Post on 02-Jun-2018
8/10/2019 Fsica Mdica ICRU60
1/22
ICRU REPORT 60.
Fundamental Quantities
and Units for lonizing
Radiation
lssued: 30 December 1998
IN.TERNATIONAL COMMISSION ON RADIATION
UNITS ANO MEASUREMENTS
791O WOODMONT AVEN UEBETHESDA, MARYLAND 20814
U.S.A.
Stralingsbeschermingsdienst TU/e
Leergang 3, 2000-2001
8/10/2019 Fsica Mdica ICRU60
2/22
8/10/2019 Fsica Mdica ICRU60
3/22
Fundamental Quantities and
Units for Ionizing RadiationIntroduction
This report supersedes PartA of ICRU Report 33 (ICRU, 1980), dealing with quantities and units forgeneral use. Part B of ICRU Report 33, coveringquantities and units for use in radiation protection,has already been replaced by ICRU Report 51 (ICRU,
1993a) entitled Quantities and Units in Radiation
Protection Dosimetry.The present report deals with the fundamental
- ; ..- {Uantities and units for ionizing radiation. Drafts ofits main sections, namely radiometry, interactioncoefficients and dosimetry, have been published forcomment in the ICRU News. The ICRU appreciatesthe assistance rendered by scientific bodies andindividuals who submitted comments, and hopesthat this process will facilitate the acceptance of thereport.
The report is structured in five majar sections,
each of which is followed by tables summarizing, foreach quantity, its symbol, unit and the relation used
in its definition.
Section 1 deals with terms and mathematicalconventions used throughout the report.
Section 2, entitled Radiometry, presents quantities required for the specification of radiation fields.Two classes of quantities are used referring either tothe number of particles or to the energy transportedy them. Accordingly, the definitions of radiometric
' - ,..J.uantities are grouped into pairs. Both scalar andvectorial quantities are defined.
Interaction coe:fficients and related quantities arecovered in Section 3. The fundamental interaction
coefficient is the cross section. All other coefficientsdefined in this section can be expressed in terms ofcross section or differential cross section. The defin-
tion of the linear energy transfer (LET) given in thepresent report differs from that given previously(ICRU, 1980) by the inclusion ofthe binding energyfor all collisions.
Section 4 deals with dosimetric quantities whichdescribe the processes by which particle energy is
converted and finally deposited in matter. Accordingly, the definitions of dosimetric quantities arepresented in two parts entitled Conversion ofEnergyand Deposition ofEnergy, respectively. The first partincludes a new quantity, cerna (converted energy perunit mass) for charged particles, paralleling kerma
(kinetic energy released per unit mass) for uncharged particles. Cerna differs from kerma in thatcerna involves the energy lost in electronic collisionsby the incoming charged particles while kerma involves the energy imparted to outgoing chargedparticles . In the second part on deposition of energy,a new quantity termed energy deposit is introduced.
Energy deposit, i.e., the energy deposited in a singleinteraction, is the fundamental quantity in terms ofwhich all other quantities presented in the sectioncan be defined. These are the traditional stochasticquantities, energy imparted, lineal energy and specific energy, the latter leading to the non-stochasticquantity absorbed dose.
Quantities related to radioactivity are defined inSection 5.
Much work has been devoted to the current docu ment to ensure it is scientifically rigorous and asconsistent as possible with similar publications used
in other fields of physics. It is hoped that this reportrepresents a modest step towards a universal scientific language.
1
8/10/2019 Fsica Mdica ICRU60
4/22
l. General Considerations
This section deals with terms and mathematical
conventions used throughout the report.
1.1 Quantities and Units
Quantities, when used for the quantitative description of physical phenomena or objects, are generally
called physical quantities. A unit is a selected reference sample of a quantity with which other quanti
ties of the same kind are compared. Every quantity
may be expressed as the product of a numerical valueand a unit. As a quantity remains unchanged when
the unit in which it is expressed changes, its numeri
cal value is modified accordingly.Quantities can be multiplied or divided by one
another resulting in other quantities. Thus, all quan
tities can be derived from a set of base quantities.The resulting quantities are called derived quantities.
Asystem 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 other thanthe number 1 occur in the expressions of derived
units.
The ICRU recommends the use of the International System of U its (SI) (BIPM, 1998). In thissystem, the base units are metre, kilogram, second,
ampere, kelvin, mole, and candela, for the base
quantities length, mass, time, electric current, ther
modynamic temperature, amount of substance, and
luminous intensity, respectively.
Sorne derived SI units are given special names,such as coulomb for ampere second. Other derived
units are given special names only when they areused with certain derived quantities. Special names
currently in use in this restricted category are
becquerel (equal to reciproca! second for activityof a radionuclide) and gray (equal to joule perkilogram for absorbed dose, kerma, cerna and spe
cific energy). Sorne examples of SI units are given in
Table 1.1.
There are also a few units outside of the intemational system that may be used with SI. For sorne of
these, their values in terms of SI units are obtained
experimentally. Two of these are used in current
ICRU documents-electron volt (symbol eV) and
(unified) atomic mass unit (symbol u). Others, such
as day, hour and minute, are not coherent with thesystem but, because of long usage, are permitted to
be used with SI (see Table 1.2).
Decimal multiples and submultiples of SI units2 can be formed using the SI prefixes (see Table 1.3).
TABLE 1.1-SIunits used in this report
Category ofunits Quantity N ame Symbol
SI base units length metre m
mass kilogram kg
time second S
amount of substance mole mol
SI derived units with electric charge coulomb especial names energy joule J(general use) solid angle steradian sr
power watt wSI derived units with activity becquerel Bq
special names absorbed dose, gray Gy
(restricted use) kerma, cerna, spe-
cific energy
1.2 Ionizing Radiation
Ionization produced by particles is the process bywhich one or more electrons are liberated in colli sions of the particles with atoms or molecules. Thismay be distinguished from excitation, which is atransfer of electrons to higher energy levels in atomsor molecules and generally requires less energy.
