Guif General Atomic lncerporo+od P. 0. Box 608,S en Diego, Calitornia 921 12 - e AEC RESEARCH AND CiA-8280 ~EVELOPMENT REPORT INTEGRAL NEUTRON THERMALIZATION ANNUAL SUMMARY REPORT OCTOBER 1, 1966 THROUGH SEPTEMBER 30, 1967 Prepared under Contract AT(04-3) - 167 Project Agreement No. 2 for the San Francisco Operations Office Us S. Atomic Energy Commission Report written by: Work done by: J. R. Beyster Y* D. Naliboff 3. R. Beyster E. L. Slaggie H. M. Antunez R. A. Moore H. M. Antunez D. Sprevak G. M. Borgonovi J. M. Neill G. M. Borgonovi C. A. Stevens W. Brouwer C. A. Preskitt 6. W. Carriveau J. A. Young G. W, Carriveau E. L. Slaggie T. Gozani J. C. Young K. Crosbie D. Sprevak Do H. Houston T. Ciozani C. A. Stevens J. U, Koppel D. H, Houston J. A. Young Y. D. Naliboff J. U. Koppel J. C. Young J. M. Neill This document is ByI1LICLY R$I+EA§ABLl%i October 30, 1.967 DISCLAIMER This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency Thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. DISCLAIMER Portions of this document may be illegible in electronic image products. Images are produced from the best available original document. OTHER REPORTS IN THIS SERIES - GA-2544 10/1/60-0/30/61 - GA-3542 10/1/61-9/30/62 GA-4659 - 1 O/ 1/62-9/30/63 - P GA-5798 10/1/63-9/30/64 c - GA-6824 10/1/64-9/30/65 - GA-7480 10/1/65-9/30/66 P ii C ONT ENT S Page 1. INTRODUCTION AND SUMMARY . . . . . . . . . 1 . . . 2. NEUTRON THERMALIZATION IN H20 AND D20. 5 2. 1 Introduction . . . . . . . . . . . . . . 5 . . 2. 2 Single Differential Scattering from Light Water 7 2.3 Total Cross Section of H20 . . . . . . . . . 7 2. 4 Multiple Scattering in Double Differential . . . . . . . . . . . . . Measurements 8 . . 3. NEUTRON THERMALIZATION IN POLYETHYLENE 13 3. 1 Introduction . . . . . . . . . . . . . . 13 . . . . 3. 2 Angular Scattering Cross Section of CH2 13 4. NEUTRON THERMALIZATION IN BENZENE AND DIPHENYL . . . . , . . . . . . . . . . 15 a 4.1 Introduction . . . . . . . . . . . . . . 15 4.2 Total Cross Section of Benzene. . . . . . . . 16 4. 3 Angular Scattering Cross Section of C6H6 . . . . 19 4.4 A Model for the Description of the Molecular . . . . . . . Dynamics of Diphenyl (C12-Hlo) 22 4. 5 Thermal Neutron Spectra in Diphenyl and at a . . . . . . . . Diphenyl-DZO Interface 29 . 5. NEUTRON THERMALIZATION IN ZIRCONIUM HYDRIDE 42 5.1 Introduction , . . . . , . . . . . 42 e a . . . 5. 2 Central Force Model for Zirconium Hydride 42 5. 3 Angular Scattering by Zirconium Hydride at Elevated Temperatures . . . . . . . . . 46 . . . . 6. NEUTRON THERMALIZATION IN Be AND Be0 54 6. 1 Introduction . . . . . . . . . . . . . 54 6, 2 First Principles Calculation of Phonon Dispersion . . . . . . . . . Curves in Beryllium Metal 0 54 . 6.3 Thermal Neutron Spectra in Beryllium at 77.4 K. 61 . . . . . . . . 6.4 Scattering Kernel for Be0 67 iii Page . . . . . . . . 7 SCATTERING LAWS FOR UC AND U02 71 . . . . . . . . . . . . . . 7.1 Introduction 71 . . . . . . . . 7 2 Scattering Laws for U02 and UC 72 . . . . . . . . 7.3 Central Force Model for U02 77 . . . . . . . SPECTRALSTUDIESINAU238 SPHERE 83 8 . 9 . KINETIC STUDIES IN U 23 8 . . . . . . . . . . . 96 . . . . . . . . . . . . . . Introduction 96 9.1 . . . . . . . . . . . . . . . Geometry 97 9.2 . . . . . . . . . . . . . . . Detector 97 9.3 . . . . . . . . . . . . . . Electronics 100 9.4 . . . . . . . . . . Experimental Procedure 106 9.5 . . . . . . . . . . . . . . . . Results 106 9.6 . . . . . . . . 9.7 Neutron Decay at Early. T.ime.s . . . . . . . . 1 18 Notes on the Theory 132 9.8 . . . . . . . . . . . . . . . 10 STUDIES IN U235 135 . . . . 10.1 Spectrum Measurements in a U235 Sphere 135 . . . . . . . 10.2 Dieaway Studies in U235 Sphere 140 . . . . . . . . . . . . 11. DATA DISSEMINATION 143 . . . . . . . . . . . 12 MISCELLANEOUS ANALYSES 146 . . . . . 12 1 Inclusion of Diffusive Motion in GASKET ( 7) 146 12.2 Application of Nonlinear Programming to Cross . . . . . . . . . . . . . Section Analysis 152 . 