Radiation Attenuation Methods

  • G. G. Biro
  • A. Foderaro
  • A. D. Krumbein
  • B. D. O’Reilly
  • R. Aronson
  • D. L. Yarmush
  • P. S. Mittelman
  • S. Preiser
  • F. R. Mynatt

Abstract

This chapter includes most of the analytical radiation attenuation methods. It is far from exhaustive but representative enough for an engineering volume. It includes methods which apply to either gamma rays or neutrons enough so that to place them in one or another of chapters four or five would cause duplication or omission.

Keywords

Moment Method Moment Calculation Fission Neutron Neutron Dose Discrete Ordinate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    G. G. Biro: A Monte Carlo Study of Back Scattered Gamma Radiation from a Broad Beam Normally Incident on an Infinitely Thick Homogeneous Slab. International Journal of Computer Mathematics, Vol. I, No. 2 (1965).Google Scholar
  2. [2]
    D. J. Raso: Monte Carlo Calculations on the Reflection and Transmission of Scattered Gamma Radiation, Technical Operations, Inc., TO-B 61–39 (1962).Google Scholar
  3. [3]
    D. J. Raso: Nucl. Sci. Eng. 17, 411–418 (1963).Google Scholar
  4. [4]
    D. J. Raso: Monte Carlo Computation of 100 000 1 MeV Gamma Rays Scattered by Concrete Slabs, Technical Operations, Inc., TO-B 64–31 (1964).Google Scholar
  5. [5]
    H. Goldstein and J. E. Wilkins, JR.: NYO 3075 (1954).Google Scholar
  6. [6]
    C. M. Davisson and L. A. Beach: A Monte Carlo Study of Back Scattered Gamma Radiation. Paper presented at Ans, Washington, November 26, 1962. Ans Transactions, Vol. 5, No. 2 (1962).Google Scholar
  7. [7]
    C. M. Davisson and L. A. Beach: Private communication.Google Scholar
  8. [8]
    H. Kahn: Random Sampling (Monte Carlo) Techniques in Neutron Attenuation Problems. Nucleonics 6, 27 (1950).Google Scholar
  9. [9]
    G. Goertzel and M. H. Kalos: Monte Carlo Methods in Transport Problems, Progress in Nuclear Energy, Series I, Vol. 2, New York: Pergamon Press 1958.Google Scholar
  10. [10]
    M. LeimdÖRfer: A Monte Carlo Method for the Analysis of Gamma Radiation Transport from Distributed Sources in Laminated Shields. Nukleonik 6, H. 2 (1964).Google Scholar
  11. [11]
    E. D. Cashwell and C. J. Everett: A Practical Manual on the Monte Carlo Method for Random Walk Problems, New York: Pergamon Press 1959.Google Scholar
  12. [12]
    H. Goldstein: Fundamental Aspects of Reactor Shielding, Reading, Mass.: Addison-Wesley 1959.Google Scholar
  13. [13]
    R. A. Liedke and H. A. Steinberg: A Monte Carlo Code for Gamma Ray Transmission Through Laminated Slab Shields, AD 203641 (Wadc 58–80) (1958).Google Scholar
  14. [14]
    H. Kahn: Use of Different Monte Carlo Sampling Techniques, Symposium on Monte Carlo Methods, New York: Wiley 1954.Google Scholar
  15. [15]
    S. K. Penny, D. K. Trubey, and M. B. Emmett: Ogre, Ornl-3805 (1966).Google Scholar
  16. [16]
    J. Spanier: Monte Carlo Methods and Their Application to Neutron Transport Problems, Wapd-195 (UC-34, Tid-4500, 15th Ed.) (1959).Google Scholar
  17. [17]
    H. Goldstein: Personal communication.Google Scholar
  18. [18]
    J. R. Lamarsh, A. I. Lieberman, and M. O. Vas-Sell: Selected Nuclear Data for Monte Carlo Calculations, G. C. Dewey (1958).Google Scholar
  19. [19]
