fundamental quantities and units for · pdf file · 2014-06-06these activities do...

FUNDAMENTAL QUANTITIES AND UNITSFOR IONIZING RADIATION (Revised)

THE INTERNATIONAL COMMISSION ONRADIATION UNITS AND

MEASUREMENTS

OCTOBER 2011

Published by Oxford University Press

ICRU REPORT No. 85

Journal of the ICRU Volume 11 No 1 2011

at Henry Ford H

ospital - Sladen Library on January 16, 2012

http://jicru.oxfordjournals.org/D

ownloaded from

http://jicru.oxfordjournals.org/

Editor’s Note

The original version of ICRU Report 85 published in the JICRU, Vol. 11, No. 1, 2011, had a number of unfor-tunate typographical errors. The ultimate responsibility for the failure to catch these errors on page proofsrests, of course, with the Editor. The basic nature of this Report and the errors in rather importantsummary tables of SI prefixes, quantities, and units, suggested strongly that a completely corrected Reportbe made available. Thus, this version (Report 85a) corrects those and other errors, and it is hoped that thiscorrected version is typographically error-free. If further errors are indeed detected, please contact theICRU so that these can be corrected in a future update.

Stephen M. SeltzerScientific Editor, JICRUGaithersburg, Maryland

at Henry Ford H



ownloaded from


FUNDAMENTAL QUANTITIES AND UNITSFOR IONIZING RADIATION (Revised)

Report Committee

S. M. Seltzer (Chairman), National Institute of Standards and Technology, Gaithersburg, Maryland USAD. T. Bartlett, Abingdon, United Kingdom

D. T. Burns, Bureau International des Poids et Mesures, Sevres, FranceG. Dietze, Braunschweig, Germany

H.-G. Menzel, European Organization for Nuclear Research (CERN), Geneva, SwitzerlandH. G. Paretzke, Institute for Radiation Protection, Neuherberg, Germany

A. Wambersie, Catholic University of Louvain, Brussels, Belgium

Consultants to the Report Committee

J. Tada, Riken Yokohama Institute, Yokohama, Japan

The Commission wishes to express its appreciation to the individuals involved in the preparation of thisReport for the time and efforts that they devoted to this task and to express its appreciation to theorganizations with which they are affiliated.

All rights reserved. No part of this book may be reproduced, stored in retrieval systems or transmitted inany form by any means, electronic, electrostatic, magnetic, mechanical photocopying, recording orotherwise, without the permission in writing from the publishers.

British Library Cataloguing in Publication Data. A Catalogue record of this book is available at the BritishLibrary.

at Henry Ford H



ownloaded from


The International Commission on Radiation Units andMeasurements

Introduction

The International Commission on Radiation Unitsand Measurements (ICRU), since its inception in1925, has had as its principal objective the develop-ment of internationally acceptable recommendationsregarding:

(1) quantities and units of radiation and radioactivity,(2) procedures suitable for the measurement

and application of these quantities in clinicalradiology and radiobiology, and

(3) physical data needed in the application of theseprocedures, the use of which tends to assureuniformity in reporting.

The Commission also considers and makes similartypes of recommendations for the radiation protec-tion field. In this connection, its work is carriedout in close cooperation with the InternationalCommission on Radiological Protection (ICRP).

Policy

The ICRU endeavors to collect and evaluatethe latest data and information pertinent to theproblems of radiation measurement and dosimetryand to recommend the most acceptable values andtechniques for current use.

The Commission’s recommendations are keptunder continual review in order to keep abreast ofthe rapidly expanding uses of radiation.

The ICRU feels that it is the responsibility ofnational organizations to introduce their owndetailed technical procedures for the developmentand maintenance of standards. However, it urgesthat all countries adhere as closely as possible tothe internationally recommended basic concepts ofradiation quantities and units.

The Commission feels that its responsibility liesin developing a system of quantities and units havingthe widest possible range of applicability. Situationscan arise from time to time for which an expedientsolution of a current problem might seem advisable.Generally speaking, however, the Commission feels

that action based on expediency is inadvisablefrom a long-term viewpoint; it endeavors to baseits decisions on the long-range advantages to beexpected.

The ICRU invites and welcomes constructivecomments and suggestions regarding its rec-ommendations and reports. These may be trans-mitted to the Chairman.

Current Program

The Commission recognizes its obligation toprovide guidance and recommendations in the areasof radiation therapy, radiation protection, and thecompilation of data important to these fields, and toscientific research and industrial applications ofradiation. Increasingly, the Commission is focusingon the problems of protection of the patient andevaluation of image quality in diagnostic radiology.These activities do not diminish the ICRU’s commit-ment to the provision of a rigorously defined set ofquantities and units useful in a very broad range ofscientific endeavors.

The Commission is currently engaged in theformulation of ICRU Reports treating the followingsubjects:

Alternatives to Absorbed Dose for Quantificationand Reporting of Low Doses and OtherHeterogeneous Exposures

Bioeffect Modeling and Biologically EquivalentDose Concepts in Radiation Therapy

Concepts and Terms for Recording and ReportingGynecologic Brachytherapy

Harmonization of Prescribing, Recording, andReporting Radiotherapy

Image Quality and Patient Dose in ComputedTomography

Key Data for Measurement Standards in theDosimetry of Ionizing Radiation

Measurement and Reporting of Radon ExposureOperational Radiation Protection Quantities for

External RadiationPrescribing, Recording, and Reporting Ion-Beam

Therapy

doi:10.1093/jicru/ndOxford University Press

# International Commission on Radiation Units and Measurements 2011

Journal of the ICRU Vol 11 No 1 (2011) Report 85

at Henry Ford H



ownloaded from


Small-Field Photon Dosimetry and Applications inRadiotherapy

The Commission continually reviews radiationscience with the aim of identifying areas in whichthe development of guidance and recommendationscan make an important contribution.

The ICRU’s Relationship with OtherOrganizations

In addition to its close relationship with the ICRP,the ICRU has developed relationships with nationaland international agencies and organizations. Inthese relationships, the ICRU is looked to forprimary guidance in matters relating to quantities,units, and measurements for ionizing radiation, andtheir applications in the radiological sciences. In1960, through a special liaison agreement, theICRU entered into consultative status with theInternational Atomic Energy Agency (IAEA).The Commission has a formal relationship with theUnited Nations Scientific Committee on the Effectsof Atomic Radiation (UNSCEAR), whereby ICRUobservers are invited to attend annual UNSCEARmeetings. The Commission and the InternationalOrganization for Standardization (ISO) informallyexchange notifications of meetings, and the ICRU isformally designated for liaison with two of the ISOtechnical committees. The ICRU also enjoys astrong relationship with its sister organization, theNational Council on Radiation Protection andMeasurements (NCRP). In essence, these organiz-ations were founded concurrently by the same indi-viduals. Presently, this long-standing relationship isformally acknowledged by a special liaison agree-ment. The ICRU also exchanges reports with thefollowing organizations:

Bureau International de Metrologie LegaleBureau International des Poids et MesuresEuropean CommissionCouncil for International Organizations of Medical

SciencesFood and Agriculture Organization of the United

NationsInternational Council for ScienceInternational Electrotechnical CommissionInternational Labour OfficeInternational Organization for Medical PhysicsInternational Radiation Protection AssociationInternational Union of Pure and Applied Physics

United Nations Educational, Scientific and CulturalOrganization

The Commission has found its relationship withall of these organizations fruitful and of substantialbenefit to the ICRU program.

Operating Funds

In recent years, principal financial support hasbeen provided by the European Commission, theNational Cancer Institute of the US Department ofHealth and Human Services, and the InternationalAtomic Energy Agency. In addition, during the last10 years, financial support has been received fromthe following organizations:

American Association of Physicists in MedicineBelgian Nuclear Research CentreCanadian Nuclear Safety CommissionElectricite de FranceHelmholtz Zentrum MunchenHitachi, Ltd.International Radiation Protection AssociationInternational Society of RadiologyIon Beam Applications, S.A.Japanese Society of Radiological TechnologyMDS NordionNational Institute of Standards and TechnologyNederlandse Vereniging voor RadiologiePhilips Medical Systems, IncorporatedRadiological Society of North AmericaSiemens Medical SolutionsUS Department of EnergyVarian Medical Systems

In addition to the direct monetary support pro-vided by these organizations, many organizationsprovide indirect support for the Commission’sprogram. This support is provided in many forms,including, among others, subsidies for (1) the timeof individuals participating in ICRU activities,(2) travel costs involved in ICRU meetings, and(3) meeting facilities and services.

In recognition of the fact that its work is madepossible by the generous support provided by allof the organizations supporting its program, theCommission expresses its deep appreciation.

Hans-Georg MenzelChairman, ICRU

Geneva, Switzerland

FUNDAMENTAL QUANTITIES AND UNITS FOR IONIZING RADIATION

at Henry Ford H



ownloaded from


Fundamental Quantities and Units for Ionizing Radiation

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2. General Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.1 Quantities and Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2 Ionizing Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.3 Stochastic and Non-Stochastic Quantities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.4 Mathematical Conventions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3. Radiometry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.1 Scalar Radiometric Quantities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113.1.1 Particle Number, Radiant Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113.1.2 Flux, Energy Flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123.1.3 Fluence, Energy Fluence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123.1.4 Fluence Rate, Energy-Fluence Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133.1.5 Particle Radiance, Energy Radiance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3.2 Vector Radiometric Quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143.2.1 Vector Particle Radiance, Vector Energy Radiance . . . . . . . . . . . . . . . . . . . . . . . 143.2.2 Vector Fluence Rate, Vector Energy-Fluence Rate . . . . . . . . . . . . . . . . . . . . . . . . 143.2.3 Vector Fluence, Vector Energy Fluence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

4. Interaction Coefficients and Related Quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

4.1 Cross Section. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174.2 Mass Attenuation Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174.3 Mass Energy-Transfer Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184.4 Mass Stopping Power. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194.5 Linear Energy Transfer (LET) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194.6 Radiation Chemical Yield . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204.7 Ionization Yield in a Gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204.8 Mean Energy Expended in a Gas per Ion Pair Formed . . . . . . . . . . . . . . . . . . . . . . . . . . 20

5. Dosimetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

5.1 Conversion of Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235.1.1 Kerma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235.1.2 Kerma Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245.1.3 Exposure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

doi:10.1093/jicru/ndr012Oxford University Press



at Henry Ford H



ownloaded from


5.1.4 Exposure Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255.1.5 Cema . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255.1.6 Cema Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

5.2 Deposition of Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265.2.1 Energy Deposit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265.2.2 Energy Imparted. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265.2.3 Lineal Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275.2.4 Specific Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275.2.5 Absorbed Dose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275.2.6 Absorbed-Dose Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

6. Radioactivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

6.1 Decay Constant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296.2 Activity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296.3 Air-Kerma-Rate Constant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33


at Henry Ford H



ownloaded from


Preface

The International Commission on Radiation Unitsand Measurements (ICRU) was originally conceivedat the First International Congress of Radiology in1925 as the International X-Ray Unit Committee,later to become the International Commission onRadiological Units before adopting its current name.Its primary objective was to provide an internation-ally agreed upon unit for measurement of radiationas applied in medicine. The ICRU established thefirst internationally acceptable unit for exposure,the rontgen, in 1928. In 1950, the ICRU expandedits role to consider all concepts, quantities, and unitsfor ionizing radiation, encompassing not onlymedical applications but also those in industry, radi-ation protection, and nuclear energy. The ICRU hascontinued to recommend new quantities and unitsas the need arose, for example, absorbed dose (1950),the rad (1953), fluence (1962), kerma (1968), andcema (1998).