When charged particles have slowed down suffi
ciently, ionization becomes less likely or impossibleand the particles increasingly dissipate their remain-
TABLE 1.2-Some unts used with the SI
Category ofunits Quantity Name Symbol
Units widely used time minute min
hour hday d
Units whose values in energy electron volta eVSI are obtained mass (unified) atomie mass u
experimentally unita
a 1eV= 1.602 177 33(49) 10-19J. 1u= 1.660 540 2(10) 10-27kg. The digits in parentheses are the one-standard-deviation
uncertainty in the last digits ofthe given value (CODATA, 1986).
TABLE 1.3-Sl prefixesa
Factor Pref ix Symbol Factor Prefix Symbol
1024 yotta y w-1 deci d1021 zetta z w-2 centi e1018 exa E w-3 milli m1015 peta p w-s micro J.l1012 tera T w-9 nano n109 giga G 10-12 pico p1Q6 mega M 10-15 femto f103 kilo k 10-18 atto a
102
hecto h 10-21
zepto z
101 deca da lQ-24 yocto y,....---......_....,
a The prefix symbol attached to the unit symbol constitutes anew symbol, e.g., 1fm2 = no-15 m)2 = w-30 m2.
8/10/2019 Fsica Mdica ICRU60
5/22
I
----Ing energy in other processes such as excitation orelastic scattering. Thus, near the end oftheir range,charged particles that were ionizing become nonionizing.
The term ionizing radiation refers to charged
particles (e.g., electrons or protons) and unchargedparticles (e.g.,photons or neutrons) that can produceionizations in a medium. In the condensed phase, thedifference between ionization and excitation can
become blurred. A pragmatic approach for dealingwith this ambiguity is to adopt a threshold for theenergy that can be transferred to the medium at thelocations called energy transfer points (see Section4.2.1). This implies cut-off energies below whichcharged particles are not considered to be ionizing.Below such energies, their ranges are minute. Hence,
the choice of the cut-off energies does not materially
affect the spatial distribution of energy depositionxcept at the smallest distances that may be of----concern in microdosimetry. The choice of the thresh
old value depends on the application; for example, a
-value of 10eV- may be appropriate for radiobiology.
1.3 Stochastic and Non-Stochastic Quantities
Differences between results from repeated observations are common in physics. These can arise fromimperfect measurement systems, or from the factthat many physical phenomena are subject to inherent fiuctuations. Thus, one distinguishes between anon-stochastic quantity with its unique value and a
stochastic quantity, the values of which follow aprobability distribution. In many instances, thisdistinction is not significant because the probabilitydistribution is very narrow. For example, the measurement of an electric current commonly involveso many electrons that fiuctuations contribute negli-
-":.tibly to inaccuracy in the measurement. Althoughsimilar considerations often apply to radiation, fluctuations can play a significant role, and may need to
be considered explicitly.Certain stochastic processes follow a Poisson distri
bution, a distribution uniquely determined by itsmean value. A typical example of such a process isradioactive decay. However, more complex distributions are involved in energy deposition. In thisreport, because of their relevance, four stochasticquantities are defined explicitly, namely energy deposit, e (see Section 4.2.1), energy imparted, e (seeSection 4.2.2), lineal energy, y (see Section 4.2.3), andspecific energy, z (see Section 4.2.4).
For example, the specific energy,z, is defined asthe quotient ofthe energy imparted, e, and the mass,m. Repeated measurements would provide an est
mate of the probability distribution of z and of itsfirst moment, z,which approaches the absorbed dose,.J, (see Section 4.2.5) as the mass becomes small.Knowledge of the distribution of z may not be
required for the determination of the absorbed dose,
D. However, knowledge of the distribution of zcorresponding to a known D can be important because in the irradiated mass element, m, the effectsof radiation are more closely related to z than to D,
and the values ofz can differ greatly fromD for smallvalues of m (e.g.,biological cells).
1.4 Mathematical Conventions
To permit characterization of a radiation field andits interactions with matter, many of the quantitiesdefined in this report are considered as functions ofother quantities. For simplicity in presentation, thearguments on which a quantity depends often willnot be stated explicitly. In sorne instances, the distribution of a quantity with respect to another quantitycan be defined. The distribution function of a discretequantity, such as the particle number N, (see Section2.1.1) will be treated as if it were continuous, since Nis usually a very large number. Distributions withrespect to energy are Jrequently required. For example, the distribution offluence (see Section 2.1.3)with respect to particle energy is given by (see Eq.2.1.6a)
8/10/2019 Fsica Mdica ICRU60
6/22
2. Radiometry
Radiation measurements and investigations of
adiation effects require various degrees of specifica- - on of the radiation field at the point of interest.
- . adiation fields consisting of various types of par-
eles, such as photons, electrons, neutrons, or pro
-. 1ns, are characterized by radiometric quantities
- hich apply in free space and in matter.
Two classes of quantities are used in the character
_ation of a radiation field, referring either to the
Limber of particles or to the energy transported by
- 1em.Accordingly, most ofthe definitions ofradiomet
ic quantities given in this report can be grouped into
. airs.
Both scalar and vectorial quantities are used in
radiometry and here they are treated separately.
Formal definitions of quantities deemed to be of
particular relevance are presented in boxes. Equiva
lent definitions which are used in particular applica
tions are given in the text. Distributions of sorne
radiometric quantities with respect to energy are given when they will be required later in the report.
An extended set of quantities relevant to radiometry
is presented in Tables 2.1 and 2.2.
2.1 Scalar Radiometric QuantitiesConsideration of radiometric quantities begins
with the definition of the most general quantities
associated with the radiation field, namely, theparticle number, N, and the radiant energy, R (seeSection 2.1.1). The full description of the radiation
field, however, requires information on the type and
the energy of the partid es as well as on their spatial,
directional and temporal distributions. In the pre
sent report, the specification of the radiation field is
achieved with increasing detail, by defining radiomet
ric quantities through successive differentiations of
N andR with respect to time, area, volume, direction or energy. Thus, these quantities relate to a particu
lar value of each variable of differentiation. This
procedure provides the simplest definitions of quan
tities such as fluence and energy fluence (see Section
2.1.3), often used in the common situation where
radiation interactions are independent of the direc
tion and temporal distribution of the incoming par
ticles.
The scalar radiometric quantities defined in this
reportare used also for fields of optical and ultravio
let radiations, sometimes under different names.
