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© ISO 2014 – All rights reserved ISO/TC 12/SC N Date: 2014-10-01 ISO/WD 80000-10 ISO/TC 12/SC /WG 19 Secretariat: SIS Quantities and units — Part 10: Atomic and nuclear physics Grandeurs et unités — Partie 10: Physique atomique et nucléaire Warning This document is not an ISO International Standard. It is distributed for review and comment. It is subject to change without notice and may not be referred to as an International Standard. Recipients of this draft are invited to submit, with their comments, notification of any relevant patent rights of which they are aware and to provide supporting documentation. Document type: International Standard Document subtype: Document stage: (20) Preparatory Document language: E E:\usr_PTB\AA1\ISO_TC12\WG19\Subgroup_10\Revision\ISO_80000-10_WD_20141001.docx STD Version 2.5a ISO/WD 80000-10 Copyright notice This ISO document is a working draft or committee draft and is copyright-protected by ISO. While the reproduction of working drafts or committee drafts in any form for use by participants in the ISO standards development process is permitted without prior permission from ISO, neither this document nor any extract from it may be reproduced, stored or transmitted in any form for any other purpose without prior written permission from ISO. Requests for permission to reproduce this document for the purpose of selling it should be addressed as shown below or to ISO's member body in the country of the requester: [Indicate the full address, telephone number, fax number, telex number, and electronic mail address, as appropriate, of the Copyright Manager of the ISO member body responsible for the secretariat of the TC or SC within the framework of which the working document has been prepared.] Reproduction for sales purposes may be subject to royalty payments or a licensing agreement. Violators may be prosecuted. ii © ISO 2014 – All rights reserved ISO/WD 80000-10 Contents Page Foreword ............................................................................................................................................................ iv Introduction ......................................................................................................................................................... v 1.1 Arrangements of the tables .................................................................................................................. v 1.2 The quantities ........................................................................................................................................ v 1.3 The units ................................................................................................................................................. v 1.3.1 General ................................................................................................................................................... v 1.3.2 Remark on units for quantities of dimension one, or dimensionless quantities........................... vi 1.4 Numerical statements in this International Standard ....................................................................... vi 1.5 Special remarks ................................................................................................................................... vii 1.5.1 Quantities ............................................................................................................................................. vii 1.5.2 Special units ........................................................................................................................................ vii 1.5.3 Stochastic and non-stochastic quantities ........................................................................................ vii 2 Scope ...................................................................................................................................................... 1 3 Normative references ............................................................................................................................ 1 4 Names, symbols, and definitions ........................................................................................................ 1 5 Quantities, units and definitions .......................................................................................................... 1 Annex A (informative) Non-SI units used in atomic and nuclear physics ................................................... 1 Bibliography ........................................................................................................................................................ 2 © ISO 2014 – All rights reserved iii ISO/WD 80000-10 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 ISO technical committees. Each member body interested in a subject for which a technical committee has been established has the right to be represented on that committee. International organizations, governmental and non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the International 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. The main task of technical committees is to prepare International Standards. Draft International Standards adopted by the technical committees are circulated to the member bodies for voting. 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 patent rights. ISO shall not be held responsible for identifying any or all such patent rights. ISO 80000-10 was prepared by Technical Committee ISO/TC 12, Quantities and units, Subcommittee SC , . This second edition cancels and replaces the first edition (ISO 80000-10, First edition, 2009), clauses, tables and annex of which have been technically revised. ISO 80000 consists of the following parts, under the general title Quantities and units: Part 1: General Part 2: Mathematics Part 3: Space and time Part 4: Mechanics Part 5: Thermodynamics Part 7: Light and Radiation Part 8: Acoustics Part 9: Physical chemistry and molecular physics Part 10: Atomic and nuclear physics Part 11: Characteristic numbers Part 12: Solid state physics IEC 80000 consists of the following parts, under the general title Quantities and units: Part 6: Electromagnetism Part 13: Information science and technology Part 14: Telebiometrics related to human physiology iv © ISO 2014 – All rights reserved ISO/WD 80000-10 Introduction 1.1 Arrangements of the tables The tables of quantities and units in this International Standard are arranged so that the quantities are presented on the left-hand side and the units on the right-hand side of one line of the table. All units between two full lines on the right-hand side belong to the quantities between the corresponding full lines on the left-hand side. 1.2 The quantities The names in English and in French of the most important quantities within the field of this International Standard are given together with their symbols and, in most cases, their definitions. These names and symbols are recommendations. The definitions are given for identification of the quantities in the International System of Quantities (ISQ), listed on the left-hand side 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 the definitions. 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 equal footing. When two types of italic letters exist (for example as with ϑ and θ; φ and φ ; a and a; g and g), only one of these is given. This does not mean that the other is not equally acceptable. It is recommended that such variants not be given different meanings. A symbol within parentheses implies that it is a reserve symbol, to be 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. The gender of the French name is indicated by (m) for masculine and (f) for feminine, immediately after the noun in the French name. 1.3 The units 1.3.1 General The names of units for the corresponding quantities are given together with the international symbols and the definitions. These unit names are language-dependent, but the symbols are international and the same in all languages. For further information, see the SI Brochure (8th edition, 2006, updated in 2014) 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 on Weights and Measures (Conférence Générale des Poids et Mesures, CGPM). The coherent SI units and their decimal multiples and submultiples formed with the SI prefixes are recommended, although the decimal multiples and submultiples are not explicitly mentioned. b) Some non-SI units are then given, namely those accepted by the International Committee for Weights and Measures (Comité International des Poids et Mesures, CIPM), or by the International Organization of Legal Metrology (Organisation Internationale de Métrologie Légale, OIML), or by ISO and IEC, for use with the SI. Such units are separated from the SI units in the item by use of a broken line between the SI units and the other units. © ISO 2014 – All rights reserved v ISO/WD 80000-10 c) Non-SI units currently accepted by the CIPM for use with the SI are given in small print (smaller than the text size) in the “Remarks” column. d) Non-SI units that are not recommended are given only in annexes in some parts of this International Standard. These annexes are informative, in the first place for the conversion factors, and are not integral parts 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. f) Other non-SI units given for information, especially regarding the conversion factors, are given in informative annexes in some parts of this International Standard. 