Thus, quantities and units for ionizing radiationrepresent the most basic element of the core

mission of the ICRU. This is evidenced by theseries of Reports on fundamental quantities andunits: Report 10a, Radiation Quantities and Units(1962); Report 11, Radiation Quantities and Units(1968); Report 19, Radiation Quantities and Units(1971); Report 33, Radiation Quantities and Units(1980); and Report 60, Fundamental Quantitiesand Units for Ionizing Radiation (1998). This listexcludes those Reports that primarily include rec-ommendations for quantities and units specificallyintended for radiation protection, which are devel-oped in liaison and collaboration with theInternational Commission on Radiation Protection(ICRP).

The development of the present Report wasprompted by a few criticisms of Report 60, andwhile basically introducing no new quantities itdoes strive for more-precisely worded definitionsand clarity.

Stephen M. Seltzer




at Henry Ford H



ownloaded from


Abstract

Definitions of fundamental quantities, and theirunits, for ionizing radiation are given, which rep-resent the recommendation of the International

Commission on Radiation Units and Measurements(ICRU).




at Henry Ford H



ownloaded from


1. Introduction

There has been a gradual evolution in the estab-lishment and definitions of fundamental quantitiesfor ionizing radiation since the formation of theICRU (see, e.g., the series of separate Reports onquantities and units: ICRU, 1962; 1968; 1971;1980; 1998). The goal is a set of quantities (andtheir units) of use in the measurement of and intransport calculations for ionizing radiation inpractical applications. The definitions of thesequantities should be precise and logically consist-ent, and possess the utmost scientific validity andmathematical rigor. Although much progress hasbeen made toward this goal, the effort has no doubtfallen short of perfection due to compromisesamong the unavoidable ambiguities inherent in thereal natural world and the need nonetheless for abasic set of useful quantities.

This Report supersedes ICRU Report 60,Fundamental Quantities and Units for IonizingRadiation (1998). Definitions are not radicallychanged: rather, the refinements presented in thisReport mainly correct oversights in the previousReport and in some cases provide additional clarifi-cation. It was felt, however, that a new Report wouldestablish a complete current reference for funda-mental quantities and units for ionizing radiation.This Report does not deal with quantities and unitsspecifically intended for use in radiation protection,which were covered in ICRU Report 51 (1993a) andwhich are currently under review by the ICRU.

The quantities and units for ionizing radiationdealt with in this Report include those for radiome-try, interaction coefficients, dosimetry, and radioac-tivity. The ICRU appreciates the assistance renderedby scientific bodies and individuals who commentedon aspects of ICRU Report 60, and a number ofthese comments have informed the refinementsincluded in the present Report. The remainder ofthis Report is structured in five subsequent majorSections, each of the last four of which is followed bytables summarizing for each quantity its symbol,unit, and the relationship used in its definition.

Section 2 deals with terms and mathematicalconventions used throughout the Report.

Section 3, entitled Radiometry, presents quan-tities required for the specification of radiationfields. Two classes of quantities are used, referringeither to the number of particles or to the energytransported by them. Accordingly, the definitions ofradiometric quantities are grouped into pairs. Bothscalar and vector quantities are defined.

Interaction coefficients and related quantitiesare covered in Section 4. The fundamental inter-action coefficient is the cross section. All othercoefficients defined in this Section can beexpressed in terms of cross section or differentialcross section. The current Report adds the defi-nition of the ionization yield, Y, to provide alogical connection between the radiation chemicalyield and the mean energy expended in a gas perion pair formed. Explicit language is now includedin the definition of W, the mean energy expendedin a gas per ion pair formed, to clarify what ismeant by “ion pair” (ICRU, 1979) in order to avoidpossible confusion.

Section 5 deals with dosimetric quantities thatdescribe the results of processes by which particleenergy is converted and finally deposited inmatter. Accordingly, the definitions of dosimetricquantities are presented in two parts entitledConversion of Energy and Deposition of Energy,respectively. The first part includes refinement ofthe definition of g as the fraction of the kineticenergy of liberated charged particles that is lostin radiative processes in the material, and explicitspecification of dry air in the definition ofexposure. In the second part on deposition ofenergy, the definitions of kerma and of exposureare refined to explicitly include the kinetic energyof all charged particles emitted in the decay ofexcited atoms/molecules or nuclei, and consider-ation of elapsed time is acknowledged in the spe-cifications of energy imparted, particularly incases involving the production of radionuclides bythe incident particle(s). Energy deposit, i.e., theenergy deposited in a single interaction, is thebasis in terms of which all other quantities pre-sented in the Section can be defined. These are




at Henry Ford H



ownloaded from


the traditional stochastic quantities (which arenow so labeled as they are defined): energyimparted, lineal energy, and specific energy, thelatter leading to the non-stochastic quantityabsorbed dose.

Quantities related to radioactivity are defined inSection 6.

The current document strives for an incrementalimprovement in scientific rigor and yet to remainas consistent as possible with earlier ICRU Reportsin this series and in similar publications used inother fields of physics. It is hoped that this Reportrepresents a modest step toward a universal scien-tific language.


6

at Henry Ford H



ownloaded from


2. General Considerations

This Section deals with terms and mathematicalconventions used throughout the Report.

2.1 Quantities and Units

Quantities, when used for the quantitativedescription of physical phenomena or objects, aregenerally called physical quantities. A unit is aselected reference sample of a quantity with whichother quantities of the same kind are compared.Every quantity is expressed as the product of anumerical value and a unit. As a quantity remainsunchanged when the unit in which it is expressedchanges, its numerical value is modified accordingly.

Quantities can be multiplied or divided by oneanother resulting in other quantities. Thus, allquantities can be derived from a set of base quan-tities. The resulting quantities are called derivedquantities.

A system of units is obtained in the same way byfirst defining units for the base quantities, the baseunits, and then forming derived units. A system issaid to be coherent if no numerical factors otherthan the number 1 occur in the expressions ofderived units.

The ICRU recommends the use of theInternational System of Units (SI) (BIPM, 2006). Inthis system, the base units are meter, kilogram,second, ampere, kelvin, mole, and candela, for thebase quantities length, mass, time, electric current,thermodynamic temperature, amount of substance,and luminous intensity, respectively.

Some derived SI units are given special names,such as coulomb for ampere second. Other derivedunits are given special names only when they areused with certain derived quantities. Specialnames pertaining to ionizing radiation currently inuse in this restricted category are becquerel (equalto reciprocal second for activity of a radionuclide),gray (equal to joule per kilogram for absorbed dose,kerma, cema, and specific energy), and sievert(equal to joule per kilogram for dose equivalent,ambient dose equivalent, directional dose equival-ent, and personal dose equivalent). Some examplesof SI units are given in Table 2.1.

There are also a few units outside of the inter-national system that may be used with SI. Forsome of these, their values in terms of SI units areobtained experimentally. Two of these are used incurrent ICRU documents: electron volt (symbol eV)and (unified) atomic mass unit (symbol u). Others,such as day, hour, and minute, are not coherentwith the system but, because of long usage, are per-mitted to be used with SI (see Table 2.2).

Decimal multiples and submultiples of SI unitscan be formed using the SI prefixes (see Table 2.3).

2.2 Ionizing Radiation

Ionization produced by particles is the process bywhich one or more electrons are liberated in col-lisions of the particles with atoms or molecules.This can be distinguished from excitation, which isa transfer of electrons to higher energy levels inatoms or molecules and generally requires lessenergy.

When charged particles have slowed down suffi-ciently, ionization becomes less likely or impossible,and the particles increasingly dissipate theirremaining energy in other processes such as exci-tation or elastic scattering. Thus, near the end oftheir range, charged particles that were ionizingcan be considered to be non-ionizing.

The term ionizing radiation refers to chargedparticles (e.g., electrons or protons) and unchargedparticles (e.g., photons or neutrons) that canproduce ionizations in a medium or can initiatenuclear or elementary-particle transformationsthat then result in ionization or the production ofionizing radiation. In the condensed phase, thedifference between ionization and excitation canbecome blurred. A pragmatic approach for dealingwith this ambiguity is to adopt a threshold for theenergy that can be transferred to the medium. Thisimplies cutoff energies below which charged par-ticles may be assumed not to be ionizing (unlessthey can initiate nuclear or elementary-particletransformations). Below such energies, theirranges are minute. Hence, the choice of the cutoffenergies does not materially affect the spatial




at Henry Ford H



ownloaded from


distribution of energy deposition except at thesmallest distances that can be of concern in micro-dosimetry. The choice of the threshold valuedepends on the application; for example, a value of10 eV might be appropriate for radiobiology.

2.3 Stochastic and Non-StochasticQuantities

Differences between results from repeated obser-vations are common in physics. These can arise

from imperfect measurement systems, or from thefact that many physical phenomena are subject toinherent fluctuations. Quantum-mechanical issuesaside, one often needs to distinguish between anon-stochastic quantity with its unique value and astochastic quantity, the values of which follow aprobability distribution. In many instances, thisdistinction is not significant because the probabilitydistribution is very narrow. For example, themeasurement of an electric current commonlyinvolves so many electrons that fluctuations con-tribute negligibly to inaccuracy in the

Table 2.1. SI units used in this Report

Category of units Quantity Name Symbol

SI base units length meter mmass kilogram kgtime second samount of substance mole mol

SI derived units electric charge coulomb Cwith special names energy joule J(general use) solid angle steradian sr

power watt W

SI derived units activity becquerel Bqwith special names absorbed dose, kerma, gray Gy(restricted use) cema, specific energy

Table 2.3. SI prefixesa

Factor Prefix Symbol Factor Prefix Symbol

1024 yotta Y 1021 deci d1021 zetta Z 1022 centi c1018 exa E 1023 milli m1015 peta P 1026 micro m

1012 tera T 1029 nano n109 giga G 10212 pico p106 mega M 10215 femto f103 kilo k 10218 atto a102 hecto h 10221 zepto z101 deca da 10224 yocto y

aThe prefix symbol attached to the unit symbol constitutes a new symbol, e.g., 1 fm2 ¼ (10215 m)2 ¼ 10230 m2.