The equivalence between the various terminologies is noted in connection with the relevant defini
tions.
4
2.1.1 :particle Number, Radiant Energy
The particle number, N, is the number of particles 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 energyE (excluding rest energy),
the radiant energy,R, is equal to the productNE.The distributions, NE and RE, of the particlenumber and the radiant energy with respect toenergy are given by
(2.1.1a)
and
RE= dR/dE, (2.1.1b)
where dN is the number of particles with energy
betweenE andE + dE and dR is their radiant energy.The two distributions are related by
(2.1.2)
The volumic particle number, n, is given by
n = d.NidV, (2.1.3)
where dN is the number of particles inthe volume dV.nis also termed number density ofparticles (ISO, 1993).
2.1.2 Flux, Energy Flux
The flux,N, is the quotient of dN by dt, where dNis the increment of the particle number in thetime interval dt, thus
. dNN=-
dt
Unit: s-1
The energy flux,R, is the quotient of dR by dt,.where dR is the increment of radiant energy inthe time interval dt, thus
.dRR=dt
Unit: W
-----.....\
8/10/2019 Fsica Mdica ICRU60
7/22
,__ These quantities frequently refer to a limited
spatial region, e.g., the flux of particles emergingfrom a collimator. For source emission, the flux in all
directions is generally considered.
For visible light and related electromagnetic radia
tions, the energy flux is defined as power emitted,transmitted, or received in the form of radiation and
termed radiant flux or radiant power (CIE, 1987).
The term flux has been employed for the quantity
termed fluence rate in the present report (see Section
2.1.4). This usage is discouraged because of the
possible confusion with the above definition offiux.
2.1.3 Fluence, Energy Fluence
The fiuence, 4>, is the quotient of dNby da, wheredN is the number of particles incident on a sphere
The distributions, 4>E and '/!E, of the fiuence andenergy fiuence with respect to energy are given by
cpE = dcJJ/dE (2.1.6a)
and
(2.1.6b)
where d4> is the fiuence of particles of energy between E and E + dE and d1JI' is their energy fiuence.
The relationship between the two distributions is
given by
(2.1.7)
The energy fiuence is related to the quantity
radiant exposure defined, for fields ofvisible light, as
the quotient of the radiant energy incident on a
surface element by the area of that element (CIE,
..-- of cross-sectional area da, thus
dN4>=-
da
Unit: m-2
The energy fiuence, P, is the quotient of dR byda, where dR is the radiant energy incident on asphere of cross-sectional area da, thus
dR
1Jt=-da
Unit: Jm-2
The use of a sphere of cross sectional area da expresses in the simplest manner the fact that one
considers an area da perpendicular to the direction
uf each particle. The quantities fluence and energy
fiuence are applicable in the common situation in which
radiation interactions are independent of the directionof the incoming particles. Incertain situations, quantities (defined below) involving the differential solid angle,
d!2, in a specified direction are required.
In dosimetric calculations, fiuence is frequently
expressed in terms of the lengths of the particle trajecto
ries. It can be shown that the fiuence, cJJ, is given by
4> = dl/dV, (2.1.4)
where dl is the sum ofthe particle trajectory lengthsin the volume dV.
For a radiation field that does not vary over the
time interval, t, and which is composed of particleswith velocity u, the fluence, 4>, is given by
1987). When a parallel beam is incident atan angle ewith the normal direction to a given surface element,the radiant exposure is equal to 1JI' cos e.
2.1.4 Fluence Rate, Energy Fluence Rate
The fiuence rate, , is the quotient of d4>by dt,where d4> is the increment of the fiuence in thetime interval dt, thus
d
= nut,
where n is the volumic particle number.
(2.1.5)
8/10/2019 Fsica Mdica ICRU60
8/22
2.1.5 Particle Radiance, Energy Radiance
. .The particle radiance, 27 is the quotient of dn.E and 1.P'n,E of the vectorialparticle radiance and the vectorial energy radiance,with respect to energy, are given by
. .
lPn.E = D4>n,E (2.2.1a)and
(2.2.lb)
8/10/2019 Fsica Mdica ICRU60
9/22
'------w' here
8/10/2019 Fsica Mdica ICRU60
10/22
tl>n m-2 s-1 sr-1 fl n Sect. 2.2.1
'l'n wm-2 sr-1 fltJtn Sect. 2.2.1
vo um c par c enumber n
volumic radiant
m-3 dN/dV Eq. 2.1.3 tion of vecto-
rial energy
energy w Jm-3
dR/dVradiance
n.Eenergy distribu- vector a u-tion of ence rate < volumic par-
ticle number nE m-3 J-1vectorial energy
dnldE fluence rate '1'
energy distribu"' energy str u-tion of tion of vecto-
volumic rial fluence
radiant rate
8/10/2019 Fsica Mdica ICRU60
11/22
1
3. Interaction Coefficients and Related Quantities
Interaction processes occur between radiation and
matter. In an interaction, the energy or the direction(or both) of the incident partele is altered or the particleis absorbed. The interaction may be followed by theemission of one or several secondary particles. Thelikelihood of such interactions is characterized by interaction coefficients. They refer to a specific interactionprocess, type and energy ofradiation, target or material.
The fundamental interaction coefficient is thecross section (see Section 3.1). All other interactioncoefficients defined in this report can be expressed interms of cross sections or differential cross sections.
Interaction coefficients and related quantities discussed in this section are listed in Table 3.1.
3.1 Cross Section
The cross section, u, of a target entity, for aparticular interaction produced by incidentcharged or uncharged particles, is the quotient ofPby 4>, where P is the probability of that interaction for a single target entity when subjected tothe particle fluence, 4>, thus
p
u= cp
Unit: m2
A special unit often used for the cross section is the barn, b, defined by
1b = 10-28 m2 = 100 fm2
A full description of an interaction process requires, inter alia, the knowledge of the distributionsof cross sections in terms of energy and direction of
3.2 Mass Attenuation Coefficient
The mass attenuation coefficient, J.LIp, of amaterial, for uncharged particles, is the quotientof dN/Nbyp dl, where dN/N is the fraction of
particles that experience interactions in traversing a distance dl in the material ofdensityp, thus
J.L 1 dN-=--p pdlN'
Unit: m2 kg- 1
J.L is the linear attenuation coefficient. The probability that at normal incidence a particle undergoes aninteraction in a ma:teriallayer ofthickness dl is J.L dl.