    M. LeimdÖRfer: On the Use of Monte Carlo Methods for Calculating the Deep Penetration of Neutrons in Shields, Transactions of Chalmers University of Technology, Gothenburg, Sweden, No. 287 (1964).Google Scholar
  20. [20]
    K. Parker: The Aldermaston Nuclear Data Library as at May, 1963, Awre 0–70/63.Google Scholar
  21. [21]
    K. Parker: Neutron Cross Sections of U 235 and U 238 in the Energy Range 1 keV — 15 MeV, Part I, Awre 0–7963 (1964).Google Scholar
  22. [22]
    K. Parker: Neutron Cross Sections of 235U and 238U in the Energy Range 1 keV — 15 MeV, Part II, Awre 0–82 /63 (1963).Google Scholar
  23. [23]
    L. Forsberg: Neutron Cross Sections for Aluminum, AE-117 (1963).Google Scholar
  24. [24]
    The Unc Nuclear Data Library. United Nuclear Corporation, White Plains, N. Y.Google Scholar
  25. [25]
    R. L. Ashley and W. F. Kreger (Editors): Neutron Attenuation in Optically Thick Shields, American Nuclear Society Ans-SD-1 (1964).Google Scholar
  26. [26]
    M. L. Worn,: Monte Carlo Calculations of Neutron Number Spectra and Buildup Factors in Infinite Conical Configurations, Nasa TN D-1434 (1962).Google Scholar
  27. [27]
    D. J. Hughes and R. B. Schwartz: Neutron Cross Sections, Bnl-325, 2nd Ed. (1958).Google Scholar
  28. [28]
    H. Goldstein: Fast Neutron Data for Oxygen Nda-Memo-15C-15, Aec (1953).Google Scholar
  29. [29]
    H. Steinberg, J. Heitner, and R. Aronson: Fantasia and Triprod — Shielding Codes for the 1103A Univac, Wadc 59–443 (1960).Google Scholar
  30. [30]
    H. Steinberg, J. Heitner, and R. Aronson: Fantasia II and Triprod II — Shielding Codes for the Ibm 7090 ML-Tdr-64–52 (1964).Google Scholar
  31. [31]
    W. Guber and M. Shapiro: A Description of the Sane and Sage Programs, Unucor-633, United Nuclear Corp. 1963. Interim Report.Google Scholar
  32. [32]
    M. R. Fleishman: A Sane-Sage Users Guide, Unucor-634, United Nuclear Corp. 1963. Interim Report.Google Scholar
  33. [33]
    B. Eisenman and E. Hennessy: Adonis — An Ibm 7090 Monte Carlo Shielding Code Which Solves for the Transport of Neutrons or Gamma Rays in Three-Dimensional Rectangular Geometry, Unucor-635, United Nuclear Corp. 1963. Interim Report.Google Scholar
  34. [34]
    R. Goldstein: Fission Neutron Attenuation Through Several Metallic Hydrides (Sponsored by F. R. Nakache), United Nuclear Corp. 1964. Interim Report.Google Scholar
  35. [35]
    B. Eisenman and F. R. Nakache: Unc-Sam, A Fortran Monte Carlo System for the Evaluation of Neutron or Gamma-Ray Transport in Three-Dimensional Geometry, Unc-5093, United Nuclear Corp. 1964. Interim Report.Google Scholar
  36. [36]
    M. Leimdörfer: On the Transformation of the Transport Equation for Solving Deep Penetration Problems by the Monte Carlo Method, Transactions of Chalmers University of Technology, Gothenburg, Sweden, No. 286 (1964).Google Scholar
  37. [37]
    U. Fano, L. V. Spencer, and M. J Berger: Penetration and Diffusion of X-Rays, in S. Flügge (Ed.): Encyclopedia of Physics, Vol. Xxxviii/2, Berlin/Göttingen/Heidelberg: Springer 1959.Google Scholar
  38. [38]
    K. Parker, D. T. Goldman, and L. Wallin: Paper CN 23/28, Iaea Conference on Neutron Data, Paris, Oct. 1966.Google Scholar
  39. [39]
    G. G. Biro and L. J. Lidofsky: A Semi Analytical Model for Mathematical Simulation of Gamma-Ray Transport Through Shielding, Ans Transactions, Vol. 9, No. 2 (1966).Google Scholar
  40. [40]
    G. H. Peebles and M. S. Plesset: Phys. Rev. 81, 430 (1951).ADSMATHCrossRefGoogle Scholar
