NCRP REPORT No 108 CONCEPTUAL BASIS FOR CALCULATIONS OF ABSORBED-DOSE DISTRIBUTIONS Recommendations of the NATIONAL COUNCIL ON RADIATION PROTECTION AND MEASUREMENTS Issued March 31, 1991 Sexond Reprinting February 1, 1995 National Council on Radiation Protection and Measurements 7910 WOODMONT AVENUE / Bethesda, MD 20814 LEGAL NOTICE This report was prepared by the National Council on Radiation Protection and Measurements (NCRP) The Council strives to provide accurate, complete and useful information in i t reports However, neither the NCRP, the members of NCRP,other persons contributing to or assisting in the preparation of this report, nor any person acting on the behalf of any of these parties: (a) makes any warranty or representation, express or implied, with respect to the accuracy, completeness o r usefulness of the information contained in this report, or that the use of any information, method or process disclosed in this report may not infringe on privately owned rights; or (b) assumes any liability with respect to the use of, or for damages resulting from the use of any information, method or process disclosed in this report, under the Civil Rights Act of 1964 Section 701 et seq as amended 42 U.S.C.Section 2000e et seq (Titk VII1 or any other strrtutory or common law theory gooerning liability Library of Congress Cataloging-in-PublicationData Conceptual basis for calculations of absorbed-dose distributions p cm.-(NCRP report; no 108) Includes bibliographical references and index ISBN 0-929600-16-9 Radiation dosimetry Ionizing radiation-Measurement I National Council on Radiation Protection and Measurements 11 Series QC795.32.RX66 539.7'22'0287-dc20 1991 91-9135 CIF' Copyright National Council on Radiation Protection and Measurements 1991 All rights reserved This publication is protected by copyright No part of this publication may be reproduced in any form or by any means, including photocopying, or utilized by any information storage and retrieval system without written permission from the copyright owner, except for brief quotation in critical articles or reviews Preface The idea for this report emerged, in the early 1970's, from the need of a n NCRP Scientific Committee to characterize the beta-ray depthdose distribution in connection with immersion doses It was realized, however, that the calculation of such a distribution was only a small part of the very much larger task concerned with the theoretical, mathematical and computational concepts involved in the development of absorbed-dose distributions in general To address this issue in an allencompassing manner, the NCRP formed Scientific Committee 52 on the Conceptual Basis of Calculations of Dose Distribution In either external or internal irradiation, the absorbed dose is usually non-uniform in any structure and, in particular, in the human body This non-uniformity is to be distinguished from the stochastic variations that exist even in regions where the dose is uniform and that are the subject of microdosimetry and not this report Many illustrations of absorbed dose non-uniformity come to mind: for example, the absorbed-dose distributions from hot particles, from internal emitters, from radiation therapy, from radiation accidents and from environmental radiation There can even be additional non-uniformity with respect to time of the non-uniform distribution, for example, in the redistributions of administered radioactivity in the body For all absorbed-dose calculations, there is a source (or sources) of radiation and a receptor (or receptors) of some of the energy of this radiation, with or without intervening material between the source and receptor The calculation of absorbed-dose distributions requires specification of the sources and receptors, characterization of their geometrical