1.3.2 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 out explicitly. 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 are recommended. 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 the ratio 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 as derived quantities of dimension one. The units radian and steradian are thus equal to one; they may either be omitted, or they may be used in expressions for derived units to facilitate distinction between quantities of different kind but having the same dimension. 1.4 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”, and the sign := is used to denote “is by definition equal to”. Numerical values of physical quantities that have been experimentally determined always have an associated measurement uncertainty. This uncertainty should always be specified. In this International Standard, the magnitude 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 to apply 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. The numerical example given above may be interpreted to mean that the best estimate of the numerical value of the 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 the standard uncertainty 0.000 32 m and the probability distribution of the values of l. vi © ISO 2014 – All rights reserved ISO/WD 80000-10 1.5 1.5.1 Special remarks Quantities Numerical values of physical constants defined in ISO 80000-10 are quoted in the consistent values of the fundamental physical constants published in CODATA recommended values”. See the CODATA website: http://physics.nist.gov/cuu/constants/index.html 1.5.2 Special units Individual scientists should have the freedom to use non-SI units when they see a particular scientific advantage in their work. For this reason, non-SI units that are relevant for atomic and nuclear physics are listed in Annex A. 1.5.3 Stochastic and non-stochastic quantities Differences between results from repeated observations are common in physics. These can arise from imperfect measurement systems, or from the fact that many physical phenomena are subject to inherent fluctuations. Therefore one often needs to distinguish between a non-stochastic quantity with its unique value and a stochastic quantity, the values of which follow a probability distribution. In many instances, the distinction is not significant because the probability distribution is very narrow. For example, the measurement of an electric current commonly involves so many electrons that fluctuations contribute negligibly to inaccuracy in the measurement. However, as the limit of zero electric current is approached, fluctuations can become manifest. This case of course requires a more careful measurement procedure, but perhaps more importantly illustrates that the significance of stochastic variations of a quantity can depend on the magnitude of the quantity. Similar considerations apply to ionizing radiation; fluctuations can play a significant role, and in some cases need to be considered explicitly. Stochastic quantities such as the energy imparted and the specific energy imparted (item 10-84.2) but also the number of particle traversals across microscopic target regions and their probability distributions have been introduced as they describe the discontinuous nature of the ionizing radiations as a determinant of radiochemical and radiobiological effects. In radiation applications involving large numbers of ionizing particles, e.g. in medicine, radiation protection and materials testing and processing, these fluctuations are adequately represented by the expected values of the probability distributions. “Non-stochastic quantities” such as the particle fluence (item10-44), the absorbed dose (item 1084.1) and the kerma (item10-89) are based on these expected values. © ISO 2014 – All rights reserved vii WORKING DRAFT ISO/WD 80000-10 Quantities and units — Part 10: Atomic and nuclear physics — 2 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. 3 Normative references The following referenced documents are indispensable for the application of this document. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (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 and radiation ISO 80000-9:2009, Quantities and units — Part 9: Physical chemistry and molecular physics 4 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. ATOMIC AND NUCLEAR PHYSICS © ISO 2014 – All rights reserved QUANTITIES 1 WORKING DRAFT 5 ISO/WD 80000-10 Quantities, units and definitions Quantity Unit Item No. Remarks Name Symbol Definition Symbol 10-1.1 atomic number, proton number fr numéro (m) atomique, nombre (m) de protons Z number of protons in an atomic nucleus 1 A nuclide is a species of atom with specified numbers of protons and neutrons. Nuclides with the same value of Z but different values of N are called isotopes of an element. The ordinal number of an element in the periodic table is equal to the atomic number. The atomic number equals the charge of the nucleus divided by the elementary charge (item 10-5.1). See the Introduction, 1.3.2. 10-1.2 neutron number fr nombre (m) de neutrons N number of neutrons in an atomic nucleus 1 Nuclides with the same value of N but different values of Z are called isotones. N – Z is called the neutron excess number. 10-1.3 nucleon number, mass number fr nombre (m) de nucléons, nombre (m) de masse A number of nucleons in an atomic nucleus 1 A=Z+N Nuclides with the same value of A are called isobars. 10-2 rest mass, proper mass fr masse (f) au m( X), mX for particle X, mass (ISO 80000-4:2006, item 4-1) of that particle at rest kg Specifically, for an electron: me = 9.109 382 91(40) ⋅ 10-31 kg © ISO 2014 – All rights reserved 1 ISO/WD 80000-10 Quantity Unit Item No. Remarks Name Symbol Definition repos, masse (f) propre 10-3 Symbol Rest mass is often denoted u Da rest energy fr énergie (f) au repos E0 energy E0 of a particle at rest m0 . 1 dalton is equal to 1/12 times the mass of a free carbon 12 atom, at rest and in its ground state J E0 = m c , 2 0 0 where m0 is the rest mass (item 10-2) of that particle, and c0 is the speed of light in vacuum (ISO 80000-7:2008, item 7-4.1) 10-4.1 atomic mass, nuclidic mass fr masse (f) atomique, masse (f) nucléidique m( X ), ma rest mass (ISO 80000-4:2006, item 4-1) of an atom or a nuclide X in the ground state kg For a nuclide X, the rest mass may be denoted m(X). u Da 10-4.2 ma is called the relative atomic mass. mu unified atomic mass constant fr constante (f) unifiée de masse mu 1/12 of the mass (ISO 80000-4:2006, item 4-1) of an atom of the nuclide 12C in the ground state at rest kg Da 2 1 u is equal to 1/12 times the mass of a free carbon 12 atom, at rest and in its ground state 1 Da = 1 u = 1 dalton is equal to 1/12 times the mass of a free carbon 12 atom, at rest and in its ground state 1 Da = 1 u = © ISO 2014 – All rights reserved ISO/WD 80000-10 Quantity Unit Item No. Remarks Name Symbol Definition Symbol u atomique 10-5.1 elementary charge fr charge (f) élémentaire e quantum of electric charge, equal to the charge of the proton and opposite to the charge of the electron (IEV-113-05-17) C 10-5.2 charge number, ionization number fr nombre (m) de charge, charge (f) ionique c for a particle, the electric charge (IEC 80000-6:2008, item 6-2) divided by the elementary charge (item 10-5.1) 1 10-6.1 Planck constant fr constante (f) de Planck h fundamental physical constant which governs, inter alia, the relation between the frequency f of electromagnetic radiation and the energy E = h f of the corresponding photons (ISO 80000-4:2006, item 4-37) J·s 10-6.2 reduced Planck constant fr constante (f) de Planck réduite h Planck constant (item 10-6.1 )divided by 2π J·s A particle is said to be electrically neutral if its charge number is equal to zero. The charge number of a particle can be positive, negative, or zero. The state of charge of a particle may be presented as a superscript to the symbol of that particle, e.g., H + , He + + , Al3+ , Cl − , S− − , N 3− h= h 2π h is sometimes known as h bar or the Dirac constant. 