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ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies(ISO member bodies). The work of preparing International Standards is normally carried out through ISOtechnical committees. Each member body interested in a subject for whom a technical committee has beenestablished has the right to be represented on that committee. International organizations, governmental andnon-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with theInternational Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
Draft International Standards adopted by the technical committees are circulated to the member bodies forvoting. Publication as an International Standard requires approval by at least 75 % of the member bodies
casting a vote.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patentrights. ISO shall not be held responsible for identifying any or all such patent rights.
International Standard ISO 80000-10 was prepared by Technical Committee ISO/TC 12, Quantities and units,in co-operation with IEC/TC 25, Quantities and units.
This first edition of ISO 80000-10 cancels and replaces ISO 31-9:1992 and ISO 31-10:1992. It alsoincorporates Amendments ISO 31-9:1992/Amd.1:1998 and ISO 31-10:1992/Amd.1:1998. The major technicalchanges from the previous standards are the following:
Annex A and Annex B to ISO 31-9:1992 have been deleted (as they are covered by ISO 80000-9);
Annex C to ISO 31-9:1992 has become Annex A;
Annex D to ISO 31-9:1992 has been deleted;
the presentation of numerical statements has been changed;
the Normative references have been changed;
items 10-33 and 10-53 from ISO 31-10:1992 have been deleted;
new items have been added;
many definitions have been re-formulated;
newer values for fundamental constants have been used.
ISO 80000 consists of the following parts, under the general title Quantities and units:
Part 1: General
Part 2: Mathematical signs and symbols to be used in the natural sciences and technology
The tables of quantities and units in this International Standard are arranged so that the quantities arepresented on the left-hand pages and the units on the corresponding right-hand pages.
All units between two full lines on the right-hand pages belong to the quantities between the corresponding fulllines on the left-hand pages.
Where the numbering of an item has been changed in the revision of a part of ISO 31, the number in thepreceding edition is shown in parenthesis on the left-hand page under the new number for the quantity; a dashis used to indicate that the item in question did not appear in the preceding edition.
0.2 Tables of quantities
The names in English and in French of the most important quantities within the field of this InternationalStandard are given together with their symbols and, in most cases, their definitions. These names andsymbols are recommendations. The definitions are given for identification of the quantities in the InternationalSystem of Quantities (ISQ), listed on the left hand pages of the table; they are not intended to be complete.
The scalar, vector or tensor character of quantities is pointed out, especially when this is needed for thedefinitions.
In most cases only one name and only one symbol for the quantity are given; where two or more names or
two or more symbols are given for one quantity and no special distinction is made, they are on an equalfooting. When two types of italic letters exist (for example as with ϑ and θ ; φ and φ ; a and a; g and g ), only oneof these is given. This does not mean that the other is not equally acceptable. It is recommended that suchvariants not be given different meanings. A symbol within parentheses implies that it is a reserve symbol, tobe used when, in a particular context, the main symbol is in use with a different meaning.
In this English edition, the quantity names in French are printed in an italic font, and are preceded by fr . Thegender of the French name is indicated by (m) for masculine and (f) for feminine, immediately after the noun inthe French name.
0.3 Tables of units
0.3.1 General
The names of units for the corresponding quantities are given together with the international symbols and thedefinitions. These unit names are language-dependent, but the symbols are international and the same in alllanguages. For further information, see the SI Brochure (8th edition, 2006) from BIPM and ISO 80000-1.
The units are arranged in the following way:
a) The coherent SI units are given first. The SI units have been adopted by the General Conference onWeights and Measures (Conférence Générale des Poids et Mesures, CGPM). The coherent SI units andtheir decimal multiples and submultiples formed with the SI prefixes are recommended, although thedecimal multiples and submultiples are not explicitly mentioned.
b) Some non-SI units are then given, namely those accepted by the International Committee for Weightsand Measures (Comité International des Poids et Mesures, CIPM), or by the International Organization ofLegal Metrology (Organisation Internationale de Métrologie Légale, OIML), or by ISO and IEC, for usewith the SI.
Such units are separated from the SI units in the item by use of a broken line between the SI units andthe other units.
c) Non-SI units currently accepted by the CIPM for use with the SI are given in small print (smaller than thetext size) in the “Conversion factors and remarks” column.
d) Non-SI units that are not recommended are given only in annexes in some parts of this InternationalStandard. These annexes are informative, in the first place for the conversion factors, and are not integralparts of the standard. These deprecated units are arranged in two groups:
1) units in the CGS system with special names;
2) units based on the foot, pound, second, and some other related units.
e) Other non-SI units given for information, especially regarding the conversion factors, are given ininformative annexes in some parts of this International Standard.
0.3.2 Remark on units for quantities of dimension one, or dimensionless quantities
The coherent unit for any quantity of dimension one, also called a dimensionless quantity, is the number one,symbol 1. When the value of such a quantity is expressed, the unit symbol 1 is generally not written outexplicitly.
EXAMPLE 1 Refractive index n = 1,53 × 1 = 1,53
Prefixes shall not be used to form multiples or submultiples of this unit. Instead of prefixes, powers of 10 arerecommended.
EXAMPLE 2 Reynolds number Re = 1,32 × 103
Considering that the plane angle is generally expressed as the ratio of two lengths and the solid angle as theratio of two areas, in 1995 the CGPM specified that, in the SI, the radian, symbol rad, and steradian, symbol sr,are dimensionless derived units. This implies that the quantities plane angle and solid angle are considered asderived quantities of dimension one. The units radian and steradian are thus equal to one; they may either beomitted, or they may be used in expressions for derived units to facilitate distinction between quantities ofdifferent kind but having the same dimension.
0.4 Numerical statements in this International Standard
The sign = is used to denote “is exactly equal to”, the sign ≈ is used to denote “is approximately equal to”, andthe sign := is used to denote “is by definition equal to”.
Numerical values of physical quantities that have been experimentally determined always have an associatedmeasurement uncertainty. This uncertainty should always be specified. In this International Standard, themagnitude of the uncertainty is represented as in the following example.