Table 2.2. Some units used with the SI

Category of units Quantity Name Symbol

Units widely used time minute minhour hday d

Units whose values in SI areobtained experimentally

energy electron volta eVmass (unified) atomic mass unita u

a1 eV ¼ 1.602176487(40) � 10219 J, and 1 u ¼ 1.660538782(83) � 10227 kg. The digits in parentheses are the one-standard-deviationuncertainty in the last digits of the given value (Mohr et al., 2008).


8

at Henry Ford H



ownloaded from


measurement. However, as the limit of zero electriccurrent is approached, fluctuations can becomemanifest. This case of course requires a morecareful measurement procedure, but perhaps moreimportantly illustrates that the significance of sto-chastic variations of a quantity can depend on themagnitude of the quantity. Similar considerationsapply to ionizing radiation; fluctuations can play asignificant role, and in some cases need to be con-sidered explicitly. On a practical level, this Reportadopts the convention that a quantity whose under-lying distribution at microscopic levels is normallyof little interest and that is customarily expressedin terms of a mean value will not be defined expli-citly as stochastic.

Certain stochastic processes follow a Poisson dis-tribution, a distribution uniquely determined by itsmean value. A typical example of such a process isradioactive decay.1 However, more complex distri-butions are involved in energy deposition. In thisReport, because of their relevance, four stochasticquantities are defined explicitly, namely energydeposit, 1i (see Section 5.2.1), energy imparted, 1

(see Section 5.2.2), lineal energy, y (see Section5.2.3), and specific energy, z (see Section 5.2.4). Forexample, the specific energy, z, is defined as thequotient of the energy imparted, 1, and the mass,m. Repeated measurements would provide an esti-mate of the probability distribution of z and of itsfirst moment or mean, �z, the latter approaching theabsorbed dose, D (see Section 5.2.5), as the massbecomes small. Knowledge of the distribution of zis not required for the determination of theabsorbed dose, D. However, knowledge of the distri-bution of z corresponding to a known D can beimportant because in the irradiated mass element,m, the effects of radiation can be more closelyrelated to z than to D, and the values of z can differgreatly from D for small values of m (e.g., biologicalcells).

2.4 Mathematical Conventions

To permit characterization of a radiation fieldand its interactions with matter, many of the quan-tities defined in this Report are considered as func-tions of other quantities. For simplicity inpresentation, the arguments on which a quantity

depends often will not be stated explicitly. In someinstances, the distribution of a quantity withrespect to another quantity can be defined. The dis-tribution function of a discrete quantity, such asthe particle number N (see Section 3.1.1), will betreated as if it were continuous, as N is usually avery large number. Distributions with respect toenergy are frequently required, as are other differ-ential forms of defined quantities. This Reportfollows the previous practice of often introducingintegral forms of quantities prior to their represen-tation in differential forms. For example, fluence isdefined at the start of Section 3.1.3, followed bythat of the distribution of fluence with respect toparticle energy, given by (see Eq. 3.1.8a)

FE ¼ dF=dE; ð2:4:1Þ

where dF is the fluence of particles of energybetween E and E þ dE. Such distributions withrespect to energy are denoted in this Report byadding the subscript E to the symbol of the distrib-uted quantity. This results in a change of physicaldimensions; thus, the unit of F is m22, whereas theunit of FE is m22 J21 (see Tables 3.1 and 3.2).

Quantities related to interactions, such as themass attenuation coefficient, m/r, (see Section 4.2)or the mass stopping power, S/r (see Section 4.4),are functions of the particle type and energy, andone might, if necessary, use a more explicit notationsuch as m(E)/r or S(E)/r. For a radiation field withan energy distribution, mean values such as �m=rand �S=r, weighted according to the distribution ofthe relevant quantity, are often useful. Forexample,

�m

r¼ÐmðEÞ=r½ �FE dEÐ

FE dE

¼ 1

F

ðmðEÞ=r½ �FE dE

� �ð2:4:2Þ

is the fluence-weighted mean value of m/r.Stochastic quantities are associated with prob-

ability distributions. Two types of such distri-butions are considered in this Report, namely thedistribution function (symbol F) and the probabilitydensity (symbol f ). For example, F(y) is the prob-ability that the lineal energy is equal to or lessthan y. The probability density f(y) is the derivativeof F(y), with f(y) being the probability that thelineal energy is between y and y þ dy.

1Radioactive decay is inherently governed by the binomialdistribution. However, for sufficiently large values of thenumber of radioactive atoms that one usually deals with, thePoisson distribution is an excellent approximation of thebinomial distribution.

General Considerations

9

at Henry Ford H



ownloaded from


3. Radiometry

Radiation measurements and investigations ofradiation effects require various degrees of specifi-cation of the radiation field at the point of interest.Radiation fields consisting of various types of par-ticles, such as photons, electrons, neutrons, orprotons, are characterized by radiometric quan-tities that apply in free space and in matter.

Two classes of quantities are used in the charac-terization of a radiation field, referring either tothe number of particles or to the energy trans-ported by them. Accordingly, most of the definitionsof radiometric quantities given in this Report canbe grouped into pairs.

Both scalar and vector quantities are used inradiometry, and here they are treated separately.Formal definitions of quantities deemed to be ofparticular relevance are presented in boxes.Equivalent definitions that are used in particularapplications are given in the text. Distributions ofsome radiometric quantities with respect to energyare given when they will be required later in theReport. This extended set of quantities relevant toradiometry is summarized in Tables 3. 1 and 3. 2.

3.1 Scalar Radiometric Quantities

Consideration of radiometric quantities beginswith the definition of the most general quantitiesassociated with the radiation field, namely the par-ticle number, N, and the radiant energy, R (seeSection 3.1.1). The full description of the radiationfield, however, requires information on the typeand the energy of the particles as well as on theirdistributions in space, direction, and time. Thismost differential form is the basic field quantityfrom a radiation-transport perspective, and defi-nitions of quantities in terms of integrals of such aquantity might seem to better represent mathemat-ical rigor. However, the physical processes relevanthere do not preclude differentiation. Thus, in thepresent Report, the specification of the radiationfield is achieved with increasing detail by definingscalar radiometric quantities through successivedifferentiations of N and R with respect to time,area, volume, direction, or energy.2 Thus, these

quantities relate to a particular value of each vari-able of differentiation. This procedure provides thesimplest definitions of quantities such as fluenceand energy fluence (see Section 3.1.3), often usedin the common situation in which radiation inter-actions are independent of the direction and timedistribution of the incoming particles.

The scalar radiometric quantities defined in thisReport are used also for fields of optical and ultra-violet radiations, sometimes under different names.In this Report, the equivalence between thevarious terminologies is often noted in connectionwith the relevant definitions.

3.1.1 Particle Number, Radiant Energy

The particle number, N, is the number of par-ticles that are emitted, transferred, or received.

Unit: 1

The radiant energy, R, is the energy (excludingrest energy) of the particles that are emitted,transferred or received.

Unit: J

For particles of energy E (excluding rest energy),the radiant energy, R, is equal to the product NE.

The distributions, NE and RE, of the particlenumber and the radiant energy with respect toenergy are given by

NE ¼ dN=dE; ð3:1:1aÞ

and

RE ¼ dR=dE; ð3:1:1bÞ

where dN is the number of particles with energybetween E and E þ dE, and dR is their radiantenergy. The two distributions are related by

RE ¼ ENE: ð3:1:2Þ

2Mathematically, the differentials are understood to be ofexpected or mean values of the quantities.




at Henry Ford H



ownloaded from


The particle number density3, n, is given by

n ¼ dN=dV; ð3:1:3aÞ

where dN is the number of particles in the volume dV.Similarly, the radiant energy density, u, is given by

u ¼ dR=dV: ð3:1:3bÞ

The distributions, nE and uE, of the particle numberdensity and the radiant energy density with respectto energy are given by

nE ¼ dn=dE; ð3:1:4aÞ

and

uE ¼ du=dE: ð3:1:4bÞ

The two distributions are related by

uE ¼ EnE: ð3:1:5Þ

3.1.2 Flux, Energy Flux

The flux, _N, is the quotient of dN by dt, wheredN is the increment of the particle number inthe time interval dt, thus

_N ¼ dN

dt:

Unit: s2l

The energy flux, _R, is the quotient of dR by dt,where dR is the increment of radiant energy inthe time interval dt, thus

_R ¼ dR

dt:

Unit: W

These quantities frequently refer to a limitedspatial region, e.g., the flux of particles emergingfrom a collimator. For source emission, the flux of par-ticles emitted in all directions is generally considered.

For visible light and related electromagnetic radi-ations, the energy flux is defined as power emitted,transmitted, or received in the form of radiation andtermed radiant flux or radiant power (CIE, 1987).

The term flux has been employed in other textsfor the quantity termed fluence rate in the presentReport (see Section 3.1.4). This usage is discour-aged because of the possible confusion with theabove definition of flux.

3.1.3 Fluence, Energy Fluence

The fluence, F, is the quotient of dN by da,where dN is the number of particles incident ona sphere of cross-sectional area da, thus

F ¼ dN

da:

Unit: m22

The energy fluence, C, the quotient of dR by da,where dR is the radiant energy incident on asphere of cross-sectional area da, thus

C ¼ dR

da:

Unit: J m22

The use of a sphere of cross-sectional area daexpresses in the simplest manner the fact that oneconsiders an area da perpendicular to the directionof each particle. The quantities fluence and energyfluence are applicable in the common situation inwhich radiation interactions are independent of thedirection of the incoming particles. In certain situ-ations, quantities (defined below) involving thedifferential solid angle, dV, in a specified directionare required.

In dosimetric calculations, fluence is frequentlyexpressed in terms of the lengths of the particle trajec-tories. It can be shown (Papiez and Battista, 1994;and references therein) that the fluence, F, is given by

F ¼ dl

dV; ð3:1:6Þ

where dl is the sum of the lengths of particle trajec-tories in the volume dV.

For a radiation field that does not vary over thetime interval, t, and is composed of particles withvelocity v, the fluence, F, is given by

F ¼ nvt; ð3:1:7Þ

where n is the particle number density.

3This quantity was previously termed volumic particle number(ICRU, 1998). Recognizing that the terms volumic and massicare not commonly used in English, this Report reverts to theconvention (IUPAC, 1997) that density indicates per volume andspecific indicates per mass (additionally, surface . . . densityindicates per area, linear . . . density indicates per length, andrate indicates per time). However, the adjectives massic ¼ permass, volumic ¼ per volume, areic ¼ per area, and lineic ¼ perlength (ISO, 1993) are acceptable and recognized for theirconvenience.