6.1 and 6.2 into ISO 80000-1 © ISO 2014 – All rights reserved 3 ISO/WD 80000-10 Quantity Unit Item No. Remarks Name 10-7 Symbol Bohr radius fr rayon (m) de Bohr a0 Definition the radius of the electron orbital in the hydrogen atom in its ground state in the Bohr model of the atom a0 = Symbol m The radius of the electron orbital in the H atom in its ground state is a 0 in the Bohr model of the atom. 4πε 0 h 2 , me e 2 where ε0 is the electric constant (IEC 80000-6:2008, item 6-14.1), h is the reduced Planck constant (item 10-6.2), me is the rest mass of electron (item 10-2), and –10 ångström (Å), 1 Å := 10 m Å e is the elementary charge (item 10-5.1) 10-8 Rydberg constant fr constante (f) de Rydberg R∞ spectroscopic constant that determines the wave numbers of the lines in the spectrum of hydrogen m -1 The quantity Ry = R∞ ⋅ hc0 is called the Rydberg energy. e2 , R∞ = 8πε 0 a0 hc0 where e is the elementary charge (item 10-5.1), ε 0 is the electric constant (IEC 80000-6:2008, item 6-14.1), a0 is the Bohr radius (item 10-7), h is the Planck constant (item 10-6.1), and c0 is the speed of light in vacuum (ISO 80000-7:2008, item 7-4.1) 10-9 Hartree energy fr énergie (f) de Hartree EH , Eh quantity related to the energy of the electron in a hydrogen atom in its ground state EH = e2 4πε 0 a0 , J The energy of the electron in an H atom in its ground state is EH . EH = 2 R∞ ⋅ hc0 where e is the elementary charge (item 10-5.1), 4 © ISO 2014 – All rights reserved ISO/WD 80000-10 Quantity Unit Item No. Remarks Name Symbol Definition Symbol ε 0 is the electric constant (IEC 80000-6:2008, item 6-14.1), and a0 is the Bohr radius (item 10-7) 10-10.1 10-10.2 magnetic dipole moment fr moment (m) magnétique µ Bohr magneton fr magnéton (m) de Bohr µB for a particle or nucleus, a vector quantity causing a change to its energy (ISO 80000-5:2007, item 5-20.1) ∆W in an external magnetic of field flux density B (IEC 800006:2008, item 6-21) nuclear magneton fr magnéton (m) 2 the absolute value of the magnetic moment of an electron in a state with orbital quantum number l = 1 (item 10-14.3) due to its orbital motion µN © ISO 2014 – All rights reserved A·m 2 µB is the absolute value of the magnetic moment of an electron in a state with orbital quantum number l = 1 (item 1014.3) due to its orbital motion. eh , 2me where e is the elementary charge (item 10-5.1), and h is the reduced Planck constant, and me is the rest mass of electron (item 10-2) the absolute value of the magnetic moment of a nucleus For an atom or nucleus, this energy is quantized and can be written as W = g ⋅ µx ⋅ M ⋅ B , where g is the appropriate g factor (item 10-15.1 or item 10-15.2), µx is mostly the Bohr magneton or nuclear magneton (item 10-10.2 or item 10-10.3), M is the magnetic quantum number (item 10-14.4), and B is the magnitude of the magnetic flux density. See also IEC 80000-6:2008, item 6-23. ∆W = − µ ⋅ B µB = 10-10.3 A·m A·m 2 Subscript N stands for nucleus. For the neutron magnetic moment, subscript n is used. The magnetic moments of protons 5 ISO/WD 80000-10 Quantity Unit Item No. Remarks Name Symbol nucléaire Definition µN = Symbol and neutrons differ from this quantity by their specific g factors (item 10-15.2). eh , 2mp where e is the elementary charge (item 10-5.1), h is the reduced Planck constant, and mp is the rest mass of proton (item 10-2) 2 10-11 spin fr spin (m) s internal angular momentum (ISO 80000-4:2006, item 4-12) of a particle or a particle system kg·m ·s 10-12 total angular momentum fr moment (m) cinétique total J vector quantity in a quantum microsystem composed of the vectorial sum of angular momentum Λ (ISO 80000-4:2006, item 4-12) and spin s (item 10-11) J·s –1 Spin is an additive vector quantity. In atomic and nuclear physics, orbital angular momentum is usually denoted by V l or L instead of Λ . The magnitude of J is quantized so that J 2 = h 2 j ( j + 1) , where j is the total angular momentum quantum number (item 1014.6). Total angular momentum and magnetic dipole moment have the same direction. j is not the magnitude of the total angular momentum J but its projection onto the quantization axis, divided by h . 10-13.1 γ gyromagnetic ratio, magnetogyric ratio, gyromagnetic coefficient fr coefficient (m) quotient of the magnetic dipole moment by the angular momentum µ =γ ⋅J , where µ is the magnetic dipole moment (item 10-10.1), and J is the total angular momentum (item 10-12) 6 2 A·m /(J·s) 2 -1 1 A·m /(J·s) = 1 A·s/kg = 1 T ·s -1 The systematic name is “gyromagnetic coefficient”, but “gyromagnetic ratio” is more usual. The gyromagnetic ratio of the proton is © ISO 2014 – All rights reserved ISO/WD 80000-10 Quantity Unit Item No. Remarks Name Symbol Definition Symbol gyromagnétique denoted by γp . The gyromagnetic ratio of the neutron is denoted by γ n . 10-13.2 gyromagnetic ratio of the electron, magnetogyric ratio of the electron, gyromagnetic coefficient of the electron fr coefficient (m) gyromagnétique de l'électron γe quotient of the electron magnetic dipole moment by the angular momentum 2 A·m /(J·s) µ = γe ⋅ J , where µ is the magnetic dipole moment (item 10-10.1), and J is the total angular momentum (item 10-12) © ISO 2014 – All rights reserved 7 ISO/WD 80000-10 Quantity Unit Item No. Remarks Name 10-14.1 Symbol quantum number fr nombre (m) quantique n, l, m, j, s, F Definition number describing a particular state of a quantum microsystem Symbol 1 Electron states determine the binding energy E = E (n, m, j, s ) in an atom. Capitals L, M, J, S are usually used for the whole system. The spatial probability distribution of an electron is given by 2 ψ , where ψ is its wave function. For an electron in an H atom in a non-relativistic approximation, the wave function can be presented as ψ (r , ϑ, ϕ ) = Rnl (r ) ⋅ Yl m (ϑ, ϕ ) where r , ϑ, ϕ are spherical coordinates (ISO 80000-2:2009, item 2-16.3) with respect to the nucleus and to a given (quantization) axis, Rnl (r ) is the radial distribution function, and Yl m (ϑ , ϕ ) are spherical harmonics. In the Bohr model of one-electron atoms, n, l, and m define the possible orbits of an electron about the nucleus. See the Introduction, 1.3.2. 10-14.2 principal quantum number fr nombre (m) quantique principal n 8 atomic quantum number related to the number n − 1 of radial nodes of one-electron wave functions 1 In the Bohr model, n = 1,2,...., ∞ is related to the binding energy of an electron and the radius of spherical orbits (principal axis of the elliptic orbits). © ISO 2014 – All rights reserved ISO/WD 80000-10 Quantity Unit Item No. Remarks Name Symbol Definition Symbol For an electron in an H atom, the semi2 classical radius of its orbit is rn = a0 n and 2 its binding energy is En = EH n . 10-14.3 10-14.4 10-14.5 orbital angular momentum quantum number fr nombre (m) quantique du moment cinétique orbital, nombre (m) quantique orbital l , li L magnetic quantum number fr nombre (m) quantique magnétique m, mi M spin quantum number fr nombre (m) quantique du spin s atomic quantum number related to the orbital angular momentum l of a one-electron state 1 r 2 l = h 2l (l − 1) , l = 0,1,....n − 1 . where l is the orbital angular momentum. li refers to a specific particle i; L is used for the whole system. An electron in an H atom for l = 0 appears as a spherical cloud. In the Bohr model, it is related to the form of the orbit. atomic quantum numbers related to the z component lz, jz or sz, of the orbital, total, or spin angular momentum 1 l z = ml h , j z = m j h , and s z = ms h , with the ranges from -l to l, from -j to j, and ± 1 2 , respectively. mi refers to a specific particle i ; M is used for the whole system. Subscripts l, s, j, etc., as appropriate, indicate the angular momentum involved. characteristic quantum number of a particle, related to its 2 2 spin angular momentum s : s = h s( s + 1) © ISO 2014 – All rights reserved 1 Fermions have s = 1 2 or s = 3 2 . Bosons have s = 0 or s = 1. The total spin quantum number S of an atom is related to the total spin (angular momentum), which is the sum of the spins of the electrons. 9 ISO/WD 80000-10 Quantity Unit Item No. Remarks Name Symbol Definition Symbol It has the possible values S = 0,1,2.... for even Z and S = 10-14.6 10-14.7 total angular momentum quantum number fr nombre (m) quantique du moment cinétique total j, ji , J nuclear spin quantum number fr nombre (m) quantique de spin nucléaire I quantum number in an atom describing the magnitude of total angular momentum J (item 10-12) 1 1 3 , ,.... for odd Z. 2 2 ji 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 of total angular momentum J (item 10-12). The two values of j are l ± 1/ 2. (See item 10-14.3.) Here, “total” does not mean “complete”. quantum number related to the total angular momentum J of a nucleus in any specified state, normally called nuclear spin: 1 J 2 = h 2 I ( I + 1) Nuclear spin is composed of spins of the nucleons (protons and neutrons) and their (orbital) motions. In principle there is no upper limit for the nuclear spin quantum number. It has possible values I = 0,1,2.... for even A and 1 3 I = , ,.... for odd A. 2 2 In nuclear and particle physics, J is often used. 10-14.8 hyperfine structure quantum number fr nombre (m) quantique de F quantum number of an atom describing the inclination of the nuclear spin with respect to a quantization axis given by the magnetic field produced by the orbital electrons 1 The interval of F is I − J , I − J + 1 , ..., I+J. This is related to the hyperfine splitting of the atomic energy levels due to the interaction between the electron and 10 © ISO 2014 – All rights reserved ISO/WD 80000-10 Quantity Unit Item No. Remarks Name Symbol Definition Symbol nuclear magnetic moments. structure hyperfine 10-15.1 Landé factor, g factor of atom g fr facteur (m) de Landé d'un atome ou d'un électron, facteur (m) g d'un atome ou d'un électron 10-15.2 g factor of nucleus or nuclear particle fr facteur (m) g d'un noyau ou d'une particule nucléaire quotient of the magnetic dipole moment of an atom by the product of the total angular momentum and the Bohr magneton g= 1 The Landé factor can be calculated from the expression g ( L, S , J ) = µ , J ⋅ µB 1 + ( g e − 1) ⋅ where µ is magnitude of magnetic dipole moment (item 1010.1), J is total angular momentum quantum number (item 1014.6), and quotient of the magnetic dipole moment of an atom by the product of the total angular momentum and the Bohr magneton g= g e is the g factor of the electron See the Introduction, 1.3.2. 