EXAMPLE l = 2,347 82(32) m
In this example, l = a(b) m, the numerical value of the uncertainty b indicated in parentheses is assumed toapply to the last (and least significant) digits of the numerical value a of the length l . This notation is used
when b represents the standard uncertainty (estimated standard deviation) in the last digits of a. Thenumerical example given above may be interpreted to mean that the best estimate of the numerical value ofthe length l , when l is expressed in the unit metre is 2,347 82, and that the unknown value of l is believed to
lie between (2,347 82 − 0,000 32) m and (2,347 82 + 0,000 32) m with a probability determined by thestandard uncertainty 0,000 32 m and the probability distribution of the values of l .
0.5 Special remarks
0.5.1 Quantities
The fundamental physical constants given in ISO 80000-10 are quoted in the consistent values of thefundamental physical constants published in “2006 CODATA recommended values”. See the CODATAwebsite: http://physics.nist.gov/cuu/constants/index.html.
0.5.2 Special units
Individual scientists should have the freedom to use non-SI units when they see a particular scientificadvantage in their work. For this reason, non-SI units which are relevant for atomic and nuclear physics arelisted in Annex A.
Quantities and units —Part 10:Atomic and nuclear physics
1 Scope
ISO 80000-10 gives the names, symbols, and definitions for quantities and units used in atomic and nuclear
physics. Where appropriate, conversion factors are also given.
2 Normative references
The following referenced documents are indispensable for the application of this document. For datedreferences, only the edition cited applies. For undated references, the latest edition of the referenceddocument (including any amendments) applies.
ISO 80000-3:2006, Quantities and units — Part 3: Space and time
ISO 80000-4:2006, Quantities and units — Part 4: Mechanics
ISO 80000-5:2007, Quantities and units — Part 5: Thermodynamics
IEC 80000-6:2008, Quantities and units — Part 6: Electromagnetism
ISO 80000-7:2008, Quantities and units — Part 7: Light
ISO 80000-9:2009, Quantities and units — Part 9: Physical chemistry and molecular physics
3 Names, symbols, and definitions
The names, symbols, and definitions for quantities and units used in atomic and nuclear physics are given on
c for a particle, the electriccharge(IEC 80000-6:2008, item6-2) divided by theelementary charge (item10-5.1)
A particle is said to be electricallyneutral if its charge number is equalto zero.The charge number of a particle canbe positive, negative, or zero.The state of charge of a particle may
be presented as a superscript to thesymbol of that particle, e.g.
3 = 3H , He , Al , Cl , S , N+ ++ + − −
10-6.1(9-7 )
Planck constant
fr constante (f)de Planck
h elementary quantum ofaction (ISO 80000-4:2006,item 4-37)
µ for a particle or nucleus,vector quantity causing anincrement
W ∆ = ⋅- µ B
to its energy W (ISO 80000-5:2007, item5-20.1) in an externalmagnetic field withmagnetic flux density B (IEC 80000-6:2008, item6-21)
For an atom or nucleus, this energy isquantized and may be written as
XW g MB= µ
where g is the appropriate g -factor(item 10-15.1 or item 10-15.2),
X µ is mostly the Bohr magneton ornuclear magneton (item 10-10.2 oritem 10-10.3), is the magneticquantum number (item 10-14.4), and B is the magnitude of the magneticflux density.
See also IEC 80000-6:2008, item
6-23.
10-10.2(9-11.2 )
Bohr magneton
fr magnéton (m)de Bohr
B µ B
e2
e
m=
µ
where e is the elementarycharge (item 10-5.1), and
em is the rest mass ofelectron (item 10-2)
B µ = 927,400 915(23) × 10 –26 J T –1
[2006 CODATA recommendedvalues].
B µ is magnetic moment of an
electron in a state with orbitalquantum number 1l = (item 10-14.3)due to its orbital motion.
10-10.3(9-11.3) nuclear magnetonfr magnéton (m)
nucléaire
Ν µ N
p2em
= µ
where e is the elementarycharge (item 10-5.1), and
Subscript N stands for nucleus. Forthe neutron magnetic moment,subscript n is used. The magneticmoments of protons or neutrons differfrom this quantity by their specific g -factors (item 10-15.2).
10-11
(—)
spin
fr spin (m)
s internal angular
momentum(ISO 80000-4:2006, item4-12) of a particle or aparticle system
number describingparticular state of aquantum microsystem
Electron states determine the binding
energy ( , , , ) E E n m j s=
in an atom.Capitals L, M , J , S are usuallyused for the whole system.
The spatial probability distribution ofan electron is given by
2ψ where ψ
is its wave function. For an electron inan H-atom in a non-relativisticapproximation, it can be presented as
( , , ) ( ) Y ( , )mnl l r R r ψ ϑ ϕ ϑ ϕ = ⋅
where, ,r ϑ ϕ are spherical coordinates
(ISO 80000-2:2009, item 2-16.3) withrespect to the nucleus and to a given(quantization) axis,
( )nl R r is the radial distributionfunction and Y ( , )m
l ϑ ϕ are sphericalharmonics.
In the Bohr model of one-electronatoms, n , l and m define thepossible orbits of an electron aroundthe nucleus.
10-14.2(9-23)
principal quantumnumber
fr nombre (m)quantique principal
n atomic quantum numberrelated to the number 1n − of radial nodes of one-electron wave functions
In the Bohr model, 1, 2, ,n = ∞… isrelated to the binding energy of anelectron and the radius of sphericalorbits (principal axis of the ellipticorbits).
For an electron in an H-atom, thesemi-classical radius of its orbit is
20nr a n= and its binding energy is
2H /n E E n= .
10-14.3(9-18)
orbital angularmomentumquantumnumber
fr nombre (m)quantique dumomentcinétiqueorbital,
nombre (m)quantiqueorbital
, ,il l L atomic quantum numberrelated to the orbitalangular momentum l of aone-electron state
2 2 1( )l l l = + , 0 1 1, , ,l n= −… .
il refers to a specific particle i;
L is used for the whole system.
An electron in an H-atom for 0l = appears as a spherical cloud. In theBohr model, it is related to the form ofthe orbit.
related to the the z -component z l , z j or z s of the orbital, total or spinangular momentum
z l l m= , z j j m= , z s s m= with the
ranges from l − to l , from j− to j,and ±1/2, respectively.
im refers to a specific particle i; M is used for the whole system.