relationships and consideration of the physical interactions of the radiations involving attenuation, scattering and the production of secondary radiations All these processes are considered in the basic transport equation, the general theorems and properties and the methods of solution of which are described in the transport theory The report is a systematic presentation, discussion and compilation of all the concepts involved It contains some complicated mathematics that will be of interest to the mathematically knowledgeable, but that should not discourage those not mathematically inclined iv / PREFACE The text of the report contains detailed explanations of all the concepts and of the consequences of the equations so that, even omitting the mathematics, a broad and comprehensive understanding can be obtained of what is entailed in the calculation of an absorbed-dose distribution The cutoff date for the report is about two years ago and, hence, the report is lacking in the most current references However, this field does not evolve at a rapid pace and the current literature is, therefore, not abundant and can be reviewed easily In accord with the recommendations of NCRP Report No 82, SI Units in Radiation Protection and Measurements, as of January 1990, only SI units are used in the text Readers needing factors for conversion of SI to conventional units are encouraged to consult Report No 82 This report was prepared by NCRP Scientific Committee 52 on Conceptual Basis of Calculations of Dose Distributions Serving on the Committee during the preparation of this report were: Harald H Rossi, Chairman 105 Larchdale Avenue Upper Nyack, New York R G Alsmiller, Jr Engineering Physics and Mathematics Division Oak Ridge National Laboratory Oak Ridge, Bnnessee William C Roesch 1646 Butternut Richland, Washingtan Martin J Berger 5011 Elm Street Bethesda, Maryland Lewis V Spencer Post Office Box 87 Hopkinsville, Kentucky Albrecht M Kellerer GSF Institut fiir Strahlungbiologie Neuherberg, Germany Marco A Zaider Radiological Research Laboratory Columbia University New York, New York NCRP Secretariat: Thomas Fearon (1976-80) J a m e s A Spahn, Jr (1981) J a m e s T Walker (1982-84) Constantine J Maletskos (1985-91) The Council wishes to express its appreciation to the Committee members for the time and effort devoted to the preparation of this report PREFACE, V Especial thanks are due to Marco Zaider for his contribution to the editing of scientific aspects of this report Warren K Sinclair President Bethesda, Maryland March 1991 Contents Introduction 1.1 The Concept of Absorbed Dose 1.2 Dose Measurement and Dose Calculation 1.3 Elements of Dose Calculations Transport Formalisms 2.1 Concepts in Dose Calculations 2.2 Transport Equation Sources 3.1 Specification of Sources 3.2 Simplified Representations of Sources Receptors Cross Sections 5.1 Schematization 5.2 General Aspects of Required Cross Sections Transport Theory-General Theorems and 1 6 14 14 15 17 20 20 22 Properties 26 6.1 Integral Form of the Transport Equation 26 6.2 Iterative Solutions (Orders of Scattering) 27 6.3 Density Scaling Theorem 28 6.4 Fano's Theorem 29 6.5 Energy Conservation 29 6.6 Superposition 30 6.7 Adjoint Transport Equation 31 6.8 Reciprocity 33 6.9 Transport Equations in Commonly Used Coordinate Systems 34 Transport Theory-Methods of Solution 36 7.1 Introduction 36 7.2 Radiation Equilibrium and Space-Integrated Radiation Fields 38 7.3 Continuous Slowing-Down Approximation (CSDA) 40 7.4 Numerical Integration Over Energy 43 7.5 Elementary Problems Involving Particle Direction 45 7.5.1 Thin-Foil Charged Particle Problems 45 7.6 Penetration Studies 47 7.6.1 The Moment Method 47 7.6.2 Discrete-Ordinates Transport Codes 49 ' CONTENTS vii 7.6.2.1 Neutron-Photon Transport 49 7.6.2.2 Dosimetry Calculations By