The reciproca! of J.L is called the mean free path ofan uncharged particle.
The linear attenuation coefficient, J.L, depends onthe density, p, of the absorber. This dependence is
largely removed by using the mass attenuation
coefficient,J.LIp.The mass attenuation coefficient can be expressed
in terms of the total cross section, cr. The mass
attenuation coefficient is the product of u and N.JM,
where NA is the Avogadro constant and M is themolar mass of the target material, thus
(3.2.1)
where aJ is the component cross section relating to
interaction of typeJ.Relation 3.2.1 can be written as
J.L nt
1 -
all emergent particles resulting from the interaction.
Such distributions, sometimes called differential cross
-=-a
p p '(3.2.2)
sections, are obtained by differentiations of awithrespect to energy and solid angle (see Eq. 3.4.2).
If incident particles of a given type and energy canundergo different and independent types of interaction in a target entity, the resulting cross section,
sometimes called the total cross section, u, is expressed by the sum of the component cross sections,a:, hence
where nt is the volumic number oftarget entities, i.e.,the number of target entities in a volume element
divided by its volume.
The mass attenuation coefficient of a compound
material is usually treated as if the latter consisted
of independent atoms. Thus,
u=_ aJ = -::PJ,. J
and UJ is the component crosssection relating to an interaction of typeJ.
of type L, aL the total cross section for an entity L,and uL,J the cross section of an interaction of typ'eJfor a single target entity of type L. Relation 3.2.3,
which ignores the changes in the molecular, chemi- 9
8/10/2019 Fsica Mdica ICRU60
12/22
di/el
cal or crystalline environment of an atom, is justi:fiedin most cases, but can occasionally lead to errors, forexample in the interaction of low-energy photonswith molecules (Hubbell, 1969).
3.3 Mass Energy Transfer Coefficient
The mass energy transfer coefficient, 11-tr/p, ofa material, for uncharged particles, is the quotient of dRtr/Rbyp dl, where dRu:IR is the fractionof incident radiant energy that is transferred to kinetic energy of charged particles by interactions, in traversing a distance dl in the material ofdensity p, thus
Unit: m2 kg- 1
In calculations relating to photons, the binding energy is usually included in the mass energy transfer coefficient. In materials consisting of elements ofmodest atomic number, this is generally signi:ficant
below photon energies of 1keV.If incident uncharged particles of a given type and
energy can produce several types of independentinteractions in a target entity, the mass energy
transfer coefficient can be expressed in terms of thecomponent cross sections, CIJ,by the relation
(3.3.1)
wherefJ is the average fraction of the incident particleenergy that is transferred to kinetic energy of chargedpartides in an interaction of typeJ,NA is the Avogadroconstant and Mis the molar mass ofthe target material.
The mass energy transfer coefficient is related to themass attenuation coefficient, p.,/p,by the equation
11-tr J.L
where (nt)L and crL,J have the same meaning as in Eq.3.2.3 and fL.J is the average fraction of the incident
particle energy that is transferred to kinetic energyof charged particles in an interaction oftype J with a
target entity of type L. Relation 3.3.3 implies thesame approximations as relation 3.2.3.The product of JLtriP for a material and (1 - g),
where g is the fraction of the energy of liberatedcharged particles that is lost in radiative processes inthe material, is called the mass energy absorption coefficient,J.Lerlp,of the material for uncharged partid es.
The mass energy absorption coefficient of a compound material depends on the stopping power (seeSection 3.4) of the material. Thus its evaluationcannot, in principie, be reduced to a simple summation of the mass energy absorption coefficient of theatomic constituents (Seltzer, 1993). Such a summa
tion can provide an adequate approximation whenthe value ofg is sufficiently small.
3.4 Mass Stopping Power
The mass stopping power, SIp, of a material, forcharged particles, is the quotient of dE by p dl,where dE is the energy lost by a charged particlein traversing a distance dl in the material ofdensity p, thus
S 1dE
p p dl.
Unit: Jm2 kg-1
E may be expressed in eV and, hence, SIp may beexpressed in eV m2 kg-1 or sorne convenient multiples or submultiples, such as MeV cm2 g-1
S =dE/dl denotes thelinear stopping power.The mass stopping power can be expressed as a
sum of independent components by
where
o:.0...,;>
ao.
.::::
where
-=- f,p p
(3.3.2)
( = s., isthe mass electronic (or collision)P P
stopping power due to collisions with
electrons,
The mass energy transfer coefficient of a com
pound materi'al is usually treated as if the latterconsisted of independent atoms. Thus,
(:) = Srad is themass radiative stopping
P rad Ppower dueto emission ofbremsstrahlung
-11-tr -1""' (nt)L "" fL,J (J'L,J, (3.3.3)in the electric fields of atomic nuclei
0 p p L J or atomic electrons,
8/10/2019 Fsica Mdica ICRU60
13/22
1-1(dEl) =-Snuc is the mass nuclear stopping The linear energy transfer, LJ., can also be ex P nuc P
power 1 dueto elastic Coulomb collisions
in which recoil energy is imparted to
atoms.
pressed by
LJ.d.Eke.J.
=Se- , (3.5.1)
In addition, one can consider energy losses due to
inelastic nuclear processes.The separate mass stopping power components
can be expressed in terms of cross sections. Forexample, the mass electronic (or collision) stopping
power for an atom can be expressed as
(3.4.2)
vhere NA is the Avogadro constant, M the molar- mass of the atom, Z its atomic number, da/dw the
differential cross section (per atomic electron) forcollisions and w is the energy loss.
Forming the quotient SetfP greatly reduces, butdoes not eliminate, the dependence on the density ofthe material (see ICRU, 1984, 1993b, where thedensity effect and the stopping powers for com
pounds are discussed).
