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BS ISO

80000-10:2009

ICS 01.060

NO COPYING WITHOUT BSI PERMISSION EXCEPT AS PERMITTED BY COPYRIGHT LAW

BRITISH STANDARD

Quantities and units

Part 10: Atomic and nuclear physics

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This British Standard

was published under the

authority of the Standards

Policy and Strategy

Committee on 31 January

2010

© BSI 2010

ISBN 978 0 580 54870 3

Amendments/corrigenda issued since publication

Date Comments

BS ISO 80000-10:2009

National foreword

This British Standard is the UK implementation of ISO 80000-10:2009.

It supersedes BS ISO 31-10:1992 and BS ISO 31-9:1992 which are

withdrawn.

The UK participation in its preparation was entrusted to Technical

Committee SS/7, General metrology, quantities, units and symbols.

A list of organizations represented on this committee can be obtained on

request to its secretary.

This publication does not purport to include all the necessary provisions

of a contract. Users are responsible for its correct application.

Compliance with a British Standard cannot confer immunity

from legal obligations.

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Reference number ISO 80000-10:2009(E)

© ISO 2009

INTERNATIONALSTANDARD

ISO80000-10

First edition2009-12-01

Quantities and units —

Part 10:Atomic and nuclear physics

Grandeurs et unités —

Partie 10: Physique atomique et nucléaire

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Published in Switzerland

ii © ISO 2009 – All rights reserved

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Contents Page

Foreword ............................................................................................................................................................iv

Introduction........................................................................................................................................................vi

1 Scope ......................................................................................................................................................1

2 Normative references............................................................................................................................1

3 Names, symbols, and definitions ........................................................................................................1

Annex A (informative) Non-SI units used in atomic and nuclear physics ..................................................66

Bibliography......................................................................................................................................................67

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Foreword

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

Part 3: Space and time

Part 4: Mechanics

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Introduction

0.1 Arrangements of the tables

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.

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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

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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.

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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

the following pages.

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ATOMIC AND NUCLEAR PHYSICS QUANTITIES

Item No. Name Symbol Definition Remarks

10-1.1(9-1)

atomic number,proton number

fr numéro (m) atomique,

nombre (m) de protons

Z number of protons in anatomic nucleus

A nuclide is a species of atom withspecified numbers of protons andneutrons.

Nuclides with the same value of Z but different values of N are calledisotopes of an element.

The ordinal number of an element inthe periodic table is equal to theatomic number.

The atomic number equals the chargeof the nucleus in units of theelementary charge (item 10-5.1).

10-1.2(9-2 )

neutron number

fr nombre (m) deneutrons

N number of neutrons in anatomic nucleus

Nuclides with the same value of N but different values of Z are calledisotones.

N Z − is called the neutron excessnumber.

10-1.3(9-3)

nucleon number,mass number

fr nombre (m) denucléons,

nombre (m) demasse

A number of nucleons in anatomic nucleus

A Z N = +

Nuclides with the same value of A arecalled isobars.

10-2(9-5.1)(9-5.2 )(9-5.3)

rest mass,proper mass

fr masse (f) au repos,

masse (f) propre

X( )m ,

Xm

for particle X, mass(ISO 80000-4:2006, item4-1) of that particle at rest

Specifically,

for an electron:31

e 9,109 382 15(45) 10 kgm −= × ;

for a proton:27

p 1,672 621 637(83) 10 kgm −= × ;

for a neutron:27

n 1,674 927 211(84) 10 kgm −= ×

[2006 CODATA recommendedvalues].

Rest mass is often denoted 0m .

10-3(—)

rest energy

fr énergie (f) au repos

0 E for a particle,2

0 0 0 E m c=

where 0m is the rest mass

(item 10-2) of that particle,

and 0c is the speed of

light in vacuum

(ISO 80000-7:2008, item

7-4.1)

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UNITS ATOMIC AND NUCLEAR PHYSICS

Item No. Name Symbol Definition Conversion factors and remarks

10-1.a one 1 See the Introduction, 0.3.2.