12

at Henry Ford H



ownloaded from


The distributions, FE and CE, of the fluence andenergy fluence with respect to energy are given by

FE ¼dF

dE; ð3:1:8aÞ

and

CE ¼dC

dE; ð3:1:8bÞ

where dF is the fluence of particles of energybetween E and E þ dE, and dC is their energyfluence. The relationship between the two distri-butions is given by

CE ¼ EFE: ð3:1:9Þ

The energy fluence is related to the quantityradiant exposure defined, for fields of visible light,as the quotient of the radiant energy incident on asurface element by the area of that element (CIE,1987). When a parallel beam is incident at an angleu with the normal direction to a given surfaceelement, the radiant exposure is equal to C cos u.

3.1.4 Fluence Rate, Energy-Fluence Rate

The fluence rate, F , is the quotient of dF by dt,where dF is the increment of the fluence in thetime interval dt, thus

F ¼ dF

dt:

Unit: m22 s2l

The energy-fluence rate, C , is the quotient of dCby dt, where dC is the increment of the energyfluence in the time interval dt, thus

C ¼ dC

dt:

Unit: W m22

In radiation-transport literature, these quantitieshave also been termed particle flux density andenergy flux density, respectively. Because the worddensity has several connotations, the term fluencerate is preferred.

For a radiation field composed of particles of vel-ocity v, the fluence rate, F , is given by

F ¼ nv; ð3:1:10Þ

where n is the particle number density.

3.1.5 Particle Radiance, Energy Radiance

The particle radiance, FV, is the quotient of dFby dV, where dF is the fluence rate of particlespropagating within a solid angle dV around aspecified direction, thus

FV ¼dF

dV:

Unit: m22 s21 sr21

The energy radiance, CV, is the quotient of dCby dV, where dC is the energy fluence rate ofparticles propagating within a solid angle dVaround a specified direction, thus

CV ¼dC

dV:

Unit: W m22 sr21

The specification of a direction requires twovariables. In a spherical coordinate system withpolar angle u and azimuthal angle w, dV is equal tosin u du dw.

For visible light and related electromagneticradiations, the particle radiance and energy radi-ance are termed photon radiance and radiance,respectively (CIE, 1987).

The distributions of particle radiance and energyradiance with respect to energy are given by

FV;E ¼dFV

dE; ð3:1:11aÞ

and

CV;E ¼dCV

dE; ð3:1:11bÞ

where dF V is the particle radiance for particles ofenergy between E and E þ dE, and dC V is theirenergy radiance. The two distributions are relatedby

CV;E ¼ EFV;E: ð3:1:12Þ

The quantity F V;E is sometimes termed angularflux or phase flux in radiation-transport theory.

Apart from aspects that are of minor importancein the present context (e.g., polarization), the fieldof any radiation of a given particle type is comple-tely specified by the distribution, FV;E, of the par-ticle radiance with respect to particle energy, asthis defines number, energy, local density, andarrival rate of particles propagating in a given

Radiometry

13

at Henry Ford H



ownloaded from


direction. This quantity, as well as the distributionof the energy radiance with respect to energy, canbe considered as basic in radiometry.

3.2 Vector Radiometric Quantities

As radiometric quantities are primarily con-cerned with the flow of radiation, it is appropriateto consider some of them as vector quantities.Vector quantities are not needed in those cases forwhich the corresponding scalar quantities areappropriate, e.g., in deriving dosimetric quantitiesthat are independent of the particle direction. Inother instances, vector quantities are useful, andthey are important in theoretical considerationsrelated to radiation fields and dosimetric quan-tities. There is, in general, no simple relationshipbetween the magnitudes of a scalar quantity andthe corresponding vector quantity. However, in thecase of a unidirectional field, they are of equal mag-nitude. The use of boldface symbols distinguishesthe vector quantities introduced in this Sectionfrom the corresponding scalar quantities.

The vector quantities, defined in this Section, areobtained by successive integrations of the quan-tities vector particle radiance and vector energyradiance (see Section 3.2.1). Vector quantities areused extensively in radiation-transport theory, butoften with a different terminology. The equival-ences are indicated for the convenience of thereader.

3.2.1 Vector Particle Radiance, VectorEnergy Radiance

The vector particle radiance, FV, is the productof V by FV , where V is the unit vector in thedirection specified for the particle radiance FV,thus

FV ¼ VFV:

Unit: m22 s2l sr21

The vector energy radiance, CV, is the productof V by CV, where V is the unit vector in thedirection specified for the energy radiance CV ,thus

CV ¼ VC V:

Unit: W m22 sr2l

The magnitudes jFVj and jCVj are equal to FV

and CV, respectively.

The distributions FV;E and CV;E of the vectorparticle radiance and the vector energy radiance,with respect to energy, are given by

FV;E ¼ VFV;E; ð3:2:1aÞ

and

CV;E ¼ VCV;E; ð3:2:1bÞ

where FV;E and CV;E are the distributions of theparticle radiance and the energy radiance, respect-ively, with respect to energy.

In radiation-transport theory, FV;E is sometimescalled angular current density, phase-space currentdensity, or directional flux.

3.2.2 Vector Fluence Rate, VectorEnergy-Fluence Rate

The vector fluence rate, F , is the integral of FV

with respect to solid angle, where FV is thevector particle radiance in the direction specifiedby the unit vector V, thus

F ¼ðFV dV:

Unit: m22 s21

The vector energy-fluence rate, C , is the integralof CV with respect to solid angle, where CV isthe vector energy radiance in the direction speci-fied by the unit vector V, thus

C ¼ðCV dV:

Unit: W m22

The vectorial integration determines both direc-tion and magnitude of the vector fluence rate andof the vector energy-fluence rate. The scalar quan-tities fluence rate and energy-fluence rate can beobtained in a similar way according to

F ¼ðFV dV; ð3:2:2aÞ

and

C ¼ðCV dV: ð3:2:2bÞ

It is important that these quantities not be con-fused with the vector counterparts. In particular, itneeds to be recognized that the magnitude of vectorfluence rate and of vector energy-fluence rate


14

at Henry Ford H



ownloaded from


Panos

Highlight

change from zero in an isotropic field to F and C

in a unidirectional field.The vector fluence rate is sometimes referred to

as current density in radiation-transport theory.

3.2.3 Vector Fluence, Vector Energy Fluence

The vector fluence, F, is the integral of F withrespect to time, t, where F is the vector fluencerate, thus

F ¼ðFdt:

Unit: m22

The vector energy fluence, C, is the integral ofC with respect to time, t, where C is the vectorenergy-fluence rate, thus

C ¼ðCdt:

Unit: J m22

The distributions FE and CE of the vector fluenceand vector energy fluence, with respect to energyare given by

FE ¼dF

dE¼ðFEdt; ð3:2:3aÞ

and

CE ¼dC

dE¼ðCEdt; ð3:2:3bÞ

where dF is the vector fluence of particles ofenergy between E and E þ dE, and dC is theirvector energy fluence.

The vector energy fluence, C, can be obtainedfrom the distribution F V;E according to

C ¼ððð

VEFV;Edt dV dE: ð3:2:4Þ

It should be noted that the (vectorial) integrationof FV;E over time, energy, and solid angle resultsin a point function in space, but this is not thecase when the integration is over area. It ismeaningful to integrate, for instance, the scalarproduct C . da over a given area a to obtain thenet flow of radiant energy through this area.Integration with respect to a particular surfacemust take account of the (three-dimensional)shape of the surface and its orientation, becausethe number of particles in a given direction,intercepted by a surface, depends on the angle ofincidence.

Table 3.1. Scalar radiometric quantities

Namea Symbol Unit Definition Appearance in the Report

particle number N 1 – Section 3.1.1radiant energy R J – Section 3.1.1energy distribution of particle number NE J21 dN/dE Eq. 3.1.1aenergy distribution of radiant energy RE 1 dR/dE Eq. 3.1.1bparticle number density n m23 dN/dV Eq. 3.1.3aradiant energy density u J m23 dR/dV Eq. 3.1.3benergy distribution of particle number density nE m23 J21 dn/dE Eq. 3.1.4aenergy distribution of radiant energy density uE m23 du/dE Eq. 3.1.4bflux _N s21 dn/dt Section 3.1.2energy flux _R W dR/dt Section 3.1.2energy distribution of flux _NE s21 J21 dN/dE –energy distribution of energy flux _RE s21 dR/dE –fluence F m22 dN/da Section 3.1.3energy fluence C J m22 dR/da Section 3.1.3energy distribution of fluence FE m22 J21 dF/dE Eq. 3.1.8aenergy distribution of energy fluence CE m22 dC/dE Eq. 3.1.8bfluence rate F m22 s21 dF/dt Section 3.1.4energy-fluence rate C W m22 dC/dt Section 3.1.4energy distribution of fluence rate FE m22 s21 J21 dF=dE –energy distribution of energy-fluence rate CE m22 s21 dC=dE –particle radiance F V m22 s21 sr21 dF=dV Section 3.1.5energy radiance _CV W m22 sr21 dC =dV Section 3.1.5energy distribution of particle radiance FV;E m22 s21 sr21 J21 dFV=dE Eq. 3.1.11aenergy distribution of energy radiance CV;E m22 s21 sr21 dC V=dE Eq. 3.1.11b

aThe expression “distribution of a quantity with respect to energy” has been replaced in this table by the shorthand expression “energydistribution of the quantity.”

Radiometry

15

at Henry Ford H



ownloaded from


Table 3.2. Vector radiometric quantities

Namea Symbol Unit Definition Appearance in the Report

vector particle radiance FV m22 s21 sr21 VFV Section 3.2.1vector energy radiance CV W m22 sr21 VC V Section 3.2.1energy distribution of vector particle radiance FV;E m22 s21 sr21 J21 V _FV;E Eq. 3.2.1aenergy distribution of vector energy radiance CV;E m22 s21 sr21 VCV;E Eq. 3.2.1bvector fluence rate F m22 s21

ÐFVdV Section 3.2.2

vector energy-fluence rate C W m22ÐCVdV Section 3.2.2

energy distribution of vector fluence rate FE m22 s21 J21ÐFV;EdV –

energy distribution of vector energy-fluence rate CE m22 s21ÐCV;EdV –

vector fluence F m22ÐFdt Section 3.2.3

vector energy fluence C J m22ÐCdt Section 3.2.3

energy distribution of vector fluence FE m22 J21ÐFEdt Eq. 3.2.3a

energy distribution of vector energy fluence CE m22ÐCEdt Eq. 3.2.3b

aThe expression “distribution of a quantity with respect to energy” has been replaced in this table by the shorthand expression “energydistribution of the quantity.”


16

at Henry Ford H



ownloaded from


4. Interaction Coefficients and Related Quantities

Interaction processes occur between radiationand matter. In an interaction, the energy or thedirection (or both) of the incident particle is alteredor the particle is absorbed. The interaction mightbe followed by the emission of one or several sec-ondary particles. The likelihood of such inter-actions is characterized by interaction coefficients.They refer to a specific interaction process, typeand energy of radiation, and target or material.

