Prepared by numerous specialists
E. P. Blizard t, A. B. Chilton,
M. Grotenhuis, A. Honig, Th. A. Jaeger
H. H. Eisenlohr Coordinating Editor
Sponsored by International Atomic Energy Agency Vienna
Volume I Shielding Fundamentals and Methods
Springer-Verlag Berlin Heidelberg GmbH 1968
With 467 Figures
ISBN 978-3-662-23757-1 ISBN 978-3-662-25858-3 (eBook) DOI 10.1007/978-3-662-25858-3
All rights reserved No part of this book may be translated or reproduced in
any form without written permission from Springer-Verlag Berlin Heidelberg GmbH 1968
© Springer-Verlag Berlin Heidelberg 1968 Originally published by Springer-Verlag Berlin • Heidelberg in 1968
Softcover reprint of the hardcover 1st edition 1968
Library of Congress Catalog Card Number 68-19816
The use of general descriptive names, trade names, trade marks, etc. in this publicationevenifthe former are not especially identified, is not to be taken as a sign that such names, as understood by the Trade
Marks and Merchandise Marks Act, may accordingly be used by anyone
Title-No, 1416
Prepared by numerous specialists
E. P. Blizard t, A. B. Chilton,
M. Grotenhuis, A. Honig, Th. A. Jaeger
H. H. Eisenlohr Coordinating Editor
Sponsored b International Atomic Energy Agency Vienna
Volume I Shielding Fundamentals and Methods
Springer-Verlag Berlin Heidelberg GmbH 1968
With 467 Figures
ISBN 978-3-662-23757-1 ISBN 978-3-662-25858-3 (eBook) DOl 10.1007/978-3-662-25858-3
All rights reserved No part of this book may be translated or reproduced in
any form without written permission from Springer-Verlag Berlin Heidelberg GmbH 1968
©Springer-Verlag Berlin Heidelberg 1968 Originally published by Springer-Verlag Berlin • Heidelberg in 1968
Softcover reprint of the hardcover 1st edition 1968
Library of Congress Catalog Card Number 68-19816
The use of general descriptive names, trade names, trade marks, etc. in this publicationevenifthe former are not especially identified, is not to be taken as a sign that such names, as understood by the Trade
Marks and Merchandise Marks Act, may accordingly be used by anyone
Title-No, 1416
IN MEMORIAM
1916-1966
EvERITT P. BLIZARD has had a greater effect on the development of the science and technology of radiation shielding than any other single person. Almost from the inception of the nuclear programs for peaceful purposes, he assumed a position of leadership in the field of radiation shielding which he never relinquished until his death. Although his activities have been centered on the research programs of his own coun­ try. the United States, thrOugh his participation in numerous international conferences he has also had a major effect on the programs of other countries. Radiation shielding of all types, throughout the world, has thus felt his touch as experimenter, teacher, administrator, editor, and advisor.
It was inconceivable that a comprehensive shielding handbook could have been started without his advice and collaboration, and EvERITT P. BLIZARD -in spite of his many other duties- generously agreed to serve as one of the editors. The first intima­ tion of his last illness came within two years afterwards, and it is characteristic of him that he tried for some months to continue work on Compendium manuscripts after his failing strength forced him to give up all his other duties at the Oak Ridge National Laboratory.
By his death, the editors have lost a close friend and an inspiring collaborator; the shielding profession has lost a great leader; and the world has lost an outstanding citizen.
List of Editors and Contributors Editors
jAEGER, R. G. Universitat Mainz, Institut fiir Klinische Strahlenkunde, 65 Mainz, F.R.G.; formerly member of Physikalisch-Technische Bundesanstalt, Braunschweig, and Senior Officer in the International Atomic Energy Agency, Vienna, Division of Isotopes.- Chapter 1, Sections 2.1., 2.2.
BLIZARD t. E. P. Formerly Oak Ridge National Laboratory, Oak Ridge, Tennessee 37 830, U.S.A.
CHILTON, A. B.
207 Nuclear Engineering Laboratory, University of Illinois, Urbana, Illinois 61 801, U.S.A. Chapters 4, 8
GROTENHUIS, M. Argonne National Laboratory, 9700 South Cass Avenue, Argonne, Illinois 60439, U.S.A. Section 2.J., Chapters J, 5
HoNIG, A.
Brno Technical University, Hlinky 48, Brno, C.S.S.R.- Chapter 9
JAEGER, TH. A. Bundesanstalt fiir Materialpriifung, Abteilung Bauwesen, 1 Berlin 45, F. R. G.; (Technische Univer­ sitat Berlin, Fakultat fiir Bauingenieurwesen, 1 Berlin 12). - Chapters 6, 7, 10
EISENLOHR, H. H.
Contributors to Volume I AALTO, E.
Imatran Voima Osakeyhti6, Box 10 138, Helsinki 10, Finland. -Sections 8.2.3., 8.2.7.
ALTER, J. Israel Atomic Energy Commission, Nuclear Research Centre-Negev., P.O. Box 9001, Beer Sheva, Israel. Section 6.8.
ARNOLD, E. D. Chemical Technology Division, Oak Ridge National Laboratory, P.O. Box X, Oak Ridge, Tennessee 37 830, U.S.A.- Sections 2.1.2, 2.3.1.1.
ARONSON, R. New York University, University Heights, New York, N.Y. 10 453, U.S.A. -Section 3.3.2.
AVERY, A. F. Winfrith Shielding Group, Building 51 OT, Atomic Energy Research Establishment, Harwell, Didcot, Berkshire, U.K. -Section 5.2.2.2.
BERGELSON, B. R. Institute of Theoretical and Experimental Physics, Moscow M-259, U.S.S.R.- Sections 8.2.1., 8.2.2.
BERGER, M. J. National Bureau of Standards, Washington, D. C. 20 234, U.S.A. -Sections 4.1 .. 4.2.
BIRO, G. G. Gibbs & Hill Inc., Consulting Engineers, 393 Seventh Avenue, New York, N.Y. 10 001, U.S.A. Section 3.1.
BLIZARD f, E. P. Formerly Oak Ridge National Laboratory, Oak Ridge, Tennessee 37 830 U.S.A. -Sections 6.1., 6 7.
BONILLA, C. F. School of Engineering and Applied Science, Columbia University, 520 West 120th Street, New York, N.Y. 10 027, U.S.A.- Sections 7.4.1.-7.4.5.
BRODER, D. L. Institute of Physics and Power Engineering, Obninsk, U.S.S.R. -Section 5.J.
VI List of editors and contributors
BRYAN, Jr., F. A. Research Triangle Institute, Box 12 194, Research Triangle Park, North Carolina 27 709, U.S.A. Section 4.3.1.3.
BuNEMANN, D. Gesellschaft fiir Kernenergieverwertung in Schiffbau und Schiffahrt m.b.H., Institut fiir Reaktor­ physik, 2057 Geesthacht-Tesperhude, F.R.G.- Section 4.3.2.
BURRILL, E. A. High Voltage Engineering Corporation, 703 Welch Road, Suite F-I, Palo Alto, California 94 304, U.S.A.- Sections 2.2.1.1., 2.2.1.2.
BURRUS, W. R. Oak Ridge National Laboratory. Present address: Tennecomp, Inc., Box J, Oak Ridge, Tennessee 37 830, U.S.A.- Sections 8.1.6., 8.1.7., 8.2.6.
BuTLER, J. Winfrith Shielding Group, Building 51 OT, Atomic Energy Research Establishment, Harwell, Didcot, Berkshire, U.K. -Section 5.2.2.2.
CHILTON, A. B.
207 Nuclear Engineering Laboratory, University of Illinois, Urbana, Illinois 61 801, U.S.A. Sections 4.3.1.1., 4.3.1.2.
CLAIBORNE, H. c. Oak Ridge National Laboratory, P.O. Box X, Oak Ridge, Tennessee 37 830, U.S.A. Sections 7.1., 7.3., 8.2.5.
CLARKE, E. T. Technical Operations, Inc., Burlington, Massachusetts 02 103, U.S.A.- Section 4.5.3.
CLIFFORD, C. E.
CLIFFORD, c. E.
Oak Ridge National Laboratory, P.O. Box X, Oak Ridge, Tennessee 37 830, U.S.A.- Section 8.2.5.
EGoRov, Yu. A. Atomic Energy Institute, Kurchatov, Moscow, U.S.S.R. -Section 5.2.1.2.
FoDERARo, A. Nuclear Engineering Department, The Pennsylvania State University, 231 Sackett Building, Uni­ versity Park, Pennsylvania 16 802, U.S.A.- Sections 3.2., 6.1.-6.6., 6.8., 7.2.
FRENCH, R. L. Radiation Research Associates, Inc., 1506 West Terrell Avenue, Fort Worth, Texas 76 104, U.S.A. Section 5.4.2.
GoussEv, N. G. Institute of Biophysics (The Ministry of Public Health of u.S.S.R.), Lhivopisnaya 22, Moscow D-182, U.S.S.R.- Sections 1.3., 6.1., 6.4., 6.5., 6.6.5.-6.6.8.
GRONROOS, H. California Institute of Technology, Jet Propulsion Laboratory, 4800 Oak Grove Drive, Pasadena, California 91103, U.S.A. -Section 5.2.3.2.
GROTENHUIS, M. Argonne National Laboratory, 9700 South Cass Avenue, Argonne, Illinois 60 439, U.S.A. Sections 2.3.2.1., 2.3.2.4.
HoovER, L. J. Nuclear Engineering DepaTtment, The Pennsylvania State University, 231 Sackett Building, Uni­ versity Park, Pennsylvania 16 802, U.S.A.- Section 7.2.
HuBBELL, J. H.
National Bureau of Standards, Washington, D. C. 20 234, U.S.A.- Sections 4.1., 4.2.
HUDDLESTON, c. M. U.S. Naval Radiological Defense Laboratory, San Francisco, California 94 135, U.S.A. Sections 8.1.1- 8.1.5.
KEEPIN, G. R. Los Alamos Scientific Laboratory, University of California, P.O. Box 1663, Los Alamos, New Mexico 87 544, U.S.A.- Section 2.3.1.2.