10-2.a kilogram kg

10-2.b dalton,unified atomicmass unit

Da

u

1 dalton is equal to 1/12 timesthe mass of a free carbon 12atom, at rest and in its groundstate

1 Da = 1 u = 1,660 538 782(83) × 10 –27 kg[2006 CODATA recommendedvalues].

10-3.a joule J

(continued)

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10-4.1(9-4.1)

atomic mass,nuclidic mass

fr masse (f)atomique,

masse (f)nucléidique

X( )m ,

am

rest mass(ISO 80000-4:2006, item4-1) of a neutral atom or anuclide X in the groundstate

a

u

m

m

is called the relative atomic

mass.

10-4.2(9-4.2 )

unified atomicmass constant

fr constante (f)unifiée demasseatomique

um 1/12 of the mass(ISO 80000-4:2006, item4-1) of a neutral atom ofthe nuclide 12C in theground state at rest

um = 1,660 538 782(83) × 10 –27 kg


10-5.1(9-6 )

elementarycharge

fr charge (f)élémentaire

e negative of electric charge(IEC 80000-6:2008,item 6-2) of the electron

e = 1,602 176 487(40) × 10 –19 C[2006 CODATA recommendedvalues].

10-5.2(—)

charge number,ionizationnumber

fr nombre (m) decharge,

charge (f)ionique

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)

h = 6,626 068 96(33) × 10 –34 J s[2006 CODATA recommendedvalues].

Energy E of harmonic vibration offrequency f can change for

multiples of E hf ω∆ = = only.

10-6.2(—) reduced Planckconstant

fr constante (f)de Planckréduite

π2h=

where h is the Planckconstant (item 10-6.1)

= 1,054 571 628(53) × 10 –34 J s [2006 CODATA recommendedvalues].

is sometimes known as hbar or theDirac constant.

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10-4.a kilogram kg


Da, u 1 dalton is equal to 1/12 timesthe mass of a free carbon 12atom, at rest and in its groundstate

1 Da = 1 u = 1,660 538 782(83) × 10 –27 kg[2006 CODATA recommendedvalues].

10-5.a coulomb C

10-6.a joule second J · s

(continued)

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10-7(9-8 )

Bohr radius

fr rayon (m) deBohr

0a π 20

0 2e

4 εa

m e=

where ε0 is the electricconstant(IEC 80000-6:2008, item6-14.1), is the reduced Planckconstant (item 10-6.2),

em is the rest mass ofelectron (item 10-2), ande is the elementarycharge (item 10-5.1)

0a = 0,529 177 208 59(36) × 10 –10 m


The radius of the electron orbital inthe H-atom in its ground state is 0a inthe Bohr model of the atom.

10-8(9-9)

Rydberg constant

fr constante (f)de Rydberg

R∞

π

2

0 0 08

e R

ε a hc∞ =

where e is the elementarycharge (item 10-5.1),

0ε is the electric constant(IEC 80000-6:2008, item6-14.1),

0a is the Bohr radius (item10-7),

h is the Planck constant(item 10-6.1), and

0c is the speed of light invacuum(ISO 80000-7:2008, item7-4.1)

R∞ =

10 973 731,568 527(73) m –1 [2006 CODATA recommendedvalues]

The quantity 0 y R R hc∞= ⋅ is calledRydberg energy.

10-9(9-10 )

Hartree energy

fr énergie (f) deHartree

H E , h E

π

2

H0 04

e E

ε a=

where e is the elementary

charge (item 10-5.1),0ε is the electric constant

(IEC 80000-6:2008, item6-14.1), and

0a is the Bohr radius (item10-7)

H E = 4,359 743 94(22) × 10 –18 J


The energy of the electron in

H-atom in its ground state is H E − .

H 02 E R hc∞= ⋅ .

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10-7.a metre m ångström (Å), 1 Å := 10 –10 m

10-8.a metre to thepower minusone

m –1

10-9.a joule J

(continued) p

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10-10.1(9-11.1)

magnetic dipolemoment

fr moment (m)magnétique

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


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

pm is the rest mass ofproton (item 10-2)

Ν µ = 5,050 783 24(13) × 10 –27 J T –1 [2006 CODATA recommendedvalues].

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

Spin is an additive vector quantity.