  41. [41]
    G. G. Biro: Simulation of Radiation Transport, A Semi Analytical Model. Columbia University (1967).Google Scholar
  42. [1]
    H. Goldstein and J. E. Wilkins, JR.: Calculation of the Penetration of Gamma Ray, Nyo-3075 (June 30, 1954 ).Google Scholar
  43. [1]
    E. Amaldi: The Production and Slowing Down of Neutrons, In: “Encyclopedia of Physics”, ed. by S. Flügge, Vol. Xxxviii/2, Berlin/Göttingen/ Heidelberg: Springer 1959, pp. 18–22.Google Scholar
  44. [2]
    J. Certaine: A Solution of the Neutron Transport Equation, Introduction and Part I, Nyo-3081 (July 1954).Google Scholar
  45. [3]
    Reactor Physics Constants“, 2nd Ed., Anl-5800, Division of Technical Information, Usaec (July (1963).Google Scholar
  46. [4]
    R. D. Evans: The Atomic Nucleus, New York: McGraw-Hill 1955, pp. 410–417.MATHGoogle Scholar
  47. [5]
    D. Halliday: Introductory Nuclear Physics, 2nd Ed., New York: Wiley 1955, pp. 314–322.MATHGoogle Scholar
  48. [6]
    M. Blatt and V. F. Weisskopf: Theoretical Nuclear Physics, New York: Wiley 1952, pp. 365–374.MATHGoogle Scholar
  49. [7]
    A. M. Weinberg and E. P. Wigner: The Physical Theory of Neutron Chain Reactors, 6nd Ed., University of Chicago Press 1958, p. 104, Eq. 9.Google Scholar
  50. [8]
    U. Fano, L. V. Spencer, and M. J. Berger: The Penetration and Diffusion of X-Rays, in “Encyclopedia of Physics”, ed. by S. Flügge, Berlin/ Göttingen/Heidelberg: Springer 1959, pp. 724–730.Google Scholar
  51. [9]
    H. Goldstein and J. E. Wilkins: Calculation of the Penetration of Gamma Rays, Final Report, Ch. 4, Nyo-3075 (June 1954).Google Scholar
  52. [10]
    H. Goldstein: Fundamental Aspects of Reactor Shielding, Reading, Mass.: Addison-Wesley 1959.Google Scholar
  53. [11]
    J. Certaine: A Solution of the Neutron Transport Equation, Part II: Nda-Univac Moment Calculations, Nyo-6268 (May 1955).Google Scholar
  54. [12]
    Ref. [9, pp. 32–34].Google Scholar
  55. [13]
    Ref. [8,pp. 693–696 and p. 725, Eq. 12.5].Google Scholar
  56. [14]
    Ref. [8,pp. 746–749].Google Scholar
  57. [15]
    L. V. Spencer: Penetration and Diffusion of X-Rays, Mathematical Techniques, Nbs Report 1442 (March 1952).Google Scholar
  58. [16]
    J. Certaine: A Solution of the Neutron Transport Equation, Part Iii: Reconstruction of a Function from its Moments, Nyo-6270 (July 1956).Google Scholar
  59. [17]
    Ref. [8, pp. 739–746].Google Scholar
  60. [18]
    Ref. [8, Ch. 5].Google Scholar
  61. [19]
    L. V. Spencer and U. Fano: J. Res. Nat. Bur. Standards 46, 446 (1951).CrossRefGoogle Scholar
  62. [20]
    A. R. Ptitsyn: Finding the Space-Energy Distribution of Neutrons from a Plane Source in an Infinite Medium. Soviet Journal of Atomic Energy 9, 738–741 (1960).CrossRefGoogle Scholar
  63. [21]
    G. C. Wicx: Phys. Rev. 75, 738 (1949).ADSCrossRefGoogle Scholar
  64. [22]
    A. R. Ptitsyn: Using the Method of Moments to Calculate the Space-Energy Distribution of Neutron Density from Plane and Point Sources in an Infinite Medium. Soviet Journal of Atomic Energy 10, 117–126 (1961).Google Scholar
  65. [23]
    Neutron Attenuation in Optically Thick Shields, American Nuclear Society, Ans-SD-1 (April 1964).Google Scholar
  66. [24]
    Ref. [1, p. 295].Google Scholar
  67. [25]
    Ref. [8, pp. 713–724].Google Scholar
  68. [26]
    H. Goldstein: Private communication.Google Scholar