List of editors and contributors
KovALEV, E. E. The Ministry Public Health of U.S.S.R., Rachmanovsky 3, Moscow, U.S.S.R. Sections 6.1.-6.3., 6.6.1.-6.6.4.
KRUMBEIN, A. D.
United Nuclear Corporation, Research and Engineering Center, Grasslands Road, Elmsford, New York 10 523, U.S.A.- Section 3.3.1.
KUKHTEVICH, V. I. Institute of Physics and Power Engineering, Obninsk, U.S.S.R.- Sections 5.2.3.1., 5.4.1.2.
LAFORE, P. Commissariat a l'Energie Atomique, Centre d'Etudes Nuc!eaires de Fontenay-aux-Roses, Fontenay­ aux-Roses, Seine, France.- Section 5.2.1.1.
LEDoux, ] . C. Nuclear Division, Flow Corporation, 6060 Duke Street-Suite 101, Alexandria, Virginia 22 302, U.S.A. Sections 8.1.1.-8.1.5.
LEIMDORFER, M .. Industri-Matematik AB, De Geersgatan 8, Stockholm NO, Sweden.- Sections 4.4., 5.4.1.1.
1\'IADEY, RICHARD
Physics Department, Clarkson College of Technology, Potsdam, New York 13 676, U.S.A. Section 2. 2. 2. 1.
MAERKER, R. E. Oak Ridge National Laboratory, P.O. Box X, Oak Ridge, Tennessee 37 830, U.S.A.- Section 8.2.5.
MAIENSCHEIN, F. C. Oak Ridge National Laboratory, P.O. Box X, Oak Ridge, Tennessee 37 830, U.S.A. Sections 2.3.1.3., 2.3.1.4.
MARABLE, J. H. Oak Ridge National Laboratory, P.O. Box X, Oak Ridge, Tennessee 37 830, U.S.A.- Section 7.2.
MASHKOVICH, v. P. Moscow Engineering Physical Institute, Moscow M-409, U.S.S.R.- Sections 8.2.1., 8.2.2.
McARTHY, A. E. Argonne National Laboratory, 9700 South Cass Avenue, Argonne, Illinois 60 439, U.S.A. Section 2.3.2.4.
MEHL, ]. G. International Atomic Energy Agency, Karntnerring, Vienna, Austria. Present address: Gesellschaft fiir Kernforschung m.b.H., Postfach 947, 75 Karlsruhe, F.R.G. -Section 1.2.
MITTELMAN, P. s. MAGI (Mathematical Applications Group, Inc.), 180 South Broadway, White Plains, New York 10 605, U.S.A. -Section 3.3.3.
MORGAN, I. L. Texas Nuclear Corporation, P.O. Box 9267-Allandale Station, Austin, Texas 78 756, U.S.A. Section 2.3.2.2.
MYNATT, F. R. Computing Technology Center, Union Carbide Corporation, Nuclear Division, P.O. Box P, Oak Ridge, Tennessee 37 830, U.S.A.- Section 3.3.4.
NETECHA, M. E. Atomic Energy Institute, Kurchatov, Moscow, U.S.S.R.- Section 5.2.1.2.
NILSSON, ]. The Axel Johnson Institute for Industrial Research, Nynashamn, Sweden.- Section 8.2.4.1.
O'REILLY, B. D. Atomics International, A Division of North American-Rockwell Corporation, 8900 De Soto Avenue, Canoga Park, California 91 304, U.S.A.- Section 3.3.1.
PREISER, S. Polytechnic Institute of Brooklyn, 333 Jay Street, Brooklyn, New York 11 201, U.S.A. Section 3.3.3.
RICHTER, G. Gesellschaft fiir Kernenergieverwertung in Schiffbau und Schiffahrt m.b.H., Institut fiir Reaktor­ physik, 2057 Geesthacht-Tesperhude, F.R.G. -Section 4.3.2.
VIII List of editors and contributors
Rossr, H. H. Radiological Research Laboratory, Department of Radiology, College of Physicians and Surgeons, Columbia University, 630 West 168th Street, New York, N.Y. 10 032, U.S.A. -Section 1.1.
SANDLIN, R. Saab Aktiebolag, Linkiiping, Sweden- Sections 8.2.4.1., 8.2.7.
ScHAEFFER, N. M. Radiation Research Associates, Inc., 1506 West Terrell Avenue, Fort Worth, Texas 76 104, U.S.A. Section 4.5.2.
SELPH, w. Radiation Research Associates, Inc., 1506 West Terrell Avenue, Fort Worth, Texas 76 104, U.S.A. Section 5. 1.
SONNEMANN, G. 30 Hurdle Fence Drive, Avon, Connecticut 06 001, U.S.A. -Sections 7.4.6., 7.5.
SuscHNY, 0. International Atomic Energy Agency, Kii.rntnerring, Vienna, Anstria.- Section 2.1.1.
THOMAS, R. H. Stanford University, Health Physics and Occupational Health, 67 Encina Hall, Stanford, California 94 305, U.S.A. - Section 2.2.2.2.
TRUBEY, D. K. Radiation Shielding Information Center, Oak Ridge National Laboratory, P.O. Box X, Oak Ridge, Tennessee 37 830, U.S.A. -Sections 2.3.2.3., 5.2.2.1.
TsYPIN, S. G. Institute of Physics and Power Engineering, Obninsk, U.S.S.R.- Sections 5.2.3.1., 5.3.
VESELKIN, A. P. Atomic Energy Institute, Kurchatov, Moscow, U.S.S.R.- Section 5.2.1.2.
VESELY, w. E. 201 Nuclear Engineering Laboratory, University of Illinois, Urbana, Illinois 61 801, U.S.A. Sections 8.2.4.2., 8.3.
WELLS, M. B. Radiation Research Associates, Inc., 1506 West Terrell Avenue, Fort Worth, Texas 76 104, U.S.A. Section 5. 4.2.
WIDERDE, R. Swiss Federal Institute of Technology, Ziirich, Switzerland. -Sections 2.2.1.3., 2.2.1.4.
WYCKOFF, H. 0. Armed Forces Radiobiology Research Institute, Defense Atomic Support Agency, Bethesda, Maryland 20 014, U.S.A.- Section 1.1.
YARMUSH, D. L. Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, N.Y. 10 012, U.S.A.- Section 3.3.2.
Preface
The need has arisen for a comprehensive handbook for engineers faced with problems of radiation shielding design. Although there are several excellent books on shielding, they either do not give enough consideration to the many practical design problems, or are limited to special aspects of the subject.
Recognizing the universal need, the International Atomic Energy Agency decided to sponsor the publication ofthe present Engineering Compendium on Radiation Shield­ ing. At the first editorial discussions it was agreed that, if such a book were to be undertaken, it would be appropriate not only to create a useful design tool for the practising engineer but also to include well-referenced basic data for the research worker. Although trying to keep the book down to a reasonable size, the editors have aimed at a complete presentation of the subject, covering and linking both the tech­ nology and the science of shielding.
Efforts to make terms and definitions consistent throughout have been only partially successful, owing to the continuing development of new ideas. However, inconsisten­ cies that could not be eliminated are identified whenever possible.
The Engineering Compendium on Radiation Shielding is arranged as follows: Vol. I, "Shielding Fundamentals and Methods", explains basic concepts, gives fundamental data, and describes analytical methods; it also contains data and formulae of an applied nature. Vol. II, "Shielding Materials and Design", deals fully with the prop­ erties of shielding materials and with the practical design problems associated with gamma and neutron radiations in industrial, scientific and medical applications of atomic energy. Typical numerical examples are given to illustrate shield analysis. The editors hope that with this arrangement the handbook will completely fulfil the need of all those engaged in radiation shielding, and also believe that it will be useful in teaching at colleges and universities.
Dr. E. P. BLIZARD is named as an editor because of his great efforts in getting the Compendium started. His untimely death denied us his valuable help in the later editorial work.
The participation and contributions of three of the divisions of the International Atomic Energy Agency, the Division of Life Sciences (formerly the Division of Iso­ topes), the Division of Nuclear Power and Reactors, and the Division of Health and Safety are gratefully acknowledged. These divisions were represented by Messrs. H. H. EISENLOHR, A. MERTON and J. G. MEHL. Valuable work by the translation staff of the IAEA is also greatly appreciated.
The Board of Editors are also grateful to the United States Atomic Energy Com­ mission for financially supporting their meetings.
The editors have been particularly pleased by the close co-operation that has existed between them and the representatives of Springer-Verlag, who were always willing to meet the exacting demands made on them, many of which were beyond normal publishing requirements.
July 1968 The Editors
1. 2. Irradiation limits
1.3. Relationship between dose equivalent (absorbed dose) and fluence (flux density)
Chapter 2
Radiation Sources
2.2. Particle accelerators 0
2. 2.1. Electron accelerators 2.2.1.1. X-ray generators 2.2.1.20 Van de Graaff and other direct electron accelerators . 2.2.1.3. Betatrons and synchrotrons. . . . o . 2.2.1.4. Linear electron accelerators ("Linacs")
2.2.2. Nucleon accelerators 0 . 0 . . . 0 0 . 2.2.2.1. Nucleon accelerators in general . 2. 2. 2. 2. Proton synchrotron accelerators
2.3. Nuclear reactors . . o . o o o o o o
2. 3.1. Radiation from nuclear fission 0 2.3.1.1. Prompt fission neutrons 2.3.1.2. Delayed fission neutrons 2.3.1.3. Prompt-fission ga=a rays. 2.3.J.4. Fission-product gamma rays
2.3.2. Radiation from secondary interactions 2.3.2.1. Capture gamma rays 2.3.2.2. Gamma rays from inelastic neutron scattering 2.3.2.3. Photoneutrons . . . . 2o3.2.4. Activation gamma rays o o . o . 0 . . . .
Chapter 3
3.1. Application of the Monte Carlo method to shielding 0
3.2. Point kernel methods.
3.3o Transport method o o
3.3.1o Neutron attenuation in hydrogenous media by the method of moments
3.302. Matrix methods . . o o o o o 0
3.3.3o Direct integration methods (Niobe)
3.3.4. The discrete ordinates method (Sn)
6
12
20
20
30
36
49 49 56
101
124
127
4. 2. Photon atomic cross sections.