the Method of Discrete Ordinates 7.7 Spectral Equilibrium and Related Concepts 7.7.1 Aspects Applicable to All Radiations 7.7.2 Electrons 7.7.3 Photons and Neutrons 7.8 Radiation Quasi-equilibrium 7.8.1 Transient Equilibrium 7.8.2 Non-uniform Sources 7.8.3 Non-uniformity in the Internal Dosimetry of Radionuclides 7.8.4 Non-uniform Media Monte-CarloMethods 8.1 Principles 8.2 Analog Monte-Carlo and Variance-Reduction Bchniques 8.3 Transport Codes 8.3.1 Neutron-Photon Transport a t Energies 520 MeV 8.3.2 Electron-Photon Cascades 8.3.3 Nucleon-Meson Transport a t Energies >20 MeV 8.3.4 Dosimetric Calculations Geometric Considerations 9.1 Absorbed Dose in Receptor Regions 9.2 Reciprocity Theorem 9.3 Isotropic Point-Source Kernels 9.4 Point-Pair Distance Distributions and Geometric Reduction Factors 10 Calculation of the Dose Equivalent List of Symbols Appendix A Information about Cross Sections for Transport Calculations A.l Photon Cross Sections A.l.l Photoelectric Effect A.1.2 Fluorescence Radiation and Auger Electrons A 1.3 Incoherent (Compton) Scattering A.1.4 Pair Production A.1.5 Coherent (Rayleigh) Scattering A.1.6 Photonuclear Effect A.1.7 Attenuation Coefficient A.1.8 Energy-Absorption Coefficient A.1.9 Photon Cross-Section Compilations viii / CONTENTS A.2 Cross Sections for Charged Particles 113 A.2.1 Elastic Scattering of Electrons by Atoms 113 A.2.2 Elastic Scattering of Protons by Atoms 117 A.2.3 Scattering of Electrons by Atomic Electrons 119 A.2.4 Scattering of Protons by Atomic Electrons 120 A.2.5 Electron Bremsstrahlung 122 A.2.6 Continuous Slowing-Down Approximation 126 A.2.7 Stopping Power 128 A.3 Neutron Cross Sections 139 A.3.1 Classification of Interactions 139 A.3.2 Data Compilations 143 A.3.3 Kerma Factors 145 ~ Nuclear Cross Sections for Charged Particles a t High Energies 147 A.4.1 Interactions of Pions below 100 MeV 147 A.4.2 Nuclear Interactions of Hadrons above 100 MeV 153 Appendix B Examples of Absorbed-Dose and DoseEquivalent Calculations 167 B.1 Absorbed Dose from Neutrons in Tissue-Equivalent Material 167 B.2 Shielding of Manned Space Vehicles Against Galactic Cosmic-Ray Protons and Alpha Particles 172 B.3 Skyshine for Neutron Energies 5400 MeV 178 Appendix C A Compilation of Geometric Reduction Factors for Standard Geometries 185 C.l The Autologous Case (A = B) 185 C.2 The Heterologous Case (A # B) 188 References 197 Introduction 1.1 The Concept of Absorbed Dose The effects of radiation on matter are initiated by processes in which atoms and molecules of the medium are ionized or excited Over a wide range of conditions, it is a n excellent approximation to assume that the average number of ionizations and excitations is proportional to the amount of energy imparted to the medium by ionizing radiation1 in the volume of interest The absorbed dose, that is, the average amount of energy imparted to the medium per unit mass, is therefore of central importance for the production of radiation effects, and the calculation of absorbed-dose distributions in irradiated media is the focus of interest of the present report It should be pointed out, however, that even though absorbed dose is useful as an index relating absorbed energy to radiation effects, it is almost never sufficient; it may have to be supplemented by other information, such as the distributions of the amounts of energy imparted to small sites, the correlation of the amounts of energy imparted to adjacent sites, and so on Such quantities are termed stochastic quantities Unless otherwise stated, all quantities considered in this report are non-stochastic A discussion concerning stochastic quantities is given in ICRU Report 33 (ICRU, 1980) The absorbed dose, D, is defined (ICRU, Report 33) as the quotient of d by dm: where d2 is the mean energy imparted by ionizing radiation to