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10-10.a ampere squaremetre

A · m2

10-11.a kilogram metre

squared persecond

kg · m2 · s –1

(continued)

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10-12(—)

total angularmomentum

fr moment (m) cinétiquetotal

J vector quantity in aquantum microsystemcomposed of angularmomentum(ISO 80000-4:2006, item4-12) and spin s (item10-11)

In atomic and nuclear physics, orbitalangular momentum is usuallydenoted by l or L instead of .

The magnitude of J is quantized sothat ( )12 2 J j j= + , where j is thetotal angular momentum quantumnumber (item 10-14.6).

Total angular momentum andmagnetic dipole moment have thesame direction.

j is not the magnitude of the totalangular momentum J but its

projection onto the quantization axis,divided by .

10-13.1(9-12 )

gyromagneticratio for electron,

magnetogyricratio for electron,

gyromagneticcoefficient forelectron

fr coefficient (m)

gyro-magnétiquede l'électron

eγ eγ = J

where is the magneticdipole moment (item10-10.1), and J is the total angularmomentum (item 10-12)

10-13.2(9-12 )

gyromagneticratio,

magnetogyricratio,

gyromagneticcoefficient

fr coefficient (m)gyro-magnétique

γ γ = J

where is the magnetic

dipole moment (item10-10.1), and J is the total angularmomentum (item 10-12)

The systematic name is“gyromagnetic coefficient”, but“gyromagnetic ratio” is more usual.

The gyromagnetic ratio of the protonis denoted by

pγ .

pγ = 2,675 222 099(70) × 108 s –1 T –1


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10-12.a joule second J · s

10-13.a ampere squaremetre per joule second

A · m2/(J · s) 1 A · m2/(J · s) = 1 A · s/kg = 1 T –1 · s –1

(continued)

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10-14.1(—)

quantum number

fr nombre (m)quantique

n, l , m,

j, s, F

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.

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10-14.4(9-24)

magneticquantumnumber

fr nombre (m)quantiquemagnétique

, ,im m M atomic quantum numbers

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 = …

3 512 2 2, , , for odd A.

In nuclear and particle physics, J isoften used.

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10-14.8(9-22)

hyperfinestructurequantumnumber

fr nombre (m)quantique destructurehyperfine

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

g -factor of the proton is

p g = 5,585 694 713(46)

[2006 CODATA recommended values].

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10-16.1(9-14.1)

Larmor angularfrequency

fr pulsation (f) deLarmor

Lω L

e2

eω B

m

=


em is the rest mass of electron(item 10-2), and B is magnetic flux density(IEC 80000-6:2008, item6-21)

The quantity

πL L / 2ν ω=

is called the Larmor frequency.

10-16.2(9-14.2 )

nuclearprecession

angularfrequency

fr pulsation (f) de précessionnucléaire deLarmor

Nω Nω B= γ

where γ is the gyromagneticcoefficient (item 10-13.2),and B is magnetic flux density(IEC 80000-6:2008, item 6-21)

10-17(9-15 )

cyclotron angularfrequency

fr puIsation (f)cycIotron

cω

c

qω B

m=

where q is electric charge(IEC 80000-6:2008, item 6-2) of

the particle, m is its mass(ISO 80000-4:2006, item 4-1),and B is the magnitude of themagnetic flux density(IEC 80000-6:2008, item 6-21)

The quantityπc c / 2ν ω=

is called the cyclotron frequency.

10-18(9-16 )

nuclearquadrupolemoment

fr moment (m)quadripolaire

nucléaire

Q 2 21/ 3 d( ) ( ) ( , , )Q e z r ρ x y z V = −∫in the quantum state with thenuclear spin in the fielddirection ( ) z , where ( , , ) ρ x y z

is the nuclear electric chargedensity (IEC 80000-6:2008,item 6-3), e is the elementarycharge (item 10-5.1),

2 2 2 2r x y z = + + , and

dV is the volume elementd d d x y z

The electric nuclear quadrupolemoment is eQ .

This value is equal to the z -component of the diagonalizedtensor of quadrupole moment.

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10-16.a radian persecond

rad/s See the Introduction, 0.3.2.

10-16.b second to thepower minusone

s –1

10-17.a radian persecond

rad/s

10-17.b second to thepower minus

one

s –1

10-18.a metre squared m2

(continued)

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10-19(9-17 )

nuclear radius

fr rayon (m)nucléaire

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=


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)

α = 1/137,035 999 679(94)[2006 CODATA recommendedvalues].