Subscripts l , s , j, etc., asappropriate, indicate the angularmomentum involved.
10-14.5(9-19)
spin quantumnumber
fr nombre (m)quantiquedu spin
s characteristic quantumnumber of a particle,related to its spin angular
momentum s : s s +
2 2 1( )s =
Fermions have 1/ 2 s = or 3 / 2 s = .Observed bosons have 0 s = or 1 s = .The total spin quantum number
S of
an atom is related to the total spin(angular momentum), which is thesum of the spins of the electrons.It has the possible values
0,1, 2,S = … for even Z and
S = …31
2 2, , for odd Z .
10-14.6(9-20)
total angularmomentumquantumnumber
fr nombre (m)quantique dumomentcinétiquetotal
, ,i j j J quantum number in anatom describingmagnitude of totalangular momentum J
(item 10-12)
i j refers to a specific particle i; J is used for the whole system.
Care has to be taken, as quantum
number J is not the magnitude oftotal angular momentum J (item10-12).
The two values of j are l ± 1/ 2.(See item 10-14.3.)
Here, “total” does not mean“complete”.
10-14.7(9-21)
nuclear spinquantumnumber
fr nombre (m)quantiquede spinnucléaire
I quantum number relatedto the total angularmomentum J of a
nucleus in any specifiedstate, normally callednuclear spin:
2 2 ( 1) I I I = +
Nuclear spin is composed of spins ofthe nucleons (protons and neutrons)
and their (orbital) motions.In principle there is no upper limit forthe nuclear spin quantum number. Ithas possible values 0,1,2 I = … foreven A and I = …
F quantum number of anatom describinginclination of the nuclearspin with respect to aquantization axis givenby the magnetic fieldproduced by the orbitalelectrons
The interval of F is I J − , I J − + 1, ...,
I J + .
This is related to the hyperfine splitting ofthe atomic energy levels due to theinteraction between the electron andnuclear magnetic moments.
10-15.1(9-13.1)
Landé factor ofatom or electron,
g -factor of atomor electron
fr facteur (m)de Landéd'un atomeou d'unélectron,
facteur (m) g d'un atome
ou d'unélectron
B
µ g
J =
where µ is magnitude ofmagnetic dipole moment(item 10-10.1), J is total angularmomentum quantumnumber (item 10-14.6),and B µ is the Bohrmagneton (item 10-10.2)
These quantities are also called g -values.
The Landé factor can be calculated fromthe expression
e
( , , )( 1) ( 1) ( 1)
1 ( 1)2 ( 1)
g L S J
J J S S L L g
J J
=
+ + + − ++ − ⋅
+
where
e g = −2,002 319 304 362 2(15)
is the g -factor of the electron
[2006 CODATA recommended values].
10-15.2(9-13.2)
g -factor ofnucleus or
nuclear particle
fr facteur (m) g d'un noyau
ou d'une particulenucléaire
B
µ g
Iµ
=
where µ is magnitude ofmagnetic dipole moment(item 10-10.1), I is nuclear angularmomentum quantumnumber (item 10-14.7),and B µ is the Bohrmagneton (item 10-10.2)
The g -factors for nuclei or nucleons areknown from measurements; e.g. the
R conventional radius ofsphere in which thenuclear matter is included
This quantity is not exactly defined. Itis given approximately for nuclei intheir ground state only by
1/ 30 R r A=
where 150 1,2 10 mr −
×≈ and A is
the nucleon number.
10-20(9-25 )
fine-structureconstant
fr constante (f)de structurefine
α
π
2
0 04
eα
ε c=
where e is the elementarycharge (item 10-5.1),
0ε is the electric constant(IEC 80000-6:2008, item6-14.1), is the reducedPlanck constant (item10-6.2), and 0c is thespeed of light in vacuum(ISO 80000-7:2008, item7-4.1)
This is a factor historically related tothe change and splitting of atomic
energy levels due to relativisticeffects.
10-21(9-26 )
electron radius
fr rayon (m) de
l'électron
er
π
2
e 2
0 e 04
er
ε m c
=
where e is the elementarycharge (item 10-5.1),
0ε is the electric constant(IEC 80000-6:2008, item6-14.1), em is the restmass of electron (item10-2), and 0c is the speedof light in vacuum(ISO 80000-7:2008, item7-4.1)
This quantity corresponds to theelectrostatic energy E of a charge
distributed inside a sphere of radiuser as if all the rest energy (item 10-3)
of the electron were attributed to theenergy of electromagnetic origin,using the relation 2
e 0 E m c= .
er = 2,817 940 289 4(58) × 10 –19 m
[2006 CODATA recommendedvalues].
10-22(9-27)
Comptonwavelength
fr longueur (f) d'onde deCompton
C λ C
0
h λ
mc=
where h is the Planckconstant (item 10-6.1),m is the rest mass (item10-2) of a particle, and
0c is the speed of light invacuum(ISO 80000-7:2008, item7-4.1)
The wavelength of electromagneticradiation scattered from free electrons(Compton scattering) is larger thanthat of the incident radiation by amaximum of C2 λ .
of the number N of atomsor nuclei in a system, dueto spontaneous emissionfrom these atoms or nucleiduring an infinitesimal timeinterval, divided by itsduration t d (ISO 80000-3:2006, item3-7), thus
1 d
d
N λ
N t = −
For exponential decay, this quantity isconstant.
If more decay channels occur, then
a λ λ= ∑ where a λ denotes the
probability of decay to a specifiedfinal state and the sum is taken over
all final states. Further,1
λτ
= .
10-27(9-31) mean lifetime,mean life
fr vie (f) moyenne
τ 1τ λ
=
where λ is the decayconstant (item 10-26)
Mean lifetime is the expectation of thelifetime of an unstable particle or anexcited state of a particle.
10-28(9-32 )
level width
fr largeur (f) deniveau
Γ Γ
τ =
where is the reducedPlanck constant (item10-6.2) and τ is the meanlifetime (item 10-27)
Level width is the uncertainty of theenergy of an unstable particle or anexcited state of a system due to theHeisenberg principle.