matter of mass dm The energy, E,imparted to the volume containing dm is defined as 'Ionizing radiation consists of directly ionizing and indirectly ionizing radiation Directly ionizing radiations are charged particles (electrons,positrons, protons, alpha particles, heavy ions) with sufficient kinetic energy to ionize or excite atoms or molecules Indirectly ionizing radiations are uncharged particles (photons, neutrons) that set in motion directly ionizing radiation (charged particles) or that can initiate nuclear transformations / INTRODUCTION where Ei, (E,,,) is the sum of energies of all the charged and uncharged ionizing particles that enter (leave)the volume, excluding rest mass energies, and XQ is the algebraic sum of all changes (decreases: positive sign; increases: negative sign) of rest-mass energy in mass-energy transformations occumng in the volume A few clarifications of Equation (1.1) are necessary a t this point The energy imparted results from random discrete energy deposition events by individual ionizing particles andlor their secondaries The quantity E is therefore stochastic in nature and governed by a (normalized) probability distribution function fv(d where V is the volume containing m The mean value of e, is the quantity referred to in the definition, Equation (1.1).In addition, this equation implies a limiting process2such that V + The absorbed dose, Dfi), is thus defined a t a given position ? in the irradiated object (see footnote 2), and is a non-stochastic quantity Furthermore, in general D c ) changes with and this variation is termed the "dose distribution." A second important aspect refers to the temporal pattern of dose accumulation Let be the dose increment at ? during the time interval CtJt+dtl This equation defines the absorbed-dose rate, D@,t) This aspect is important in understanding the relation between dose and biological effect A final remark concerns the relation between.dose and its stochastic counterpart, the specific energy, z, defined as z = dm (1.5) The specific energy is always measured in a non-zero volume, V, and its mean value, 2, has the value of the average absorbed dose, Dv, in that volume of 2Becauseof the discrete manner in which energy is imparted, the limiting process V- is obviouely an idealization At all times the volume V should contain a large number of atoms and molecules THENCRP 221 United States Environmental Protection Agency United States Navy United States Nuclear Regulatory Commission The NCRP values highly the participation of these organizations in the liaison program The Council's activities are 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Guictance on Radiation Received in Spate Activities (1989) Qwlity Assurance for Diagnostic Imaging (1988) Exposure of the U.S Population fiom Diagnostic Medical Radiation (1989) 226 NCRP PUBLICATIONS Exposure o f the U.S Population from Occupational Radiation (1989) Medical X-Ray, Electron Beam and Gamma-Ray Protection for Energies Up to 50 MeV (Equipment Design, Performance and Use) (1989) Control of Radon in Houses (1989) The Relative Biological Effectiveness of Radiations ofDifferent Quality (1990) Radiation Protection for Medical and Allied Health Personnel (1989) Limit for Exposure to "Hot Particles" on the Skin (1989) Implementation of the Principle of As Low As Reasonably Achievable (ALARA) for Medical and Dental Personnel ( 1990) Conceptual Basis for Calculations of Absorbed-Dose Distributions (1991) Effects of Ionizing Radiation on Aquatic Organisms (1991) Some Aspects of Strontium Radiobiology (1991) Developing Radiation Emergency Phns fordcademic, Medical or Industrial Facilities (1991) Calibration ofsurvey Instruments Used i n Radiation Protection for the Assessment of Ionizing Radiation Fields and Radioactive Surface Contamination (1991) Exposure