12 3 Correction for Finite Length of Flight Path in Single . . . . . . . . . Differential Cross Sections 163 . 13 IMPROVEMENT IN LINAC AND EXPERIMENTAL . . . . . . . . . . . . . . . CAPABILSTIES 167 . . . . . . . . 13.1 LINAC Facility Improvements 167 . . . . . . 13 2 Intermediate Energy Neutron Detector 168 . . . . . . . . . . 13.3 Lithium Glass Detector 171 . . . . . . . . . . . . 13.4 On-Line Computer 176 . . . . . . . . . . . . . . . REFERENCES 184 - APPENDIX A AB INITIO CALCULATIONS OF PHONON DISPERSION CURVES - APPENDIX B NEUTRON SPECTRA ACROSS A URANIUM SLAB u4 iv LIST OF FIGURES Figure Page . . . . . . . 2. 1 Measured total cross section of H 0 9 2 2. 2 Ratio of predicted to observed total cross section for . . . . . . . . . . . . . . . H 2 0 e . . 10 4.1 Geometry for angular scattering and total cross section . . . . . . . . . . . . . . measurements. 17 4. 2 Comparison of experimental and calculated total cross 1 sections for benzene. . . . . . . . . . . . . 18 . . . 4. 3 Angular scattering cross section of benzene . 21 a . . 4.4 Average cosine of the scattering angle for benzene. 23 4. 5 Angular scattering cross sections for benzene; compari- . . . . . . . . . son of two experimental results 24 4. 6 Geometry of the diphenyl molecule; the distances are . . . . given in angstroms and the angles in degrees 25 4. 7 Definition of the valence coordinates for the in-plane . . . . . . . . . . . . . . . . vibrations 27 4. 8 Definition of the valence coordinates for the out-of-plane . . . . . . . . . . . . . . . Vibrations 28 4.9 Definitions and least squares values for a 9-parameter VFF for the out-of-plane vibrations of diphenE 1. The . . force constants are in units of erg/rad . 30 4. 10 Definitions and least squares values for a 17-parameter VFF for the in-plane vibrations of diphenyl. Stretch con- stants are in units of mdyn/rad; bending and torsion con- stants are in units of mdyn Ao/rad2. . . . . . . . 31 4.11 Frequency spectrum of hydrogen atoms in C12H10 (The . . . . set of frequencies about .38 eV are not shown) 32 4. 12 Geometrical arrangement for spectral measurements at . . . . . . . . . a D20-diphenyl measurement. 36 4. 12 Comparison of experimental and calculated neutron s ec- . tra in benzene (5.9 barns/H atom; infinite medium)B’=O 37 V Figure Page 0 4. 14 Neutron spectra in diphenyl at 80 C as a function of . . . . . . . . . . . . poison concentration. 39 4. 15 Thermal neutron spectra in the diphenyl-D 0 interface 0 . . . . . . . 2 . . . . . assembly at 80 C . 40 . 5.1 Infinite medium neutron spectrum in borated ZrH 45 1.75 5.2 Zirconium hydride sample holder used at elevated temperatures . . . . . . . . . . . . 47 5.3 Calculated multiple scattering correction factor for single . differential scattering by zirconium hydride at 2960 K. 48 5.4 Calculated multiple scattering correction factor for single . differential scattering by zirconium hydride at 700 0K . 49 5.5 Comparison of measured angular scattering cross sec- tions of zirconium hydride at 2960 K for two different . . . . . . . . . . . . sample thicknesses 50 e U 5.6 Angular scattering cross section of zirconium hydride at r 70O0K.. . . . . . . . . . 52 o . e a a 5. 7 Comparison of angular scattering cross sections of . . . zirconium hydride for different temperatures 53 e 6. 1 Comparison of diagonal elements of X(Iq) +4G, q4tG4) as cal- culated with 11 OPW to the dielectric constant of an . . . . . . . . . electrongas 56 a e e e . . 6. 2 Dielectric function for beryllium. 57 a e e . 6.3 Diagonal terms of the screening matrix for 37 OPW 58 6.4 Phonon dispersion curves for beryllium for the (0001) . . . . . . . . . direction. 60 a e 6.5 Configuration for spectral measurements in Be at 77.4 0K 62 6.6 Spatial foil activities in the beryllium assembly (Axial Distribution) . . . . 64 e e a e a e 6. 