4.3. Broad beam attenuation . .
4. 3.1. Homogenous mixtures 4. 3.1.1. General . . . 4.3.1.2. Buildup factor 4.3.1.3. Differential energy spectra
4. 3. 2. Multilayered shields
4.4. The backscattering of photons .
4.5. Air scattering . . . . . . . .
4.5.2. Energy and angle distributions in air for gamma rays .
4.5.3. Photon fields near earth-air interface . . . . . ...
5.1. Interaction processes . . . . . .
5.2 Attenuation in hydrogenous media (Methods and results) 261
5.2.1. Diffusion and age diffusion methods 261 5.2.1.1. Two-group method . . 261 5.2.1.2. Multi-group method . . . . 264
5.2.2. Removal-diffusion combination 270 5.2.2.1. Combination diffusion methods 270 5.2.2.2. Removal-diffusion theory. . . 273
5.2.3. Removal theory . . . . . . . . . . 301 5.2.3.1. Removal cross-section method of neutron penetration 301 5.2.3.2. Energy dependent removal cross-sections in fast neutron shielding theory 305
5.3. Attenuation in non-hydrogenous media 322
5.4. Neutron scattering . . . . . . . . . 330
5.4.1. The backscattering of neutrons 330 5.4.1.1. Theory . . . . . . 330 5.4.1.2. Example . . . . . . 346
5. 4. 2. The air-scattering of neutrons 350
Chapter 6
6.1. Point and extended sources
6.2. Line sources . .
6.6. Derivation of formulae . . .
6. 7. Geometrical transformations .
363
367
368
374
387
393
403
411
7. 2. Heat generation by neutrons. . . . . . . . . . . .
7.3. Analytical solutions for heat generation distributions in regular geometric~
7.4. Temperature distribution in radiation shields
7.4.1. Introduction . . . . . . . . .
7.4.3. Heat conduction within shields: Discussion of principles aud simplified methods of analysis .......... .
417
438
441
450
450
450
453
7.4.5. Techniques for the solution of complex thermal problems . . . . . . . . . . . . . 460
7.4.6. Solution of the nondimensionalized heat conduction equation by the usc of finite integral transform techniques . . . . . . . . . . . . . . 462
7.5. Radiation induced thermal stresses in long hollow cylinders . . . . . . . . 473
Chapter 8
8. 1.1. General comments . .
8.1.2. Straight cylindrical duct.
8.1. 5. Rectangular ducts with more than one right-angle bend
8.1.6. Random voids and lumps
8.1. 7. Regular geometric void shapes
8.2. Attenuation of neutrons
8.2.1. Empty cylindrical ducts
8.2.2. Straight cylindrical ducts, filled with material differing from shield material
8.2.3. Liquid filled cylindrical ducts
8.2.4. Annular (cylindrical) ducts. 8.2.4.1. Straight ducts 8.2.4.2. Stepped ducts
8.2.5. Neutron attenuation in rectangular ducts
8.2.6. Voids in neutron shields ....... .
8.2. 7. Fast neutron dose in a material surrounding a cylindrical duct
8.3. Neutron streaming .
Chapter 9: Nuclear, Physical and Mechanical Properties and Technology of Shielding Materials
Chapter 10: Shield Design and Engineering
487
487
487
488
488
489
490
495
497
497
508
512
by H. 0. 'WYCKOFF and H. H. Rossi
1.1.1. INTRODUCTION The quantities and units useful in radiation shield­
ing have been considered on an international scale by the International Commission on Radiological Units and Measurements (ICRU) since 1928, when the roentgen was specified as a unit of what was then termed the "X-ray intensity" [I]. In 1953 the same organization defined the quantity "absorbed dose" applicable to any radiation and recommended that its (special) unit be the rad (equal to 100 ergs/g) [2]. More recent consideration of radiation quan­ tities and units by the Commission culminated in a report on the subject in 1962 [3]. Most national and other international organizations are accepting these definitions of the ICRU. The 1962 ICRU report is, therefore, a primary reference for this section of the Compendium. Direct quotations from this report and the 1963 Report of the ICRP-ICRU RBE-Committee [ 4] will appear in sans serif type in this chapter. In some instances these definitions will be followed by brief comments.
As used here the term "quantity" denotes a phy­ sical entity used for the precise description of a phenomenon and defined so as to be measurable [5]. A unit is a particular sample of a quantity of such magnitude that it is assigned the measure "1". Samples of different magnitude are then expressed by the product of their measure and the unit. A common unit is one 'vhich is the product or quotient of the fundamental units. Occasionally a unit has a special name and is associated with a particular quantity. Such units are called special units.
Thus, according to the above definition, the quantity specifies the type of phenomenon under consideration and the measure and unit indicate the magnitude. It is obvious that~except for special units-a unit by itself conveys no information regarding the type of phenomenon under conside­ ration.
The 1962 ICRU report also contains definitions of general terms that do not denote quantities in the sense referred to above:
Directly ionizing particles are charged particles ( elec­ trons, protons, <X- particles, etc.) having sufficient kinetic energy to produce ionization by collision.
1 Engineering Compendium, Vol. I
Indirectly ionizing particles are uncharged particles (neutrons, photons, etc.) which can liberate directly ionizing particles or can initiate a nuclear transformation.
Ionizing radiation is any radiation consisting of di­ rectly or indirectly ionizing particles or a mixture of both.
Comment: It is true that an indirectly ionizing par­ ticle produces an ion in the act of liberating a directly ionizing particle. For example the first step in the photo­ electric effect is that a photon ejects a high speed elec­ tron from an atom which then becomes a positive ion. Such a photon is nevertheless not considered as directly ionizing radiation since it is not a charged particle as required by the definition above.
A nuclide is a species of atom having specified num­ bers of neutrons and protons in its nucleus.
Comment: Some authors wish to distinguish between nuclear isomers by the addition of "and given nuclear energy state". However, this formulation has not vet been generally adopted. According to the definition given here, nuclear isomers constitute the same nuclide.
The energy imparted by ionizing radiation to the matter in a volume is the difference between the sum of the energies of all the directly and indirectly ionizing particles which have entered the volume and the sum of the energies of all those which have left it, minus the energy equivalent of any increase in rest mass that took place in nuclear or elementary particle reactions within the volume.
Notes: (a) The above definition is intended to be exactly equivalent to the previous meanings given by the ICRU to "energy retained by matter and made locally available" or "energy which appears as ionization, excitation, or changes of chemical bond energies". The present formulation specifies what energy is to be in­ cluded without requiring a lengthy, and possibly in­ complete, catalogue of the different types of energy transfer.
(b) Ultimately, most of the energy imparted will be degraded and appear as heat. Some of it, however, may appear as a change in interatomic bond energies. More­ over, during the degradation process the energy will diffuse and the distribution of heat produced may be different from the distribution of imparted energy. For
2 1. Dosimetric fundamentals and irradiation limits [Ref. p. 5
these reasons the energy imparted cannot always be equated with the heat produced.
(c) The quantity energy imparted to matter in a given volume is identical with the quantity often called integral absorbed dose in that volume.
Comment: This definition is provided as a basis for the definition of absorbed dose (see below).
Three general types of quantities are of interest for radiation shielding. These are material radiation quantities, physical radiation quantities and bio­ physical radiation quantities.
The first two types must be distinguished because of the statistical nature of radiation and its inter­ actions. The material quantities are those that for a given type and energy of radiation are functions of the material only-regardless of the amount of radiation received or the rate at which it is deliver­ ed. Consequently in a determination of their magnitude a sufficient number of interactions can be observed to assure that an unambiguous numeri­ cal value is obtained; that is, one with an insigni­ ficant statistical uncertainty. Hence the quotients of these quantities may be expressed as ordinary differential quotients (see Sec. 1.1.2.).
However, for quantities that are proportional to the amount of radiation received or the rate at which it is delivered, the number of interactions in a specific mass or time may be so small that sta­ tistical considerations enter. Thus the energy ab­ sorbed in a given small mass may be different from that in an adjacent equal mass and an unambiguous quotient of absorbed energy by mass can then be deduced only from an averaging process or as a result of repeated experimental determinations. The symbol Ll is employed in the definition of the quantities that may be concerned in such averaging procedures. All such quantities are listed in the section entitled "Physical Radiation Quantities"' (see Sec. 1.1.3.).
The third type of quantity considered here, the biophysical quantity, depends not only on physical considerations, but also on biological factors of importance in radiation protection. These quanti­ ties are considered in Sec. 1.1. 4.
1.1.2. MATERIAL RADIATION QUANTITffiS
The mass attenuation coefficient (p/~) of a material for indirectly ionizing particles is the quotient of dN by the product of ~. N, and dl where N is the number of particles incident normally upon a layer of thickness dl and density ~. and d N is the number of particles that experience interactions in this layer.
(1.1.-1)
Notes: (a) The term "interactions" refers to processes whereby the energy or direction of the indirectly ionizing particles is altered.
(b) For X- or gamma radiations
f.lTGGcohX -=-+-+--+-. ~ ~ ~ ~ ~
(1.1.-2)
where •I ~ is the mass photoelectric attenuation coeffi­ cient, uf ~ is the total Compton mass attenuation coeffi­ cient,Gcoh/ (!is the mass attenuation coefficient for coher­ ent scattering, and "/~ is the pair-production mass attenuation coefficient.
The mass energy transfer coefficient (PKI ~) of a material for indirectly ionizing particles is the quotient of dEK by the product of E.~ and dl, where Eis the sum of the energies (excluding rest energies) of the indirectly ionizing particles incident normally upon a layer of thick­ ness dl and density~. and dEK is the sum of the kinetic energies of all the charged particles liberated in this layer.
I'K dEK - = E'i ----,;z (1.1.-3)
Notes: (a) The relation between energy fluence and kerma may be written as
K = F PK. (1.1.-4) 1) e
(b) For X- or gamma rays of energy hv
/'K 'l'a Ga Xa -=-+-+-.
( •I ~ = the photoelectric mass attenuation coefficient, ~ = average energy emitted as fluorescent radiation per photon absorbed.) and
Ga a Ee -=fih.