1 The g factors for nuclei or nucleons are known from measurements µ , I ⋅ µN where µ is magnitude of magnetic dipole moment (item 10-10.1), I is nuclear angular momentum quantum number (item 1014.7), and µ N is the nuclear magneton (item 10-10.2) © ISO 2014 – All rights reserved J ( J + 1) + S (S + 1) − L(L + 1) , 2 J ( J + 1) where µB is the Bohr magneton (item 10-10.2) g These quantities are also called g values. 11 ISO/WD 80000-10 Quantity Unit Item No. Remarks Name 10-16.1 10-16.2 10-17.1 Symbol Larmor angular frequency fr pulsation (f) de Larmor ωL Definition the frequency that the electron angular momentum vector precesses about the axis of an external magnetic field Symbol rad·s -1 s -1 ν L = ωL 2π is called the Larmor frequency. e ωL = B, 2me nuclear precession angular frequency fr pulsation (f) de précession nucléaire de Larmor ωN cyclotron angular frequency fr puIsation (f) cycIotron ωc where e is the elementary charge (item 10-5.1), me is the rest mass of electron (item 10-2), and B is magnetic flux density (IEC 80000-6:2008, item 6-21) the frequency that the nucleus angular momentum vector precesses about the axis of an external magnetic field The quantity See the Introduction, 1.3.2. rad·s -1 s -1 rad·s -1 s -1 ωN = γ ⋅ B , where γ is the gyromagnetic ratio (item 10-13.1), and B is magnetic flux density (IEC 80000-6:2008, item 6-21) quotient of the product of the electric charge of a particle and the magnetic field, by the particle mass q ωc = B , m The quantity vc = ωc 2π is called the cyclotron frequency. 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 the magnetic flux density (IEC 80000-6:2008, item 6-21) 12 © ISO 2014 – All rights reserved ISO/WD 80000-10 Quantity Unit Item No. Remarks Name 10-17.2 gyroradius, Larmor radius fr puIsation (f) cycIotron Symbol rg , rL Definition radius of circular movement of a particle with mass m (ISO 80000-4:2006, item 4-1), velocity v (ISO 80000-3:2006, item 3-8.1), and electric charge q (IEC 80000-6:2008, item 6-2), moving in a magnetic field with magnetic flux density B (IEC 80000-6:2008, item 6-21): rg = 10-18 nuclear quadrupole moment fr moment (m) quadripolaire nucléaire Q Symbol rad·s -1 s -1 The quantity vc = ω 2π is called the cyclotron frequency. m v×B qB2 the z component of the diagonalized tensor of nuclear quadrupole moment ( e )∫ (3z Q= 1 2 − r 2 ) ρ ( x, y, z )dV in the quantum state with the nuclear spin in the field direction (z), where m 2 The electric nuclear quadrupole moment is eQ. This value is equal to the z component of the diagonalized tensor of quadrupole moment. ρ ( x, y, z ) is the nuclear electric charge density (IEC 80000-6:2008, item 6-3), e is the elementary charge (item 10-5.1), r 2 = x 2 + y 2 + z 2 , and dV is the volume element dxdydz © ISO 2014 – All rights reserved 13 ISO/WD 80000-10 Quantity Unit Item No. Remarks Name 10-19 Symbol nuclear radius fr rayon (m) nucléaire R Definition conventional radius of sphere in which the nuclear matter is included Symbol m This quantity is not exactly defined. It is given approximately for nuclei in their ground state by R = r 0 A where r0 ≈ 1.2 × 10 −15 1/ 3 , m , and A is the nucleon number. Nuclear radius is usually expressed in –15 femtometres. 1 fm = 10 m. 10-20 fine-structure constant fr constante (f) de structure fine α fundamental constant characterizing the strength of electromagnetic interaction α= 1 This is a factor historically related to the change and splitting of atomic energy levels due to relativistic effects. See the Introduction, 1.3.2. m This quantity corresponds to the electrostatic energy E of a charge distributed inside a sphere of radius re as e2 , 4πε0 hc0 where e is the elementary charge (item 10-5.1), ε0 is the electric constant (IEC 80000-6:2008, item 6-14.1), h is the reduced Planck constant (item 10-6.2), and c0 is the speed of light in vacuum (ISO 80000-7:2008, item 7-4.1) 10-21 electron radius fr rayon (m) de l'électron re the radius of a sphere such that the relativistic electron energy is distributed uniformly re = e2 4πε0mec02 , where e is the elementary charge (item 10-5.1), ε0 is the electric constant (IEC 80000-6:2008, item 6-14.1), if all the rest energy (item 10-3) of the electron were attributed to the energy of electromagnetic origin, using the relation E = me c02. me is the rest mass of electron (item 10-2), and c0 is the speed of light in vacuum (ISO 80000-7:2008, item 14 © ISO 2014 – All rights reserved ISO/WD 80000-10 Quantity Unit Item No. Remarks Name Symbol Definition Symbol 7-4.1) 10-22 Compton wavelength fr longueur (f) d'onde de Compton λC quotient of Plank constant by the product of the mass of the particle and the speed of light in vacuum λC = m The wavelength of electromagnetic radiation scattered from free electrons (Compton scattering) is larger than that of the incident radiation by a maximum of 2 λ C. kg Da u See item 10-2.b. Quantities 10-23.1 and 10-23.2 are usually expressed in daltons kg If the binding energy of the orbital electrons h , mc0 where h is the Planck constant (item 10-6.1), m is the rest mass (item 10-2) of a particle, and c0 is the speed of light in vacuum (ISO 80000-7:2008, item 7-4.1) 10-23.1 mass excess fr excès (m) de masse ∆ the increase between the mass of an atom and its mass number in atomic mass units ∆ = ma − A ⋅ m u where ma is the rest mass (item 10-2) of the atom, A is its nucleon number (item 10-1.3), and mu is the unified atomic mass constant (item 10-4.2) 10-23.2 mass defect fr défaut (m) de masse B the sum of the product of the proton number and the hydrogen atomic mass, and the neutron rest mass, less the rest mass of the atom 2 is neglected, Bco is equal to the binding energy of the nucleus See item 10-2.b. B = Zm( 1H) + Nmn − ma , where Z is the proton number (item 10-1.1) of the atom, 1 1 m( H) is atomic mass (item 10-4.1) of H , N is neutron number (item 10-1.2), mn is the rest mass (item 10-2) of the neutron, and Da u 1 Da = 1 u = Quantities 10-23.1 and 10-23.2 are usually expressed in daltons ma is the rest mass (item 10-2) of the atom © ISO 2014 – All rights reserved 15 ISO/WD 80000-10 Quantity Unit Item No. Remarks Name 10-24.1 Symbol relative mass excess fr excès (m) de masse relatif ∆r Definition quotient of mass excess by the unified atomic mass constant 1 See the Introduction, 1.3.2. ∆r = ∆ / m u , where 10-24.2 Symbol relative mass defect fr défaut (m) de masse relatif Br ∆ is the mass excess (item 10-23.1)and mu is the unified atomic mass constant (item 10-4.2) quotient of mass defect by the unified atomic mass constant 1 Br = B / mu , where B is the mass defect (item 10-23.2) and mu is the unified atomic mass constant (item 10-4.2) 10-25.1 packing fraction fr facteur (m) de tassement f quotient of relative mass excess by the nucleon number 1 See the Introduction, 1.3.2. f = ∆r / A Where ∆r is relative mass excess (item 10-24.1) and A is the nucleon number (item 10-1.3) 10-25.2 binding fraction fr facteur (m) de liaison b quotient of relative mass defect by the nucleon number 1 b = Br / A , where Br is relative mass defect (item 10-24.2) and A is the nucleon number (item 10-1.3) 10-26 decay constant, disintegration constant fr constante (f) de désinté- λ quotient of –dN/N by dt, where dN/N is the mean fractional change in the number of nuclei in a particular energy state due to spontaneous transformations in time interval dt, thus s -1 For exponential decay, this quantity is constant. For more than one decay channel occur, λ = ∑ λa , where λa denotes the decay 16 © ISO 2014 – All rights reserved ISO/WD 80000-10 Quantity Unit Item No. Remarks Name Symbol gration, constante (f) de décroissance 10-27 mean lifetime, mean life fr vie (f) moyenne Definition λ=− τ 1 λ constant for a specified final state and the sum is taken over all final states. 