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

=


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


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 .

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10-19.a metre m Nuclear radius is usually expressed

in femtometres. 1 fm= 10

–15

m.


10-21.a metre m

10-22.a metre m

(continued)

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10-23.1(9-28.1)

mass excess

fr excès (m) demasse

∆ a um Am∆ = −

where am is the rest mass(item 10-2) of the atom, A is its nucleon number(item 10-1.3), and

um is the unified atomic

mass constant (item10-4.2)

10-23.2(9-28.2 )

mass defect

fr défaut (m) demasse

B 1n aH( ) B Zm Nm m= + −

where Z is the proton

number (item 10-1.1) ofthe atom, 1H( )m is atomicmass (item 10-4.1) of 1H, N is neutron number

(item 10-1.2), nm is therest mass (item 10-2) of

the neutron, and am is therest mass (item 10-2) ofthe atom

If the binding energy of the atomic

electrons is neglected, 20 Bc is equal

to the binding energy of the nucleus.

10-24.1(9-29.1)

relative massexcess

fr excès (m) demasse relatif

r ∆ r u/ m∆ = ∆

where ∆ is the massexcess (item 10-23.1) and

um is the unified atomic

mass constant (item10-4.2)

10-24.2(9-29.2 )

relative massdefect

fr défaut (m) demasse relatif

r B r u/ B B m=

where B is the mass

defect (item 10-23.2) and

um is the unified atomicmass constant (item

10-4.2)10-25.1(9-30.1)

packing fraction

fr facteur (m) detassement

f r / f A= ∆

where ∆r is relative mass

excess (item 10-24.1) and A is the nucleon number(item 10-1.3)

10-25.2(9-30.2)

binding fraction

fr facteur (m) deliaison

b r /b B A=

where r B is relative massdefect (item 10-24.2) and

A is the nucleon number(item 10-1.3)

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10-23.a kilogram kg


Da, u See item 10-2.b. 1 Da = 1 u = 1,660 538 782(83) × 10 –27 kg[2006 CODATA recommendedvalues].

Quantities 10-23.1 and 10-23.2 areusually expressed in daltons.



(continued)

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10-26(9-36 )

decay constant,disintegrationconstant

fr constante (f)de désinté-gration,

constante (f) dedécroissance

λ relative variation d / N N

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)

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10-26.a second to thepower minusone

s –1

10-27.a second s

10-28.a joule J

10-28.b electronvolt eV kinetic energy acquired by anelectron in passing through apotential difference of 1 V invacuum

1 eV = 1,602 176 487(40) × 10 –19 J[2006 CODATA recommendedvalues].

10-29.a becquerel Bq 1 Bq := 1 s –1 The becquerel is a special name forsecond to the power minus one, tobe used as the coherent SI unit ofactivity.

curie, (Ci), 1 Ci := 3,7 × 1010 Bq

10-30.a becquerel perkilogram

Bq/kg

(continued)

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10-31(9-35 )

activity density,volumic activity,activityconcentration

fr activité (f)volumique

Ac A

Ac

V

=

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

spectrum in a betadisintegration process

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10-31.a becquerel percubic metre

Bq/m3

10-32.a becquerel persquare metre

Bq/m2

10-33.a second s

10-34.a joule J

10-34.b electronvolt eV See 10-28.b. 1 eV = 1,602 176 487(40) × 10 –19 J[2006 CODATA recommended

values].

10-35.a joule J

10-35.b electronvolt eV See 10-28.b. 1 eV = 1,602 176 487(40) × 10 –19 J


(continued)

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10-36(9-40 )

betadisintegrationenergy

fr énergie (f) dedésinté-gration bêta

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

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10-36.a joule J

10-36.b electronvolt eV See 10-28.b. 1 eV = 1,602 176 487(40) × 10 –19 J[2006 CODATA recommendedvalues].


10-38.a joule J

10-38.b electronvolt eV See 10-28.b. 1 eV = 1,602 176 487(40) × 10 –19 J[2006 CODATA recommended

values].

(continued)

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10-39.1(10-3.1)

cross-section

fr section (f)efficace

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.