3.5 Linear Energy Transfer (LET)
The linear energy transfer or restricted linear electronic stopping power, L,1, of a material, for charged particles, is the quotient of dE.1
by dl, where dE.1 is the energy lost by a chargedparticle due to electronic collisions in traversing a
distance dl, minus the sum ofthe kinetic energiesof all the electrons released with kinetic energies
in excess of Ll, thus
where Se1 is the linear electronic stopping power and
d.Eke.J. is the sum ofthe kinetic energies, greater than' of all the electrons released by the charged
particle traversing a distance dl.The definition expresses the following energy
balance: energy lost by the primary charged par
ticle in collisions with electrons, along a track
segment dl, minus energy carried away by secon
dary electrons having kinetic energies greater than Ll,
equals energy considered as 'locally transferred',
although the definition specifies an energy cutoff, .:1,
and not a range cutoff.
This definition differs from that previously given
(ICRU, 1980) in two respects. First,L.1 now includesthe binding energy for all collisions. As a conse
quence, L0 refers to the energy lost that does not
reappear as kinetic energy of released electrons.
Second, the threshold of the kinetic energy of the
released electrons is now Ll as opposed to Ll minus thebinding energy.
In order to simplify notation, .:1 may be ex
pressed in eV. Then L100 is understood to be thelinear energy transfer for an energy cutoff of 100 eV.Lx, which is equal to Seb may be replaced by L andis sometimes termed unrestricted linear e rzergytransfer.
3.6 Radiation Chemical Yield
The radiation chemical yield, G(x), of an en tity, x, is the quotient ofn(x) by E, where n(x) is themean amount of substance of that entity pro
duced, destroyed, or changed in a system by theenergy imparted, E, to the matter of that system,thus
Unit: Jm-1
E .1 may be expressed in eV and henceL .1 may beexpressed in eV m-1,or sorne convenient multiples or
Unit: mol J-1
G(x)n(x)=-.
E
submultiples, such as keV .um-1.
1The established term "mass nuclear stopping power" is amisnomer because it does not pertain to nuclear interactions.
The mole is the amount of substance of a system which contains as many elementary entities as thereare atoms in 0.012 kg of carbon-12. The elementary
entities must be specified and may be atoms, molecules, ions, electrons, other particles or specitledgroups of such particles (BIPM, 1998).
A related quantity, called G value, has been de- 11
8/10/2019 Fsica Mdica ICRU60
14/22
fined 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)- 1.AG value of1 (100 eV)- 1corresponds toaradiation chemical yield of0.104 ,umolJ-1.
In salid state theory, a concept similar to W is theaverage energy required for the formation of ahole-electron pair.
T.-\.BLE 3.1-Interaction coefficients and related quantities
3.7 Mean Energy Expended in a Gas per IonPairFormed
The mean energy expended in a gas per ionpair form.ed, W,is the quotient ofE byN, whereN is the mean number of ion pairs formed whenthe initial kinetic energyE of a charged particle iscompletely dissipated in the gas, thus
E
W=N.
Unit: J
:Name
cross sectionmass attenua
tion coeffi
cient
linear attenua
tion coeffi
cient
mean free path
mass energy
transfer coef
ficient
mass energy
absorption
coefficient
mass stopping
Symbol Unit
\Vhere it appearsDefinition inthe report
PfcJ> Sect. 3.1
d.Nip dlN Sect. 3.2
d.NIN dl Sect. 3.2N dlld.N Sect. 3.2
dRtriP dl R Sect. 3.3
(.Ltrlp) (1-g) Sect. 3.3
W may also be expressed in eV.It follows from the definition of W that the ions
produced by bremsstrahlung or other secondary
power
linear stopping
power
linear energy
Slp J m2 kg- 1 dE!p dl
dE/dl
Sect. 3.4
Sect. 3.4
radiation emitted by the charged particles are includedinN.
In certain cases, it may be necessary to focus
transferradiation
chemical
dEjdl Sect.3.5
attention on the variation in the mean energy ex pended per ion pair along the path of the particle; then the concept of a differential W is required, as
yield
meanenergy
expended in agas perion
G(x) mol J-1 n(x)/e Sect. 3.6
defined in ICRU Report 31 (ICRU, 1979). pairformed w J EIN Sect. 3.7
2
8/10/2019 Fsica Mdica ICRU60
15/22
4. Dosimetry
The effects of radiation on matter depend on theradiation field, as specified by the radiometric quantities defined in Sections 2.1 and 2.2, and on theinteractions between radiation and matter, as characterized by the interaction quantities defined inSections 3.1 to 3.5. Dosimetric quantities, which aredevised to provide a physical measure to correlatewith actual or potential effects, are, in essence,
products of radiometric quantities and interactioncoefficients. In calculations, the values of the relevant quantities of each type must be known, while measurements often do not require this information.
Radiation interacts with matter in a series ofprocesses in which particle energy is converted and
finally deposited in matter. The dosimetric quanti,ies which describe these processes are presented
--below in two sections dealing with the conversionand with the deposition of energy.
The quantity dEtr includes the _kinetic energy of
the Auger electrons.For a fiuence, e[>, of uncharged particles of energy
E, the kerma,K, in a specified material is given by
K = c[>EJ1t!p, (4.1.1)
where J.Lt!P is the mass energy transfer coefficient ofthe material for these particles.
The kerma per unit :fiuence, K/4>, is termed thekerma coefficient for uncharged particles of energyEin a specified material. The term kerma coefficient isused in preference to the term kerma factor previously used as the word coefficient implies a physicaldimension whereas the word factor does not.
In dosimetric calculations, the kerma, K, is usually expressed in terms of the distribution, c[>E, of theuncharged particle fiuence with respect to energy(see Eq. 2.1.6a). The kerma,K, is then given by
4.1 Conversion ofEnergy
The term conversion of energy refers to the trans
K = f c[>EE J.Ltr dE, p
(4.1.2)
fer of energy from ionizing particles to secondaryionizing particles. The quantity kerma relates to thekinetic energy of the charged particles liberated byuncharged particles; the energy expended againstthe binding energies, usually a relatively small
component, is, by definition, not included. In addition to kenna, a quantity called cema is defined whichrelates to the energy lost by charged particles (e.g.,electrons, protons, alpha particles) in collisions withatomic electrons. By definition, the binding energies areincluded. Cerna differs from kerma in that cerna involves the energy lost in electronic collisions by theincoming charged particles while kerma involves the
,, nergy imparted to outgoing charged particles.