1 dN N dt the reciprocal of the decay constant τ= Symbol s Mean lifetime is the expected value of the lifetime of an unstable particle or an excited state of a particle. J Level width is the uncertainty of the of an unstable particle or an excited state of a system due to the Heisenberg principle. kinetic energy acquired by an electron in passing through a potential difference of 1 V in vacuum The term energy level refers to the configuration of the distribution function of the density of states. Energy levels may be discrete like those in an atom or may have an finite width like e.g. this item or like e.g the valence or conduction band in solid state physics. Energy levels are applicable to both real and virtual particles, e.g. electrons and phonons, respectively. , where λ is the decay constant (item 10-26) 10-28 10-29 level width fr largeur (f) de niveau activity fr activité (f) Γ quotient of the reduced Plank constant by the mean lifetime h , τ where h is the reduced Planck constant (item 10-6.2) and Γ= A τ is the mean lifetime (item 10-27) eV quotient of –dN by dt, where dN is the mean change in the number of nuclei in a particular energy state due to spontaneous nuclear transformations in the time interval dt Bq A=− © ISO 2014 – All rights reserved dN dt For exponential decay, A = λN , where λ is the decay constant (item 10-26). The becquerel is a special name for second to the power minus one, to be used as the coherent SI unit of activity. 17 ISO/WD 80000-10 Quantity Unit Item No. Remarks Name Symbol Definition Symbol -1 1 Bq = 1 s 10 1 Ci := 3.7 × 10 Bq Ci 10-30 quotient of the activity A (item 10-29) of a sample by the mass (ISO 80000-4:2006, item 4-1) of that sample Bq/kg specific activity, massic activity fr activité (f) massique a activity density, volumic activity, activity concentration fr activité (f) volumique cA surface-activity density, areic activity fr activité (f) surfacique as 10-33 half life fr période (f) radioactive T1/ 2 mean time (ISO 80000-3:2006, item 3-7) required for the decay of one half of the atoms or nuclei s For exponential decay, T1/ 2 = (ln2) / λ . 10-34 alpha disintegration energy fr énergie (f) de désintégration alpha Qα sum of the kinetic energy (ISO 80000-3:2006, item 4-27.3) of the α particle produced in the disintegration process and the recoil energy (ISO 80000-5:2007, item 5-20.1) of the product atom in the reference frame in which the emitting nucleus is at rest before its disintegration J The ground-state alpha disintegration energy, Qα,0, also includes the energy of any nuclear transitions that take place in the daughter produced. 10-31 10-32 a= A m quotient of the activity A (item 10-29) of a sample by the volume (ISO 80000-3:2006, item 3-4) V of that sample cA = Bq·m -3 Bq·m -2 A V quotient of the activity A (item 10-29) of a sample by the total area (ISO 80000-3:2006, item 3-3) of the surface S of that sample This value is usually defined for flat sources, where S corresponds to the total area of surface of one side of the source. as = A / S 18 eV © ISO 2014 – All rights reserved ISO/WD 80000-10 Quantity Unit Item No. Remarks Name Symbol Definition Symbol 10-35 maximum betaparticle energy fr énergie (f) bêta maximale Eβ maximum kinetic energy (ISO 80000-5:2007, item 5-20.1) of the emitted beta particle produced in the nuclear disintegration process J eV The maximum kinetic energy corresponds to the highest energy of the beta spectrum See 10-28 10-36 beta disintegration energy fr énergie (f) de désintégration bêta Qβ sum of the maximum beta-particle kinetic energy (item 1035) and the recoil energy (ISO 80000-5:2007, item 5-20.1) of the atom produced in the reference frame in which the emitting nucleus is at rest before its disintegration J For positron emitters, the energy for the production of the annihilation radiation created in the combination of an electron with the positron must be added to the sum mentioned in the definition. eV The ground-state beta disintegration energy, Qβ,0 , also includes the energy of any nuclear transitions that take place in the daughter product. See 10-28 10-37 internalconversion factor fr facteur (m) de conversion interne α ratio of the number of internal conversion electrons to the number of gamma quanta emitted by the radioactive atom in a given transition, where a conversion electron represents an orbital electron emitted through the radioactive decay 1 The quantity α / (α + 1) is also used and called the internal-conversion fraction. Partial conversion fractions referring to the various electron shells K, L, ... are indicated by αK , αL , K , αK / αL is called the K-to-L internal conversion ratio. 10-38.1 reaction energy fr énergie (f) de réaction Q in a nuclear reaction, the sum of the kinetic energies (ISO 80000-4:2006, item 4-27.3) and photon energies (ISO 80000-5:2007, item 5-20.1) of the reaction products minus the sum of the kinetic and photon energies of the reactants © ISO 2014 – All rights reserved J For exothermic nuclear reactions, Q > 0. eV For endothermic nuclear reactions, Q < 0 . See 10-28 19 ISO/WD 80000-10 Quantity Unit Item No. Remarks Name Symbol Definition 10-38.2 resonance energy fr énergie (f) de résonance Er , Eres kinetic energy (ISO 80000-4:2006, item 4-27.3) of an incident particle, in the reference frame of the target, corresponding to a resonance in a nuclear reaction 10-39.1 cross section fr section (f) efficace σ for a specified target entity and for a specified reaction or process produced by incident charged or uncharged particles of a given type and energy, the mean number of such reactions or processes divided by the incident-particle fluence (item 10-44) 10-39.2 total cross section fr section (f) efficace totale σtot, σT sum of all cross sections (item 10-39.1) corresponding to the various reactions or processes between an incident particle of specified type and energy (ISO 80000-5:2007, item 5-20.1) and a target entity Symbol The energy of the resonance corresponds to the difference of the energy levels involved of the nucleus m m The type of process is indicated by subscripts, e.g., absorption cross section σa, scattering cross section σs , fission cross section σf . -28 b b 20 2 1 barn (b) = 10 2 m 2 In the case of a narrow unidirectional beam of incident particles, this is the effective cross section for the removal of an incident particle from the beam. See the Remarks for item 10-53. -28 2 1 barn (b) = 10 m © ISO 2014 – All rights reserved ISO/WD 80000-10 Quantity Unit Item No. Remarks Name 10-40 10-41 10-42 10-43.1 Symbol direction distribution of cross section fr section (f) efficace directionnelle σΩ energy distribution of cross section fr section (f) efficace spectrique σE direction and energy distribution of cross section fr section (f) efficace directionnelle spectrique σΩ, E volumic cross section, macroscopic cross-section fr section (f) efficace macroscopique, section (f) efficace volumique Σ Definition cross section for ejecting or scattering a particle into a specified direction, divided by the solid angle d Ω (ISO 80000-3:2006, item 3-6) around that direction: Symbol 2 m ·sr -1 Quantities 10-40, 10-41 and 10-42 are sometimes called differential cross sections. σ Ω = dσ dΩ quotient of cross section (item 10-39.1) for a process in which the energy (ISO 80000-5:2007, item 5-20.1) of the ejected or scattered particle is between E and E+dE, by dE m ·J 2 -1 2 -1 σ E = dσ dE quotient of cross section (item 10-39.1) for ejecting or scattering a particle into specified direction and with an energy between E and E+dE, by the product of solid angle d Ω (ISO 80000-3:2006, item 3-6) around that direction and dE m ·J ·sr -1 σ Ω,E = d 2σ dΩdE product of the number density na of the atoms and of the cross-section σ a for a given type of atoms Σ = naσ a © ISO 2014 – All rights reserved m -1 When the target particles of the medium are at rest, Σ = 1 l , where l is the mean free path (item 10-73). See the Remarks for item 10-50. 21 ISO/WD 80000-10 Quantity Unit Item No. Remarks Name 10-43.2 10-44 Symbol volumic total cross section, macroscopic total cross-section fr section (f) efficace totale macroscopique, section (f) efficace totale volumique Σtot, Σ T particle fluence fr fluence (f) de particules Φ Definition product of the number density na of the atoms and of the Symbol m -1 m -2 cross-section σ tot for a given type of atoms: Σ tot = n a σ tot the quotient of dN by da, where dN is the mean number of particles incident on a sphere of cross-sectional area da, thus Φ= dN da The word “particle” is usually replaced by the name of a specific particle, for example proton fluence. A flat area of size dA crossed perpendicularly by a number of dN particles results in the particle fluence Φ= dN dA A plane area of size dA crossed at an angle α with respect to the surface normal by a number of dN particles results in the particle fluence Φ = 22 © ISO 2014 – All rights reserved dN cos(α )dA ISO/WD 80000-10 Quantity Unit Item No. Remarks Name 10-45 Symbol particle fluence rate fr débit (m) de fluence de particules Φ& Definition quotient of the increment of the particle fluence dΦ (item 10-44) in a time interval (ISO 80000-3:2006, item 3-7) dt by that time interval Symbol -2 m ·s dΦ Φ& = dt -1 The word “particle” is usually replaced by the name of a specific particle, for example proton fluence rate. The distribution function expressed in & and Φ& , terms of speed and energy, Φ v E ∫ ∫ & = Φ& dv = Φ& dE . are related to by Φ v E This quantity has also been termed particle flux density. Because the word “density” has several connotations, the term “fluence rate” is preferred. For a radiation field composed of particles of velocity v, the fluence rate is equal to n ⋅ v , where n is the particle number density. See Remarks for 10-44. 