostat 24.9 1.5650 1.8872 1.5870 1.9343 0.981 0.987 Reference 24.6 1.0913 1.3078 1.1025 1.3017 Cryostat 23.0 4.6520 3.3763 4.6484 3.4648 0.978 0.984 Reference 24.3 3.3338 2.4082 3.3294 2.3820 Cryostat -77 0.7009 4.7875 0.6968 4.8442 0.990 0.996 Reference 23.8 0.4369 2.9914 0.4414 2.9976 Cryostat -110 1.6448 5.1177 1.6552 5.2372 0.990 0.996 Reference 21.5 1.0006 3.1157 1.0030 3.1063 Cryostat -195 2.7937 2.1199 2.2713 1.7484 0.979 0.982 Reference 23.9 2.2910 1.7290 2.2947 1.7030 Cryostat -195 0.9449 2.9287 0.7537 2.3624 0.983 0.986 Reference 25.3 1.0165 3.1125 1.0110 3.0970 - 26 - TABLE 8 RESULTS FOR tEUTRON CAPTURE K Th232 Temp 233 Mi g(T) Irradiation Location Pa g(20) Activity Activity Cryostat 24.9 0.9706 5.4660 0.9847 5.5241 0.994 0.994 Reference 24.6 0.6767 3.9123 0.6744 3.9322 Cryostat -110 0.9002 5.0901 0.9114 5.1130 1.019 1.019 Reference 21.5 0.5435 3.1259 0.5395 3.0890 Cryostat -195 0.8233 2.0271 0.7280 1.7597 1.002 1.000 Reference 23.9 0.6903 1.7088 0.7131 1.7228 Cryostat -195 3.0332 2.8352 2.4875 2.4053 1.029 1.027 Reference 25.3 3.1955 3.0737 3.1273 3.1173 - 27 - TABLE 9 RESULTS SOR MUTRON INDUCED flSSION CF U233 U233 u233 Irradiation Location Temp Fission // (°C) Product Act. Activity g(20) 1 Cryostat 24.9 1.7023 1.8530 1.7097 1.8900 1.008 1.008 Reference 24.6 1.1758 1.2903 1.1780 1.3119 2 Cryostat 23.4 1.1500 1.0710 1.1641 1.0462 0.997 0.997 Reference 23.4 0.7916 0.7232 0.7868 0.7165 3 Cryostat 23.0 1.1402 3.3515 1.1339 3.3394 1.006 1.006 Reference 24.3 0.8172 2.3913 0.7955 2.3798 4 Cryostat -77 1.1291 4.7155 1.1289 4.6971 1.012 1.012 Reference 23.8 0.7006 2.9502 0.7123 3.0076 6 Cryostat -195 1.0710 1.9668 1.0000 1.8284 1.010 1.008 Reference 23.9 0.9329 1.7203 0.9275 1.7215 7 Cryostat -195 0.8788 2.6584 0.8231 2.4976 1.017 1.015 Reference 25.3 0.9980 3.0778 1.0106 3.1089 - 28 - TABLE 10 RESULTS FOR NEUTRON CAPTURE BY Cu63 Irradiation Location Temp Cu64 Mn g(T) # (°C) Activity Activity Mn g(20) Cryostat 24.9 3.6096 1.9396 3.5681 1.8821 0.992 0.992 Reference 24.6 2.4585 1.2987 2.4639 1.3019 Cryostat 23.4 2.3061 1.0884 2.2522 1.0543 1.002 1.002 Reference 23.4 1.5324 0.7249 1.5114 0.7091 Cryostat 23.0 2.0587 3.3472 2.0192 3.3244 1.011 1.011 Reference 24.3 1.4373 2.3958 1.4315 2.3491 Cryostat -77 2.1567 4.8819 2.0810 4.6733 1.006 1.006 Reference 23.8 1.3048 2.9642 1.3152 2.9785 Cryostat -110 2.2113 5.2354 2.1416 5.0188 1.006 1.006 Reference 21.5 1.2954 3.0819 1.2998 3.0671 Cryostat -195 3.4662 2.3111 2.7460 1.7690 0.990 0.989 Reference 23.9 2.6123 1.6957 2.6143 1.6964 Cryostat -195 1.3220 3.2765 1.0055 2.4639 0.993 0.992 Reference 25.3 1.2502 3.0635 1.2536 3.0644 - 29 - TABLE 11 ESTIMATED RANDOM ERRORS FOR REACTION RATE RATIOS Ratio Error Lu/Mn +1.3 In/Mn +0 • 7 Au/Mn +0.6 Cu/Mn +0.9 U233/Mn +1.3 U235/Mn +0.6 Pu23'/Mn +0.9 Th/Mn +1.5 U238/Mn +1.0 - 30 ' REFERENCE WHEEL CRYOSTAT • • • W Figure 1: Plan View of the ZED-2 Reactor Core - 31 - VENT SUPPORT LUG 4 '0' RING SEAL EXPANDED POLYSTYRENE . INSULATION \ ALUMINUM SPACER LIQUID NITROGEN MODERATOR CONTAINER ALUMINUM SPACER WEIGHT ATTACHMENT LUG •c-•„..*-•- —i- 1 1 1 I •" 1 1 ... ! 1 1 401- • • 0h— • • -40h • • • • • * • • • • • a • - • • - -80h • • • • • • • • Ill -I2O|- • • - • • • K 111 • • 0. • LAST N2 FILL • • • £ -I60U- • • _ • •• t • '•"••-..: -200|- 1 i — i L 1.... l_ i i i 8 9 10 II 12 13 14 15 16 TIME (HOURS) Figure 3: Cooling and Warming Curve for the Cold Moderator - 33 - 177 Hi ~56~ Mn ACTIVITY RATIO 1.0 ' 1.0 24°C 56 Mn ACTIVITY /o (ARBITRARY UNITS) -195 °C / / 0-5 0.5 24°C - I95°C 10 20 30 40 50 RADIAL POSITION (mm) Figure 4: Mn Activity and Lu /Mn Activity Ratio versus Radial Position in a Solid Cylindrical Block of Wax at 24°C and at -195°C - 34 - PARAFFIN WAX EXPANDED POLYSTYRENE SLOTS FOR LOCATIONS OF FOILS THERMOCOUPLES FOIL POSITIONS Figure 5: Section and Plan of the Hollow Cold Moderator Assembly 2.0- 9(20) 1.8- 1.6- 1.4- 1.2- I 1.0 -200 -150 -100 -50 50 100 150 200 250 300 NEUTRON TEMPERATURE,T PC) 0.8 0.6- JhA Figure 6: Ratio of g-factors versus Neutron Temperature for Capture by Lu . The Dashed Line is Based on ENDF/B-V Data J 1.08- 11 g (T) \ 1.06- 9 (20) f" 1.04- f \. 