Criteriu for Medical Diagnostic Ultrasound:I Criteria Based on Thermal Mechanisms (1992) Maintaining Radiution Protection Records (1992) Risk Estimutes for Radiation Protection (1993) Limitation of Exposure to Ionizing Radiation (1993) Research Needs for Radiation Protection ( 1993) Radiation Protection in the Mineral Extraction Industry (1993) A Practical Guide to the Determination of Human Exposure to Radiofrequency Fields (1993) Binders for NCRP reports are available Two sizes make it possible to collect into small binders the "old series" of reports (NCRPReports Nos 8-30) and into large binders 'he more recent publications (NCRP Reports Nos 32-119) Each binaer will accommodate from five to seven reports The binders carry the identification WCRP Reports" and come with label holders which permit the user 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No NCRP Commentaries Title Krypton-85 in the Atmosphere-With Specific Reference to the Public Health Significance of the Proposed Controlled Release at Three Mile Island (1980) Preliminary Evaluation of Criteria for the Disposal of Trans uranic Contaminated Waste (1982) Screening Techniques for Determining Compliance with Environmental Standards-Releases of Radionuclides to the Atmosphere (1986),Revised (1989) Guidelines for the Release of Waste Water from Nuclear Facilities with Special Reference to the Public Health Significance of the Proposed Release of Treated Waste Waters at Three Mile Island (1987) Review of the Publication, Living Without Landfills (1989) Radon Exposure of the U.S Population-Status of the Problem (1991) 228 NCRP PUBLICATIONS Misadministration of Radioactive Material in MedicineScientific Background (1991) Uncertainty in NCRP Screening Models Relating to A t m spheric Transport, Deposition and Uptake by Humans (1993) Proceedings of the Annual Meeting No Title Perceptions of Risk, Proceedings of the Fifteenth Annual Meeting held on March 14-15, 1979 (including Taylor Lecture No 3) (1980) Critical Zss~lesin Setting Radiation Dose Limits, Proceedings of the Seventeenth Annual Meeting held on April 89, 1981 (including Taylor Lecture No 5) (1982) Radiation Protection a n d New Medical Diagnostic Approaches, Proceedings of the Eighteenth Annual Meeting held on April 6-7, 1982 (including Taylor Lecture No 6) (1983) Environmental Radioactivity, Proceedings of the Nineteenth Annual Meeting held on April 6-7,1983 (including Taylor Lecture No 7) (1983) Some Issues Important in Developing Basic Radiation Protection Recommendations, Proceedings of the Twentieth Annual Meeting held on April 4-5,1984 (including Taylor Lecture No 8) (1985) Radioactive Waste, Proceedings of the Twenty-first Annual Meeting held on April 34,1985 (including Taylor Lecture No 9) (1986) Nonionizing Electromagnetic Radiations and Ultrasound, Proceedings of the Twenty-second Annual Meeting held on April 2-3, 1986 (including Taylor Lecture No 10) (1988) New Dosimetry at Hiroshima andNagasaki andZts Zmplications for Risk Estimates, Proceedings of the Twenty-third Annual Meeting held on April 8-9,1987 (including Taylor Lecture No 11)(1988) Radon, Proceedmgs of the Twenty-fourth Annual Meeting held on March 30-31, 1988 (including Taylor Lecture No 12) (1989) Radiation Protection Today-The NCRP at Sixty Years, Proceedings of the Twenty-fifth Annual Meeting held on April 5-6, 1989 (including Taylor Lecture No 13)(1990) NCRP PUBLICATIONS / 229 Health and Ecological Implications of Radioactively Contaminated Environments, Proceedings of the Twentysixth Annual Meeting held on April 45,1990 (including Taylor Lecture No 14) (1991) Genes, Cancer and Radiation Protection, Proceedings of the Twenty-seventh Annual Meeting held on April 3-4,1991 (including Taylor Lecture No 15) (1992) Radiation Protection in Medicine, Proceedings of