4.1.1 Kerma2
The kerma, K, is the quotient of dEtr by dm,where dEtr is the sum of the initial kinetic energies of all the charged particles liberated by
uncharged particles in a mass dm of material,thus
where J.Lt/p is the mass energy transfer coefficient ofthe material for uncharged particles of energy E.
The expression of kenna in terms of :fiuence impliesthat one can refer to a value ofkerma or kerma rate for aspecified material at a point in free space, or inside a
different material. Thus, one can speak., for example, ofthe air kerma ata point inside a water phantom.
Although kerma is a quantity which concernsinitial transfer of energy to matter, it is sometimes
used as an approximation to absorbed dose. Equality of absorbed dose and kerma is approached to thedegree that charged particle equilibrium exists, thatradiative losses are negligible, and that the energy of
the uncharged particles is large compared to thebinding energy of the released charged particles.Charged particle equilibrium exists at a point if thedistribution of the charged particle radiance withrespect to energy (see Eq. 2.1.9a) is constant withindistances equal to the maximum charged particle range.
4.1.2 Kerma Rate
Unit: Jkg-1
dEtrK= dm.
The kerma rate, k, is the quotient of dK by dt,where dK is the increment of kerma in the time interval dt, thus
The special name for the unit of kerma is gray(Gy).
2 netic nergy eleased per unit mass.
Unit: J kg-1
s-1
Ifthe special name gray is used, the unit ofkermarate is gray per second (Gy s-1).
13
8/10/2019 Fsica Mdica ICRU60
16/22
cpE-
4.1.3 Exposure
The exposure, X, is the quotient of dQ by dm,where dQ is the absolute value ofthe total chargeofthe ions of one sign produced in air when all theelectrons and positrons liberated or created by
photons in air ofmass dm are completely stoppedin air, thus
Unit: ekg-1
The ionization produced by Auger electrons isincluded in dQ. The ionization due to photons emit
ted by radiative processes (i.e.,bremsstrahlung andfluorescence photons) is not to be included in dQ.Except for this difference, significant at high energies, the exposure, as defined above, is the ionizationanalogue of the air kerma. Exposure can be ex
pressed in terms of the distribution, ct>E, of thefluence with respect to the photon energy, E, and themass energy transfer coefficient, 1-Lt!p, for air and forthat energy as follows
4.1.5 Cema3
The cema, e, is the quotient of dECby dm, wheredEe is the energy lost by charged particles, exceptsecondary electrons, in electronic collisions in amass dm of a material, thus
dEC
e= dm
Unit: Jkg-1
The special name ofthe unit of cerna is gray (Gy).
The energy lost by charged particles in electroniccollisions includes the energy expended against binding energy and any kinetic energy of the liberated
electrons, referred to as secondary electrons. Thus,energy subsequently lost by all secondary electronsis excluded from dEc.
The cerna, e, can be expressed in terms of thedistribution ct>E, ofthe charged particle fluence, withrespect to energy (see Eq. 2.1.6a). According to thedefinition of cerna, the distribution cpE does notinclude the contribution of secondary electrons to the
fluence. The cerna, e, is thus given by
(4.1.3) e= fcpESe
-1
dE=f L:o
dE,p p
(4.1.4)
where e is the elementary charge, W is the meanenergy expended in air per ion pair formed, g is thefraction of the energy of the electrons liberated byphotons that is lost in radiative processes in air.
For photon energies of the order of 1MeV or below,where the value of g is small, Eq. 4.1.3 may beapproximated byX = e1W K(1 -g), whereK is theair kerma for primary photons andg is the meanvalue ofg averaged over the distribution of the airkerma with respect to the electron energy.
where Selpis the mass electronic stopping power of aspecified material for charged particles of energy E,and Loo is the corresponding unrestricted linearenergy transfer.
For charged particles of high energies, it may beundesirable to disregard energy transport by secondary electrons of all energies. A modified concept,
restricted cema, e;1, (Kellerer et al., 1992) is thendefined as the integral
As in the case of kerma, it may be convenient torefer to a value of exposure or of exposure rate in free
eJ.=fL!l
4>E:- dE.p
(4.1.5)
space or at a point inside a material different from air; one can speak, for example, of the exposure at a
point inside a water phantom.
4.1.4 Exposure Rate
The exposure rate,X, is the quotient of dXby dt,where dX is the increment of exposure in the time interval dt, thus
Unit: ekg-1s-114
This di:ffers from the integral in Eq. 4.1.4 in thatLxis replaced by L!l and that the distribution ct>E: nowincludes secondary electrons with kinetic energiesgreater than .1. For .1 = oo, restricted cerna isidentical to cerna.
The expression of cerna and restricted cerna interms of fluence implies that one can refer to theirvalues for a specified material at a point in freespace, or inside a different material. Thus, one can
speak, for example, of tissue cerna in air (Kellerer etal., 1992).
The quantities called cerna and restricted cernacan be used as approxirnations to absorbed dose fromcharged particles. Equality of absorbed dose and
3 -.onverted nergy per unit mass.
8/10/2019 Fsica Mdica ICRU60
17/22
\._ .;ema is approached to the degree that secondaryelectron equilibrium exists and that radiative lossesand those due to elastic nuclear collisions are negligible. Such an equilibrium is achieved at a point ifthe fluence of secondary electrons is constant within
distances equal to their maximum range. For restricted cerna, only partial secondary electron equilibrium, up to kinetic energy Ll, is required.
4.1.6 Cema Rate
The cerna rate, , is the quotient of dC by dt, where dC is the increment of cerna in the time interval dt, thus
- Unit: Jkg-1s-1
If the special name gray is used, the unit of cernarate is gray per second (Gy s-1).
4.2 Deposition of Energy
In this section, certain stochastic quantities areintroduced.Energy deposit is the fundamental quantity in terms of which all other quantities presented
here can be defined.
4.2.1 Energy Deposit
The energy deposit, Ei, is the energy deposited ina single interaction, i, thus
where Ein is the energy of the incident ionizingparticle (excluding rest energy), Eout is the sum ofthe energies of all ionizing particles leaving the
interaction (excludingrest energy), Q is the changein the rest energies of the nucleus and of all
particles involved in the interaction (Q > 0: decrease of rest energy; Q < 0: increase of restenergy).
