Download Quantities and units — Part 10: Atomic and nuclear physics

© 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.
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Document type: International Standard
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© 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.
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© 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