7 Thermal neutron spectra in poisoned beryllium (0. 25 . . . . . barns/Be atom at 2200 in/sec) at 77.4OK. 66 6. 8 Variation of thermal neutron spectrum in beryllium with . . . . . . . temperature 68 a a e e . 6. 9 Total cross section of beryllium oxide. 70 a. 1 Variation of CV/3R with cutoff frequency and temperature . . . . . . for a Debye model 74 e a e a v i Fig ur e Page 8. 1 Geometry of the 20 in. diam depleted uranium sphere. 84 8. 2 Photograph of the 20 in. diam uranium sphere in the . . . . . . . . . . . experimental room 85 23 8 8. 3 Calculated effect of target water coolant on the U sphere spectra. . . . . . . . . . . 86 e 8. 4 Source spectrum for a U238 target due to Gayther and . . . . . . . . . . Goode. * . 89 8. 5 Leakage flux spectrum from the air cooled uranium target. . . . . . . . . . . . . . . 90 a 8. 6 Comparison of measured and calculated neutron spectra . . . . at position C in the U238 sphere 94 e a 8. 7 Comparison of measured and calculated neutron spectra . . . . . . . at position M in the U238 sphere. 95 a . . 9.1 Electronic block diagram for the kinetic studies 99 9.2 Electronic block diagram for the linear channel "stretcher" used to check the discriminator in the fast kinetic studies 102 9.3 Alpha spectrum from the Pu238 contaminated Np237 foil. 103 . . . . 9.4 Calibration and linearity checks of the TAC 105 e 9.5 Instantaneous decay constants at (a) R = 11.8 crns and . . . . . (b) R = 20.23 cms in the uranium sphere 110 e 9. 6 Spatial dependence of the time behavior of the neutron flux in the U238 sphere (U235 conversion foil) 112 a 9. a Wide range decay of the neutron population in the deple- . . . . . . ted uranium sphere 115 a e 9. 8 Decay curve (a) and instantaneous decay constants (b) measured by U235 conversion foil at R = 17.37 cms . . . . . . . . (Position D). 116 a e . 9.9 Decaying neutron flux measured at Positions 1 and F'. 120 9.10 Instantaneous decay constants measured at Positions 1, . . . . . . . . . . . . . . C ' a n d F ' 121 e . 9.11 Instantaneous decay constants measured at R = 11.4 cm 123 23 7 9.12 Decaying neutron flux measured by the Np conversion . . . . . foilat Positions C'and D' . 124 v i i 7- Figure Page 23 7 9. 13 Decay constants measured by the Np conversion foil at Positions C' and D' . . . . . . . . . . . 126 23 7 9. 14 Decay constants at lag times measured by the Np . . . . . . conversion foilat Positions C'and F' 127 9. 15 Pertinent cross sections of U 235, u238 , and Np 23 7 . . 129 23 5 . . . 10.1 Geometry for spectral studies in a U sphere. 136 235 . . . . . . . . . 10.2 Photograph of the U sphere 138 10.3 Comparison of theoretical and measured neutron spectra . . . . . . . at the center of a U235 sphere 139 e 23 5 . . . 10.4 Calculated angular spectra in the U sphere 141 e 12.1 Comparison of diffusive and free recoil treatments of . . . . . . . . . . translational modes in H20 151 12.2 Constrained and unconstrained least squares fit to the . . . . . . . . . i data points in Table 12. 1 160 12.3 Everywhere positive law order polynomial approxima- tion to a highly peaked cross section . . . . . . . 162 12.4 Variation of correction factor C with incident neutron P. . . . . . . . . energy for zirconium hydride. 166 13. 1 Photograph of the intermediate energy neutron detector . . . . . . . . . (XED) during construction 170 e 13.2 Electronic block diagram incorporating the NE-908 . lithium glass detector . . 173 e e e 13.3 Response of the lithium glass detection system to a Po-Be source . . . . . . . 174 a a e 13.4 Energy dependence of the transmission through the . . . . . NE-908 lithium glass 175 * e e 13.5 Geometry for calculating the efficiency of the NE-908 . . . . lithium glass detector 178 a e a 13. 6 Block diagram of the data acquisition system designed . . . . . . around the CDC-1700 computer 180 e . . 13.7 CDC- 1700 computer with interfacing equipment , 181 a c v i i i