10-29(9-33)(10 -49)
activity
fr activité (f)
A variation d N ofspontaneous number ofnuclei N in a particularenergy state, in a sampleof a radionuclide, due tospontaneous nucleartransitions from this stateduring an infinitesimal timeinterval, divided by itsduration dt (ISO 80000-3:2006, item
3-7), thus:d
d
N A
t = −
For exponential decay, A λ N = ,where λ is the decay constant (item10-26).
10-30(9-34)
specific activity,massic activity
fr activité (f)massique
a Aa
m=
where A is the activity(item 10-29) of a sampleand m is its mass(ISO 80000-4:2006, item4-1)
where A is the activity(item 10-29) of a sampleand V is its volume(ISO 80000-3:2006, item3-4)
10-32(—)
surface activitydensity,
areic activity
fr activité (f)surfacique
sa s /a A S =
where S is the total area(ISO 80000-3:2006, item3-3) of the surface of a
sample and A is itsactivity (item 10-29)
This value is usually defined for flatsources, where S corresponds to thetotal area of surface of one side of thesource.
10-33(9-37 )
half-life
fr période (f)radioactive
1/2T average duration(ISO 80000-3:2006, item3-7) required for the decayof one half of the atoms ornuclei
For exponential decay, 1/2 (ln2)/T λ= .
10-34(9-38 )
alphadisintegrationenergy
fr énergie (f ) dedésinté-gration alpha
αQ sum of the kinetic energy(ISO 80000-3:2006, item4-27.3) of the α -particleproduced in thedisintegration process andthe recoil energy(ISO 80000-5:2007, item5-20.1) of the productatom in the referenceframe in which the emittingnucleus is at rest before itsdisintegration
The ground-state alpha disintegration
energy, α,0Q , also includes theenergy of any nuclear transitions that
take place in the daughter produced.
10-35(9-39)
maximum beta-particle energy
fr énergie (f) bêtamaximale
β E maximum energy(ISO 80000-5:2007, item5-20.1) of the energy
βQ sum of the maximum betaparticle kinetic energy(item 10-35) and therecoil energy(ISO 80000-5:2007, item5-20.1) of the atomproduced in the referenceframe in which the emittingnucleus is at rest before itsdisintegration
For positron emitters, the energy forthe production of an electron pair hasto be added to the sum mentioned inthe definition.
The ground-state beta disintegrationenergy, β,0Q , also includes theenergy of any nuclear transitions that
take place in the daughter product.
10-37(9-41)
internalconversionfactor
fr facteur (m) deconversioninterne
α ratio of the number ofinternal conversionelectrons to the number of
gamma quanta emitted bythe radioactive atom in agiven transition
The quantity / 1( )α α + is also used
and may be called the internal
conversion fraction.Partial conversion fractions referringto the various electron shells K, L, ...are indicated by K L, ,α α …,
K L/α α is called the K to L internalconversion ratio.
10-38.1(10-1)
reaction energy
fr énergie (f) deréaction
Q in a nuclear reaction, thesum of the kinetic energies(ISO 80000-4:2006, item4-27.3) and photon
energies(ISO 80000-5:2007, item5-20.1) of the reactionproducts minus the sum ofthe kinetic and photonenergies of the reactants
For exothermic nuclear reactions,0Q > .
For endothermic nuclear reactions,
0Q <
.
10-38.2(10-2 )
resonance energy
fr énergie (f) derésonance
r E , res E kinetic energy(ISO 80000-4:2006, item4-27.3) of an incidentparticle, in the referenceframe of the target,corresponding to aresonance in a nuclearreaction
σ for a specified targetparticle and for a specifiedreaction or processproduced by incidentcharged or unchargedparticles of specified typeand energy, the meannumber of such reactionsor processes divided bythe incident-particlefluence (item 10-44)
The type of process is indicated by
subscripts, e.g. absorption cross-section aσ , scattering cross-section
sσ , fission cross-section f σ .
10-39.2(10-3.2 )
total cross-section
fr section (f)efficacetotale
totσ , Tσ sum of all cross-sections(item 13-36.1)corresponding to thevarious reactions orprocesses between anincident particle ofspecified type and energy(ISO 80000-5:2007, item5-20.1) and a targetparticle
In the case of a narrow unidirectionalbeam of incident particles, this is theeffective cross-section for the removalof an incident particle from the beam.See the Remarks for item 10-53.
Ωσ cross-section for ejectingor scattering a particle intoan elementary cone,divided by the solid angledΩ (ISO 80000-3:2006,item 3-6) of that cone:
dΩσ σ Ω= ∫
10-41(10-5 )
spectralcross-section
fr section (f)efficacespectrique
E σ cross-section (item10-39.1) for a process inwhich the energy(ISO 80000-5:2007, item5-20.1) of the ejected or
scattered particle is in aninterval of energy, dividedby the range d E of thisinterval
d E σ σ E = ∫
10-42(10-6 )
spectral angularcross-section
fr section (f)efficacedirectionnelle
spectrique
,Ω E σ cross-section (item10-39.1) for ejecting orscattering a particle into anelementary cone withenergy E
(ISO 80000-5:2007, item5-20.1) in an energyinterval, divided by thesolid angle dΩ (ISO 80000-3:2006, item3-6) of that cone and therange d E of that interval:
, d dΩ E σ σ Ω E = ∫∫
Quantities 10-40, 10-41 and 10-42are sometimes called differentialcross-sections.
In accordance with conventions used
in other parts of this InternationalStandard, angular and spectral cross-
sections are indicated by the use ofsubscripts. Information about
incoming and outgoing particles maybe added between parentheses, e.g.
σ Ω , E (n E 0,p E ϑ ) orσ Ω , E (n E 0,p) or σ Ω , E (n,p).
The cross-section for a process inwhich an incoming neutron of energy
0 E causes the ejection of a protonwithin the energy interval [ d ], E E E +
and in the elementary cone with solidangle dΩ, about the scattering angle
ϑ , is σ Ω , E (n E 0,p E ϑ ) dΩ d E .