10-46 radiant energy fr énergie (f) rayonnante R mean energy (ISO 80000-5:2007, item 5-20.1), excluding rest energy (item 10-3), of the particles that are emitted, transferred, or received J For particles of energy E (excluding rest energy), the radiant energy, R, is equal to the product N ⋅ E where N is the number of the particles that are emitted, transferred, or received The distributions, N E and RE , of the particle number and the radiant energy with respect to energy are given by N E = dN dE and RE = dR dE , respectively, where dN is the number of particles with energy between E and E + dE , and dR is their radiant energy. The two distributions are related by © ISO 2014 – All rights reserved 23 ISO/WD 80000-10 Quantity Unit Item No. Remarks Name Symbol Definition Symbol RE = E ⋅ N E . 10-47 energy fluence Ψ fr fluence (f) énergétique 10-48 the quotient dR by da, where dR is the radiant energy incident on a sphere of cross-sectional area da, thus Ψ= energy-fluence rate fr débit (m) de fluence énergétique Ψ& J·m -2 dR da quotient of the energy fluence by the time interval W·m -2 -2 -1 Mostly, symbol Ψ& is used instead of ψ . dΨ , Ψ& = dt where dΨ is the increment of the energy fluence (item 1047) in the time interval dt (ISO 80000-3:2006, item 3-7) 10-49 particle current density fr densité (f) de courant de particules J , ( S) vector whose component in direction of an area normal is given by J n = ∫ ΦΩ (θ , α ) cos(θ )dΩ m ·s Usually the word “particle” is replaced by the name of a specific particle, for example proton current. Symbol S is recommended when there is a possibility of confusion with the symbol J for electric current density. For neutron current, the symbol J is generally used. The distribution functions expressed in terms of speed and energy, J v and J E , are related to J by J = ∫ J v dv =∫ J E dE . 24 © ISO 2014 – All rights reserved ISO/WD 80000-10 Quantity Unit Item No. Remarks Name 10-50 10-51 10-52 10-53 10-54 10-55 Symbol linear attenuation coefficient fr coefficient (m) d'atténuation linéique µ, µl mass attenuation coefficient fr coefficient (m) d'atténuation massique µm molar attenuation coefficient fr coefficient (m) d'atténuation molaire µc atomic attenuation coefficient fr coefficient (m) d'atténuation atomique µa half-value thickness fr épaisseur (f) de demiatténuation d1/2 total linear S , Sl Definition for uncharged particles of a given type and energy the quotient of dN/N by dl, where dN/N is the mean fraction of the particles that experience interactions in traversing a distance dl in a given material µ= Symbol m -1 µ is equal to the macroscopic total crosssection Σ tot for the removal of particles from the beam. 1 dN dl N quotient of the linear attenuation coefficient µ (item 10-50) by the mass density ρ (ISO 80000-4:2006, item 4-2) of the medium -1 m·kg µm = µ ρ quotient of linear attenuation coefficient µ (item 10-50) by the amount c of-substance concentration (ISO 80000-9:2009, item 9-13) of the medium -1 m·mol µc = µ c linear attenuation coefficient µ (item 10-50) divided by the number density (ISO 80000-9:2009, item 9-10.1) n of the atoms in the substance m 2 µ is equal to the total cross-section σ tot for the removal of particles from the beam. See also item 10-39.2. µa = µ n thickness (ISO 80000-3:2006, item 3-1.4) of the attenuating layer that reduces the quantity of interest of a unidirectional beam of infinitesimal width to half of its initial value m for charged particles of a given type and energy the quotient of dE by dx, where dE is the mean energy lost by J·m © ISO 2014 – All rights reserved For exponential attenuation, d 1 = ln(2)/µ 2 . The quantity of interest is often the air kerma or exposure. -1 Also called stopping power. 25 ISO/WD 80000-10 Quantity Unit Item No. Remarks Name Symbol stopping power fr pouvoir (m) d'arrêt linéique total Definition Symbol S =− dE dx eV·m 10-56 total atomic stopping power fr pouvoir (m) d'arrêt atomique total Sa total mass stopping power fr pouvoir (m) d'arrêt massique total Sm 10-58 mean linear range fr parcours (m) moyen linéaire 10-59 mean mass range fr parcours (m) moyen en masse 10-57 Both electronic losses and radiative losses are included. The ratio of the total linear stopping power of a substance to that of a reference substance is called the relative linear stopping power. See also item 10-88. the charged particles in traversing a distance dx in the given material, thus total linear stopping power S (item 10-55) divided by the number density (ISO 80000-9:2009, item 9-10.1) n of the atoms in the material -1 2 J·m 2 eV·m Sa = S n 2 -1 total linear stopping power S (item 10-55) divided by the mass density ρ (ISO 80000-4:2006, item 4-2) of the material J·m ·kg Sm = S ρ eV·m ·kg R, Rl mean total rectified path length (ISO 80000-3:2006, item 31.1) travelled by a particle in the course of slowing down to rest in a given material averaged over a group of particles having the same initial energy (ISO 80000-5:2007, item 520.1) m Rρ , ( Rm ) mean linear range R (item 10-58) divided by the mass density ρ (ISO 80000-4:2006, item 4-2) of the material kg·m 2 The ratio of the total mass stopping power of a material to that of a reference material is called the relative mass stopping power. -1 -2 Rρ = R ρ 26 © ISO 2014 – All rights reserved ISO/WD 80000-10 Quantity Unit Item No. Remarks Name 10-60 linear ionization fr ionisation (f) linéique Symbol N il Definition quotient of the average total charge dq of all positive ions produced by an ionizing charged particle over an infinitesimal element of path dl (ISO 80000-3:2006, item 31.1, by dl, divided by the elementary charge e Nil = 10-61 10-62 total ionization fr ionisation (f) totale Ni average energy loss per elementary charge produced fr perte (f) moyenne d'énergie par paire d'ions formée Wi Symbol m -1 Ionization due to secondary ionizing particles, etc., is included. 1 dq e dl total mean charge, divided by the elementary charge, e , of all positive ions produced by an ionizing charged particle along its entire path and along the paths of any secondary charged particles 1 initial kinetic energy Ek (ISO 80000-4:2006, item 4-27.3) of an ionizing charged particle divided by the total ionization Ni (item 10-61) produced by that particle J N = ∫ N i dl See Remarks for item 10-60. See the Introduction, 1.3.2. Wi = Ek N i The name “average energy loss per ion pair formed” is usually used, although it is ambiguous.The quantity Si / Ni , sometimes called the average energy per ion pair formed, should not be confused with Wi . In ICRU Report 85a, the mean energy expended in a gas per ion pair formed, W , is the quotient of E by N, where N is the mean total liberated charge of either sign, divided by the elementary charge when the initial kinetic energy E of a charged particle introduced into the gas is completely dissipated in the gas. Thus W = E N . It eV © ISO 2014 – All rights reserved follows from the definition of W that the ions produced by bremsstrahlung or other secondary radiation emitted by the initial and secondary charged particles are included in N. 27 ISO/WD 80000-10 Quantity Unit Item No. Remarks Name Symbol Definition Symbol 2 -1 10-63 mobility fr mobilité (f) µ , µm average drift speed (ISO 80000-3:2006, item 3-8.1) imparted to a charged particle in a medium by an electric field, divided by the electric field strength (IEC 800006:2008, item 6-10) m ·V ·s 10-64.1 particle number density fr nombre (m) volumique de particules n quotient of the mean number N of particles in the volume V by volume m ion number density, ion density fr nombre (m) volumique d'ions n+ , n− recombination coefficient, recombination factor fr coefficient (m) de recombinaison α diffusion coefficient, diffusion coefficient for particle number density D , Dn 10-64.2 10-65 10-66 -3 -1 n is the general symbol for the number density of particles. n=N V The distribution functions expressed in terms of speed and energy, nv and nE , are related to n by quotient of the number of positive and negative ions N + and N − , respectively, in the volume V (ISO 80000-3:2006, item 3-4), by that volume n+ = N + V , n− = N − V n = ∫ n v dv = ∫ n E dE . coefficient in the law of recombination + The word “particle” is usually replaced by the name of a specific particle, for example neutron number density. m ·s 3 -1 The widely used term “recombination factor” is not correct because “factor” should only be used for quantities with dimension 1. 