  69. [27]
    R. C. Lewis: Private communication.Google Scholar
  70. [28]
    R. K. Paschall: The Age of Fission Neutrons to Indium Resonance Energy in Iron-Water Mixtures — I. Experiment. Journal of Nuclear Energy Parts A and B 20, 25–35 (1966).CrossRefGoogle Scholar
  71. [29]
    Ref. [1, pp. 65–68].Google Scholar
  72. [30]
    W. N. Hess: Summary of High Energy Nucleon-Nucleon Cross Section Data. Reviews of Modern Physics 30, 368 (1958).ADSCrossRefGoogle Scholar
  73. [31]
    R. D. Albert and T. A. Welton: Wapd-15 [1950), declassified with deletions [ 1955 ).Google Scholar
  74. [32]
    Tx. Rockwell (Ed.): Aec Reactor Shielding Design Manual, New York: McGraw-Hill 1956, pp. 6–7.Google Scholar
  75. [33]
  76. [34]
    Ref. [10, pp. 281–288, 292–294].Google Scholar
  77. [35]
    C. H. Blanchard: On the Multiple Scattering of Neutrons in Hydrogen-like Substances. Nucl. Sci. Eng. 3, 113–128 (1958).Google Scholar
  78. [36]
    Ref. [5,p. 118, Eq. 4] and Ref. [7, p. 281, Eq. 10.2].Google Scholar
  79. [37]
    A. D. Krumbein: Summary of Nda Unclassified Results of Moments Calculations for the Penetration of Neutrons Through Various Materials, Nda 92–2 Rev. (August 1957).Google Scholar
  80. [38]
    A. F. Avery, Aere (Harwell): Private communication.Google Scholar
  81. [39]
    H. Goldstein: Fast Neutron Data for Oxygen, Nda 15C - 15 (November 1953).Google Scholar
  82. [40]
    M. H. Kalos et al.: Revised Cross Sections for Neutron Interactions with Oxygen and Deuterium, Unc-5038 (August 1962).Google Scholar
  83. [41]
    R. Aronson et al.: Penetration of Neutrons from Point Monoenergetic Sources in Water, Nyo-6269 (December 1954).Google Scholar
  84. [42]
    D. K. Trubey: Calculation of Fission-Source Thermal-Neutron Distribution in Water by the Transfusion Method, Ornl-3487 (August 1964).Google Scholar
  85. [43]
    E. S. Troubetzkoy: Fast Neutron Cross Sections of Iron, Silicon, Aluminum and Oxygen, Nda 2111–3, Vol. C (November 1959); also in Reactor Handbook, 2nd Ed., Vol. Iii, Part B, Shielding New York: Interscience 1962, pp. 234–235.Google Scholar
  86. [44]
    H.Goldstein: Neutron Cross Sections for Neutron Attenuation Problem Proposed by the American Nuclear Society Shielding Division, Contribution 63–3–1 Division of Nuclear Science and Engineering, Columbia University (March 30, 1963 ).Google Scholar
  87. [45]
    B. J. Henderson and H. A. Gerardo: Private communication.Google Scholar
  88. [46]
    H. Goldstein: Some Recent Calculations on Penetration of Fission Neutrons in LiH, Nda-42, Aug. 1957 (Declassified April 1966 ).Google Scholar
  89. [47]
    J. Certaine and R. Aronson: Distribution of Fission Neutrons in Water at the Indium Resonance Energy, Nda 15C - 40 (June 1954).Google Scholar
  90. [48]
    Ref. [10, p. 350].Google Scholar
  91. [49]
    R. Aronson et al.: Penetration of Neutrons from a Point Isotropic Fission Source in Water, Nyo6267 (September 1954).Google Scholar
  92. [50]
    Ref. [49].Google Scholar
  93. [51]
    A. Foderaro and F. Obenshain: Neptune, Part I: The History Generating Code, Wapd-TN-517 (August 1955).Google Scholar
  94. [52]
    J. Certaine et al.: Renupak, An Ibm-704 Program for Neutron Moment Calculations, Nda 2120–3 (December 1959).Google Scholar
  95. [53]
    J. Replogle, Modric: A One Dimensional Neutron Diffusion Code for the Ibm-7090, K-1520 (1962).Google Scholar