Sometimes, the incoming and
outgoing particles are indicated bysubscripts, in which case the
subscript Ω or E indicating theangular or spectral character could be
placed in the superscript position, e.g.,
n,p 0( )Ω E σ E or ,n,pΩ E σ .
If, however, the subscripts Ω or E are omitted completely from the
cross-section symbol, the angular orspectral character of the cross-section then follows only from theoccurrence of the variable ϑ or E for
the outgoing particles between the
parentheses, e.g. σ n,p( E 0, E ϑ ) orσ n,p( E ϑ ).
These variables should then never beomitted.
Instead of “spectral”, the terms“distribution with respect to energy” or“energy distribution” can be used (seeICRU Report 60, 1998).
Σ sum of the cross-sections(item 10-39.1) for areaction or process of aspecified type over allatoms or other entities in agiven 3D domain, dividedby the volume(ISO 80000-3:2006, item3-4) of that domain
10-43.2
(10-7.2 )
volumic total
cross-section,macroscopic totalcross-section
fr section (f)efficacetotalemacro-scopique,
section (f)efficacetotalevolumique
tot Σ , T Σ sum of the total cross-
sections (item 10-39.1) forall atoms or other entitiesin a given 3D domain,divided by the volume(ISO 80000-3:2006, item3-4) of that domain
1 1 ... j j Σ n σ n σ = + + +
where jn is the number density and
jσ the cross-section for entities of
type j. When the target particles ofthe medium are at rest, 1/ Σ l = ,
where l is the mean free path (item10-73).
See the Remarks for item 10-50.
10-44(10-8 )
particle fluence
fr fluence (f) de particules
Φ at a given point of space,the number d N ofparticles incident on asmall spherical domain,divided by the cross-sectional area d A (ISO 80000-3:2006, item3-3) of that domain:
d
d
N Φ=
A
The word “particle” is usually replacedby the name of a specific particle, forexample proton fluence.
When a flat source is used, forparticles passing perpendicularlythrough the surface, this value is thenumber of particles passing throughthe surface of the flat source dividedby the total area of that surface.
where dΦ is the incrementof the particle fluence(item 10-44) during aninfinitesimal time intervalwith duration dt
(ISO 80000-3:2006, item3-7)
The word “particle” is usually replacedby the name of a specific particle, forexample proton fluence rate.
Mostly, symbol Φ is used instead ofθ .
The distribution function expressed interms of speed and energy, θ
v and
E θ , are related to θ by
d d E θ θ θ E = =∫ ∫vv .
This quantity has also been termedparticle flux density. Because the
word “density” has severalconnotations, the term “fluence rate”is preferred. For a radiation fieldcomposed of particles of velocity v,the fluence rate is equal to nv, wheren is the particle number density.
See Remarks for 10-44.
10-46(—)
radiant energy
fr énergie (f)rayonnante
R energy(ISO 80000-5:2007, item5-20.1), excluding restenergy (item 10-3), of theparticles that are emitted,transferred or received
For particles of energy E (excludingrest energy), the radiant energy, R, isequal to the product NE where N is
the number of the particles that areemitted, transferred or received
The distributions, E N and E R , of the
particle number and the radiantenergy with respect to energy are
given by d d/ E E N N = and d d/ E E R R= where d N is the number of particles
with energy between E and d E E + , and d R is their radiant energy. The
the sum of the radiantenergies d R (item 10-46),exclusive of rest energy, of
all particles incident on asmall spherical domain,
divided by the cross-sectional area d A
(ISO 80000-3:2006, item3-3) of that domain:
d
d
RΨ
A=
10-48(10-11)
energy fluencerate
fr débit (m) defluenceénergétique
ψ d
d
Ψ ψ
t =
where dΨ is the incrementof the energy fluence (item10-47) during aninfinitesimal time intervalwith duration dt (ISO 80000-3:2006, item3-7)
Mostly, symbol Ψ is used instead ofψ .
Symbol ψ is lower case psi.
10-49(10-12 )
particle current
fr densité (f) decourant de particules
J , ( S ) vector quantity, theintegral of whose normalcomponent over anysurface is equal to the netnumber N of particlespassing through thatsurface in an infinitesimaltime interval divided by itsduration dt
(ISO 80000-3:2006, item
3-7): n d d /d A N t ⋅ =∫ J e
where nd Ae is the vector
surface element(ISO 80000-3:2006, item3-3)
Usually the word “particle” is replacedby the name of a specific particle, forexample proton current.
Symbol S is recommended when
there is a possibility of confusion withthe symbol J for electric currentdensity. For neutron current, thesymbol J is generally used. The
distribution functions expressed interms of speed and energy, J
where J is magnitude ofthe current rate (item10-49) of a beam ofparticles parallel to the x -direction
µ is equal to the macroscopic total
cross-section tot Σ for the removal ofparticles from the beam.
10-51(10-14)
mass attenuationcoefficient
fr coefficient (m)d'atténuationmassique
m µ /m µ µ ρ=
where is the linearattenuation coefficient(item 10-50) and ρ is the
mass density(ISO 80000-4:2006, item4-2) of the medium
10-52(10-15 )
molar attenuationcoefficient
fr coefficient (m)d'atténuationmolaire
c µ /c µ µ c=
where is the linearattenuation coefficient(item 10-50) and c is theamount-of-substanceconcentration(ISO 80000-9:2009, item9-13) of the medium
10-53(10-16 )
atomicattenuationcoefficient
fr coefficient (m)d'atténuationatomique
a µ a / µ µ n=
where is the linearattenuation coefficient(item 10-50) and n is thenumber density(ISO 80000-9:2009, item9-10.1) of the atoms in thesubstance
µ is equal to the total cross-section
totσ for the removal of particles fromthe beam.
See also item 10-39.2.
10-54(10-17 )
half-valuethickness
fr épaisseur (f) de demi-atténuation
1/2d thickness(ISO 80000-3:2006, item3-1.4) of the attenuatinglayer that reduces thequantity of interest of aunidirectional beam to halfof its initial value
For exponential attenuation,
1/2 (ln2)/d µ= .