( af e = total Compton mass Ee = average energy of the scattered photon.) and
"• = :!...(1 _ 2mc2 )
(1.1.-8)
("/ ~ = mass attenuation coefficient for pair production, m c2 = rest energy of the electron.)
The mass energy-absorption coefficient (Pen/e) of a material for indirectly ionizing particles is pK/e (1- G), where G is the proportion of the energy of secondary charged particles that is lost to bremsstrahlung in the material.
Notes: (a) When the material is air, Pen/~ is propor­ tional to the quotient of exposure by fluence 2).
(b) PK/~ and Pen/~ do not differ appreciably unless the kinetic energies of the secondary particles are com­ parable with or larger than their rest energy.
Comments: 1) The linear attenuation coefficient, linear energy transfer coefficient, and linear energy absorption coefficient may be obtained by multiplying the mass attenuation coefficient, mass energy transfer coefficient, and mass energy absorption coefficient, respectively, by the density of the material, f!· Similarly, the various atomic attenuation, transfer and absorption coefficients are obtained bydividingthe mass coefficients by the number of atoms per gram.
') See Sec. 1.1.3., Eqs. (1.1.-15) and (1.1.-17). ') See Sec. 1.1.3. (d).
Ref. p. 5] 1.1. Radiation quantities and units 3
2) The expressions in the notes for /len/e and pxfe assume that nuclear interactions are not important. An extra term for such interactions may be required for X- or gamma-ray energies in excess of a few MeV.
The mass stopping power Sf e of a material for charged particles is the quotient of dEs by the product of dl and e. where dEs is the average energy lost by a charged particle of specified energy in traversing a path length til, and e is the density of the medium.
S 1 dEs --e = --e (il' (1.1.-s>
Note: dEs denotes energy lost due to ionization, electronic excitation and radiation. For some purposes it is desirable to consider stopping power with the exclu­ sion of bremsstrahlung losses. In this case S must be multiplied by an appropriate factor that is less than unity.
The linear energy transfer (L) of charged particles in a medium is the quotient of dEL by dl, where dEL is the average energy locally imparted to the medium by a charged particle of specified energy in traversing a distance of dl.
L = dEL dl
(1.1.-10)
Notes: (a) The term "locally imparted" may refer either to a maximum distance from the track or to a maximum value of discrete energy loss by the particle beyond which losses are no longer considered as local. In either case the limits chosen should be specified.
(b) The concept of linear energy transfer is different from that of stopping power. The former refers to energy imparted within a limited volume, the latter to loss of energy regardless of where this energy is absorbed.
Comment: It has been suggested [ 4) that the term "locally imparted" refer to the maximum energy loss and that this energy loss (in eV) be noted by a sub­ script. Thus L 100 would be a value of L obtained when tracks due to secondary particles (delta rays) with ener­ gies of 100 eV or more are counted as separate tracks. L 00 (or LET 00) is equal to the product of mass stopping power and density.
The average energy ( W) expended in a gas per ion pair formed is the quotient of E by Nw, where Nw is the average number of ion pairs formed when a charged particle of initial kinetic energy E is completely stopped by the gas.
W=_!__, Nw
(1.1.-11)
Notes: (a) The ions arising from the absorption of bremsstrahlung emitted by the charged particles are to be counted in Nw').
(b) In certain cases it may be necessary to consider the variation in W along the path of the particle, and a differential concept is then required, but is not specific­ ally defined here.
The specific gamma ray constant (F) of a gamma­ emitting nuclide is the quotient of l' (LIXfLit) by A. where LIXfLit is the exposure rate at a distance l from a point source of this nuclide having an activity A and Ll has the meaning indicated in Sec. 1.1.1.
l 2LIX F= ALit. (1.1.-12)
,.
Special units of specific gamma ray constant are Rm2h-' Ci-' or any convenient multiple of this•).
Note: It is assumed that the attenuation in the source and along lis negligible. However, in the case of radium the value of r is determined for a filter thickness of 0.5 mm of platinum and in this case the special units are Rm 2h-'g-1 or any convenient multiple of this.
1.1.3. PHYSICAL RADIATION QUANTITIES
The particle fluence 3 ) or fluence (@) of particles is the quotient of LIN by Lla, where LIN is the number of particles which enter a sphere•) of cross-sectional area Lla and Ll has the meaning indicated in Sec. 1.1.1.
@~LIN Lla · (1.1.-13)
The particle flux density or flux density (</>) of particles is the quotient of Llrp by Lit, whereLI@ is the particle flu­ ence in time Lit and Ll has the meaning indicated in Sec. 1.1.1.
-!. = Lj(li p ~· 0~~~
Note: This quantity may also be referred to as particle fluence rate.
The energy fluence (F) of particles is the quotient of LIEF by Lla, where LIEF is the sum of the energies, ex­ clusive of rest energies, of all the particles which enter a sphere4) of cross-sectional area Lla and Ll has the meaning indicated in Sec. 1.1.1.
LIEF F =LiB' (1.1.-15)
The energy flux density or intensity (I) is the quotient ofLIF by Lit, whereLIFis the energy fluence in the time Lit and Ll has the meaning indicated in Sec. 1.1.1.
I= ~~. (1.1.-16)
Note: This quantity may also be referred to as energy fluence rate.
The kerma5 ) (K) is the quotient of LIEK by Lim, where LIEK is the sum of the initial kinetic energies of all the charged particles liberated by indirectly ionizing particles in a volume element of the specified material, Am is the mass of the matter in that volume element and Ll has the meaning indicated in Sec. 1.1.1.
LIEK K = Lim . (1.1.-17)
1) This note (a} is revised. •) In regard to the abbreviation Ci for the unit Curie see
Report on the Com. Consultatif pour les etalons de mesure des radiations ionisantes. 4e session, 1963 (Paris, Gauthier­ Villars&Co.),seeEq. (1.1.-25). ConcerningRseeEq. (1.1.-19).
a) This quantity is the same as the quantity, nvt, com­ monly used in neutron physics.
f.) This quantity is sometimes defined with reference to a plane of area Ja, instead of a sphere of cross-sectional area Lla. The plane quantity is less useful for the present purposes and it will not be defined. The two quantities are equal for a uni-directional beam of particles perpendicularly incident upon the plane area.
5) Various other methods of specifying a radiation field have been used, e.g., for a neutron source the ufirst collision dose" in a standard material at a specified point.
4 1. Dosimetric fundamentals and irradiation limits [Ref. p. 5]
Notes: {a) Since LIEK is the sum of the initial kinetic energies of the charged particles liberated by the in­ directly ionizing particles, it includes not only the kinetic energy these charged particles expend in collisions but also the energy they radiate in bremsstrahlung. The energy of any charged particles is also included when these are produced in secondary processes occuring within the volume element. Thus the energy of Auger electrons is part of LIEK.
(b) In actual measurements Lim should be so small that its introduction does not appreciably disturb the radiation field. This is particularly necessary if the medium for which kerma is determined is different from the ambient medium; if the disturbance is appreciable an appropriate correction must be applied.
{c) It may often be convenient to refer to a value of kerma rate for a specified material in free space or at a point inside a different material. In such a case the value will be that which would be obtained if a small quantity of the specified material were placed at the point of interest. It is, however, permissible to make a statement such as: "The karma for air at the pointp inside a water phantom is ... ". Recognizing that this is a shorthand version of the fuller description given above.
{d) A fundamental physical description of a radiation field is the intensity {energy flux density) at all relevant points. For the purpose of dosimetry, however, it may be convenient to describe the field of indirectly ionizing particles in terms of the kerma rate for a specified ma­ terial. A suitable material would be air for electromag­ netic radiation of moderate energies, tissue for all radia­ tions in medicine or biology, or any relevant material for studies of radiation effects.
Karma can also be a useful quantity in dosimetry when charged particle equilibrium exists at the position and in the material of interest, and bremsstrahlung losses are negligible. It is then equal to the absorbed dose at that point. In beams of X- or gamma rays or neutrons, whose energies are moderately high, transient charged-particle equilibrium can occur; in this condition the kerma is just slightly less than the absorbed dose. At very high energies the difference becomes appreciable. In general, if the range of directly ionizing particles becomes com­ parable with the mean free path of the indirectly ionizing particles, no equilibrium will exist.
The kerma rate is the quotient of LIK by Lit, where LIK is the increment in kerma in time Lit and Ll has the mean­ ing indicated in Sec. 1.1.1.
The exposure (X) is the quotient of Ll Q by Lim, where LIO is the sum of the electrical charges on all the ions of one sign produced in air when all the electrons {nega­ trons and positrons), liberated by photons in a volume element of air whose mass is Lim, are completely stopped in air and Ll has the meaning indicated in Sec. 1.1.1.
LIO X~ Lim. (1.1.-18)
1 R ~ 2.58·10-4 C/kg. (1.1.-19) 1)
1 ) This unit is numerically identical with the old one defined as 1 e.s.u. of charge per 0.001293 gram of air. Cis the abbreviation for Coulomb.
Notes: (a) The words "charges on all the ions of one sign" should be interpreted in the mathematically ab­ solute sense.
(b) The ionization arising from the absorption of bremsstrahlung emitted by the secondary electrons is notto be included inLIQ. Except forth is small difference, significant only at high energies, the exposure as defined above is the ionization equivalent of the kerma in air.
(c) With present techniques it is difficult to measur~ exposure when the photon energies involved lie above a few MeV or below a few keV.
(d) As in the case of kerma it may often be convenient to refer to a value of exposure or of exposure rate in free space or at a point inside a material different from air. In such a case the value will be that which would be determined for a small quantity of air placed at the point of interest. It is, however, permissible to make a state­ ment such as: 'The exposure atthe pointp inside a water phantom is ... ".
The exposure rate is the quotient of LIX by Lit, where LIX is the increment in exposure in time Lit and Ll has the meaning indicated in Sec. 1.1.1.
LIX Exposure rate ~ Lit . {1.1.-20)
The absorbed dose (D) is the quotient of Ll£o by Lim, where Ll£o is the energy imparted by ionizing radiation to the matter in a volume element, Lim is the mass of the matter in that volume element and L1 has the meaning indicated in Sec.1.1.1.