  96. [54]
    M. Kalos and H. Goldstein: Neutron Cross Section Data for Carbon, Nda 12–16 (March 1956).Google Scholar
  97. [55]
    Anp Quarterly Progress Report, p. 122, Ornl1649 (December 1953).Google Scholar
  98. [56]
    H. Alter et al.: Monte Carlo Calculations of the Slowing Down Moments in Hydrocarbons, Naasr-Memo-5655 (1960).Google Scholar
  99. [57]
    H. Alter: Calculation of Neutron Age and Moments of the Neutron Slowing Down Density Distribution in Hydrocarbons, Naa-SR-6866 (November 1961).Google Scholar
  100. [58]
    S. S. Rosen, United Nuclear Corp.: Private communication.Google Scholar
  101. [59]
    Ref. [23].Google Scholar
  102. [60]
    R. Goldstein: Fission Neutron Attenuation Through Several Metallic Hydrides, Unc Phys/ Math Memo 3348 (February 1964).Google Scholar
  103. [60a]
    D. J. Hughes and J. A. Harvey: Neutron Cross Section, 6nd Ed., Bnl-325 (July 1958).Google Scholar
  104. [61]
    N. Tralli et al.: Neutron Cross Sections for Ti, K, Mg, N, Al, Si, Na, O and Mn, Unc-5002 (January 1962).Google Scholar
  105. [62]
    J. H. Ray: Private communication.Google Scholar
  106. [63]
    Ref. [3,Table 2.6].Google Scholar
  107. [64]
    D. K. Trubey and M. B. Emmett: Some Calculations of Fast Neutron Distributions in Ordinary Concrete from Point and Plane Isotropic Fission Sources, Ornl-Rsic-4 (June 1965).Google Scholar
  108. [65]
    Ref. [43,Vol. A].Google Scholar
  109. [66]
    E. S. Troubetzkoy et al.: Fast Neutron Cross Sections of Mn, Ca, S and Na, Nda 2133–4 (1961).Google Scholar
  110. [67]
    B. J. Henderson: Conversion of Neutron or Gamma–Ray Flux to Absorbed Dose Rate, Xdc 59–8–179 (1959). Available from Reactor Shielding Information Center Oak Ridge, Tenn.Google Scholar
  111. [68]
    J. Butler: The Status of Theoretical Methods for Reactor Shield Design, Aeww-R361 (March 1964) Fig. 3.7 (Solid dots).Google Scholar
  112. [69]
    See Sec. 3.3.3. of this Compendium.Google Scholar
  113. [70]
    H. Goldstein, J. G. Sullivan, Jr., R. R. Cove-You, W. E. Kinney, and R. R. Bate: Calculations of Neutron Age in H2O and other Materials, Ornl2639, p. 7 (July 1961).Google Scholar
  114. [71]
    T. R. Jaworowski, Measurement of Spatial Distribution of Neutrons in Water from a Fission Source. Trans. Amer. Nucl. Soc. 5, 380 (1962).Google Scholar
  115. [72]
    Ref. [23].Google Scholar
  116. [73]
    J. Butler: The Status of Theoretical Methods for Reactor Shield Design, Aeew-R 361 (March 1964).Google Scholar
  117. [74]
    D. K. Trubey and M. B. Emmett: Trans. Amer. Nuclear Soc. 7, 357 (1964).Google Scholar
  118. [75]
    D. K. Trubey and M. B. Emmett: A Comparison of First and Last Flight Expectation Values Used in an 05R Monte Carlo Calculation of Neutron Distributions in Water, Ornl-R S1C -3 (May 1965).Google Scholar
  119. [76]
    D. R. Otis: Neutron and Gamma Rav Attenuation from a Fission Source in Water–Comparison of Theory and Ltsf Measurements, Ornl CF 57–3–48 (March 1957).Google Scholar
  120. [77]
    J. Certaine and H. Goldstein: Penetration of 14 MeV Neutrons in Water, Nda 15–97 (August 1957).Google Scholar
  121. [78]
    R. S. Caswell et al.: Nucl. Sci. Eng. 2, 143 (1957)Google Scholar
  122. R. S. Caswell et al.: Phys. Rev. 94, 786 A (1954).Google Scholar
  123. [79]