Unit: J
E may also be expressed in eV.Ei may be considered as the energy deposited at the
point of interaction, which is called the transferpoint, i.e., the location where an ionizing particleloses kinetic energy. The quantum-mechanical uncertainties ofthis location are ignored.
The energy deposits and transfer points, without- -rurther details of the interactions that cause them,
are sufficient for a description ofthe spatial distribution of energy deposition by ionizing particles.
4.2.2 Energy Imparted
The energy imparted, E, to the matter in a givenvolume is the sum of all energy deposits in thevolume, thus
where the summation is performed over all en
ergy deposits, Ei, in that volume.
Unit: J
E may also be expressed in eV.
The energy deposits over which the summation isperformed may belong to one or more (energy deposition) events; for example, they may belong to one orseveral statistically independent partid e tracks. Theterm event denotes the imparting of energy to matter by statistically correlated particles. Examplesinclude a proton and its secondary electrons, anelectron-positron pair or the primary and secondary
particles in nuclear reactions.
If the energy imparted to the matter in a given volume is dueto a single event, it is equal to the sumof the energy deposits in the volume associated with
the event.If
the energy imparted to the matter in agiven volume is dueto several events, it is equal tothe sum of the individual energies imparted to thematter in the volume due to each event.
The mean energy imparted, , to the matter in a
given volume equals the radiant energy, Rim of allthose charged and uncharged ionizing particles whichenter the volume minus the radiant energy, Rouh ofall those charged and uncharged ionizing particleswhich leave the volume, plus the sum, Q, of allchanges of the rest energy of nuclei and elementaryparticles which occur in the volume (Q > 0: decreaseofrest energy; Q < 0: increase ofrest energy), thus
(4.2.1)
4.2.3 Lineal Energy
The lineal energy, y, is the quotient of Esby l,where Es is the energy imparted to the matter in a given volume by a single (energy deposition)
event and l is the mean chord length of thatvolume, thus
Unit: Jm-115
8/10/2019 Fsica Mdica ICRU60
18/22
Es is the sum of the energy deposits E in a volume
from a single event and may be expressed in eV.
Hence y may be expressed in multiples and submul
tiples ofeV and m, e.g., in keV .um-1.The mean chord length of a volume is the mean
length of randomly oriented chords (uniform isotropic randomness) through that volume. For a convexbody, it can be shown that. the mean chord length, l,equals 4V/A, where V is the volume and A is thesurface area (Cauchy, 1850; Kellerer, 1980).
It is useful to consider the probability distribution
ofy. The value of the distribution function, F(y), isthe probability that the lineal energy due to a single
(energy deposition) event is equal to or less than y.
The probability density, f(y), is the derivative ofF(y), thus
dF(y)
probability that a specific energy less than or equal
to z is deposited if one event has occurred Theprobability density, {1(z), is the derivative of F1(z),
thus
(4.2.4)
For convex volumes, y and the increment, z, ofspecific energy due to a single (energy deposition)
event are related by
pA
y=--z, (4.2.5)
where A is the surface area of the volume, and p isthe density of matter in the volume.
f(y) =d.Y. (4.2.2) 4.2.5 Absorbed DoseF(y) andf(y) are independent of absorbed dose andabsorbed dose rate.
4.2.4 Specific Energy
The absorbed dose, D, is the quotient of dbydm, where d is the mean energy imparted to
matter ofmass dm, thus
The specific energy (imparted), z, is the quotient of E by m, where E is the energy imparted tomatter ofmass m, thus
E
Unit: J kg-1
dD= dm.
Unit: Jkg-1
z =-.m
The special name for the unit of absorbed dose is gray(Gy).
The special name for the unit of specific energy is gray (Gy).
The specific energy may be due to one or more(energy deposition) events. The distribution function,F(z), is the probability that the specific energyis equal to or less thanz. The probability density,
f(z), is the derivative ofF(z), thus
dF(z)f(z) = . (4.2.3)
F(z) andf(z) depend on absorbed dose. The probabil
ity density f(z) includes a discrete component (a
Dirac delta function) atz = O for the probability of noenergy deposition.
The distribution function of the specific energy
deposited in a single event, F1(z), is the conditional
16
In the limit of a small domain, the mean specific
energyz is equal to the absorbed doseD.
4.2.6 Absorbed Dose Rate
The absorbed dose rate,D, is the quotient of dDby dt, where dD is the increment of absorbed dosein the time interval dt, thus
. dD
D =dt.
Unit: J kg-1s-1
If the special name gray is used, the unit ofabsorbed dose rate is gray per second (Gy s-1).
8/10/2019 Fsica Mdica ICRU60
19/22
coefficient J rn2 kg-1 Gyrn2 K/4> Sect. 4.1.1kerma rate k J kg-1 s-1 Gy s-1 dKJdt Sect. 4.1.2
irnparted E
lineal energy yJJrn-1
E
Esfl
Sect. 4.2.2
Sect. 4.2.3
specific
energy z g- Gy elm ect. . . absorbed
dose D J kg-1 Gy de/dm Sect. 4.2.5absorbed
dose rate iJ J kg-1s-1 Gy s-1 dD/dt Sect. 4.2.6
o
J-.TABLE 4.1-Dosimetric quantities- Conversion of energy TABLE 4.2-Dosimetric quantities-Deposition ofenergy >,
"" Where it appears '\'here it EName Symbol Unit Definition in the report appears a;
in the
kerma K J kg-1 Gy d.Eu-fdm Sect. 4.1.1 N ame Symbol Unit Definition reponkerma
energy
deposit E J En- Eout + Q Sect. 4.2.1exposure X e kg- 1 dQ/dm Sect. 4.1.3 energyexposure rate x e kg- 1 s-1 cL"G'dt Sect. 4.1.4cerna e J kg-1 Gy d.Ecldm Sect. 4.1.5restricted cerna c.l J kg-1 Gy Sect. 4.1.5cerna rate e J kg-1 s-1 Gy s-1 dC/dt Sect.4.1.6
17
8/10/2019 Fsica Mdica ICRU60
20/22
5. Radioactivity
The term radioactivity refers to those spontaneoustransformations that involve changes ofthe nuclei of
atoms. The energy released in such transformationsis emitted as photons and/or other radiations.