.1£o D ~ Lim. (1.1.-21)
The special unit of absorbed dose is the rad.
1 rad = 100 ergfg = 1/100 J/kg. (1.1.-22)
Note: J is the abbreviation for Joule.
Comment: To avoid confusion with the abbreviation for "radian" it is considered acceptable by ICRU to use the abbreviation "rd" for the "rad".
The absorbed dose rate is the quotient of LID by Lit, where LID is the increment in absorbed dose in time Lit and Ll has the meaning indicated in Sec. 1.1.1.
Absorbed dose rate = LID . Lit
(1.1.-23)
A special unit of absorbed dose rate is any quotient of the rad by a suitable unit of time (rad/d, rad/min, rad/h. etc.).
The activity {A) of a quantity of a radioactive nuclide is the quotient of LIN by Lit, where tJN is the number of nuclear transformations which occur in this quantity in time Lit and Ll has the meaning indicated in Sec. 1.1.1.
LIN A =Lit. {1.1.-24)
1 Ci = 3.7·1010 [s- 1] (exactly). (1.1.-25)
Note: In accordance with the former definition of the curie as a unit of quantity of a radioactive nuclide, it was customary and correct to say: "Y Curies of P-32 were administered ... ". It is still permissible to make such
1.1. Radiation quantities and units 5
statements rather than use the longer form which is now correct: "A quantity of P-32 was administered whose activity was Y Curies."
1.1.4. BIOPHYSICAL RADIATION QUANTITIES
1.1.4.1. DOSE EQUIVALENT
1. For protection purposes it is useful to define a quan­ tity which will be termed the "dose equivalent", (DE).
2. (DE) is defined as the product of absorbed dose, D, quality factor, (OF), dose distribution factor, (DF), and other necessary modifying factors.
(DE) = D(OF) (DF) . .... (1.1.-26)
3. The unit of dose equivalent is the "rem". The dose equivalent is numerically equal to the dose in rads multiplied by the appropriate modifying factors.
1.1.4.2. RELATION BETWEEN LAND QF
The relation between L and QF as recommended by the ICRP is given in the table below:
Table 1.1.-1. Relationship between L 00 and QF [ 4]
Loo [keVfl'm in water]
23 - 53 53 -175
10-20
1.1.4.3. EVALUATION OF DE
A joint committee of the ICRP and ICRU has considered the problem of the evaluation of DE in detail. Their recommendations [ 4] are as follows :
For a radiation involving a range of LET's the dose equivalent (DE) may be defined as:
DE= I D(L) . OF(L) . dL, 0
(1.1.-27)
where D (L) is the actual (non-normalized) dose per unit LET interval at the LET, L, and OF (L) is the quality factor for this LET.
It is useful to consider the practical problem of the assessment of DE in radiation protection surveys, since this may be carried out in a variety of ways and the choice between these will depend on the practical situation en­ countered. The accurate evaluation of DE requires a determination of absorbed dose as a function of LET. A technique has been devised to determine D (L) for particles other than electrons at LET values greater than 3.5 keV(I'm. Since the OF for virtually all electrons en­ countered in practice and for any particles having LET less than 3.5 keV(I'm is equal to unity, one may deter­ mine the D (L)oo above this limit and
lA
00
subtract the integral f D (L) dL from the total absorbed 3.5
dose 00
<f D(L) dL) 0
as measured with a tissue equivalent ionization chamber. In this way it is possible to obtain the absorbed dose delivered at an LET < 3.5 keV/1-'m which is given a OF of unity, and then to evaluate the integral
00
f D(L)·OF(L)·dL. 3.5
The total DE is given as the sum of these two terms. This method has the advantage that no explicit know­ ledge of the nature or energy of the radiation(s) is re­ quired and, for this reason, it is particularly useful in very complicated radiation fields such as exist in the vicinity of GeV accelerators. Furthermore, because it is the most exact method, it always results in the lowest value of DE since simplifications must be conservative and thus lead to overestimates. On the other hand, because of the complexity of the method and the extensive measuring equipment requirements this approach is, at present, rarely used.
Most practical DE problems consist in the evaluation of the hazard due to a mixture of neutrons and gamma radiations. The OF of neutrons as a function of neutron energy has been evaluated for neutron energies up to 10 MeV. lithe neutron energy distribution is known, the absorbed dose due to neutrons may then be multiplied by an appropriate OF to obtain the DE. If the precise neutron energy is unknown, and provided neutrons are thermal. intermediate or fast (i.e. have energies of less than 10 MeV), the absorbed doses due to neutrons and gamma rays may be evaluated separately. The sum of the former multiplied by 10 and the latter multiplied by 1 may be considered an upper limit of the DE. Finally, the simplest approach is merely to measure the total ab­ sorbed dose and multiply it by a OF of 10. While being the simplest, this method may result in an overestimate that can be as high as 10.
Comment: This formulation is applicable to dose equi­ valents of magnitudes that are less than or comparable to the maximum permissible dose equivalent. At higher doses dose rate and other factors are important, but there are as yet no firm recommendations in this area.
References [1] L. S. TAYLOR: History of the International Com­
mission on Radiological Units and Measurements (ICRU). Health Physics 1, No.3, 306 (1958).
[ 2] Recommendations of the International Commission on Radiological Units. Radiology 62, No. I, 106 (1954).
[J] Recommendations of the International Commission on Radiological Units and Measurements, Report No. lOa on Radiation Quantities and Units. Natio­ nal Bureau of Standards Handbook 84, Washing­ ton 1962.
[ 4] Report of the RBE Committee to the International Commissions on Radiological Protection and on Radiological Units and Measurements. Health Physics 9, No.4, 357 (1963).
[5] F. B. SILSBEE: Systems of Electrical Units. U. S. National Bureau of Standards, Monograph 56.
6 1. Dosimetric fundamentals and irradiation limits [Re£. p. 11
1.2. IRRADIATION LIMITS by J. MEHL
1.2.1. GENERAL CONSIDERATIONS The purpose of a radiation shield is to protect
objects that can suffer radiation damage where the irradiation can not be made less by reducing the sources' strengths, by reducing the irradiation times, or by increasing the separations between source and objects.
In order to permit adequate shielding at reason­ able cost, due consideration should be given to radiation levels which can be considered not to involve unacceptable radiation effects. Such radiation levels depend upon the response to irradiation ofthe particular object for which protec­ tion is required and on the definition of the accept­ able radiation effect.
1.2.1.1. RESPONSE OF OBJECTS TO IRRADIATION
There exists a significant difference in the radia­ tion effects in inanimate and animate objects. For inanimate objects, irradiation results in effects that manifest themselves temporarily or permanently in the irradiated object only; however, for animate objects, injuries may manifest themselves also in their descendants. Thus, in particular where ex­ posure of man must be considered, limitation of radiation levels must be governed by both, considera­ tion of radiation effects in the individual (somatic effect) and by consideration of effects to the popu­ lation (genetic effects). Normally, the response of the particular object under consideration differs with
(i) the part of the object which is irradiated, (ii) the radiation quantity,
(iii) the radiation quality, and (iv) the mode of irradiation.
If irradiation of man (or animate objects) is con­ sidered for the assessment of genetic effects, also ( v) the number of individuals subjected to radiation
and that are capable of producing descendants must be taken into account.
Irradiation of parts of the object may need conside­ ration where the object is or could possibly be near the source or within a collimated radiation beam and where shielding can be provided only for parts of the object. Normally, irradiation of the object as a whole is of interest where the object is remote from the source or in a diffuse radiation field.
The radiation quantity referred to above depends upon the source strength, the source-to-object geo­ metry'), the efficiency of shields and the time period during which the object is actually irradiated: The assessment of these factors may be complex where
(i) the source strength varies with time, (ii) the source or the object moves;
1) Unless the object is within a diffuse radiation field.
(iii) the number of sources or the number of objects which need protection exceeds unity,
and in particular where any combination of (i) - (iii) must be considered.
If the source strength varies, averaging proce­ dures can be applied. However, if the source or the object moves, numerical values of acceptable radiation levels which are applicable to the indivi­ dual object may be of little help to the designer of radiation shields. If the source is moving, it is preferable that an area around the source be defined beyond which the accepted radiation levels should not be exceeded. If the object is moving within a defined area, it is useful that radiation levels within that area do not exceed accepted limits.
Radiation quantities and units defined by ICRU (see Sec. 1.1.3.) to which reference should be made here are:
(i) exposure, X [R], (ii) absorbed dose, D [rad],
(iii) kerma, ]{ [MeVfg], (iv) energy fluence, F [MeVjcm2], and (v) particle fluence, <P [particlesorphotonsfcm2]
being the time integrals of
exposure rate [R/s], absorbed dose rate [ radjs], kerma rate [MeVjg s], energy flux density [MeVjcm' s], and particle flux density [particles orphotonsjcm's]
respectively. Design of shields is normally based on values of the flux density which apply to locations of particular interest between source and object (see Sec. 1.3.). Values of the absorbed dose are assessed where the response of irradiated objects to radiation depends on the energy absorbed per unit mass. Use of the kerma may be necessary where indirectly ionising particles (e.g. neutrons) interact with matter. For X- and gamma-radiation above a few keV up to 2 MeV data expressed in exposure values are often preferred in order to facilitate con­ trol by measurement.
Differences in energy imparted to matter per particle or photon, or differences in microscopic distribution of the absorbed energy do not affect the absorbed dose value unless the energy absorbed per unit mass is changed. Therefore the absorbed dose will be unsuitable for purpose of radiation protection where the radiation effects, either mani­ fest themselves only if the energy imparted per particle or photon exceeds certain threshold values or depend upon the microscopic distribution of th~ absorbed energy. In such cases additional factors need to be taken into account which depend upon the radiation quality.
The radiation quality is defined by the radiation type and the particle or photon energy. Absorption and scattering affects the radiation quality. It is therefore subject to variation as particles or pho-
Ref. p. 11] 1.2. Irradiation limits 7
tons interact with matter on their track from the source to the object under consideration.