1.02- i TEMPERATURE ,T(°C) \ NEUTRON 1.00 d 1 1 < 1' i -200 -150 -100 -50 0 ^50 100 150 200 250 300 0.98- \ 0.96- \ 0.94- 2 35 Figure 7: Ratio of g-factors versus Neutron Temperature for Fission of U . The points marked x were obtained with natural Uranium metal foils. 100 T50~ tOff" •250 300 NEUTRON TEMPERATURE, T(°C) Figure 8: Ratio of g-factors versus Neutron Temperature for Fission of U233 1.40- Q(T) 9(20) 1.30- 1.20- 00 00 -200 -100 -50 50 100 150 200 250 300 NEUTRON TEMPERATURE, T (°C) 0.90- 239 Figure 9: Ratio of g-factors versus Neutron Temperature For Fission of Pu Figure 10: Ratio of g-factors versus Neutron Temperature for Capture by U238 9(T) 1.04- 9(20) 1 i i 1.02- " , NEUTRON TEMPERATURE, T(°C) i I«UU • 1 1 1 1 -2< 10 -150 -100 -50 0 fl 50 ' RJO4 'SO 200 250 300 TT f-' 0.98- 0.9 6- Figure 11: Ratio of g-factors vsrsus Neutron Temperature for Capture by Th232 g(T) 1.04- 1.02- i i 1 1 1.00 1 1 1 1 1 1 -2 )0 -150 -100 -50 0 50 100 150 200 250 300 1\ NEUTRON TEMPERATURE, T(°C) 0.98- 0.96 63 Figure 12: Ratio of g-factors versus Neutron Temperature for Capture by Cu g(T) g(20) 1.04- i 1.02- 1 - 1 1 1.00 I 1 _——4 -200 -150 J[ 50 100 15i 0 20I 0 25r 0 30i 0 — "1 If I 1 0.98- i NEUTRON TEMPERATURE, T(°C) 0.96- Figure 13: Ratio of g-factors versus Neutron Temperature for Capture by Au197 g(T) 1.06- g(20) j. 1.04- I 1 1.02- i 1 1 1.00 i i i -200 -150 -100 -50 0 50 100 150 200 250 300 I NEUTRON TEMPERATURE, T <°C) 0.98- i 1 0.96- 0.94 Figure 14: Ratio of g-factors versus Neutron Temperature for Capture by In115 -.44 - APPENDIX Neutron Self-Shielding Effects for Two Foils in Close Proximity Section 2 of the report makes no mention of self-shielding or neutron-flux depression effects in the foils used. This was more complicated than usual since in almost all the measurements the neutron density at the measurement location was found by irradiating a Mn-Ni alloy foil as close as possible to the foil of interest. The geometry is illustrated in Fig Al. The two foils of materials 1 and 2 are considered to be at the centre of a large cavity where an isotopic flux of monoenergetic neutrons is maintained. The cavity is so large that the chance of a neutron passing through the foil, being scattered, and passing through it a second time is vanishingly small. It is also assumed that the foils are thin enough that activation by neutrons entering through their edges is negligible. Furthermore the scattering cross section of the foil materials is taken to be much smaller than that for absorption so that scattering in the foils can be neglected. Then, considering Fig Al, the number of neutrons entering the free surface of foil 1 at angle 9 to a normal through elemental area dS is NQ1 = 2TTJ dS cos 9 sin 0 d 0 (1) - 45 - where J is the magnitude of the constant vector flux measured in neutrons per unit area per unit time per steradian. Of these a fraction 1 - e 1 where t^ is the thickness and Mi, the absorption coefficient, will be absorbed in foil 1. The total number absorbed in foil 1 is found by integrating over 0 from 0 to "72: /2 3 6 J AQ1 = 2«-J dS / cos© sin© (l-e'^lh ^ d0 (2) which gives = 2TTJ dS (| - E-CO) where T-± = ^i tj and E3 (r^) is the exponential integral *~3 e~T% d* (3) Now considering those neutrons not absorbed in foil 1 which subsequently enter foil 2 we write for the number absorbed in foil 2. T sece T Sece A = 2TTJ dS ^ cose sine e~ l (l-e~ 2 ) d0 (4) ' Jn which reduces to 2TTJ dS (E3(T1) - ^3(rl+r2)) (5) - 46 - Similarly there are equations equivalent to 2 and 5 for neutrons which enter the foils first through the free surface of foil 2. These are AQ2 = 2TTJ dS (i - E3(r2)) (6) and A21 = 2TTJ dS (E^) - E^r^ + T^) (7) To obtain self-shielding factors for the foils we must now evaluate the activations which would obtain if no depression of the flux occurred as the neutrons passed through the foils. These are Ax = 4TT J dS T 1 (8) and A» = 4TT J dS r „ (9) The self-shielding factors G^ and G2 are given by the ratios A01 * A21 and A02 + A12 Al A2 thus: Gi = *-E3(Tl)+E3(T2)-E3(Tl + 72) (10) and G7 = t-VV^^-VW (11) - 47 - To see how these results can be applied to the present experiments a more detailed expression for the measured activity ratios must be derived. Adopting the Westcott convention the activity measured in a foil containing isotope x in a purely Maxwellian neutron spectrum may be written as A = C N a g (T) G (T) 0 (12) x xx ox x x o where: Cx is a factor accounting for efficiency of the counting apparatus used and decay of the measured activity, Nx is the number of atoms of x in 1 the foil, is the appropriate self-shielding factor, and 0O is the Westcott flux. Using this the activity ratio measured may be written as Axl where the fluxes and counting efficiencies have cancelled and T and To are the neutron temperatures in the cryostat and at the reference site respectively. Reorganization of the equation allowing that gyn = 1 for all T gives (14) In practice the N's are either assumed proportional to the foil mass (for elemental foils) or to a measured sensitivity, S (for alloys). S is measured by irradiating all the foils of one type in the same well thermalized neutron flux of temperature Tc. It is thus proprotional to the product of N and the appropriate self-shielding factor: Sxl « \l Gxl(TC> Substituting for the N's in equation 14 gives gx(T) GMn2 The first bracketed term is the activity ratio uncorrected for self shielding, the second allows for self shielding in the intercalibration irradiations, while the third accounts for self shielding in the irradiation conditions of this experiment. If elemental foils are used tne then SX2/SX1 becomes My2^^xl ( ratio of foil masses) and the ratio G^(Tc)/G^2^Tc) is identically one. In general foils are selected to have G close to unity and the variation in G from foil to foil is small (<(0.1%). Thus the second term is usually set equal to one and a small contribution made to the random error in the experiment based on the estimated variation in the intercalibration self"shielding factors. If, however, variations between foils are large enough explicit correction factors may be calculated and inserted. - 49 - Concerning the third term the simplest case is that in which the Mn and x are homogenized in a single alloy; whereupon the two ratios become unity. When separate foils are used equations 10 and 11 give suitable values for the ratios of self-shielding factors if r corresponding to the modal velocity of the appropriate Maxwellian is used. Properly speaking Maxwellian averaged values should be used but over the ranges of interest it is found that the above approximation results in errors in the ratio of G factors of <0.1%. The table below gives the value of the correction factor embodied in the third term of equation 16 for the pairs of foils used in the current measurements with the cryostat temperature at -195°c. Foils Correction Factor Mn-Ni/U233-Al 0..998 2^S 0..998 Mn-Ni/U -Al Mn-Ni/Pu -Al 0.998 Mn-Ni/Th 0.998 Mn-Ni/U nat 0.997 Mn-Ni/Au 1.005 Mn-Ni/In-Al 0.998 Mn-Ni/Cu 0.999 Lu-Mn-Al 1.000 - 50 ~ NORMAL MATERIAL I MATERIAL 2 Figure Al: Geometry for Calculation of Neutron Self-Shielding Factors for Pairs of Foils in Close Proximity ISSN 0067-0367 ISSN 0067-0367 To identify individual documents in the series Pour identifier les rapports individuelsfaisant we have assigned an AECL- number to each. partie de cette serie nous avons assigne unnumeroAECL- achacun. 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