the Twenty-eighthAnnual Meeting held on April 1-2,1992(including Taylor Lecture No.16) (1993) Lauriston S.Taylor Lectures No Title Thesquares of tireNatudNumbers in Radiation Protection by Herbert M Parker (1977) Why be Quantitative about Radiation Risk Estimates? by Sir Edward Pochin (1978) Radiaabn Pnnktion Comqts and Tmde O j j i by Hymer L Friedell (1979) [Available also in Perceptions of Risk, see above] From "Quantity ofRadiation" and "Dose" to '%xposure" and "Absorbed DoseJJ-An Historical Review by Harold Wyckoff (1980) How Well Can We Assess Genetic Risk? Not Very by James F Crow (1981) [Available also in Critical Issues in Setting Radiation Dose Limits, see abovel Ethics, Trade-offs and Medical Radiation by Eugene L Saenger (1982) [Available also in Radiution Protection and New Medical Diagnostic Approaches, see abovel The Human Environment-Past, Present and Future by Merril Eisenbud (1983) [Available also in Environmental Radioactivity, see abovel Limitation and Assessment i n Radiation Protection by Harald H Rossi (1984) [Available also in Some Isszces Important in Developing Basic Radiation Protection Recommendations, see abovel Truth (and Beauty) in Radiution Measurement by John H Harley (1985) [Available also in Radioactive Waste, see abovel Biological Effects of Non-ionizing Radiations: Cellular Properties and Interactions by Herman P Schwan (1987) [Available also in Nonionizing Electromagnetic Radiations and UZtmsound, see abovel 230 NCRP PUBLICATIONS How to be Quantitative about Radiation Risk Estimates by Seymour Jablon (1988) [Available also in New Dosimetry at Hiroshima: and Nagasaki and its Implications for Risk Estimates, see above] How Safe is Safe Enough? by Bo Lindell(1988) [Available also in Radon, see above] Radiobiology and Radiation Protection: The Past Century and Prospects for the Future by Arthur C Upton (1989) [Available also in Radiation Protection Today, see above] Radiation Protection and the Internal Emitter Saga by J Newel1 Stannard (1990) [Available also in Health and Ecological Implications of Radioactively Contaminated Environments, see abovel When is a Dose Not a Dose? by Vidor P Bond (1992) [Available also in Genes, Cancer and Radiation Protection, see above] Dose and Risk in Diagnostic Radiology: How Big? How Little? by Edward W Webster (1992)[Available also in Radiation Protection in Medicine, see abovel Science, Radiation Protection and the NCRP by Warren K Sinclair (1993) Symposium Proceedings The Control of Exposure of the Public to Ionizing Radiation i n the Event ofAccident or Attack, Proceedings of a Symposium held April 27-29, 1981 (1982) NCRP Statements No Title "Blood Counts, Statement of the National Committee on Radiation Protection," Radiology 63,428 (1954) "Statements on Maximum Permissible Dose h m Television Receivers and Maximum Permissible Dose to the Skin of the Whole Body," Am J Roentgenol., Radium Ther and Nucl Med 84, 152 (1960) and Radiology 75, 122 (1960) X-Ray Protection Standards for Home Television Receivers, Interim Statement of the National Council on Radiation Protection and Measurements (1968) Specification of Units ofNatural Uranium and Natural Thorium, Statement of the National Council on Radiation Protection and Measurements, (1973) NCRP PUBLICATIONS 231 NCRP Statement on Dose Limit for Nelltrons (1980) Control of Air Emissions of Radionuclides (1984) The Probability That a Particular Malignancy May Have Been Caused by a Specified Irradiation (1992) Other Documents The following documents of the NCRP were published outside and Statement series: of the NCRP Report, CornmenSomatic Radiation Dose for the Geneml Population, Report of the Ad Hoc Committee of the National Council on Radiation Protection and Measurements, May 1959,Science, February 19,1960, Vol 131, No 3399, pages 482-486 