    J. Certaine and R. Aronson: Distribution of Fission Neutrons in Water at the Indium Resonance Energy, Nda 15C - 40 (June 1954).Google Scholar
  124. [80]
    J. E. Hill, L. D. Roberts and T. E. Fitch: J. App. Phys. 26, 1013 (1955).ADSCrossRefGoogle Scholar
  125. [81]
    H. Alter: Age of Fission Neutrons to Indium Resonance Energy in H2O, Part II: Theory, Naasr-Memo-8662 (October 1964).Google Scholar
  126. [82]
    R. K. Paschall: Age of Fission Neutrons to Indium Resonance Energy in H2O, Part I: Experiment, Naa-SR-8621 (November 1963); see also Nste 23, 256 (1965).Google Scholar
  127. [83]
    Ref. [61].Google Scholar
  128. [84]
    J. J. Schmidt: Eandc-E-35U (1962).Google Scholar
  129. [85]
    See Ref. [52].Google Scholar
  130. [86]
    J. Certaine and M. Sullivan: Operating Instructions for Nupak, Nda 15–87 (December 1955).Google Scholar
  131. [87]
    J. Brooks and E. DE Dufour: Operating Instructions for Addition of Inelastic Scattering to Nupak, Nda-15–95 (January 1957).Google Scholar
  132. [88]
    E. R. Cohen, Canoga Park: Private communication.Google Scholar
  133. [89]
    R. A. Blaine, Tyche: A Monte Carlo Slowing Down Code, Naa-SR-7357 (June 1962).Google Scholar
  134. [90]
    Ref. [70].Google Scholar
  135. [91]
    H. Alter: The Age of Fission Neutrons to Indium Resonance Energy in Graphite, Part 2: Theory, Naa-SR-8684 (April 1964).Google Scholar
  136. [92]
    G. D. Joanou and J. S. Dudek, Gam-1: A Consistent P-1 Multigroup Code for the Calculation of Fast Neutron Spectra and Multigroup Constants, GA-1850 (June 1961).Google Scholar
  137. [93]
    G. D. Joanou, A. J. Goodjohn, and N. F. Wikner: Moments Calculations of Fermi Age in Various Moderators. Trans. Amer. Nuclear Soc. 4, 278 (1961).Google Scholar
  138. [94]
    G. D. Joanou et al.: Moments Calculations of the Fermi Age in Moderators and Moderator-Metal Mixtures, GA-2157 (August 1961).Google Scholar
  139. [1]
    A. R. Bobrowky: Naca Technical Note 1712 (1948).Google Scholar
  140. [2]
    R. Redheffer: J. Math and Phys. 41, 1 (1962).MathSciNetMATHGoogle Scholar
  141. [3]
    G. H. Peebles and M. S. Plesset: Phys. Rev. 81, 430 (1951).ADSMATHCrossRefGoogle Scholar
  142. [4]
    I. Kataoka: Paper presented at session on shielding, Third Geneva Conference on Peaceful Uses of Atomic Energy, 1964; Nucl. Sci. Abst. 18; 38235 (A/Conf. 28/P1657).Google Scholar
  143. [5]
    R. Aroxsox and D. L. Yarmush: J. Math. Phys. 7, 221 (1966)ADSCrossRefGoogle Scholar
  144. D. Yarmush, J. Zell, and R. Aronsox: Wadc Technical Report 59–772 (1960).Google Scholar
  145. [1]
    S. Preiser, G. Rabinowitz, and E. DE Dufour: A Program for the Numerical Integration of the Boltzmann Transport Equation — Niobe, Ari. Technical Report 60–314 (Dec. 1960).Google Scholar
  146. [2]
    Tables of Functions and Zeros of Functions, U.S. National Bureau of Standards, Washington, D. C., Ams-37, pp. 185–189 (1954).Google Scholar
  147. [3]
    J. Certaine and P. S. Mittelman: A Procedure for the Numerical Integration of the Boltzmann Transport Equation, Nda 10–161 (1955).Google Scholar
  148. [4]
    J. Certaine and J. Brooks: Addition of Inelastic Scattering to the Univac Moment Calculations, Nda 2015–92 (1956).Google Scholar
  149. [5]
    J. Certaine: A Solution of the Neutron Transport Equation — Part II, Nda-Univac Moment Calculations, Nyo-6268 (1955).Google Scholar
  150. [6]