The fundamental interaction coefficient is thecross section (see Section 4.1). All other interactioncoefficients defined in this Report can be expressedin terms of cross sections or differential crosssections.

Interaction coefficients and related quantitiesdiscussed in this Section are listed in Table 4.1.

4.1 Cross Section

The cross section, s, of a target entity, for aparticular interaction produced by incidentcharged or uncharged particles of a given typeand energy, is the quotient of N by F, where N isthe mean number of such interactions per targetentity subjected to the particle fluence F, thus

s ¼ N

F:

Unit: m2

A special unit often used for the cross section isthe barn, b, defined by

1 b ¼ 10�28 m2 ¼ 100 fm2:

A full description of an interaction process requires,among other things, the knowledge of the distri-butions of cross sections in terms of energy anddirection of all emergent particles resulting fromthe interaction. Such distributions, sometimescalled differential cross sections, are obtained bydifferentiations of s with respect to energy of emer-gent particles and solid angle.

If incident particles of a given type and energycan undergo different and independent types ofinteraction in a target entity, the resulting crosssection, sometimes called the total cross section, s,is expressed by the sum of the component cross sec-tions, sj, hence

s ¼X

J

sJ ¼1

F

XJ

NJ; ð4:1:1Þ

where NJ is the mean number of interactions oftype J per target entity subjected to the particlefluence F, and sJ is the component cross sectionrelating to an interaction of type J.

4.2 Mass Attenuation Coefficient

The mass attenuation coefficient, m/r, of amaterial, for uncharged particles of a given typeand energy, is the quotient of dN/N by rdl,where dN/N is the mean fraction of the particlesthat experience interactions in traversing a dis-tance dl in the material of density r, thus

m

r¼ 1

r d l

dN

N:

Unit: m2 kg21

The quantity m is the linear attenuation coeffi-cient. The probability that at normal incidence anuncharged particle undergoes an interaction in amaterial layer of thickness dl is mdl.

The reciprocal of m is called the mean free path ofan uncharged particle.

The linear attenuation coefficient, m, depends onthe density, r, of the material. This dependence islargely removed by using the mass attenuationcoefficient, m/r.

The mass attenuation coefficient can beexpressed in terms of the total cross section, s. Themass attenuation coefficient is the product of s andNA/M, where NA is the Avogadro constant, and M is




at Henry Ford H



ownloaded from


the molar mass of the target material, thus

m

r¼ NA

Ms ¼ NA

M

XJ

sJ; ð4:2:1Þ

where sJ is the component cross section relating toan interaction of type J.

Relationship 4.2.1 can be written as

m

r¼ nt

rs; ð4:2:2Þ

where nt is the number density of target entities,i.e., the number of target entities in a volumeelement divided by its volume.

The mass attenuation coefficient of a compoundmaterial is usually treated as if the latter consistedof independent atoms. Thus,

m

r¼ 1

r

XL

ðntÞL sL ¼1

r

XL

ðntÞLX

J

sL;J; ð4:2:3Þ

where (nt)L is the number density of target entitiesof type L, sL the total cross section for an entity L,and sL,J the cross section of an interaction of typeJ for a single target entity of type L. Relationship4.2.3, which ignores the effects on the cross sec-tions of the molecular, chemical, or crystallineenvironment of an atom, is justified in most cases,but can occasionally lead to errors, for example, inthe interaction of low-energy photons with mol-ecules (Hubbell, 1969) and in the interaction ofslow neutrons with molecules, particularly thosecontaining hydrogen (see, e.g., Caswell et al., 1982;Houk and Wilson, 1967; Rauch, 1994).

4.3 Mass Energy-Transfer Coefficient

The mass energy-transfer coefficient, mtr /r, of amaterial, for uncharged particles of a given typeand energy, is the quotient of dRtr/R by rdl,where dRtr is the mean energy that is trans-ferred to kinetic energy of charged particles byinteractions of the uncharged particles of inci-dent radiant energy R in traversing a distancedl in the material of density r, thus

mtr

r¼ 1

r d l

dRtr

R:

Unit: m2 kg21

The binding energies of the liberated chargedparticles are not to be included in dRtr. However,

binding energies are usually assumed negligibleand thus included in calculations of the massenergy-transfer coefficient for photons. In materialsconsisting of elements of modest atomic number,such an inconsistency with the definition canbecome important for photons with energies below1 keV. In addition, the decay of excited nuclearstates produced by interactions can contributecharged particles; this process is usually notincluded in evaluation of the mass energy-transfercoefficient for photons, but rather is treated as aseparate source term in dosimetry calculations.

If incident uncharged particles of a given typeand energy can produce several types of indepen-dent interactions in a target entity, the massenergy-transfer coefficient can be expressed interms of the component cross sections, sJ, by therelationship

mtr

r¼ NA

M

XJ

fJsJ; ð4:3:1Þ

where fJ is the quotient of the mean energy trans-ferred to kinetic energy of charged particles in aninteraction of type J by the kinetic energy of theincident uncharged particle, NA is the Avogadroconstant, and M is the molar mass of the targetmaterial.

The mass energy-transfer coefficient is related tothe mass attenuation coefficient, m /r, by theequation

mtr

r¼ m

rf ; ð4:3:2Þ

where

f ¼P

J fJsJPJ sJ

:

The mass energy-transfer coefficient of a compoundmaterial is usually treated as if the latter consistedof independent atoms. Thus,

mtr

r¼ 1

r

XL

ðntÞLX

J

fL;JsL;J; ð4:3:3Þ

where (nt)L and sL, J have the same meaning as inEq. 4.2.3, and fL, J is the quotient of the meanenergy transferred to kinetic energy of charged par-ticles in an interaction of type J with a target entityof type L by the kinetic energy of the incidentuncharged particle. Relationship 4.3.3 implies thesame approximations as relationship 4.2.3.

A fraction g of the kinetic energy transferred tocharged particles is subsequently lost on average in


18

at Henry Ford H



ownloaded from


radiative processes (bremsstrahlung, in-flightannihilation, and fluorescence radiations) as thecharged particles slow to rest in the material, andthis fraction g is specific to the material. Theproduct of mtr/r for a material and (1 2 g) is calledthe mass energy-absorption coefficient, men/r, of thematerial for uncharged particles,

men

r¼ mtr

rð1� gÞ: ð4:3:4Þ

The mass energy-absorption coefficient of a com-pound material depends on the stopping power (seeSection 4.4) of the material. Thus, its evaluationcannot, in principle, be reduced to a simple sum-mation of the mass energy-absorption coefficient ofthe atomic constituents (Seltzer, 1993). Such asummation can provide an adequate approximationwhen the value of g is sufficiently small.

4.4 Mass Stopping Power

The mass stopping power, S/r, of a material, forcharged particles of a given type and energy, isthe quotient of dE by rdl, where dE is the meanenergy lost by the charged particles in traversinga distance dl in the material of density r, thus

S

r¼ 1

r

dE

d l:

Unit: J m2 kg2l

The quantity E may be expressed in eV, andhence S/r may be expressed in eV m2 kg2l or someconvenient multiples or submultiples, such as MeVcm2 g2l.

The quantity S ¼ dE/dl denotes the linear stop-ping power.

The mass stopping power can be expressed as asum of independent components by

S

r¼ 1

r

dE

dl

� �el

þ 1

r

dE

dl

� �rad

þ1

r

dE

dl

� �nuc

; ð4:4:1Þ

where

1

r

dE

dl

� �el

¼ 1

rSel is the mass electronic (or collision4)

stopping power due to interactionswith atomic electrons resulting inionization or excitation,

1

r

dE

dl

� �rad

¼ 1

rSrad is the mass radiative stopping

power due to emission of brems-strahlung in the electric fields ofatomic nuclei or atomic elec-trons, and1

r

dE

dl

� �nuc

¼ 1

rSnuc is the mass nuclear stopping

power5 due to elastic Coulombinteractions in which recoilenergy is imparted to atoms.

In addition, one can consider energy losses due tononelastic nuclear interactions, but such processesare not usually described by a stopping power.

The separate mass stopping-power componentscan be expressed in terms of cross sections. Forexample, the mass electronic stopping power for anatom can be expressed as

1

rSel ¼

NA

MZ

ð1

ds

d1d1; ð4:4:2Þ

where NA is the Avogadro constant, M the molarmass of the atom, Z its atomic number, ds/d1 thedifferential cross section (per atomic electron) forinteractions, and 1 is the energy loss.

Forming the quotient Sel/r greatly reduces, butdoes not eliminate, the dependence on the densityof the material (see ICRU, 1984; 1993b, where thedensity effect and the stopping powers for com-pounds are discussed).

4.5 Linear Energy Transfer (LET)

The linear energy transfer or restricted linearelectronic stopping power, LD, of a material, forcharged particles of a given type and energy, isthe quotient of dED by dl, where dED is themean energy lost by the charged particles due toelectronic interactions in traversing a distancedl, minus the mean sum of the kinetic energiesin excess of D of all the electrons released by thecharged particles, thus

LD ¼dED

d l:

Unit: J m21

The quantity ED may be expressed in eV, andhence LD may be expressed in eV m2l or some con-venient multiples or submultiples, such as keVmm2l.

4The older term was “collision stopping power.” Because allinteractions can be considered “collisions,” the more specificterm “electronic” is strongly preferred.

5The established term “mass nuclear stopping power” can bemisleading because this quantity does not pertain to nuclearinteractions.

Interaction Coefficients and Related Quantities

19

at Henry Ford H



ownloaded from


The linear energy transfer, LD, can also beexpressed by

LD ¼ Sel �dE ke;D

d l; ð4:5:1Þ

where Sel is the linear electronic stopping power,and dEke, D is the mean sum of the kinetic energies,greater than D, of all the electrons released by thecharged particle in traversing a distance dl.

The definition expresses the following energybalance: energy lost by the primary charged par-ticle in interactions with electrons, along a distancedl, minus energy carried away by energetic second-ary electrons having initial kinetic energies greaterthan D, equals energy considered as “locally trans-ferred,” although the definition specifies an energycutoff, D, and not a distance cutoff.

Note that LD includes the binding energy of elec-trons for all interactions. As a consequence, L0

refers to the energy lost that does not reappear askinetic energy of released electrons. Thus, thethreshold of the kinetic energy of the released elec-trons is D as opposed to D minus the binding energy.

In order to simplify notation, D may be expressedin eV. Then L100 is understood to be the linearenergy transfer for an energy cutoff of 100 eV. If noenergy cutoff is imposed, the unrestricted linearenergy transfer, L1, is equal to Sel, and may bedenoted simply as L.