2 -1 The word “particle” is usually replaced by the name of a specific particle, for example neutron number density. For a particle of a given speed v + dn dn − =− = α ⋅ n+ n− , dt dt where n + and n− are the ion number densities (item 1064.2) of positive and negative ions, respectively, recombined during an infinitesimal time interval dt (ISO 80000-3:2006, item 3-7) proportionality constant between the particle current density J (item 10-49) and the gradient of the particle number density n (item10-64.1) J = − D ⋅ grad(n) 28 m ·s © ISO 2014 – All rights reserved ISO/WD 80000-10 Quantity Unit Item No. Remarks Name Symbol Definition Symbol fr coefficient (m) de diffusion, coefficient (m) de diffusion pour le nombre volumique de particules 10-67 10-68 Dn (v) = − diffusion coefficient for fluence rate fr coefficient (m) de diffusion pour le débit de fluence Dϕ , D particle source density fr densité (f) totale d’une source de particules S proportionality constant between the particle current density J (item 10-49) and the gradient of the particle fluence rate (item 10-45) Φ& J v ,x ∂nv / ∂x For a particle of a given speed v, m DΨ& (v) = − J = − D ⋅ grad(Φ& ) J v, x & ∂Ψ v / ∂x and v ⋅ DΨ& (v ) = − Dn (v ) mean rate of production of particles in a domain divided by the volume (ISO 80000-3:2006, item 3-4) of that domain -1 s ·m -3 The word “particle” is usually replaced by the name of a specific particle, for example proton source density. The distribution functions expressed in terms of speed and energy, S v and S E , are related to S by S = ∫ S v dv ∫ S E dE . 10-69 10-70 slowing-down density fr densité (f) de ralentissement q resonance escape p number density of particles dn that are slowed down in an infinitesimal time interval, dt , divided by dt , thus q = − -3 dn dt in an infinite medium, the probability that a neutron slowing down will traverse all or some specified portion of the range © ISO 2014 – All rights reserved -1 s ·m 1 See the Introduction, 1.3.2. 29 ISO/WD 80000-10 Quantity Unit Item No. Remarks Name Symbol probability fr facteur (m) antitrappe 10-71 Definition Symbol of resonance energies (item 10-38.2) without being absorbed lethargy fr léthargie (f) u for a neutron of kinetic energy E (ISO 80000-4:2006, item 4-27.3), 1 The lethargy is also referred to as logarithmic energy decrement See the Introduction, 1.3.2. u = ln (E0 E ) where E0 is a reference energy 10-72 average logarithmic energy decrement fr décrément (m) logarithmique moyen de l'énergie, paramètre (m) de ralentissement ζ average value of the increase in lethargy (item 10-71) in elastic collisions between neutrons and nuclei whose kinetic energy (ISO 80000-4:2006, item 4-27.3) is negligible compared with that of the neutrons 1 See the Introduction, 1.3.2. 10-73 mean free path fr libre parcours (m) moyen l, λ average distance (ISO 80000-3:2006, item 3-1.9) that particles travel between two successive specified reactions or processes m See the Remarks for item 10-43. 10-74.1 slowing-down area fr aire (f) de ralentissement L2s , L2sl in an infinite homogenous medium, one-sixth of the mean square of the distance (ISO 80000-3:2006, item 3-1.9) between the neutron source and the point where a neutron reaches a given energy (ISO 80000-5:2007, item 5-20.1) m 30 2 © ISO 2014 – All rights reserved ISO/WD 80000-10 Quantity Unit Item No. Remarks Name Symbol Definition Symbol 10-74.2 diffusion area fr aire (f) de diffusion L2 in an infinite homogenous medium, one-sixth of the mean square distance (ISO 80000-3:2006, item 3-1.9) between the point where a neutron enters a specified class and the point where it leaves this class m 2 10-74.3 migration area fr aire (f) de migration M2 sum of the slowing-down area (ISO 80000-3:2006, item 33) from fission energy to thermal energy (ISO 800005:2007, item 5-20.1) and the diffusion area for thermal neutrons m 2 10-75.1 slowing-down length fr longueur (f) de ralentissement Ls , Lsl square root of the slowing down area L2s (item 10-74.1) m diffusion length fr longueur (f) de diffusion L migration length fr longueur (f) de migration M neutron yield per fission fr nombre (m) de neutrons produits par fission ν neutron yield per absorption η 10-75.2 10-75.3 10-76.1 10-76.2 The class of neutrons must be specified. Ls = L2s 2 square root of the diffusion area L (item 10-74.2) m L = L2 , 2 square root of the migration area M (item 10-74.3) m M = M2 average number of fission neutrons, both prompt and delayed, emitted per fission event 1 average number of fission neutrons, both prompt and delayed, emitted per neutron absorbed in a fissionable 1 © ISO 2014 – All rights reserved Also called ν factor and η factor. See the Introduction, 1.3.2. ν η is equal to the ratio of the macroscopic cross section for fission to 31 ISO/WD 80000-10 Quantity Unit Item No. Remarks Name Symbol fr nombre (m) de neutrons produits par neutron absorbé Definition Symbol nuclide or in a nuclear fuel, as specified 10-77 fast fission factor fr facteur (m) de fission rapide ϕ 10-78 thermal utilisation factor fr facteur (m) d'utilisation thermique 10-79 that for absorption, both for neutrons in the fuel material. in an infinite medium, the ratio of the mean number of neutrons produced by fission due to neutrons of all energies (ISO 80000-5:2007, item 5-20.1) to the mean number of neutrons produced by fissions due to thermal neutrons only 1 The class of neutrons, e.g. thermal, must be specified. See the Introduction, 1.3.2. f in an infinite medium, the ratio of the number of thermal neutrons absorbed in a fissionable nuclide or in a nuclear fuel, as specified, to the total number of thermal neutrons absorbed 1 The class (thermal) of neutrons must be specified. See the Introduction, 1.3.2. non-leakage probability fr probabilité (f) de non-fuite Λ probability that a neutron will not escape from the reactor during the slowing-down process or while it diffuses as a thermal neutron 1 The class (thermal) of neutrons must be specified. See the Introduction, 1.3.2. 10-80.1 multiplication factor fr facteur (m) de multiplication k ratio of the total number of fission or fission-dependent neutrons produced in a time interval to the total number of neutrons lost by absorption and leakage during the same interval 1 See the Introduction, 1.3.2. 10-80.2 infinite multiplication factor fr facteur (m) de multiplication infini k∞ multiplication factor (item 10-80.1) for an infinite medium or for an infinite repeating lattice 1 For a thermal reactor, 32 k∞ = η ⋅ ε ⋅ p ⋅ f © ISO 2014 – All rights reserved ISO/WD 80000-10 Quantity Unit Item No. Remarks Name Symbol Definition Symbol 10-80.3 entry deleted (effective multiplication factor fr facteur (m) de multiplication effectif) entry deleted 10-81 entry deleted (reactivity fr réactivité (f)) entry deleted 10-82 reactor time constant fr constante (f) de temps du réacteur T duration (ISO 80000-3:2006, item 3-7) required for the neutron fluence rate (item 10-45) in a reactor to change by the factor e when the fluence rate is rising or falling exponentially s Also called reactor period. 10-83.1 energy imparted fr énergie (f) communiquée ε sum of all energy deposits in a given volume, J Energy imparted is a stochastic quantity. ε = ∑εi i where the summation is performed over all energy (ISO 80000-5:2007, item 5-20.1) deposits ε i of interaction i in that volume . eV ε i is given by ε i = ε in − ε out + Q , where ε in is the energy (ISO 80000-5:2007, item 5-20.1) of the incident ionizing particle, excluding rest energy (item 10-3), ε out is the sum of the energies (ISO 80000-5:2007, item 5-20.1) of all ionizing particles leaving the interaction, excluding rest energy (item 10-3), and Q is the change in the rest energies (item © ISO 2014 – All rights reserved 33 ISO/WD 80000-10 Quantity Unit Item No. Remarks Name Symbol Definition Symbol 10-3) of the nucleus and of all particles involved in the interaction. Q > 0 means decrease of rest energy; Q < 0 means increase of rest energy. Stochastic quantities such as the energy imparted and the specific energy imparted (item 10-84.2) and their probability distributions have been introduced as they describe the discontinuous nature of the ionizing radiations as a determinant of radiochemical and radiobiological effects. In radiation applications involving large numbers of ionizing particles, e.g. in medicine, radiation protection and materials testing and processing, these fluctuations are adequately represented by the expectation values of the probability distributions. “Non-stochastic quantities” such as the particle fluence (item10-44), the absorbed dose (item 10-84.1) and the kerma (item10-89)” are based on these expectation values. 