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10-39.a square metre m2 barn (b), 1 b := 10 –28 m2

(continued)

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10-40(10-4)

angularcross-section

fr section (f)efficacedirectionnelle

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).

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10-40.a square metreper steradian

m2/sr

10-41.a square metreper joule

m2/J

10-42.a square metreper steradian joule

m2/(sr · J)

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10-43.1(10-7.1)

volumiccross-section,

macroscopiccross-section

fr section (f)efficacemacro-scopique,

section (f)efficacevolumique

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.

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m –1

10-44.a metre to thepower minustwo

m –2

(continued)

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10-45(10-9)

particle fluencerate

fr débit (m) defluence de particules

θ , Φ d

d

Φθ

t

=

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

two distributions are related by

E E R EN = .

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10-45.a metre to thepower minustwo persecond

m –2/s

10-46.a joule J J

(continued)

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10-47

(10-10 )

energy fluence

fr fluence (f)énergétique

Ψ at a given point of space,

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

v and

E J , are related to J by

d d E E = ∫ ∫ J J J v

v= .

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10-47.a joule persquare metre

J/m2

10-48.a watt per squaremetre

W/m2

10-49.a metre to thepower minustwo persecond

m –2/s

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10-50(10-13)

linear attenuationcoefficient

fr coefficient (m)d'atténuationlinéique

µ, l µ 1 d

d

J µ

J x

= −

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.

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m –1

10-51.a metre squaredper kilogram

m2/kg

10-52.a metre squaredper mol

m2/mol


10-54.a metre m

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10-55(10-18 )

total linearstopping power

fr pouvoir (m)d'arrêtlinéique total

S , l S d /dS E x= −

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

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10-55.a joule per metre J/m

10-55.b electronvolt permetre

eV/m 1 eV/m = 1,602 176 487 (40) × 10 –19 J/m[2006 CODATA recommendedvalues].

10-56.a joule metresquared

J · m2

10-56.b electronvoltmetre squared

eV · m2 1 eV · m2 = 1,602 176 487 (40) × 10 –19 J · m2 [2006 CODATA recommendedvalues].

10-57.a joule metresquared perkilogram

J · m2/kg

10-57.b electronvoltmetre squaredper kilogram

eV · m2/kg 1 eV · m2/kg = 1,602 176 487(40) × 10 –19 J · m2/kg[2006 CODATA recommendedvalues].

10-58.a metre m

10-59.a kilogram permetre squared

kg/m2

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10-60(10-23)

linear ionization

fr ionisation (f)linéique

il N i

1 d

dl

Q N

e l

=

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

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m –1


10-62.a joule J

10-62.b electronvolt eV See 10-28.b. 1 eV = 1,602 176 487(40) × 10 –19 J[2006 CODATA recommendedvalues].

(continued)

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10-63(10-26 )

mobility

fr mobilité (f)

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.

For a particle of a given speed v,

( ) xn

J D

n x= −

∂ ∂

v,

v

v .

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10-63.a square metreper voltsecond

m2/(V · s)

10-64.a metre to thepower minusthree

m –3

10-65.a cubic metreper second

m3/s

10-66.a metre squaredper second

m2/s

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10-67(10-33)

diffusioncoefficient forfluence rate

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

10-71

(10-37 ) lethargy

fr léthargie (f)

u for a neutron of kinetic

energy E (ISO 80000-4:2006, item4-27.3),

0ln ( / )u E E =

where 0 E is a referenceenergy

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10-67.a metre m

10-68.a second to thepower minusone per cubicmetre

s –1/m3

10-69.a metre to thepower minusthree persecond

m –3/s



(continued)

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10-72(10-38 )

averagelogarithmicenergydecrement

fr décrément (m)logarithmiquemoyen del'énergie,

paramètre (m)de ralentis-sement

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

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10-73.a metre m


(continued)

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10-75.1(10-41.1)

slowing-downlength

fr longueur (f)de ralentis-sement

s L , sl L 2s s L L=

where 2s L is the slowing-

down area (item 10-74.1)

10-75.2(10-41.2 )

diffusion length

fr longueur (f) dediffusion

L 2 L L=

where 2 L is the diffusionarea (item 10-74.2)

10-75.3(10-41.3)

migration length

fr longueur (f) de

migration

2 M =

where2

M is the migrationarea (item 10-74.3)

10-76.1(10-42.1)

neutron yield perfission

fr nombre (m) deneutrons produits parfission

ν average number of fissionneutrons, both prompt anddelayed, emitted perfission event

Also called ν-factor and η-factor.