4.6 Radiation Chemical Yield

The radiation chemical yield, G(x), of an entity,x, is the quotient of n(x) by �1, where n(x) is themean amount of substance of that entity pro-duced, destroyed, or changed in a system by themean energy imparted, �1, to the matter of thatsystem, thus

GðxÞ ¼ nðxÞ�1

:

Unit: mol J21

The mole is the amount of substance of a systemthat contains as many elementary entities as thereare atoms in 0.012 kg of 12C. The elementary enti-ties must be specified and can be atoms, molecules,ions, electrons, other particles, or specified groupsof such particles (BIPM, 2006).

A related quantity, called G value, has beendefined as the mean number of entities produced,destroyed, or changed by an energy imparted of100 eV. The unit in which the G value is expressed

is (100 eV)2l. A G value of 1 (100 eV)21 correspondsto a radiation chemical yield of approximately0.1036 mmol J21.

4.7 Ionization Yield in a Gas

The ionization yield in a gas, Y, is the quotientof N by E, where N is the mean total liberatedcharge of either sign, divided by the elementarycharge, when the initial kinetic energy E of acharged particle of a given type is completelydissipated in the gas, thus

Y ¼ N

E:

Unit: J21

The quantity Y may also be expressed in eV21.The ionization yield in a gas is a particular case

of the radiation chemical yield. It follows from thedefinition of Y that the charge produced by brems-strahlung or other secondary radiation emitted bythe initial and secondary charged particles isincluded in N. The charge of the initial chargedparticle is not included in N, as this charge is notliberated in the energy-dissipation process.

4.8 Mean Energy Expended in a Gas per IonPair Formed

The mean energy expended in a gas per ion pairformed, W, is the quotient of E by N, where N isthe mean total liberated charge of either sign,divided by the elementary charge, when theinitial kinetic energy E of a charged particleintroduced into the gas is completely dissipatedin the gas, thus

W ¼ E

N:

Unit: J

The quantity W may also be expressed in eV.It follows from the definition of W that the ions

produced by bremsstrahlung or other secondaryradiation emitted by the initial and secondarycharged particles are included in N. The charge ofthe initial charged particle is not included in N.

In certain cases, it could be necessary to focusattention on the variation in the mean energyexpended per ion pair along the path of the


20

at Henry Ford H



ownloaded from


particle; then the concept of a differential W isrequired, as defined in ICRU Report 31 (ICRU,1979). The differential value, w, of the meanenergy expended in a gas per ion pair formed is thequotient of dE by dN; thus

w ¼ dE

dN; ð4:8:1Þ

where dE is the mean energy lost by a charged par-ticle of kinetic energy E in traversing a layer of gasof infinitesmal thickness, and dN is the mean totalliberated charge of either sign divided by the

elementary charge when dE is completely dissi-pated in the gas.

The relationship between W and w is given by

WðEÞ ¼ EÐEI ½dE0=wðE0Þ�

; ð4:8:2Þ

where I is the lowest ionization potential of the gas,and E’ is the instantaneous kinetic energy of thecharged particle as it slows down.

In solid-state theory, a concept similar to W is theaverage energy required for the formation of ahole–electron pair.

Table 4.1. Interaction coefficients and related quantities

Name Symbol Unit Definition Appearance inthe Report

cross section s m2 N/F Section 4.1mass attenuation coefficient m /r m2 kg21 dN/(N r dl) Section 4.2linear attenuation coefficient m m21 dN/(N dl) Section 4.2mean free path m21 m N dl/dN Section 4.2mass energy-transfer coefficient mtr /r m2 kg21 dRtr/(R r dl) Section 4.3mass energy-absorption coefficient men/r m2 kg21 (mtr/r)(1 2 g) Section 4.3mass stopping power S/r J m2 kg21 dE/(r dl) Section 4.4linear stopping power S J m21 dE/dl Section 4.4linear energy transfer LD J m21 dED /dl Section 4.5radiation chemical yield G(x) mole J21 n(x)/1 Section 4.6ionization yield in a gas Y J21 N/E Section 4.7mean energy expended in a gas per ion pair formed W J E/N Section 4.7differential mean energy expended in a gas

per ion pair formedw J dE/dN Eq. 4.8.1

Interaction Coefficients and Related Quantities

21

at Henry Ford H



ownloaded from


5. Dosimetry

The effects of radiation on matter depend on theradiation field, as specified by the radiometricquantities defined in Sections 3.1 and 3.2, and onthe interactions between radiation and matter, ascharacterized by the interaction quantities definedin Sections 4.1 to 4.5. Dosimetric quantities, whichare selected to provide a physical measure to corre-late with actual or potential effects, are products ofradiometric quantities and interaction coefficients.In calculations, the values of these quantities andcoefficients must be known, while measurementsmight not require this information.

Radiation interacts with matter in a series of pro-cesses in which particle energy is converted andfinally deposited in matter. The dosimetric quantitiesthat describe these processes are presented below intwo Sections dealing with the conversion and withthe deposition of energy. The evaluation of the quan-tities defined in this Section requires, in general, con-sideration of elapsed time. Most applications andmeasurements of ionizing radiation involve timescales of the order of seconds or minutes, so at a prac-tical level the decay of an excited atomic stateusually can be assumed to have occurred. This mightnot be the case for nuclear de-excitations or spon-taneous nuclear decays, with the obvious example ofa radionuclide produced in an interaction or pre-existing in a volume of interest.

5.1 Conversion of Energy

The term conversion of energy refers to the trans-fer of energy from ionizing particles to secondaryionizing particles. The quantity kerma pertains tothe kinetic energy of the charged particles liberatedby uncharged particles; the energy expended toovercome the binding energies, usually a relativelysmall component, is, by definition, not included. Inaddition to kerma, the quantity cema is defined thatpertains to the energy lost by charged particles (e.g.,electrons, protons, alpha particles) in interactionswith atomic electrons; by definition, the bindingenergies are included. Cema differs from kerma inthat cema involves the energy lost in electronicinteractions by the incoming charged particles,

while kerma involves the energy of outgoingcharged particles as a result of interactions byincoming uncharged particles. Both quantities, inconditions of charged-particle equilibrium, serve asapproximations to absorbed dose, kerma foruncharged and cema for charged ionizing particles.

5.1.1 Kerma6

The kerma, K, for ionizing uncharged particles,is the quotient of dEtr by dm, where dEtr is themean sum of the initial kinetic energies of allthe charged particles liberated in a mass dm ofa material by the uncharged particles incidenton dm, thus

K ¼ dEtr

dm:

Unit: J kg21

The special name for the unit of kerma is gray(Gy).

The quantity dEtr includes the kinetic energy ofthe charged particles emitted in the decay ofexcited atoms/molecules7 or in nuclearde-excitation or disintegration.

For a fluence, F, of uncharged particles of energyE, the kerma, K, in a specified material is given by

K ¼ FEmtr=r ¼Cmtr=r; ð5:1:1Þ

where mtr/r is the mass energy-transfer coefficientof the material for these particles.

The kerma per fluence, K/F, is termed the kermacoefficient for uncharged particles of energy E in aspecified material. The term kerma coefficient isused in preference to the older term kerma factor,as the word coefficient implies a physical dimensionwhereas the word factor does not.

In dosimetric calculations, the kerma, K, is usuallyexpressed in terms of the distribution, FE, of the

6Kinetic energy released per mass.7For example, Auger, Coster-Kronig, shake-off electrons.




at Henry Ford H



ownloaded from


uncharged-particle fluence with respect to energy(see Eq. 3.l.8a). The kerma, K, is then given by

K ¼ðFEE

mtr

rdE ¼

ðCE

mtr

rdE; ð5:1:2Þ

where mtr/r is the mass energy-transfer coefficient ofthe material for uncharged particles of energy E.

The expression of kerma in terms of fluencemakes it clear that one can refer to a value ofkerma or kerma rate for a specified material at apoint in free space, or inside a different material.Thus, one can speak, for example, of the air kermaat a point inside a water phantom.

Although kerma is a quantity that concerns theinitial transfer of energy to matter, it is sometimesused as an approximation to absorbed dose. Thenumerical value of the kerma approaches that ofthe absorbed dose to the degree that charged-particle equilibrium exists, that radiative losses arenegligible, and that the kinetic energy of theuncharged particles is large compared with thebinding energy of the liberated charged particles.Charged-particle equilibrium exists at a point ifthe distribution of the charged-particle radiancewith respect to energy (see Eq. 3.1.11a) is constantwithin distances equal to the maximum charged-particle range.

A quantity related to the kerma, termed the col-lision kerma, has long been in use as an approxi-mation to absorbed dose (Attix, 1979a; 1979b)when radiative losses are not negligible. The col-lision kerma, Kcol, excludes the radiative losses bythe liberated charged particles, and – for a fluence,F, of uncharged particles of energy E in a specifiedmaterial – is given by

Kcol ¼ FEmen

r¼ FE

mtr

rð1� gÞ ¼ Kð1� gÞ; ð5:1:3Þ

where men/r is the mass energy-absorption coeffi-cient of the material for uncharged particles ofenergy E, and g is the fraction of the kinetic energyof liberated charged particles that would be lost inradiative processes in that material (see Section4.3).

In dosimetric calculations, the collision kerma,Kcol, can be expressed in terms of the distribution,FE, of the uncharged-particle fluence with respectto energy as

Kcol ¼ðFEE

men

rdE ¼

ðFEE

mtr

r1� gð Þ dE

¼ K 1� �gð Þ; ð5:1:4Þ

where �g is the mean value of g averaged over the

distribution of the kerma with respect to the elec-tron energy.

The expression of collision kerma in terms of theproduct of the kerma and a radiative-loss correctionfactor evaluated for the same material as thekerma suggests that one can refer to a value of col-lision kerma or collision kerma rate for a specifiedmaterial at a point in free space, or inside a differ-ent material.

5.1.2 Kerma Rate

The kerma rate, _K, is the quotient of dK by dt,where dK is the increment of kerma in the timeinterval dt, thus

_K ¼ dK

dt:

Unit: J kg21 s21

If the special name gray is used, the unit ofkerma rate is gray per second (Gy s21).

5.1.3 Exposure

The exposure, X, is the quotient of dq by dm,where dq is the absolute value of the mean totalcharge of the ions of one sign produced when allthe electrons and positrons liberated or createdby photons incident on a mass dm of dry air arecompletely stopped in dry air, thus

X ¼ dq

dm:

Unit: C kg21

The ionization produced by electrons emitted inatomic/molecular relaxation processes is includedin dq. The ionization due to photons emitted byradiative processes (i.e., bremsstrahlung and fluor-escence photons) is not to be included in dq. Exceptfor this difference, significant at high energies, theexposure, as defined above, is the ionization ana-logue of the dry-air kerma. Exposure can beexpressed in terms of the distribution, FE, of thefluence with respect to the photon energy, E, andthe mass energy-transfer coefficient, mtr/r, for dryair and for that energy as follows:

X � e

W

ðFEE

mtr

rð1� gÞdE

� e

W

ðFEE

men

rdE; ð5:1:5Þ


24

at Henry Ford H



ownloaded from


where e is the elementary charge, W is the meanenergy expended in dry air per ion pair formed, andg is the fraction of the kinetic energy of the electronsliberated by photons that is lost in radiative pro-cesses in air. The approximation symbol in Eq. 5.1.5reflects the fact that the exposure includes thecharge of electrons or ions liberated by the incidentphotons whereas W pertains only to the charge pro-duced during the slowing down of these electrons.8

For photon energies of the order of 1 MeV orbelow, for which the value of g is small, Eq. 5.1.5can be further approximated by X � (e/W)Kair

(l 2 �g) ¼ (e/W)Kcol,air, where Kair is the dry-airkerma for primary photons and �g is the mean valueof g averaged over the distribution of the air kermawith respect to the electron energy.