Other half-value thicknesses, such asthose for attenuation, exposure andair kerma are also used.
where d E − is the energy(ISO 80000-5:2007, item5-20.1) decrement in the x -direction along anelementary path with thelength d x (ISO 80000-3:2006, item3-1.1)
Also called stopping power.
Both electronic losses and radiativelosses are included.
The ratio of the total linear stoppingpower of a substance to that of areference substance is called therelative linear stopping power.
See also item 10-88.
10-56(10-19)
total atomicstopping power
fr pouvoir (m)
d'arrêtatomiquetotal
aS a /S S n=
where S is the total linearstopping power (item10-55) and n is thenumber density(ISO 80000-9:2009, item9-10.1) of the atoms in thesubstance
10-57(10-20 )
total massstopping power
fr pouvoir (m)d'arrêtmassiquetotal
mS /mS S ρ=
where S is the total linearstopping power (item10-55) and ρ is the massdensity
(ISO 80000-4:2006, item4-2) of the sample
The ratio of the total mass stoppingpower of a substance to that of areference substance is called therelative mass stopping power.
10-58(10-21)
mean linear range
fr parcours (m)moyenlinéaire
R, l R mean total rectified pathlength (ISO 80000-3:2006,item 3-1.1) travelled by aparticle in the course ofslowing down to rest (or tosome suitable cut-offenergy) in a givensubstance under specifiedconditions averaged over
a group of particles havingthe same initial energy(ISO 80000-5:2007, item5-20.1)
10-59(10-22 )
mean mass range
fr parcours (m)moyen enmasse
R , ( m R ) ρ R R ρ=
where R is the meanlinear range (item 10-58)and ρ is the mass density(ISO 80000-4:2006, item4-2) of the sample
where e is the elementarycharge and dQ is theaverage total charge of allpositive ions producedover an infinitesimalelement of the path withlength dl (ISO 80000-3:2006, item3-1.1) by an ionizingcharged particle
Ionization due to secondary ionizingparticles, etc., is included.
10-61(10-24)
total ionization
fr ionisation (f)totale
i N by a particle, total meancharge, divided by theelementary charge, e, ofall positive ions producedby an ionizing chargedparticle along its entirepath and along the pathsof any secondary chargedparticles
id N N l = ∫
See Remarks for item 10-60.
10-62
(10-25 )
average energy
loss perelementarycharge produced
fr perte (f)moyenned'énergie par paire d'ionsformée
iW i k i/W E N =
where k E is the initialkinetic energy(ISO 80000-4:2006, item4-27.3) of an ionizingcharged particle and i N isthe total ionization (item10-61) produced by thatparticle
The name “average energy loss per
ion pair formed” is usually used,although it is ambiguous.The quantity
i i/S N , sometimes called the average
energy per ion pair formed, shouldnot be confused with iW .
In ICRU Report 60, the mean energyexpended in a gas per ion pairformed, W , is the quotient of E by N , where N is the mean number ofion pairs formed when the initialkinetic energy E of a chargedparticle is completely dissipated in thegas. Thus /W E N = where the meannumber N of ion pairs is equal to thetotal liberated charge of either signdivided by the charge of the electron.
It follows from the definition of W thatthe ions produced by bremsstrahlungor other secondary radiation emittedby the charged particles are includedin N .p
µ average drift speed(ISO 80000-3:2006, item3-8.1) imparted to acharged particle in amedium by an electricfield, divided by theelectric field strength(IEC 80000-6:2008, item6-10)
10-64.1(10-29)
particle numberdensity
fr nombre (m)volumique de
particules
n /n N V =
where N is the number ofparticles in the 3D domainwith the volume V
10-64.2(10-27 )
ion numberdensity,
ion density
fr nombre (m)volumiqued'ions
n+ , n− /n N V
+ += , /n N V
− −=
where N + and N
− are thenumber of positive andnegative ions,respectively, in a 3Ddomain with volume V (ISO 80000-3:2006, item3-4)
n is the general symbol for thenumber density of particles.
The distribution function expressed interms of speed and energy, n
v and
E n , is related to n by
d d E E n n n= =∫ ∫vv .
The word “particle” is usually replacedby the name of a specific particle, forexample neutron number density.
10-65(10-28 )
recombinationcoefficient,recombinationfactor
fr coefficient (m)de recombi-naison
α coefficient in the law ofrecombination
d d
d d
n nαn n
t t
+ −+ −
− = − =
where n+ and n− are theion number densities (item10-64.2) of positive andnegative ions,respectively, recombinedduring an infinitesimal timeinterval with duration dt (ISO 80000-3:2006, item3-7)
The widely used term “recombinationfactor” is not correct because “factor”should only be used for quantitieswith dimension 1.
10-66(10-32 )
diffusioncoefficient,
diffusioncoefficient forparticle numberdensity
fr coefficient (m)de diffusion,
coefficient (m)de diffusion
pour le nombrevolumique de
particules
D, n D in the x -direction,
xn
J D
n x= −
∂ ∂
where x J is the x -component of theparticle current (item10-49) and n is theparticle number density(item 10-64.1)
The word “particle” is usually replacedby the name of a specific particle, forexample neutron number density.
fr coefficient (m)de diffusion pour le débitde fluence
φ D , ( D) xφ
J D
φ x
= −
∂ ∂
where x J is the x -compo-nent of the particle current(item 10-49) and φ is theparticle fluence rate (item10-45)
For a particle of a given speed v,
( ) xφ
J Dφ x
= −∂ ∂
v,
v
v
and
( ) ( )φ n D D= −v v v .
10-68(10-34)
particle sourcedensity
fr densité (f)totale d’une
source de particules
S rate of production ofparticles in a 3D domaindivided by the volume(ISO 80000-3:2006, item3-4) of that element
The word “particle” is usually replacedby the name of a specific particle, forexample proton source density.
The distribution functions expressed
in terms of speed and energy, S v and E S , are related to S by
d d E E S S S = =∫ ∫vv .
10-69(10-35 )
slowing-downdensity
fr densité (f) deralentis-sement
q number density (item10-64.1) slowing downpast a given energy(ISO 80000-5:2007, item5-20.1) value in aninfinitesimal time interval,divided by the duration
(ISO 80000-3:2006, item3-7) of that interval
For a number density n andduration dt ,
d
dt
nq = − .