Due to the microstructure of biological tissue its response to radiation depends upon the microscopic distribution of the absorbed energy. Experimental findings have proven that the response of biological tissue is related to the linear energy transfer (LET). Based upon LET values which apply to specific radiation types and particle or photon energies, quality factors, QF, were recommended by ICRP [I] which if multiplied by the corresponding ab­ sorbed dose value result in a quantity that expresses on a common scale for all ionizing radiations the irradiation incurred by persons. The name re­ commended by ICRU for this quantity is the "dose equivalent", its unit the "Rem". The radiation quantities and units listed above should therefore be supplemented by
(vi) dose equivalent, DE [rem] (see Sec. 1.1.4.)1).
Numerical values of QF are given in Sec. 1.1.4.2., Table 1.1.-1, and Sec. 1.3., Tables 1.3.-1 and 1.3.-6. It should however be pointed out here that the QF values listed in these tables do not necessarily apply to all animate objects and do certainly not apply to inanimate objects.
The mode of irradiation i. e. the way in which the radiation quantity is fractionated and the rate at which each fraction is given are known to affect somatic effects due to irradiation of man and most of the animate objects. However, it appears from theoretical and experimental studies that when either the total accumulated dose received or the dose rate is very low any somatic effects will be directly proportional to the total dose and independent of the dose rate.
A linear dose-effect relationship unaffected by dose rate is in general assumed for gene-mutations. Only at intermediate and higher levels of dose rate may gene-mutations not be independent of the dose rate. Thus, after consideration of the mode of irradiation the dose equivalent still can be accepted as a radiation quantity suitable for purposes of radiation protection of man.
Radiation effects in inanimate objects may also be affected by the mode of irradiation. The response of the object under consideration rna! significantly differ from that of man and most am­ mate objects so that detailed investi~ation ~ay ~e indicated if no information on thts question lS
readily at hand.
Where genetic effects are involved the number of individuals which need. c.o:'sideration may. be taken into account by defm1t10n of a population dose average that is relevant to the assessment of genetic injury to the whole population. The nu~er~­ cal value of that population dose average whtch lS
considered acceptable may be made up by quotas assigned to various groups of the population, each group being made up by individual~ which have a similar standing with respect to bemg exposed to
1) The maximum permissible doses (M PD) are given as dose equivalents in "rem".
lA'
ionizing radiation and the exposure levels which can be permitted.
It is obvious that the efficiency of shields should be judged upon by reduction factors which apply to that radiation quantity which can best-where ne­ cessary with appropriate factors such as the quality factor- be related to the response of the object to radiation of the specific quality under consideration. Expert advice may be required for proper specifica­ tion of shielding requirements as well as for proper interpretation of shield efficiences, where the re­ sponse of the object to radiation is complex.
1.2.1.2. ACCEPTABLE RADIATION EFFECTS The problem involved in the assessment of the
radiation effect which can be accepted for a parti­ cular object is to find a reasonable balance between the drawbacks and the benefits which would result from the acceptance of the effect.
Where irradiation results from uses of radiation sources for the benefit of mankind the governing principle is to balance these benefits against the radiation risk to man. Somatic radiation effects in man which can be considered accept­ able depend on factors which do not significantly vary between members of different races and popu­ lations. Therefore it is possible for acceptable radia­ tion effects to be agreed upon internationally. However, in the case of genetic effects the factors required to find a proper balance between risks and benefits vary from country to country so that the final decision on acceptable effects must rest with each country.
Also in the case of consumer goods, if they are extremely sensitive to ionizing radiation and if they are used throughout the world it may be desirable that agreement on acceptable radiation effects be achieved at an international level (e. g. photographic film). Where protection of the object is required for technical reasons, the advantages achieved by the reduction of the radia­ tion effect are to be balanced against the costs of the protectives measures. In such cases the accept­ able effect depends upon the technical needs and can be assessed only for each particular case in question.
1.2.2. PROTECTION OF MAN Provision of adequate protection of man against
the hazards of ionizing radiation is the common objective of all nations having an interest in uses of radiation. For that reason the work of the Inter­ national Commission on Radiological Protection (ICRP) which originated in the Second Internatio­ nal Congress of Radiology in 1928, was supported by many countries. The recommendations of the Commission on the basic principles of radiation pro­ tection of man [J] served as a basis in the esta­ blishment of conventions, basic safety standards and recommendations of the specialized Agencies of the United Nations [4] [International Labour Office (ILO), International Atomic Energy Agency (IAEA)] [ 5] and in the establishment of regional
8 1. Dosimetric fundamentals and irradiation limits [Ref. p. 11
and national regulations on radiation protection. Therefore shield design for purposes of protection of man will, in general, rely on the basic recommen­ dation of ICRP.
1.2.2.1. MAXIMUM PERMISSlliLE DOSE EQUIVALENTS
The basic concept of ICRP is to ensure protection of health by deriving from previous experience, experimental data and theoretical studies "maxi­ mum perrnissible doses" (M PD) so that doses which are below these values "involve a risk that is not unacceptable to the individual and to the popula­ tion at large". Consequently, doses which are below the maximum perrnissible values should be considered perrnissible or acceptable. The concept of the MPD can be applied only if the rates by which these doses are received are low. For that reason it was necessary to supplement 111 PD values by inforrnation on the time during which these doses can be received. The recommendations are designed to limit somatic and genetic effects. There­ fore it was necessary to reduce both the dose to the population as a whole as well as the dose to the individual as much as possible. This is done by
(a) Classification of exposed individuals into the following two categories :
(i) Adults irradiated in the course of their work.
(ii) Members of the public (this group comprises among others adults and children living in the neighbourhood of radiation areas).
(b) The establishment of MPD values for indi­ viduals of each category.
(c) The establishment of a maximum permissible genetic dose to the whole population which is to be made subject to proper apportionment between various categories of individuals.
The genetic dose to a population is assessed as the annual genetically significant dose multiplied by the mean age of child bearing. The annual genetically significant dose to a population is the average gonad dose weighted for the expected number of children.
The time period of irradiation on which theM PD values are to be based depends upon whether somatic or genetic effects are to be considered. Where somatic effects need consideration in radiation protection practice, any time period up to the lifetime of the individual is of interest. In cases where genetic effects to the population are of particular concern, the time period of irradiation on which M P D values are based is the mean age of child bearing which is normally taken to be 30 years.
It is not possible in the design of shields to take into account the special conditions under which, in ICRP regulations, allowance is made for higher doses (e. g. if the dose accumulated from previous irradiation is low, or if only a part of the body is irradiated). Maximum permissible dose values re­ commended for purposes of planning and design are derived from the maximum permissible annual doses
which apply to whole body irradiation and are given astheweeklyaverageofthat dose (see Table 1.2.-1).
Table 1.2.-1. Maximum permissible annual dose equi­ valentsa) for whole-body irradiation
Category Annual MPD [rem]
in the course of their work
Mem hers of the public 5 0.5
1/10 1/100
Annual genetically significant doseb) to the population 5/30 1/300
a) These values do not include doses received from medical procedures and from natural background radiation.
b) Allocations of this dose among the various categories of individuals depend on factors which are different from country to country. Therefore the decision must rest with the competent national authorities.
It is to be noted that the Commission decided to exclude from the proposed values contributions from medical procedures and from natural back­ ground radiation. This was necessary because these contributions vary considerably from country to country. However, the Commission recommended that these contributions should be considered sepa­ rately and that contributions from medical proce­ dures should be limited to a minimum value con­ sistent with medical requirements.
In Table 1.2.-2 are listed the maximum perrnis­ sible annual doses which include allowances that
Table 1.2.-2. Maximum permissible annual dose equi­ valents for partial-body irradiation
Organ
Gonads, red bone marrow, and in the case of uniform irra­ diation, the whole body
Skin, thyroid, bone Hands, forearms,
feet, ankles All other organs
Category of individuals Adults Members
irradiated of the in the course public of their work
[rem] [rem]
75 15
0.5 3
7.5 1.5
can be applied if the exposure of the individual is essentially restricted to portions or single organs of the body.
These values are primarily used in limiting inter­ nal radiation but can also be of guidance in such cases where shielding can be provided only for parts of the body, e. g. for the trunk of the body but not for the hands or the head of the individual.
Ref. p. 11] 1.2. Irradiation limits 9
1.2.2.2. TECHNICAL AND OPERATIONAL STANDARDS
The primary objective which should be achieved by technical and operational standards is the deri­ vation of minimum requirements of structural and operational protection so that under conditions of normal operation, irradiation of persons \vould not result in doses in excess of M PD-values.
Naturally, these requirements depend upon the type of source, the type of operation and the con­ ditions under which the operation in question is performed. It is of course not possible to consider in detail all the various types of sources which are now in use and the numerous operations for which they are used. Also it is not possible to predict in detail the conditions under which all the various operations will be perfomed in which ionising ra­ diation is involved. Therefore it was necessary to demand that operations with ionizing radiations should only be permitted if a number of minimum requirements of operational protection are fulfilled which reflect on :
(i) the administrative organisation, including a system by which notification, registration, li­ censing, recording, inspection and intervention are governed,
(ii) the physical and medical surveillance of indi­ viduals and the population, including a system by which the establishment of controlled areas, individual monitoring, area monitoring, en­ vironmental monitoring, waste processing and medical tests are governed.
Fundamental principles on which the administra­ tive organisation and the medical and physical sur­ veillance should be based are contained in the basic recommendations of ICRP [3], the convention and recommendations of ILO [ 4], and the basic safety standards of IAEA [5]. These principles have been adopted in most national standards. Therefore, in determining special requirements of structural and operational protection for specific sources and ope­ rations, it can be assumed that the operations are performed in compliance with these minimum re­ quirements of operational protection. This leaves a certain flexibility to balance adequately the de­ gree of the structural protection and the degree of operational protection to be applied to operations and sources which are suitable for more detailed consideration. Detailed international recommen­ dations and standards are primarily intended to facilitate procedures of licensing of sources to be applied throughout the world and of operations to be performed everywhere in the world in order to permit that all countries can benefit from the use of ionizing radiation under safe conditions. This applies in particular to
(i) sources which can be exempted from licensing procedures,
(ii) medical radiation sources and their operation for therapeutic and diagnostic purposes re­ spectively,
(iii) industrial radiation sources and their opera­ tion, and
(iv) the international transport of radioactive materials.