As in the case of collision kerma, it can be con-venient to refer to a value of exposure or of exposurerate in free space or at a point inside a materialdifferent from air; one can speak, for example, of theexposure at a point inside a water phantom.

5.1.4 Exposure Rate

The exposure rate, _X, is the quotient of dX by dt,where dX is the increment of exposure in thetime interval dt, thus

_X ¼ dX

dt:

Unit: C kg21 s21

5.1.5 Cema9

The cema, C, for ionizing charged particles, isthe quotient of dEel by dm, where dEel is themean energy lost in electronic interactions in amass dm of a material by the charged particles,except secondary electrons, incident on dm, thus

C ¼ dEel

dm:

Unit: J kg21

The special name of the unit of cema is gray(Gy).

The energy lost by charged particles in electronicinteractions includes the energy expended to over-come the binding energy and the initial kineticenergy of the liberated electrons, referred to as sec-ondary electrons. Thus, energy subsequently lostby all secondary electrons is excluded from dEel.

The cema, C, can be expressed in terms of the dis-tribution, FE, of the charged-particle fluence, withrespect to energy (see Eq. 3.1.8a). According to thedefinition of cema, the distribution FE does notinclude the contribution of secondary electrons to thefluence, but the contributions of all other chargedparticles, such as secondary protons, alpha particles,tritons, and ions produced in nuclear interactions, areincluded in the cema. The cema, C, is thus given by

C ¼ðFE

Sel

rdE ¼

ðFE

L1

rdE; ð5:1:6Þ

where Sel/r is the mass electronic stopping power of aspecified material for charged particles of energy E,and L1 is the corresponding unrestricted linearenergy transfer. In general, the cema is evaluated asthe sum of contributions by all species of charged par-ticles, except liberated secondary electrons.

For charged particles of high energies, it mightbe undesirable to disregard energy transport bysecondary electrons of all energies. A modifiedconcept, restricted cema, CD, (Kellerer et al., 1992)is then defined as

CD ¼ðF 0E

LD

rdE: ð5:1:7Þ

This differs from the integral in Eq. 5.1.6 in thatL1 is replaced by LD and that the distribution F

0

E

now includes secondary electrons liberated in dmwith kinetic energies greater than D. For D ¼1,restricted cema is identical to cema.

The expression of cema and restricted cema interms of fluence makes it clear that one can referto their values for a specified material at a point infree space, or inside a different material. Thus, onecan speak, for example, of tissue cema in air(Kellerer et al., 1992).

The quantities cema and restricted cema can beused as approximations to absorbed dose fromcharged particles. Equality of absorbed dose andcema is approached to the degree that secondary-charged-particle equilibrium exists and that radia-tive losses and those due to elastic nuclear inter-actions are negligible. Secondary-charged-particleequilibrium is achieved at a point if the fluence ofsecondary charged particles is constant within dis-tances equal to their maximum range. For restricted

8This difference, although relatively small, tends to becomemore significant as the photon energy decreases. Additionally, Wis not constant as perhaps implied in Eq. 5.1.5, but known toincrease at low energies (ICRU, 1979). At energies for which thevariation of W with energy becomes important, one shouldconsider the effect of this increase on the relationship betweenexposure and air kerma.9Converted energy per mass.

Dosimetry

25

at Henry Ford H



ownloaded from


cema, only partial secondary-charged-particle equi-librium, up to kinetic energy D, is required.

5.1.6 Cema Rate

The cema rate, _C, is the quotient of dC by dt,where dC is increment of cema in the time inter-val dt, thus

_C ¼ dC

dt:

Unit: J kg21 s21

If the special name gray is used, the unit ofcema rate is gray per second (Gy s21).

5.2 Deposition of Energy

In this Section, certain stochastic quantities areintroduced. Energy deposit is the basis in terms ofwhich all other quantities presented here can bedefined.

5.2.1 Energy Deposit

The energy deposit, 1i, is the energy deposited ina single interaction, i, thus

1i ¼ 1in � 1out þQ;

where 1in is the energy of the incident ionizingparticle (excluding rest energy), 1out is the sum ofthe energies of all charged and uncharged ioniz-ing particles leaving the interaction (excludingrest energy), and Q is the change in the rest ener-gies of the nucleus and of all elementary par-ticles involved in the interaction (Q . 0: decreaseof rest energy; Q , 0: increase of rest energy).

Unit: J

The quantity 1i may also be expressed in eV.Note that 1i is a stochastic quantity.

Interactions with atomic electrons resulting inatomic excitation (and subsequent de-excitation)do not involve a change in rest energies of thenucleus or of elementary particles and thus haveQ ¼ 0. The restriction of 1in and 1out to energies ofionizing particles can in principle lead to a slightenergy imbalance by ignoring the net energytransport by non-ionizing particles; thus, energy ofnon-ionizing particles, e.g., very-low-energy

photons, that can leave the interaction areincluded in the energy deposit. The dimensionsover which that energy is re-absorbed can bethought to define a spatial region associated witha single interaction.

5.2.2 Energy Imparted

The energy imparted, 1 , to the matter in a givenvolume is the sum of all energy deposits in thevolume, thus

1 ¼X

i

1i;

where the summation is performed over allenergy deposits, 1i, in that volume.

Unit: J

The quantity 1 may also be expressed in eV. Notethat 1 is a stochastic quantity.

The energy deposits over which the summationis performed can belong to one or more energy-deposition events; for example, they might belongto one or several independent particle trajectories.The term energy-deposition event denotes theimparting of energy to matter by correlated par-ticles. Examples include a proton and its second-ary electrons, an electron-positron pair, or theprimary and secondary particles in nuclearreactions.

If the energy imparted to the matter in a givenvolume is due to a single energy-deposition event,it is equal to the sum of the energy deposits in thevolume associated with the energy-depositionevent. If the energy imparted to the matter in agiven volume is due to several energy-depositionevents, it is equal to the sum of the individualenergies imparted to the matter in the volume dueto each energy-deposition event.

The mean energy imparted, �1, to the matter in agiven volume equals the mean radiant energy, Rin,of all charged and uncharged ionizing particlesthat enter the volume minus the mean radiantenergy, Rout, of all charged and uncharged ionizingparticles that leave the volume, plus the meansum,

PQ, of all changes of the rest energy of

nuclei and elementary particles that occur in thevolume (Q . 0: decrease of rest energy; Q , 0:increase of rest energy); thus

�1 ¼ Rin � Rout þX

Q: ð5:2:1Þ


26

at Henry Ford H



ownloaded from


5.2.3 Lineal Energy

The lineal energy, y, is the quotient of 1s by �l,where 1s is the energy imparted to the matter ina given volume by a single energy-depositionevent, and �l is the mean chord length of thatvolume, thus

y ¼ 1s

�l:

Unit: J m21

The quantity y is a stochastic quantity. Thenumerator 1s may be expressed in eV; hence y maybe expressed in multiples and submultiples of eVand m, e.g., in keV mm2l.

The mean chord length of a volume is the meanlength of randomly oriented chords (uniform isotropicrandomness) through that volume. For a convex body,it can be shown that the mean chord length, �l, equals4V/A, where V is the volume and A is the surfacearea (Cauchy, 1850; Kellerer, 1980); thus, for a spherethe mean chord length is 2/3 of the sphere diameter.

It is useful to consider the probability distributionof y. The value of the distribution function, F(y), is theprobability that the lineal energy due to a singleenergy-deposition event is equal to or less than y. Theprobability density, f(y), is the derivative of F(y); thus

f ðyÞ ¼ dFðyÞdy

: ð5:2:2Þ

F(y) and f(y) are independent of absorbed dose andabsorbed-dose rate, but are dependent on the sizeand shape of the volume.

5.2.4 Specific Energy

The specific energy (imparted), z, is the quotientof 1 by m, where 1 is the energy imparted byionizing radiation to matter in a volume of massm, thus

z ¼ 1

m:

Unit: J kg21

The special name for the unit of speific energy isgray (Gy).

The quantity z is a stochastic quantity. Thespecific energy can be due to one or more energy-deposition events. The distribution function, F(z),is the probability that the specific energy is equalto or less than z. The probability density, f(z), is thederivative of F(z); thus

f ðzÞ ¼ dFðzÞdz

: ð5:2:3Þ

F(z) and f(z) depend on absorbed dose in the mass,m. The probability density f(z) includes a discretecomponent (in terms of a Dirac delta function) atz ¼ 0 for the probability of no energy deposition.

The distribution function of the specific energydeposited in a single energy-deposition event, Fs(z),is the conditional probability that a specific energyless than or equal to z is deposited if one energy-deposition event has occurred. The probabilitydensity, fs (z), is the derivative of Fs(z); thus

fsðzÞ ¼dFsðzÞ

dz: ð5:2:4Þ

For convex volumes, y and the increment, z, ofspecific energy due to a single energy-depositionevent are related by

y ¼ rA

4z; ð5:2:5Þ

where A is the surface area of the volume, and r isthe density of matter in the volume.

5.2.5 Absorbed Dose

The absorbed dose, D, is the quotient of d�1 bydm, where d�1 is the mean energy imparted byionizing radiation to matter of mass dm, thus

D ¼ d�1

dm:

Unit: J kg21

The special name for the unit of absorbed doseis gray (Gy).

In the limit of a small domain10, the meanspecific energy �z is equal to the absorbed dose D.

10The absorbed dose, D, is considered a point quantity, but itshould be recognized that the physical process does not allow dmto approach zero in the mathematical sense.

Dosimetry

27

at Henry Ford H



ownloaded from


5.2.6 Absorbed-Dose Rate

The absorbed-does rate, _D, is the quotient of dDby dt, where dD is the increment of absorbeddoes in the time interval dt, thus

_D ¼ dD

dt:

Unit: J kg21 s21

If the special name gray is used, the unit ofabsorbed-does rate is gray per second (Gy s21).