    R. D. Richtmyer: A Numerical Method for the Time Dependent Transport Equation, Nyo-7696 (1957).Google Scholar
  151. [7]
    D. Young: Iterative Methods for Solving Partial Difference Equations of Elliptic Type. Transactions Amer. Math. Soc. 76, 92–111 (1954).MATHCrossRefGoogle Scholar
  152. D. Yetman, B. Eisenman, and G. Rabinowitz: Description of Input Preparation and Operating Procedures for 9-Niobe, an Ibm-7090 Code, Nda 2143–18 (1961).Google Scholar
  153. J. Certaine: Integral Term for Elastic Scattering of Particles, Nda 15C - 12 (1953).Google Scholar
  154. H. Goldstein: Fundamental Aspects of Reactor Shielding, Reading, Mass.: Addison-Wesley 1959.Google Scholar
  155. [1]
    G. C. Wick: Z. Phys. 121, 702 (1943).MathSciNetADSMATHCrossRefGoogle Scholar
  156. [2]
    S. Ciiandrasekhar: Radiative Transfer, London: Oxford University Press 1950.Google Scholar
  157. [3]
    A. M. Weinberg and E. P. Wigner: The Physical Theory of Neutron Chain Reactors, Chicago: The University of Chicago Press 1958.Google Scholar
  158. [4]
    B. G. Carlson: Solution of the Transport Equation by the S n Method, Usaec Document LA 1891 (1955).Google Scholar
  159. [5]
    B. G. Carlson, C. E. Lee and W. J. Worlton: The Dsn and Tdc Neutron Transport Codes, Usaec Document Lams-2346 (1959).Google Scholar
  160. [6]
    B. G. Carlson and W. J. Worlton: Private communication.Google Scholar
  161. [7]
    W. W. Engle, M. A. Boling and B. W. Colston: Dtf II, A One-Dimensional, Multigroup Neutron Transport Program, Usaec Document Naa-SR10951 (1966).Google Scholar
  162. [8]
    K. D. Lathrop: Dtf-IV, A Fortran-IV Program for Solving the Multigroup Transport Equation with Anisotropic Scattering, Usaec Document LA-3373 (1965).Google Scholar
  163. [9]
    W. W. Engle: A Users Manual for Anisn, A One Dimensional Discrete Ordinates Transport Code with Anisotropic Scattering, Usaec Document K-1693 (1967).Google Scholar
  164. [10]
    F. R. Mynatt: A Users Manual for Dot, A Two Dimensional Discrete Ordinates Transport Code with Anisotropic Scattering. Usaec Document K-1694 (1968).Google Scholar
  165. [11]
    K. D. Lathrop and B. G. Carlson: Discrete Ordinates Angular Quadrature of the Neutron Transport Equation, Usaec Document LA-3186 (1965).Google Scholar
  166. [12]
    C. E. Lee: The Discrete Sn Approximation to Transport Theory, Usaec Document LA-2595 (1962).Google Scholar
  167. [13]
    J. R. Askew and R. J. Brissenden: Some Improvements in the Discrete Ordinate Method of B. G. Carlson for Solving the Neutron Transport Equation, Ukaea Document Aeew-R 161 (1963).Google Scholar
  168. [14]
    D. K. Trubey and M. B. Emmett: A Comparison of First and Last Flight Expectation Values Used in an 05R Monte Carlo Calculation of Neutron Distributions in Water, Usaec Document Ornlrsic-3 (1965).Google Scholar
  169. [15]
    F. B. K. Kam and F. H. S. Clark: Fission Spectrum Neutron Dose Rate Attenuation and Gamma Ray Exposure Dose Build Up Factors for Lithium Hydride. Usaec Journal Document Ornl-TM1744 (1967); Nuclear Applicationi Vol. 3, p. 433–5 (1967).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1968

Authors and Affiliations

  • G. G. Biro
  • A. Foderaro
  • A. D. Krumbein
  • B. D. O’Reilly
  • R. Aronson
  • D. L. Yarmush
  • P. S. Mittelman
  • S. Preiser
  • F. R. Mynatt

There are no affiliations available

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