10-76.2(10-42.2 )

neutron yield perabsorption

fr nombre (m) deneutrons produits parneutronabsorbé

η average number of fissionneutrons, both prompt and

delayed, emitted perneutron absorbed in afissionable nuclide or in anuclear fuel, as specified

/ν η is equal to the ratio of themacroscopic cross-section for fission

to that for absorption, both forneutrons in the fuel material.

10-77(10-43)

fast fission factor

fr facteur (m) defissionrapide

φ in an infinite medium, theratio of the mean numberof neutrons produced byfission due to neutrons ofall energies(ISO 80000-5:2007, item

5-20.1), to the meannumber of neutronsproduced by fissions dueto thermal neutrons only

The class (thermal) of neutrons mustbe specified.

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10-75.a metre m



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10-78(10-44)

thermal utilisationfactor

fr facteur (m)d'utilisationthermique

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


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


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

medium or for an infiniterepeating lattice

For a thermal reactor,.k ηε pf ∞ =

10-80.3(10-46.3)

effectivemultiplicationfactor

fr facteur (m) demultiplicationeffectif

eff k multiplication factor for afinite medium

Λeff k k ∞= .

10-81(10-47 )

reactivityfr réactivité (f)

ρ eff

eff

1k ρ

k

−=

where eff k is effective

multiplication factor (item10-80.3)

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10-82(10-48 )

reactor timeconstant

fr constante (f)de temps duréacteur

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.

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10-82.a second s

10-83.a joule J

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10-84.1(10-51.2 )

absorbed dose

fr dose (f)absorbée

D for any ionizing radiation,

dd

Dm

= ε

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).

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10-84.a gray Gy 1 Gy

:= 1 J/kg The gray is a special name for jouleper kilogram, to be used as thecoherent SI unit for these quantities.

rad (rad), 1 rad := 10 –2 Gy

10-85.a one 1

10-86.a sievert Sv 1 Sv := 1 J/kg The sievert is a special name for joule per kilogram, to be used as thecoherent SI unit for dose equivalent.

rem (rem), 1 rem :=

10 –2 Sv

(continued)

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10-87(10-53)

absorbed doserate

fr débit (m) dedoseabsorbée

D d

d

D D

t

=

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)

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10-87.a gray persecond

Gy/s 1 Gy/s = 1 W/kg

See the Remarks for item 10-84.a.

10-88.a joule per metre J/m

10-88.b electronvolt permetre

eV/m 1 eV/m = 1,602 176 487(40) × 10 –19 J[2006 CODATA recommended

values].

10-89.a gray Gy See the Remarks for item 10-84.a.

10-90.a gray persecond

Gy/s 1 Gy/s = 1 W/kg

See the Remarks for item 10-84.a.

(continued)

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10-91(10-57 )

mass energytransfercoefficient

fr coefficient (m)de transfertd’énergiemassique

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

quantity luminous exposure(ISO 80000-7:2008, item 7-39).

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10-91.a square metreper kilogram

m2/kg

10-92.a coulomb perkilogram

C/kg röntgen (R), 1 R := 2,58 × 10 –4 C/kg

(continued) p

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10-93(10-59)

exposure rate

fr débit (m)d’exposition

X d

d

X X

t

=

where d X is theincrement of exposure(item 10-92) during timeinterval with duration dt (ISO 80000-3:2006, item3-7)

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10-93.a coulomb perkilogramsecond

C/(kg · s) 1 C/(kg · s) = 1 A/kg

(concluded)

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Annex A (informative)

Non-SI units used in atomic and nuclear physics

Quantity Name of unit Symbol forunit

Value in SI units

Units accepted for use with the SI

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.

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Bibliography

[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

[8] SI Brochure, 8th edition (2006), BIPM, Sèvres

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ICS 01.060

Price based on 67 pages

© ISO 2009 – All rights reserved

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