10-70(10-36 )
resonanceescapeprobability
fr facteur (m)antitrappe
in an infinite medium, theprobability that a neutronslowing down will traverseall or some specifiedportion of the range ofresonance energies (item10-38.2) without beingabsorbed
ξ average value of theincrease in lethargy (item10-71) in elastic collisionsbetween neutrons andnuclei whose kineticenergy(ISO 80000-4:2006, item4-27.3) is negligiblecompared with that of theneutrons
10-73(10-39)
mean free path
fr libre parcours (m)moyen
l , λ average distance(ISO 80000-3:2006, item3-1.9) that particles travelbetween two successivespecified reactions orprocesses
See the Remarks foritem 10-43.
10-74.1(10-40.1)
slowing-downarea
fr aire (f) deralentis-sement
2s L , 2
sl L in an infinite homogenousmedium, one-sixth of themean square distance(ISO 80000-3:2006, item3-1.9) between theneutron source and thepoint where a neutron
reaches a given energy(ISO 80000-5:2007, item5-20.1)
10-74.2(10-40.2 )
diffusion area
fr aire (f) dediffusion
2 L in an infinite homogenousmedium, one-sixth of themean square distance(ISO 80000-3:2006, item3-1.9) between the pointwhere a neutron enters aspecified class and thepoint where it leaves thisclass
The class of neutrons must bespecified.
10-74.3(10-40.3)
migration area
fr aire (f) demigration
2
sum of the slowing-downarea (ISO 80000-3:2006,item 3-3) from fissionenergy to thermal energy(ISO 80000-5:2007, item5-20.1) and the diffusionarea for thermal neutrons
f in an infinite medium, theratio of the number ofthermal neutrons absorbedin a fissionable nuclide orin a nuclear fuel, asspecified, to the totalnumber of thermalneutrons absorbed
The class (thermal) of neutrons mustbe specified.
10-79(10-45 )
non-leakageprobability
fr probabilité (f)de non-fuite
Λ probability that a neutronwill not escape from thereactor during the slowing-down process or while itdiffuses as a thermalneutron
The class (thermal) of neutrons mustbe specified.
10-80.1(10-46.1)
multiplicationfactor
fr facteur (m) demultiplication
k ratio of the total number offission or fission-dependent neutronsproduced in a time intervalto the total number ofneutrons lost byabsorption and leakageduring the same interval
10-80.2(10-46.2 )
infinitemultiplication
factorfr facteur (m) de
multiplicationinfini
k ∞ multiplication factor (item10-80.1) for an infinite
T duration (ISO 80000-3:2006, item3-7) required for the neutronfluence rate (item 10-45) in areactor to change by the factor ewhen the fluence rate is rising orfalling exponentially
Also called reactor period.
10-83.1(10-50.1)
energy imparted
fr énergie (f)commu-niquée
ε for ionizing radiation in the matterin a given 3D domain,
ii= ∑ε ε
where the energy deposit, iε , isthe energy (ISO 80000-5:2007,item 5-20.1) deposited in a singleinteraction i , and is given by
in outi Qε ε ε = − + ,where inε is the energy(ISO 80000-5:2007, item 5-20.1)of the incident ionizing particle,excluding rest energy (item 10-3),
outε is the sum of the energies(ISO 80000-5:2007, item 5-20.1)of all ionizing particles leaving theinteraction, excluding rest energy(item 10-3), and
Q is the change in the restenergies (item 10-3) of thenucleus and of all particlesinvolved in the interaction
Energy imparted is astochastic quantity.
10-83.2(10-50.2 )
mean energyimparted
fr énergie (f)commu-niquéemoyenne
ε to the matter in a given domain,
in out R R Qε = − + ∑
where in R is the radiant energy(item 10-46) of all those chargedand uncharged ionizing particlesthat enter the domain,
out R is the radiant energy of allthose charged and unchargedionizing particles that leave thedomain, and
Q∑ is the sum of all changes ofthe rest energy (item 10-3) ofnuclei and elementary particlesthat occur in that domain
This quantity has the meaningof the expected value of theenergy imparted (item10-83.1).
Sometimes, it has been calledthe integral absorbed dose.
Q > 0 means decrease of restenergy; Q < 0 means increaseof rest energy.
where dε is the meanenergy imparted (item10-83.2) by ionizingradiation to an elementof irradiated matter withthe mass dm (ISO 80000-4:2006, item4-1)
d D m= ∫ε
where dm is the element of mass ofthe irradiated matter.
In the limit of a small domain, themean specific energy z is equal tothe absorbed dose D.
10-84.2
(10-51.1)
specific energy
impartedfr énergie (f)
commu-niquéemassique
z for any ionizing radiation,
z m
= ε
where ε is the energyimparted (item 10-83.1)to irradiated matter andm is the mass(ISO 80000-4:2006, item4-1) of that matter
z is a stochastic quantity.
In the limit of a small domain, themean specific energy z is equal tothe absorbed dose D.
The specific energy imparted can bedue to one or more (energy-deposition) events.
10-85 quality factor
fr facteur (m) de
qualité
Q factor in the calculationand measurement of doseequivalent (item 10-86), by
which the absorbed dose(item 10-84.1) is to beweighted in order toaccount for differentbiological effectiveness ofradiations, for radiationprotection purposes
Q is determined by the unrestrictedlinear energy transfer, L∞ (oftendenoted as L or LET), of chargedparticles passing through a smallvolume element at this point (thevalue of L∞ is given for chargedparticles in water, not in tissue; thedifference, however, is small).