Technical and operational standards which give detailed information on structural and operational protection requirements against risks of exposure to external radiation are contained in reports of ICRP Committees [ 6, 1], detailed operational stan­ dards of IAEA [ 8, 9] and safety regulations of ILO [ 1 OJ. These standards are kept continually under. review and are periodically subject of revi­ sion. Therefore the reader is advised to check whether numerical data, to which reference is made in this section are still in compliance with the most recent recommendations of the respective organi­ sations.
\Vhcre the type of source and the respective operations are well defined it is possible to lay down the minimum requirements of structural pro­ tection which should apply to the containment of the source. In the establishment of numerical values due consideration is given to the following aspects of each source and operation in question
(i) the distance of areas around the source to which access of persons is required,
(ii) the category of persons for which access to the areas is required and the contribution to the respective lvl PD which can be permitted from the source under consideration,
(iii) the average amount of access time required for persons of the category in question to the area under consideration (occupancy factor).
In Table 1.2.-3 are listed maximum and average exposure rates of leakage radiation in the vicinity of radiation sources which for the indicated operations comply with the standards.
Minimum requirements of structural protection to be provided through primary and secondary barriers to attenuate the useful beam and the stray radiation depend in addition to the factors referred to above on the following factors:
(iv) The average radiation output of the source at which it will be operated (work load factor), and
(v) the fraction of the work load during which the useful beam is pointed in the direction of the occupied area under consideration (use factor of the barrier).
Therefore, for installations which are similar in type, it is in general not possible to express the requirements of the respective barriers in numerical values applicable to all installations of that type. Such values must be calculated separately for each installation. Detailed guidance on these calcu­ lations has been provided by ICRP for protective barriers for X- and gamma rays [ 6]. Since it is inevitable that these calculations arc based on assumptions, it is necessary to obtain evidence of their validity by methods of physical surveillance. For that reason detailed standards on structural protection arc supplemented by detailed standards on operational protection which prescribe in more detail adequate measures of physical surveillance
10 1. Dosimetric fundamentals and irradiation limits [Ref. p. 11]
Table 1.2.-3. Maximum and average exposure rates of leakage radiation in the vicinity of radiation sources which comply with standards of reference
Type of source I Type of operation Area of reference Exposure rate Reference
Ionising radiation any 11ormal not 0.1 m from surface max. < 0.1 mremfh IAEA Safety Series exempted by the of apparatus No. 9 (1962) p. 23, standards para. 5.1.1.4 (iii) without licensing
TV set normal for use by 0.05 m from surface max. < 0. 5 mRfh ICRP Pub!. 3 (1960) the public of set p. 14, para. 119;
IAEA Safety Series No. 9 (1962) p. 23, para. 5.1.1.4 (v)
Medical X- or lektherapy 0. 0 5 m from surface max. < 100 mRfh ICRP Pub!. 3 ( 19 60) gamma-ray beam control in of source housing av. < 20mR/h p. 3 and p. II, para. >IOOkV "off" position 1. 0 m from source max.< 10mR/h 82; ICRP Pub!. 4 useful beam av. < 2mR/h (1964) p. 8, para. > 100 R/h at I m 55-56
teletherapy 1 m from source max. < I R/h or beam control in except diaphragm 0.1% of useful beam, "on" position region dose rate at 1 m
from the source transmission of < 5% of useful diaphragm beam dose rate
Medical X- or teletherapy 0. 0 5 m from surface max. < 200 mRJh gamma-ray beam control in of source housing av. < 40mRfh >100kV "off" positions) 1 m from source max. < I 0 mR/h useful beam av. < 2mR/h <100 Rfh at 1m
Medical X-ray therapy at every 5 em from surface max.< 30 Rfh ICRP Pub!. 3 (1960) specified rating of of tube housing at p. 5 tube any point accessible
to patient 1 m from focus max.< 1 R/h
Medical X-ray diagnosis at every 1 m from focus max. < 100 mRfh ICRP Pub!. 3 (1960) specified rating of p. 4 tube
Industrial X- or unspecified normal 0. 0 5 m from surface max. < 100 mR/h") ICRP Pub!. 3 (1960) gamma ray beam control in of source housing av. < 20 mRjh•) p.4; ICRP Pub!. 6
"off" positions) 1 m from source max. < 10 mR/hb) (1964) p. 70 av. < 2 mRfh•)
Industrial X-ray X -ray analysis at 0. 0 5 m from surface max. < 25 mRfh ICRP Pub!. 3 (1960) every specified of tube housing p. 13, para. 106 rating
X-ray high-voltage normal use 0.05 m from surface max. < 20 mRfh ICRP Pub!. 3 (1960) generator of housing p. 7, para. 40
occupied space within a controlled
max.< 2mRfh
area
Radioactive transport in com- external surface of max. < 0.5 mRfh•) IAEA Safety Series as specified in pliance with regula- package No. 6 (1964, revi- the regulations tions applicable to sion 1965) para.
Category I packages C-3.4 in compliance with external surface of max. < 10 mRfh•) regulations applic- package able to Category II 1 m from centre of max. < 0. 5 mRfh•) packages package in compliance with external sudace of max. < 200 mR/h') regulations applica package able to Category III 1 m from centre of max. < 10 mRjh•) packages package
a) No numerical values recommended for beam control in "on" position. b) Exemption from these specifications may be permitted according to ICRP Publ. 6. C) For large external dimension packages ( > 2m), fissile packages and low specific activity materials loads maximum ex­
posure rates apply which differ from those listed in this table.
1.2. Irradiation limits 11
to be applied to operations which have been sub­ jected to detailed consideration. It is obvious that radiation safety is only maintained where evidence can be obtained that the operations arc performed in compliance with both, the requirements of structural and of operational protection.
Since the provision of detailed information on the design of adequate shields is the primary objec­ tive of this compendium, reference to the methods of calculation of the "allowable transmission" of shields is left to the respective chapters of this book. However, it is felt that the reader should be reminded in this section of some basic principles recommended by ICRP [6] by which the determi­ nation of operational protection requirements appli­ cable to radiation installations should be governed:
(i) Plans for new installations using ionising radia­ tion or modifications of existing installations involving structural shielding should be re­ viewed by the appropriate protective organi­ sation or a qualified expert before building is commenced.
(ii) The final plans of an installation should indi­ cate the types of materials and the dimensions of all protective barriers. The positions of all windows, doors, pipes andlouvcrersshall be indi­ cated in so far as they affect the protection requirements. Such plans should have the approval of the appropriate protection organi­ sation or a qualified expert.
(iii) Routine operation shall be deferred until a radiation survey has been made and the instal­ lation found to comply with the applicable standards. The survey shall be made by the appropriate protection organisation or a quali­ fied expert. A reappraisal of the protection shall be made after every change in an existing installation. (Change is construed to mean any change that is likely to increase the radiation hazards, such as increase of work load, use factor, energy of radiation or alteration of pro­ tective barriers.) The installation should be resurveyed periodically to check that condi­ tions are still safe. The results of a survey should be submitted in a formal written report.
1.2.3. PROTECTION OF GOODS, MATERIALS AND DEVICES
1.2.3.1. INTERNATIONAL RECOMMENDA­ TIONS AND STANDARDS
Fortunately there are only few consumer goods used throughout the world that are so sensitive to irradiation that agreement on acceptable radiation effects and on standards of protection is required at an international level. In fact to date reference is made in recommendations and standards of international organisations only to unprocessed photographic emulsions. The response of photo­ graphic emulsions to ionising radiation depends largely upon the type of emulsion and the radiation quality. The acceptable radiation effect must be judged upon the purpose for which the emulsion
is used. Therefore it is difficult to recommend numerical values which apply to all emulsion types and to all types of radiation.
In the transport regulations of IAEA [9] it is laid down that packages containing radioactive material "shall be kept separated from undeveloped photographic films and plates so that these are not exposed to more than 10 mR".
In ICRP recommendations [6] it is noted that "unprocessed photographic emulsions may be dam­ aged by exposure to as little as 1 mR". The diffe­ rence in these values is probably due to the fact that the ICRP value considers the lower energies to which photographic emulsions are most sensitive. These energies can normally be ecxluded from con­ sideration where only that radiation is of real con­ cern which penetrates the walls of a transport container.
It is obvious that the radiation exposure is not a very suitable measure to define the acceptable radiation effect to photographic emulsions. How­ ever, more precision in the definition of acceptable effects would lead to a system of measurements which is difficult to apply in radiation protection practice.
1.2.3.2. SPECIAL REQUIREMENTS
Specification of structural protection require­ ments may have to take into account the protection of special goods, materials and devices within the installation. At some locations radiation levels even lower than those which can be permitted for adequate protection of man may be required. Typical examples are locations of devices for low­ level radiation measurement. The minimum de­ tectable level of the radiation to be measured by such devices may be severely affected if the level of background radiation is increased or is subject to significant change. It may be necessary to per­ form a detailed analysis on the response of the instrument to the expected quality of background radiation and to specify a shielding requirement based on the maximum level of background radia­ tion which can be permitted without affecting severely the performance of the measurements in question.
At locations within useful radiation beams or within high level radiation fields, structural pro­ tection may be indicated to prevent radiation damage of goods, materials and devices which would not withstand exposure at the levels in question over the total length of the time during which they may be exposed. This applies to activation of materials by thermal neutrons, and the structural changes of substances owing to exposure to high radiation levels. Lists of materials grouped accord­ ing to radiation levels above which radiation dam­ age may occur are listed elsewhere in this compen­ dium.
References
[I] Report at the RBE Committee to the International Commission on Radiological Protection. Health Physics 9, 357-386 (1963).
12 1. Dosimetric fundamentals and irradiation limits [Ref. p. 19
[ 2] Recommendations of the International Commis~ sian on Radiological Units ancl Measurements, Report Ko. lOa on Radiation Quantities and Units. ~ational Bureau of Standards Handbook 84, Washington 1962.
[3] Recommendations of the International Commis­ sion on Radiological Protection. (Adopted Septem­ ber 17, 1965). ICRP Publication 9, London: Per­ gamon Press 1966.