10-83.2 (10-50.2) mean energy imparted fr énergie (f) communiquée moyenne ε expectation value of the energy imparted (item10-83.1) J ε = Rin − Rout + ∑ Q , eV where Rin is the radiant energy (item 10-46) of all those charged and uncharged ionizing particles that enter the volume, Rout is the radiant energy of all those charged and Sometimes, it has been called the integral absorbed dose. Q > 0 means decrease of rest energy; Q < 0 means increase of rest energy. uncharged ionizing particles that leave the volume, and 34 © ISO 2014 – All rights reserved ISO/WD 80000-10 Quantity Unit Item No. Remarks Name Symbol Definition Symbol ∑Q is the sum of all changes of the rest energy (item 103) of nuclei and elementary particles that occur in that volume 10-84.1 (10-51.2) absorbed dose fr dose (f) absorbée D quotient of dε by dm (ISO 80000-4:2006, item 4-1), where dε is the mean energy imparted by ionizing radiation to matter of mass dm, thus D= Gy ε = ∫ Ddm , Where dm is the element of mass of the irradiated matter. In the limit of a small domain, the mean specific energy z is equal to the absorbed dose D . The absorbed dose can also be expressed in terms of the volume of the mass element by dε dm D= dε dε = dm ρ ⋅ dV where ρ is the mass density of the mass element -1 1 Gy = 1 J·kg 10-84.2 (10-51.1) 10-85 specific energy imparted fr énergie (f) communiquée massique z quality factor fr facteur (m) de qualité Q quotient of the energy imparted ε (item 10-83.1) by the mass m (ISO 80000-4:2006, item 4-1) of the matter in that volume element z= z is a stochastic quantity. In the limit of a small domain, the mean specific energy z is equal to the absorbed dose D . The specific energy imparted can be due to one or more (energy-deposition) events. ε m factor in the calculation and measurement of dose equivalent (item 10-86), by which the absorbed dose (item 10-84.1) is to be weighted in order to account for different © ISO 2014 – All rights reserved Gy 1 Q is determined by the linear energy transfer (item10-88) for ∆ → ∞ , L∞ (often 35 ISO/WD 80000-10 Quantity Unit Item No. Remarks Name Symbol Definition Symbol biological effectiveness of radiations, for radiation protection purposes denoted as L or LET), of charged particles passing through a small volume element at this point (the value of L∞ refers to water, not to tissue; the difference, however, is small). The relationship between L and Q is given in ICRP Publication 103 (ICRP, 2007). 10-86 dose equivalent fr dose (f) équivalente, [équivalent (m) de dose] H product of the absorbed dose D (item10-84.1) to tissue at the point of interest and the quality factor Q (item 10-85) at that point Sv The sievert is a special name for joule per kilogram, to be used as the coherent SI unit for dose equivalent. -1 1 Sv = 1 J·kg . H = DQ The dose equivalent at a point in tissue is given by ∞ H = ∫ Q( L) DL dL , 0 where DL = dD dL is the distribution of D in L at the point of interest. See ICRP Publication 103 (ICRP, 2007). 10-87 10-88 absorbed-dose rate fr débit (m) de dose absorbée D& linear energy transfer fr transfert (m) L∆ quotient of the increment of the absorbed dose dD (item 10-84.1) in the time interval dt (ISO 80000-3:2006, item 37), by that time interval Gy·s -1 1 Gy/s = 1 W/kg See the remarks for item 10-84.a. dD D& = dt 36 quotient of the mean energy dE∆ lost by the charged particles due to electronic interactions in traversing a distance dl, minus the mean sum of the kinetic energies in J·m -1 This quantity is not completely defined unless ∆ is specified, i.e., the maximum kinetic energy of secondary electrons © ISO 2014 – All rights reserved ISO/WD 80000-10 Quantity Unit Item No. Remarks Name Symbol Definition Symbol whose energy is considered to be “locally deposited.” ∆ may be expressed in eV. Note that the abbreviation LET specifically refers to the quantity L∞ mentioned in the remark to 10-85 excess of ∆ of all the electrons released by the charged particles, by dl linéique d’énergie L∆ = dE ∆ dl eV·m 10-89 kerma fr kerma (m) K quotient of the mean sum of the initial kinetic energies (ISO 80000-4:2006, item 4-27.3) dEtr of all the charged -1 Gy The name “kerma” is derived from Kinetic Energy Released in MAtter (or MAss or MAterial). ionizing particles liberated in a mass (ISO 80000-4:2006, item 4-1) dm of a material, by dm K= 10-90 10-91 kerma rate fr débit (m) de kerma K& mass energytransfer coefficient fr coefficient (m) de transfert d’énergie massique µ tr ρ The quantity dE tr includes also the kinetic energy of the charged particles emitted in the decay of excited atoms, molecules, or nuclei. See the Remarks for item 10-84.a. dEtr dm quotient of the increment of kerma (item 10-89) dK during time dt (ISO 80000-3:2006, item 3-7) by that time interval Gy·s -1 1 Gy/s = 1 W/kg See the Remarks for item 10-84.a. dK K& = dt for ionizing uncharged particles of a given type and energy, the quotient of dRtr R by ρ dl , µ tr 1 1 dRtr , = ρ ρ R dl where dR t r is the mean energy that is transferred to kinetic energy of charged particles by interactions of the uncharged particles of incident radiant energy R in © ISO 2014 – All rights reserved 2 -1 m ·kg µtr ρ = K& ψ , where K& is the kerma rate (item 10-90) and ψ is the energy fluence rate (item 10-48). The quantity µ en ρ = (µ tr ρ )(1 − g ) , where g is the mean fraction of the kinetic energy of the liberated charged particles 37 ISO/WD 80000-10 Quantity Unit Item No. Remarks Name Symbol Definition traversing a distance dl in the material of density 10-92 exposure fr exposition (f) X exposure rate fr débit (m) d’exposition X& that is lost in radiative processes in the material, is called the mass energyabsorption coefficient. The mass energy-absorption coefficient of a compound material depends on the stopping power of the material. Thus its evaluation cannot, in principle, be reduced to a simple summation of the mass energyabsorption coefficient of the atomic constituents. Such a summation can provide an adequate approximation when the value of g is sufficiently small. See also item 10-51. ρ for x or gamma radiation the quotient of the absolute value of the mean total electric charge dq of the ions of the same sign produced when all the electrons and positrons liberated or created by photons incident on a mass dm of dry air are completely stopped in that mass element by the mass (ISO 80000-4:2006, item 4-1) dm , X = 10-93 Symbol -1 C·kg The ionization produced by electrons emitted in atomic or molecular relaxation is included in dq. The ionization due to photons emitted by radiative processes (i.e., bremsstrahlung and fluorescence photons) is not to be included in dq. This quantity should not be confused with the quantity photon exposure (ISO 800007:2008, item 7-51), radiation exposure (ISO 80000-7:2008, item 7-18), or the quantity luminous exposure (ISO 800007:2008, item 7-39). dq dm quotient of the increment dX of the exposure (item10-92) in a time interval dt (ISO 80000-3:2006, item 3-7) by dt -1 C·kg ·s -1 -1 -1 dX X& = dt 38 -1 1 C·kg ·s = 1 A·kg © ISO 2014 – All rights reserved ISO/WD 80000-10 © ISO 2014 – All rights reserved 39 WORKING DRAFT ISO/WD 80000-10 Annex A (informative) Non-SI units used in atomic and nuclear physics Quantity Name of unit Symbol for unit Value in SI units Units accepted for use with the SI energy electron volt eV 1 eV = 1.602 176 565(35) ⋅ 10 -19 J mass unified atomic mass unit u 1u= mass dalton Da 1 Da = 1 u length astronomical unit ua 1 ua = 1.495 1.660 538 921(73)⋅10-27 kg 978 707 00 ⋅ 1011 m (exact) Natural 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 1.054 571 726(47) ⋅ 10-34 J s mass n.u. of mass (electron mass) me 9.109 382 91(40)10-31 kg time n.u. of time ħ/(mec02) 1.288 088 668 33(83)10-21 s Atomic units (a.u.) charge a.u. of charge (elementary charge) e 1.602 176 565 (35) ⋅ 10-19 C mass a.u. of mass (electron mass) me 9.109 382 91(40) ⋅10-31 kg action a.u. of action (reduced Planck constant) ħ 1.054 571 726(47) ⋅10-34 J s length a.u. of length, bohr (Bohr radius) a0 0.529 177 210 92(17) ⋅ 10-10 m energy a.u. of energy, hartree (Hartree energy) Eh 4.359 744 34(19)⋅ 10-18 J time a.u. of time ħ/Eh 2.418 884 326 502(12)⋅ 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. For completeness, the astronomical unit of length is included. © ISO 2014 – All rights reserved 1 ISO/WD 80000-10 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 the natural sciences and technology 3. IEC 60050-393:2003, International Electrotechnical instrumentation — Physical phenomena and basic concepts 4. ICRP Publication 103 (ICRP, 2007) 5. ICRU Report 85a: Fundamental Quantities and Units for Ionizing Radiation, International Commission on Radiation Units and Measurements, J. ICRU, 11, 2011 6. Mohr P.J., Taylor, B.N. and Newell, D.B. CODATA recommended values of the fundamental physical constants: 2010. Rev. Mod. Phys. 84(4), 2012, pp. 1527-1605. See also the CODATA website: http://physics.nist.gov/cuu/constants/index.html 7. SI Brochure, 8th edition (2006), Bureau International des Poids et Mesures, Sèvres, France http://www.bipm.org/en/si/si_brochure/ 2 © ISO 2014 – All rights reserved Vocabulary — Part 393: Nuclear