Table 5.1. Dosimetric quantities: conversion of energy

Name Symbol Unit Definition Appearance in the Report

kerma K J kg21 Gy dEtr/dm Section 5.1.1collision kerma Kcol J kg21 Gy K(1 2 g) Section 5.1.1kerma coefficient – J m2 kg21 Gy m2 K/F Section 5.1.1kerma rate K J kg21 s21 Gy s21 dK/dt Section 5.1.2exposure X C kg21 dq/dm Section 5.1.3exposure rate X C kg21 s21 dX/dt Section 5.1.4cema C J kg21 Gy dEel/dm Section 5.1.5restricted cema CD J kg21 Gy – Section 5.1.5cema rate C J kg21 s21 Gy s21 dC/dt Section 5.1.6

Table 5.2. Dosimetric quantities: deposition of energy


energy deposit 1i J 1in 2 1out þ Q Section 5.2.1energy imparted 1 J X

i

1i

Section 5.2.2

lineal energy y J m21 1s=�l Section 5.2.3

specific energy z J kg21 Gy 1/m Section 5.2.4absorbed dose D J kg21 Gy d�1=dm Section 5.2.5

absorbed-dose rate D J kg21 s21 Gy s21 dD/dt Section 5.2.6


28

at Henry Ford H



ownloaded from


6. Radioactivity

The term radioactivity refers to the phenomenaassociated with spontaneous transformations thatinvolve changes in the nuclei of atoms or of theenergy states of the nuclei of atoms. The energyreleased in such transformations is emitted asnuclear particles (e.g., alpha particles, electrons,and positrons) and/or photons.

Such transformations represent a stochasticprocess. The whole atom is involved in this processbecause nuclear transformations can also affect theatomic shell structure and cause emission orcapture of electrons, the emission of photons, orboth.

A nuclide is a species of atoms having a specifiednumber of protons and neutrons in its nucleus.Unstable nuclides, which transform to stable orunstable progeny, are called radionuclides. Thetransformation results in another nuclide or in atransition to a lower energy state of the samenuclide.

6.1 Decay Constant

The decay constant, l, of a radionuclide in aparticular energy state is the quotient of2dN/N by dt, where dN/N is the meanfractional change in the number of nucleiin that energy state due to spontaneousnuclear transformations in the time intervaldt, thus

l ¼ �dN=N

dt:

Unit: s2l

The quantity (ln 2)/l, commonly called thehalf life, Tl/2, of a radionuclide, is the mean timetaken for the radionuclides in the particularenergy state to decrease to one half of their initialnumber.

6.2 Activity

The activity, A, of an amount of a radionuclidein a particular energy state at a given time isthe quotient of 2dN by dt, where dN is themean change in the number of nuclei in thatenergy state due to spontaneous nuclear trans-formations in the time interval dt, thus

A ¼ �dN

dt:

Unit: s2l

The special name for the unit of activity is bec-querel (Bq).

The “particular energy state” is the groundstate of the radionuclide unless otherwise specified.

The activity, A, of an amount of a radionuclide ina particular energy state is equal to the product ofthe decay constant, l, for that state, and thenumber N of nuclei in that state, thus,

A ¼ lN: ð6:2:1Þ

6.3 Air-kerma-Rate Constant

The air-kerma-rate constant, Gd, of a radio-nuclide emitting photons is the quotient of l2 _Kd

by A, where _Kd is the air-kerma rate due tophotons of energy greater than d, at a distance lin vacuo from a point source of this nuclidehaving an activity A, thus

Gd ¼l2 _Kd

A:

Unit: m2 J kg2l

If the special names gray (Gy) and becquerel(Bq) are used, the unit of air-kerma-rate con-stant is m2 Gy Bq21 s2l.




at Henry Ford H



ownloaded from


The photons referred to in the definition includegamma rays, characteristic x rays, and internalbremsstrahlung.

The air-kerma-rate constant, a characteristicof a radionuclide, is defined in terms of anideal point source, and the term is not strictlyapplicable to a source of finite extent. In asource of finite size, attenuation and scatteringoccur, and annihilation radiation and externalbremsstrahlung can be produced. In many

cases, these processes require significantcorrections.

Any medium intervening between the source andthe point of measurement will give rise to absorptionand scattering for which corrections are needed.

The selection of the value of d depends upon theapplication. To simplify notation and ensure uniform-ity, it is recommended that d be expressed in keV. Forexample, G5 is understood to be the air-kerma-rateconstant for a photon-energy cutoff of 5 keV.

Table 6.1. Quantities related to radioactivity


decay constant l s21 2(dN/N)/dt Section 6.1half life T1/2 s (ln 2)/l Section 6.1activity A s21 Bq 2dN/dt Section 6.2air-kerma-rate constant Gd m2 J kg21 m2 Gy Bq21 s21 l2 _Kd=A Section 6.3


30

at Henry Ford H



ownloaded from


References

Attix, F. H. (1979a). “The partition of kerma to accountfor bremsstrahlung,” Health Phys. 36, 347–354.

Attix, F. H. (1979b). “Addendum to ‘The partition of kermato account for bremsstrahlung’,” Health Phys. 36, 536.

BIPM (2006). Bureau International des Poids etMesures, Le Systeme International d’Unites (SI), TheIniternational System of Units (SI), 8th ed. (BureauInternational des Poids et Mesures, Sevres).

Caswell, R. S., Coyne, J. J., and Randolph, M. L. (1982).“Kerma factors of elements and compounds forneutron energies below 30 MeV,” Int. J. Appl. Radiat.Isot. 33, 1227–1262.

Cauchy, A. (1850). “Memoire sur la rectification descourbes et la quadrature des surfaces courbes,” Mem.Acad. Sci. XXII, 3.

CIE (1987). Commission Internationale de l’Eclairage,Vocabulaire Electrotechnique International, CIEPublication 50 (845) (Bureau Central de laCommission Electrotechnique Internationale, Geneve).

Houk, T. L., and Wilson, R. (1967). “Measurements of theneutron–proton and neutron–carbon total cross sec-tions at electron-volt energies,” Rev. Mod. Phys. 39,546–547.

Hubbell, J. H. (1969). Photon Cross Sections, AttenuationCoefficients, and Energy Absorption Coefficients from10 keV to 100 GeV, NSRDS-NBS 29 (National Bureauof Standards, Washington, DC).

ICRU (1962). International Commission on RadiationUnits and Measurements. Radiation Quantities andUnits, ICRU Report 10a (Published as NationalBureau of Standards Handbook 84, U.S. GovernmentPrinting Office, Washington, DC).

ICRU (1968). International Commission on RadiationUnits and Measurements. Radiation Quantities andUnits, ICRU Report 11 (International Commission onRadiation Units and Measurements, Washington, DC).

ICRU (1971). International Commission on RadiationUnits and Measurements. Radiation Quantities andUnits, ICRU Report 19 (International Commission onRadiation Units and Measurements, Washington, DC).

ICRU (1979). International Commission on RadiationUnits and Measurements. Average Energy Required toProduce an Ion Pair, ICRU Report 31 (InternationalCommission on Radiation Units and Measurements,Bethesda, MD).

ICRU (1980). International Commission on RadiationUnits and Measurements. Radiation Quantities andUnits, ICRU Report 33 (International Commission onRadiation Units and Measurements, Bethesda, MD).

ICRU (1984). International Commission on RadiationUnits and Measurements. Stopping Powers forElectrons and Positrons, ICRU Report 37(International Commission on Radiation Units andMeasurements, Bethesda, MD).

ICRU (1993a). International Commission on RadiationUnits and Measurements. Quantities and Units inRadiation Protection Dosimetry, ICRU Report 51(International Commission on Radiation Units andMeasurements, Bethesda, MD).

ICRU (1993b). International Commission on RadiationUnits and Measurements. Stopping Powers andRanges for Protons and Alpha Particles, ICRU Report49 (International Commission on Radiation Units andMeasurements, Bethesda, MD).

ICRU (1998). International Commission on RadiationUnits and Measurements. Fundamental Quantitiesand Units for Ionizing Radiation, ICRU Report 60(International Commission on Radiation Units andMeasurements, Bethesda, MD).

IS0 (1993). International Organization for Standardization.IS0 Standards Handbook, Quantities and Units, 3rd ed.(International Organization for Standardization, Geneva).

IUPAC (1997). International Union of Pure and AppliedChemistry. Compendium of Chemical Terminology, 2nded., McNaught, A. D., and Wilkinson, A., Eds.(Blackwell Science, Oxford).

Kellerer, A. M. (1980). “Concepts of geometrical prob-ability relevant to microdosimetry and dosimetry,”p. 1049 in Proc. 7th Symp. Microdosimetry, Booz, J.,Ebert, H. G., and Hartfiel, H. D., Eds. (HarwoodAcademic Publishers, Chur, Switzerland).

Kellerer, A. M., Hahn, K., and Rossi, H. H. (1992).“Intermediate dosimetric quantities,” Rad. Res. 130,15–25.

Mohr, P. J., Taylor, B. N., and Newell, D. B. (2008).“CODATA recommended values of the fundamentalphysical constants: 2006,” Rev. Mod. Phys. 80,633–730.

Papiez, L., and Battista, J. J. (1994). “Radiance and par-ticle fluence,” Phys. Med. Biol. 39, 1053–1062.

Rauch, H. (1994). “Hydrogen detection by neutron opticalmethods,” in Neutron Scattering from Hydrogen inMaterials, Proc. 2nd Summer School on NeutronScattering, 14–20 August 1994, Zuoz, Switzerland,Furrer, A., Ed. (World Scientific, Singapore).

Seltzer, S. M. (1993). “Calculation of photon mass energy-transfer and mass energy-absorption coefficients,”Rad. Res. 136, 147–170.




at Henry Ford H



ownloaded from


Index

absorbed dose 27absorbed-dose rate 28activity 29air-kerma-rate constant 29cema 25cema rate 26collision kerma 24cross section 17decay constant 29energy deposit 26energy fluence 12energy flux 12energy imparted 26energy radiance 13energy-fluence rate 13exposure 24exposure rate 25fluence 12fluence rate 13flux 12half life 29ionization yield in a gas 20kerma 23kerma coefficient 23kerma rate 24lineal energy 27linear attenuation coefficient 17

linear energy transfer 19linear stopping power 19mass attenuation coefficient 17mass electronic (or collision) stopping power 19mass energy-absorption coefficient 19mass energy-transfer coefficient 18mass nuclear stopping power 19mass radiative stopping power 19mass stopping power 19mean energy expended in a gas per ion

pair formed20

mean free path 17particle number 11particle number density 12particle radiance 13radiant energy 11radiant energy density 12radiation chemical yield 20restricted cema 25specific energy 27vector energy fluence 15vector energy radiance 14vector energy-fluence rate 14vector fluence 15vector fluence rate 14vector particle radiance 14




at Henry Ford H



ownloaded from


fundamental quantities and units for · pdf file · 2014-06-06these activities do...

Documents