[ 4] Manual of Industrial Radiation Protection, Part L Convention and Recommendation. International Labour Office, Geneva 1963.
~5] Basic Safety Standards for Radiation Protection, Safety Series No. 9 (first revision). International Atomic Energy Agency, Vienna 1965.
[6] Report of Committee III on Protection Against X-Rays up to Energies of 3 :MeV and Beta- and
Gamma~Rays from Sealed Sources. ICRP Publi­ cation 3, London: Pergamon Press 1960.
[ 7] Report of Committee IV on Protection Against Electromagnetic Radiation Above 3 MeV and Elec­ trons, Neutrons and Protons. (Adopted 1962 with revisions adopted 1963). ICRP Publication 4, London: Pergamon Press 1964.
I 8] Safe Handling of Radioisotopes. Safety Series No. 1 (first edition with revised Appendix I). International Atomic Energy Agency, Vienna 1962.
(9J Regulations for the Safe Transport of Radioactive Materials. Safety Series No. 6 (1964 Revision). International Atomic Energy Agency, Vienna 1965.
[ 1 OJ Manual of Industrial Radiation Protection, Part II: Model Code of Safety Regulations (Ionising Radia­ tions). International Labour Office, Geneva 1959.
1.3. RELATIONSHIP BETWEEN DOSE EQUIVALENT (ABSORBED DOSE) AND FLUENCE (FLUX DENSITY)
by N. G. GoussEv
For reasons explained in detail in Sec. 1. 2. \veekly averages of the maximum permissible doses recom­ mended for purposes of planning and design (see Tables 1.2.-1, -2) arc given in units of the dose equiv­ alent [rem]. However, the design o£ shields is, in general, based upon calculations of radiation quantities such as
(i) the particle fluence [number of particles or photonsfcm2] or
(ii) the energy fluence [MeVfcm2].
Therefore it is necessary to find the appropriate relationship between the respective radiation quantities.
Table 1.3.-1. Quality factors (QF) for converting absorbed doses to dose equivalents; recommended
by ICKP
Type of radiation IQF I Type of radiation I QF
Gamma rays Thermal neutrons 3.0 X-rays Neutrons, 6 ke V 2.5 Electrons ~eutrons, 20 keV 5.0 Positrons Neutrons, 100 keV 8.0 Beta rays :Neutrons, 500 keV 10.0 Alpha particles 10 Neutrons, 1 MeV 10.5 Protons 10 N cutrons, 5 :\fe V 7.0 Heavy recoil atoms 20 Neutrons, 10 MeV 6.5
It should be made clear right at the beginning of this section that there exists to date no com­ pletely reliable or recommended mathematical model to correlate these quantities. The formulas and the tabular data obtained by them presented in this section are only intended for guidance. More precision will be achieved as further knowledge is acquired. The relationship between the dose equiv­ alent and the absorbed dose received from external radiation was discussed above. The quality factors given in Table 1.3.-1 are used in this section for converting absorbed doses to dose equivalents.
\Ve shall now consider the relationship between
(i) the absorbed dose (D) measured in rad (in air) and the particle fluence (<P) measured in par­ ticles or photonsfcm2 or the energy fluence (F) measured in MeVjcm2, or
(ii) the absorbed dose rate (P) measured in radfs (in air) and the particle flux density (if;) measur­ ed in particlesfcm2s or the energy flux density (/) measured in MeVfcm2 s
and determine the values <P0 , F 0, ¢0 and I 0 which correspond to the weekly average of the M P D applicable to workers directly engaged in radiation work (0.1 rem per 168 h week or per 40 h week, respectively).
1.3.1. THE RELATIONSHIP BETWEEN ABSORBED DOSE
RATE (IN AIR) AND PARTICLE FLUX DENSITY OR ENERGY
FLUX DENSITY (X- AND GAMMA RAYS)
The relationship between the absorbed dose rate P and the particle flux density if; or energy flux density I for monoenergetic radiation of energy E [MeV per gamma quantum] under conditions of electron equilibrium is determined by the following formula:
¢ ·E ·fJa ·1.6· lo-6
~if; 1.6 ·10-8 I fJa [radfs], (1.3.-1) where
fia is the mass absorption coefficient of gamma rays in air [cm2jg], sec Table 4.1.-9,
1.6 ·to-6 is the energy equivalent in ergs of 1 :\'IeV, 100 is the energy equivalent in ergjg of 1 rad.
The results of calculations performed in [I] for the particle and energy fluences (<P and F), and the particle and energy flux densities (if; and I) cor-
Ref. p. 19] 1.3. Relationship between dose equivalent (absorbed dose) and fluence (flux density) 13
Table 1.3.-2. Energy fluence F 0 [MeVJcm2 or ergjcm2] which corresponds to an absorbed dose of 0.1 rad, and energy flux density 10 [MeVfcm2 s] or particle flux den­ sity ¢0 [quantafcm2 s] which corresponds to an absorbed dose rate P 0 = 2.5 mrad/h
( ~ 0.1 rad/ 40 hjwcek)
Dose of 0.1 rad Dose rate of 2. 5 mrad/h corresponds to corresponds to
E fla F, [MeV] [cm2jg] pieVjcm2]
0.01 4.54 1.38 ·106 0.015 1.25 5.00·106 0.02 0.502 1.24·107 0.03 0.145 4.31· 107 0.04 0. 0622 1.00·10 8
0.05 0.0376 1.66· 108 0.06 0.0287 2.18·108
0.08 0.0234 2.67· 108
0.10 0.0233 2.68 ·108 0.15 0.0268 2.33·108 0.3 0.0288 2.17 ·108
0.4 0.0296 2.11·108
1.0 0. 0280 2.23·108 1.25 0. 0268 2.33·108
1.50 0.0256 2.44· 108
2 0.0238 2.62· 108
3 0.0211 2.96·108
6 0.0172 3.63. 108
10 0.0153 4.08·108
15 0.0142 4.40· 108
20 0.0137 4.56· 108 30 0.0136 4.60·108 40 0.0136 4.60· 10' 50 0.0137 4.56· 108 60 0.0139 4.50. 108
80 0.0143 4.37 ·108
200 0.0162 3.86·108 300 0.0169 3. 70·108
400 0.0173 3.61·108
500 0.0175 3.57 ·108
600 0.0176 3.55 ·108
800 0.0178 3.51· 10 8
1 000 0.0179 3.49. 108
1 500 0.0181 3.45. 108
2 000 0.0182 3.43·108
3 000 0.0183 3.42·108
4 000 0.0184 3.40·108 5 000 0.0186 3.36·108 8 000 0.0187 3.34·108
10 000 0.0188 3.32·108
responding to a specific value of the absorbed dose (D) and of the absorbed dose rate (P), respec­ tively, are presented in Table 1.3.~2 (see also Fig. 1.3.~1).
It should be noted that, strictly speaking, Eq. (1.3.~1) can be used only up to a gamma radia­ tion energy of 3 MeV, i.e. in that range for which the definition of the exposure (X) applies.
At higher energies, where electron cquilibriun1 is difficult to attain, on1y very approximate calcu-
I
2.21 9.56 956 8.00 34.7 2 310
12.4 86.4 4 320 43.1 299 9 980
160 698 17 400 266 1150 23 100 349 1510 25 200 427 1850 23 200 429 1860 18 600 373 1620 10 800 347 1510 5 020 338 1470 3 660 336 1460 2 920 338 1470 2 440 346 1500 1 880 357 1550 1 550 373 1620 1 300 390 1700 1 130 419 1820 912 474 2060 686 515 2240 559 552 2400 480 581 2520 420 626 2710 339 653 2840 284 704 3060 204 730 3170 158 736 3190 106 736 3190 79.8 730 3170 63.4 720 3120 52.0 699 3040 37.9 685 2970 29.7 645 2800 18.7 618 2680 13.4 592 2570 8.56 578 2510 6.27 571 2480 4. 96 568 2460 4.11 562 2440 3.05 558 2420 2.42 552 2400 1.60 549 2380 1.19 547 2370 0. 790 544 2360 0.590 538 2330 0.467 534 2320 0.290 531 2310 0.231
lations are possible with Eq. (1.3.~1); in Fig. 1.3.~1, therefore, the curves are drawn as broken lines after an energy of 3 MeV is reached.
It can be seen from Fig. 1.3.~1 that in the medium-to-high energy range the particle flux density ¢y, corresponding to a specified absorbed dose rate, falls almost linearly as energy increases, whereas the energy flux density I Y in this range hardly varies \vith energy.
For medium and high energies it may be assumed
14 1. Dosimetric fundamentals and irradiation limits [Ref. p. 19
that the energy flux density I 0 corresponding to a dose rate of 0.1 rem/40 h week (2.5 mremfh) is ap­ proximately
I, ~ 2500 MeVfcm2s or 3.2·1o-• ergfcm2 s.
To a dose of 0.1 rem corresponds an energy fluence
F 0 = 3.6·108 MeVfcm' = 580 ergfcm'.
1.3.2. THE RELATIONSHIP BETWEEN ABSORBED DOSE
RATE (IN AIR) AND FLUX DENSITY OF BETA PARTICLES AND
MONOENERGETIC ELECTRONS IN BIOLOGICAL TISSUE
For monoenergetic electrons the relationship between particle flux density </> [electronsfcm2 s] and dose rate P [radfs] at the surface of biological tissue is given by the Eq. (1.3.-2)
_I_(E!._) MeVcm' 1. 6 . 10_,~ ¢em's dx g MeV d/
P= [ra s], 100 erg
g rad (1.3.-2)
where dEfdx is ionization loss of electron energy in biological tissue [in MeVcm'fg], which can be calculated with BETHE's well-known ionization loss formula').
The quantitative relationship between dose and fluence for monoenergetic electrons in the energy range from 0.01 to 10 MeV was found in [I].
The composition of the biological tissue was taken to be: H- 10%, C- 12.3%, N- 3.5%, 0- 72.9%. The numerical values of dEfdx for the different elements were taken from [ 2]. The calculated relationships between the dose equiv­ alent, and fluence for monoenergetic electrons