Dose Effect Modifying Factors I n Radiation Protection, Report of Subcommittee M-4 (Relative Biological Effectiveness) of the National Council on Radiation Protection and Measurements, Report BNL 50073 (T-471) (1967) Brookhaven National Laboratory (National Technical Information Service Springfield, Virginia) The following documents are now superseded andlor out of print: NCRP Reports No Title X-Ray Protection (1931) [Superseded by NCRP Repart No 31 R d m Pm&tion (1934) [Superseded by NCRP Report No 41 X-Ray Protection (1936) [Superseded by NCRP Report No 61 Radium Prdection (1938) [Supersededby NCRP Repart No 131 Safe H a d i n g of Radioactive Luminow Compound (1941) [Out of Print] Medicul X-Ray Protection Up to Two Million Volts (1949) [Superseded by NCRP Report No 181 Safe Handling of Radioactive Isotopes (1949) [Superseded by NCRP Report No 301 Recommendations for WasteDisposal of Phosphorus32 and Iodine-131 for Medical Users (1951) [Out of Print] Radiological Monitoring Methods and Instruments (1952) [Superseded by NCRP Report No 571 Maximum Permissible Amounts of Radioisotopes i n the Human Body and Maximum Permissible Concentmtion+ in Air and Water (1953) [Superseded by NCRP Report No 221 Recommendations for the Disposal of Carbon-14 Wastes (1953) [Superseded by NCRP Report No 81.1 232 / NCRP PUBLICATIONS Protection Against Radiations from Radium, Cobalt-60 and Cesium-I37 (1954)[Superseded by NCRP Report No 241 Protection Against Betatron-Synchrotron Radiations Up to 100 Million Electron Volts (1954)[Superseded by NCRP Report No 511 Safe Handling of Cadavers Containing Radioactive Isotopes (1953)[Superseded by NCRP Report No 211 Radioactive-Waste Disposal i n the Ocean (1954)[Out of Print] Permissible Dose from External Sources of Ionizing Radiation (1954)including Maximum Permissible Exposures to Man, Addendum to National Bureau of Standards Handbook 59 (1958)[Superseded by NCRP Report No 391 X-Ray Prdection (1955)[Supersededby NCRP Report No 261 Regulation of Radiation Exposure by Legislative Means (1955)[Out of Print] ProtectionAgainst Neutron Radiation Up to30 Million Electron Volts (1957)[Superseded by NCRP Report No 381 Safe Handling of Bodies Containing Radiwctive Isotopes (1958)[Superseded by NCRP Report No 371 Protection Against Radiations from Sealed Gamma Sources (1960)[Superseded by NCRP Reports No 33,34 and 401 Medical X-Ray Protection Up to Three Million Volts (1961) [Superseded by NCRP Reports No 33,34,35and 361 A Manual of Radioactivity Procedures (1961)[Superseded by NCRP Report No 581 Exposure to Radiation in an Emergency (1962)[Superseded by NCRP Report No 421 Shielding for High-Energy Electron Accelerator Znstallations (1964)[Superseded by NCRP Report No 511 Medical X-Ray and Gamma-Ray Protection for Energies up to 10 MeV-Equipment Design and Use (1968)[Superseded by NCRP Report No 1021 Medical X-Ray and Gamma-Ray Protection for Energies Up to 10 MeV-Structural Shielding Design and Evaluation Handbook (1970)[Superseded by NCRP Report No 491 Basic Radiation Protection Criteria (1971)[Superseded by NCRP Report No 911 Review of the Current State ofRadiation Protection Philosophy (1975)[Superseded by NCRP Report No 911 Natuml Background Radiation in the United States (1975) [Superseded by NCRP Report No 941 Radiation Protection for Medical and Allied Health Personnel (1976)[Superseded by NCRP Report No 1051 NCRP PUBLICATIONS 53 56 58 66 91 233 Review ofNCRPRadiation Dose Limit forEmbryo and Fetus in Occupationally -Exposed Women (1977) [Out of Print] R&n Exposwv from ConswnerProdudsan&M i s o e b u s S o m (1977) [Superseded by NCRP Report No 951 A Handbook of Radioactivity Measurements Procedures, 1st ed (1978) [Superseded by NCRP Report No 58, 2nd ed.] Mammography (1980) [Out of Print] Reoommeruhhns on Limits fir Eqmm to Ionizing RacEiation (1987) [Superseded by NCRP Report No 1161 NCRP Proceedings No Title Quantitative Risk in Standards Setting, Proceedings of the Sixteenth Annual Meeting held on April 2-3, 1980 [Out of Print] Index Adjoint methods, 19, 31 Attenuation coefficient, 111 Auger electrons, 97 Bremsstrahlung, 122 Charged-particle equilibrium, 13 Compton scattering, 97 Continuous Slowing-Down Approximation, 23, 40, 126 Cross section, 9, 20 assumption for calculating, 21 distributions of, energy-transfer coefficient, 13 list of references, 25 macroscopic, mean free path, 21 mirroecopic, scattering center 21 Discrete-ordinate method, 36 codes for, 49 dosimetry calculations, 60 neutron-photon transport, 49,67 Dose, absorbed-dose rate, calculation of, 3, deterministic approach, energy imparted, h m neutrons, 167 geometric considerations, 74 internal dosimetry, 58 ionizing radiation, kerma, 13 measurement of, Monte-Carlo method, 6.72 stochastic quantities, total dose, 10 banaport equatione, 5, Dose equivalent, 84,167 Doae rate, Elastic scattering, 113 electrons, 113 neutrons, 140 protons, 117 Electron-photon transport, 68 Energy-absorption coefficient, 111 Energy conservation, 29 Energy-transfer coefficient, 13 Fano's theorem, 29 Fluorescence radiation, 97 Flux density, flux-density distribution, Geometrical factors, 74 autologous geometry, 82, 186 heterologous geometry, 82, 188 Geometric reduction factor, 76, 81 compilation of, 186 Green's theorem, Hadrons, 153 Hartree-Fock wave functions, 103 Importance function, 181 Internal dosimetry 68 Kenna, 13 charged-particle equilibrium, 13 kerma factore 146 Klein-Nishina equation, 103 Linear energy transfer (LET), 84 unrestricted (LET), 84 Mean excitation energy, 131 Mean free path, 21 Microdoeimetry, specific energy, Moment method, 24,47 Monte-Carlo technique, 6, 61 and CSDA, 66 efficiency of, 63 eventby-event, 65 transport codes, 70 variance-reduction metho&, 66 Neutron cmsa sections, 139 Neutron-photon transport, 49,67 Nucleon-meeon tramport, 70 Pair production 103 Particle current density, Particle density, Phase space,8 Photoelectric effect, 93 Photonuclear effect, 107 Pions, 147 Point-pair dietanee distribution, 76, 81 Point-source kernal, 76 differential, 75 integral, 75 isotropic, 78 Probability density function, 61 INDEX Quality factor, 84-85 Radiation equilibrium, 51 quasi-equilibrium, 56 traneient equilibrium, 57 Random (pseudorandom) number generator, 62 Rayleigh scattering, 106 Receptor, 17 absorbed dose in, 74 anthropomorphic, 17 receptor-free field, 17 reciprocity, 33 Reciprocity theorem, 77 Scattering operator, 27 Shielding, 172 Skyahine for neutrons, 178 fhurces, 6, 14 fictitious s o m a 15 monoenergetic, 16 non-uniform, 57 / 235 plane muree 16 point aourc8,16 reciprocity, 33 simplified repre~entation,15 Specific Energy, Stochastic quantities, Stopping power, 12, 128 denaity-effect correction, 132 mass stopping power, 12 'Ranslation operator, 27 lhmsport equations, 5,8,26 demity d i n g , 28 for two kind8 of particles, 12 in different coordinate eyatems, 34 integral form of, 26 iterative solution of, 27 linear and nonlinear, 10 Neumann expansion, 28 radiation equilibrium, 38 euperposition, 30 transport codes, 67 ... where the dose is uniform and that are the subject of microdosimetry and not this report Many illustrations of absorbed dose non-uniformity come to mind: for example, the absorbed- dose distributions. .. theory gooerning liability Library of Congress Cataloging-in-PublicationData Conceptual basis for calculations of absorbed- dose distributions p cm.- (NCRP report; no 108) Includes bibliographical references... development of absorbed- dose distributions in general To address this issue in an allencompassing manner, the NCRP formed Scientific Committee 52 on the Conceptual Basis of Calculations of Dose Distribution