Radioactivity is a stochastic process. The wholeatom is involved inthis process because nuclear transformations also can affect the atomic shell structure andcause emission of electrons, photons or both.
Atoms are subdivided into nuclides. A nuclide is aspecies of atoms having a specified number of protons and neutrons in its nucleus. Unstable nuclides,that transform to stable or unstable progeny, arecalled radionuclides. The transformation results inanother nuclide orina transition toa lower energy
state ofthe same nuclide.
5.1 Decay Constant
The decay constant, A, of a radionuclide in aparticular energy state is the quotient of dP by dt,where dP is the probability that a given nucleus undergoes a spontaneous nuclear transformationfrom that energy state in the time interval dt,thus
Unit: s-1
The quantity (ln 2)/A, commonly called the halflife, T112, of a radionuclide, is the mean time taken forthe radionuclides in the particular energy state todecrease to one half of their initial number.
5.2 Activity
The activity,A, ofan amount ofa radionuclide ina particular energy state at a given time, is thequotient of dN by dt, where dN is the number ofspontaneous nuclear transformations from thatenergy state in the time interval dt, thus
Unit: s-1
The activity,A, of an amount of a radionuclide in aparticular energy state is equal to the product of thedecay constant, A, for that state, and the number 1V ofnuclei in that state, thus
A=AN. (5.2.1)
5.3 Air Kerma-Rate Constant
The air kerma-rate constant, Ta, of a radionuclide emitting photons is the quotient of l 2KabyA,whereKa is the air kerma rate due to photons ofenergy greater than o, at a distance l in vacuo
from a pont source of this nuclide having anactivityA, thus
Unit: m2 J kg-1
If the special names gray (Gy) and becquerel (Bq)are used, the unit of air kerma-rate constant ism2 Gy Bq-1s-1
The photons referred to in the definition include
gamma rays, characteristic x rays, and interna!bremsstrahlung. The air kerma-rate constant, a characteristic of a
radionuclide, is defined in terms of an ideal pointsource. In a source of finite size, attenuation and scattering occur, and annihilation radiation and externa! bremsstrahlung may be produced. In sorne cases,these processes require significant corrections.
Any medium intervening between the source and
the point of measurement will give rise to absorptionand scattering for which corrections are needed.
The selection of the value of o depends upon theapplication. To simpli:fy notation and ensure unifor
mity, it is recommended that obe expressed in keV.For example, T5 is understood to be the air kermarate constant with a photon energy cutoff of 5 keV.
TABLE 5.1-Quantities related to radioactivity
Whereit
appears
in the
Name Symbol Unit Definition report
decay
The special name for the unit of activity is bec querel (Bq).
The "particular energy state" is the ground state of
constant A.
halflife Tv2
activity Aairkerma-rate con-
s-1 d.P/dt Sect. 5.1
S Cln 2)/A. Sect. 5.1s-1
Bq dN/dt Sect. 5.2
8 the radionuclide unless otherwise specified. stant T6 m2 J kg-1 m2 Gy Bq-1s-1 12K6/A Sect. 5.3
8/10/2019 Fsica Mdica ICRU60
21/22
References
BIPM (1998). Bureau International des Poids etMesures, Le Systeme International d'Units (SI),7th edition (Bureau International des Poids etMesures, Sevres).
CAUCHY, A. (1850). "Mmoire sur la rectification descourbes et la quadrature des surfaces courbes,"
tion Units and Measurements, Stopping Pou:ers
for Electrons and Positrons, ICRU Report 37 (International Commission on Radiation Units and lVIea
surements, Bethesda, MD).
ICRU (1993a). International Commission on Radia
tion Units and Measurements, Quantities and.M. moires del' Acadmie des Sciences, XXII, 3. Units in Radiation Protection Dosimetry, ICRU
CIE (1987). Commission Internationale del'Eclairage, Vocabulaire Electrotehnique Intemational, CIE Publication 50 (845) (Bureau Centralde la Commission Electrotechnique Internationale, Geneve).
CODATA (1986). Committee on Data for Science andTechnology, The 1986Adjustment of the Fundamen
tal Physical Constants, Codata Bulletin Number63 (Pergamon Press, Oxford).
'---HUBBELL, J.H. (1969).Photon cross sections, attenuation coefficients, and energy absorption coefficients(rom 10 keV to 100 GeV,NSRDS-NBS 29 (NationalBureau of Standards, Washington, DC).
ICRU (1979). International Commission on Radiation Units and Measurements, Average Energy
Required to Produce an Ion Pair, ICRU Report 31(International Commission on Radiation Unitsand Measurements, Bethesda, MD).
ICRU (1980). International Commission on Radia
tion Units and Measurements, Radiation Quantities and Units, ICRU Report 33 (InternationalCommission on Radiation Units and Measure ments, Bethesda, MD).
ICRU (1984). International Commission on Radia-
Report 51 (International Commission on Radia
tion Units and Measurements, Bethesda, MD).
ICRU (1993b). International Commission on Radia
tion Units and Measurements, Stopping Powersand Ranges for Protons and Alpha Particles, ICRUReport 49 (International Commission on Radia
tion Units and Measurements, Bethesda, MD).
ISO (1993). International Organization for Standard
ization,ISO Standards Handbook, Quantities andUnits, 3rd edition (International Organization forStandardization, Geneva).
KELLERE A.M. (1980). "Concepts of geometrical
probability relevant to microdosimetry and dosim
etry," p. 1049 in Proceedings Seventh Symposiumon Microdosimetry, Booz, J., Ebert, H.G. and Hartfiel, H.D., Eds. (Harwood Academic Publishers,Chur, Switzerland).
KELLERE A.M., HAHN, K. and Rossi, H.H. (1992).
"Intermediate dosimetric quantities," Rad. Res.130,15-25.
SELTZE S.M. (1993). "Calculation of photon mass
energy-transfer and mass energy-absorption coef
ficients,"Rad. Res. 136, 147-170.
19
8/10/2019 Fsica Mdica ICRU60
22/22