10-86(10-52 )
dose equivalent
fr dose (f)équivalente,
[équivalent (m)
de dose]
H at the point of interest intissue, H DQ=
where D is the absorbed
dose (item 10-84.1) andQ is the quality factor
(item 10-85) at that point
The dose equivalent at a point intissue is given by
0d( ) L H Q L D L
∞= ∫
where d d/ L D D L= is the distributionof L of the absorbed dose at thepoint of interest. The relationship of L is given in ICRP Publication 103(ICRP, 2007).
where d D is the incrementof absorbed dose (item10-84.1) during timeinterval with duration dt (ISO 80000-3:2006, item3-7)
10-88(10-54)
linear energytransfer
fr transfert (m)linéique
d’énergie
∆ L for ionizing charged
particles,d
d ∆
∆
E L
l =
where d ∆ E is the mean
energy lost in electroniccollisions locally to matteralong a small path throughthe matter, minus the sumof the kinetic energies ofall the electrons releasedwith kinetic energies inexcess of ∆ , anddl (ISO 80000-3:2006,item 3-1.1) is the length ofthat path
This quantity is not completelydefined unless ∆ is specified, i.e. themaximum kinetic energy of secondaryelectrons whose energy is consideredto be “locally deposited.” ∆ may beexpressed in eV.
Linear energy transfer is oftenabbreviated to LET, but the subscript ∆ or its numerical value should beappended to it.
10-89(10-55 )
kerma
fr kerma (m)
K for indirectly ionizing(uncharged) particles,
tr d
d
E K
m=
where t r d E is the mean
sum of the initial kineticenergies (ISO 80000-4:2006, item 4-27.3) of allthe charged ionizingparticles liberated byuncharged ionizing
particles in an element ofmatter, and dm is themass (ISO 80000-4:2006,item 4-1) of that element
The name “kerma” is derived fromKinetic Energy Released in MAtter (orMAss or MAterial).
The quantity t r d E includes the kinetic
energy of the charged particlesemitted in the decay of excited atomsor molecules or nuclei.
10-90(10-56 )
kerma rate
fr débit (m) dekerma
K d
d
K K
t =
where K is the incrementof kerma (item 10-89)during time interval withduration t (ISO 80000-3:2006, item3-7)
tr / µ ρ for a beam of indirectlyionizing unchargedparticles acting on thematerial,
tr tr
d1 1/
d
R µ ρ
ρ R l =
where tr d R is the meanenergy that is transferredto kinetic energy ofcharged particles byinteractions of the incidentradiation R in traversing adistance dl in the materialof density ρ
tr / / µ ρ K ψ = , where K is the kerma
rate (item 10-90) and ψ is the energyfluence rate (item 10-48).
The quantity
en tr / / 1( )( ) µ ρ µ ρ g = −
(where is the fraction of the kineticenergy of the liberated chargedparticles that is lost in radiativeprocesses in the material)is called the mass energy absorptioncoefficient.
The mass energy absorptioncoefficient of a compound materialdepends on the stopping power of thematerial. Thus its evaluation cannot,in principle, be reduced to a simplesummation of the mass energyabsorption coefficient of the atomicconstituents. Such a summation canprovide an adequate approximationwhen the value of g is sufficientlysmall.
See also item 10-51.
10-92(10-58 )
exposure
fr exposition (f)
X for X- or gamma radiation,d
d
Q X
m=
wheredQ is the absolute valueof the mean total electriccharge of the ions of thesame sign produced in dryair when all the electronsand positrons liberated orcreated by photons in an
element of air arecompletely stopped in air,anddm is the mass(ISO 80000-4:2006, item4-1) of that element
The ionization produced by electronsemitted in atomic or molecularrelaxation is included in dQ. Theionization due to photons emitted byradiative processes (i.e.bremsstrahlung and fluorescencephotons) is not to be included in dQ.
This quantity should not be confusedwith the quantity photon exposure(ISO 80000-7:2008, item 7-51),radiation exposure(ISO 80000-7:2008, item 7-18) or the
energy electronvolt eV 1 eV = 1,602 176 487 (40) · 10−19 J
mass dalton Da 1 Da = 1,660 538 782 (83) · 10−27 kg
unified atomic mass unit u 1 u = 1 Da
length astronomical unit ua 1 ua = 1,495 978 706 91 (6) · 1011 mNatural units (n.u.)
speed n.u. of speed(speed of light in vacuum)
c0 299 792 458 m/s (exact)
action n.u. of action(reduced Planck constant)
ħ 1,054 571 628 (53) · 10−34 J s
mass n.u. of mass(electron mass)
me 9,109 382 15 (45) · 10−31 kg
time n.u. of time ħ/(mec02) 1,288 088 6570 (18) · 10−21 s
Atomic units (a.u.) charge a.u. of charge
(elementary charge)e 1,602 176 487 (40) · 10−19 C
mass a.u. of mass(electron mass)
me 9,109 382 15 (45) · 10−31 kg
action a.u. of action(reduced Planck constant)
ħ 1,054 571 628 (53) · 10−34 J s
length a.u. of length, bohr(Bohr radius)
a0 0,529 177 208 59 (36) · 10−10 m
energy a.u. of energy, hartree(Hartree energy)
E h 4,359 743 94 (22) · 10−18 J
time a.u. of time ħ/ E h 2,418 884 326 505 (16) · 10−17 s
NOTE The units in this annex are those given in Table 7 in the 8th edition (2006) of BIPM's SI Brochure. Forcompleteness, the astronomical unit of length is included.
[1] ISO 80000-1, Quantities and units — Part 1: General
[2] ISO 80000-2:2009, Quantities and units — Part 2: Mathematical signs and symbols to be used in thenatural sciences and technology
[3] IEC 60050-393:2003, International Electrotechnical Vocabulary — Part 393: Nuclear instrumentation —Physical phenomena and basic concepts
[4] ICRP Publication 103 (ICRP, 2007)
[5] ICRU Report 60: Fundamental Quantities and Units for Ionizing Radiation, International Commission onRadiation Units and Measurements, Bethesda MD USA, 1998
[6] MOHR P.J. and T AYLOR B.N. CODATA recommended values of the fundamental physical constants:2002. Rev. Mod. Phys., 77(1), 2005, pp. 1-107
[7] MOHR P.J., T AYLOR B.N. and NEWELL, D.B. CODATA recommended values of the fundamental physicalconstants: 2006. Rev. Mod. Phys., 80(2), 2008, pp. 633-730. See also the CODATA website:http://physics.nist.gov/cuu/constants/index.html