ISO 80000-10:2019

INTERNATIONAL ISO
STANDARD 80000-10
Second edition
2019-08
Quantities and units —
Part 10:
Atomic and nuclear physics
Grandeurs et unités —
Partie 10: Physique atomique et nucléaire
Reference number
©
ISO 2019
© ISO 2019
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ii © ISO 2019 – All rights reserved

Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
Bibliography .41
Alphabetical index .42
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards
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ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of
electrotechnical standardization.
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described in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the
different types of ISO documents should be noted. This document was drafted in accordance with the
editorial rules of the ISO/IEC Directives, Part 2 (see www. iso. org/directives).
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.org/iso/foreword. html.
This document was prepared by Technical Committee ISO/TC 12, Quantities and units, in collaboration
with Technical Committee IEC/TC 25, Quantities and units.
This second edition cancels and replaces the first edition (ISO 80000-10:2009), which has been
technically revised.
The main changes compared to the previous edition are as follows:
— the table giving the quantities and units has been simplified;
— some definitions and the remarks have been stated physically more precisely;
— definitions in this document have been brought in line with their equivalent ones in ICRU 85a.
A list of all parts in the ISO 80000 and IEC 80000 series can be found on the ISO and IEC websites.
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www. iso. org/members. html.
iv © ISO 2019 – All rights reserved

Introduction
0  Special remarks
0.1  Quantities
Numerical values of physical constants in this document are quoted in the consistent values of the
fundamental physical constants published in CODATA recommended values. The indicated values are
the last known before publication. The user is advised to refer to the CODATA website for the latest
values, https: //physics .nist .gov/cuu/Constants/index .html.
h
The symbol  is the reduced Planck constant, it is equal to , where h is the Planck constant.
2π
0.2  Special units
1 eV is the energy acquired by an electron in passing a potential difference of 1 V in vacuum.
0.3  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. Quantum-mechanical issues aside, one often needs to distinguish between a
stochastic quantity, the values of which follow a probability distribution, and a non-stochastic quantity
with its unique, expected value (expectation) of such distributions. 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 10-81.2) 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 particle fluence (item 10-43), absorbed dose (item 10-81.1) and kerma (item 10-86.1) are based on
these expected values.
This document contains definitions based on a differential quotient of the type dA/dB in which the
quantity A is of a stochastic nature, a situation common in ionizing radiation metrology. In these cases,
quantity A is understood as the expected or mean value whose element ΔA falls into element ΔB. The
differential quotient dA/dB is the limit value of the difference quotient ΔA/ΔB for ΔB → 0. In the remarks
of the definitions falling in this category, a reference to this paragraph is made.
INTERNATIONAL STANDARD ISO 80000-10:2019(E)
Quantities and units —
Part 10:
Atomic and nuclear physics
1 Scope
This document gives names, symbols, definitions and units for quantities used in atomic and nuclear
physics. Where appropriate, conversion factors are also given.
2 Normative references
There are no normative references in this document.
3 Terms and definitions
The names, symbols, and definitions for quantities and units used in atomic and nuclear physics are
given in Table 1.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https: //www .iso .org/obp
— IEC Electropedia: available at http: //www .electropedia .org/
2 © ISO 2019 – All rights reserved
Table 1 — Quantities and units used in atomic and nuclear physics
Item No. Quantity Unit Remarks
Name Symbol Definition
10-1.1 atomic number, Z number of protons in an atomic nucleus 1 A nuclide is a species of atom with speci-
fied numbers of protons and neutrons.
proton number
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 atom-
ic number.
The atomic number equals the quo-
tient of the charge (IEC 80000-6) of
the nucleus and the elementary charge
(ISO 80000-1).
10-1.2 neutron number 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, A number of nucleons in an atomic nucleus 1 A = Z + N
mass number Nuclides with the same value of A are
called isobars.
10-2 rest mass, m(X) for particle X, mass (ISO 80000-4) of that particle at rest in kg EXAMPLE
an inertial frame
proper mass m u m(H O) for a water molecule, m for an
X 2 e
electron.
Da
Rest mass is often denoted m .
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
10-3 rest energy E energy E (ISO 80000-5) of a particle at rest: J
0 0
N m
Em= c
00 0
2 −2
kg m s
where
m is the rest mass (item 10-2) of that particle, and
c is speed of light in vacuum (ISO 80000-1)
Table 1 (continued)
Item No. Quantity Unit Remarks
Name Symbol Definition
10-4.1 atomic mass m(X) rest mass (item 10-2) of an atom X in the ground state kg
m(X)
is called the relative atomic mass.
m u
X
m
u
Da
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
10-4.2 nuclidic mass m(X) rest mass (item 10-2) of a nuclide X in the ground state kg 1 u is equal to 1/12 times the mass of a
free carbon 12 atom, at rest and in its
m u
X
ground state.
Da
1 Da = 1 u
10-4.3 unified atomic mass m 1/12 of the mass (ISO 80000-4) of an atom of the nuclide kg 1 u is equal to 1/12 times the mass of a
u
constant C in the ground state at rest free carbon 12 atom, at rest and in its
u
ground state.
Da
1 Da = 1 u
10-5.1 elementary charge e one of the fundamental constants in the SI system C
(ISO 80000-1), equal to the charge of the proton and oppo-
s A
site to the charge of the electron
10-5.2 charge number, c for a particle, quotient of the electric charge (IEC 80000-6) 1 A particle is said to be electrically neu-
and the elementary charge (ISO 80000-1) tral if its charge number is equal to zero.
ionization number
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.
+ ++ 3+ - -- 3-
H , He , Al , Cl , S , N .
4 © ISO 2019 – All rights reserved
Table 1 (continued)
Item No. Quantity Unit Remarks
Name Symbol Definition
10-6 Bohr radius a radius (ISO 80000-3) of the electron orbital in the hydro- m The radius of the electron orbital in the
gen atom in its ground state in the Bohr model of the atom: H atom in its ground state is a in the
Å
Bohr model of the atom.
4πε 
−10
ångström (Å), 1 Å: = 10 m
a =
me
e
where
ε is the electric constant (IEC 80000-6),
 is the reduced Planck constant (ISO 80000-1),
m is the rest mass (item 10-2) of electron, and
e
e is the elementary charge (ISO 80000-1)
−1
10-7 Rydberg constant R spectroscopic constant that determines the wave numbers m The quantity R = R hc is called the
∞ y ∞ 0
of the lines in the spectrum of hydrogen: Rydberg energy.
e
R =
∞
8πε ahc
00 0
where
e is the elementary charge (ISO 80000-1),
ε is the electric constant (IEC 80000-6),
a is the Bohr radius (item 10-6),
h is the Planck constant (ISO 80000-1), and
c is the speed of light in vacuum (ISO 80000-1)
Table 1 (continued)
Item No. Quantity Unit Remarks
Name Symbol Definition
10-8 Hartree energy E energy (ISO 80000-5) of the electron in a hydrogen atom eV The energy of the electron in an H atom
H
in its ground state: J in its ground state is E .
H
E
h 2 −2
kg m s
e
E =
H
4πε a
where
e is the elementary charge (ISO 80000-1),
ε is the electric constant (IEC 80000-6), and
a is the Bohr radius (item 10-6)
10-9.1 magnetic dipole μ for a particle, vector (ISO 80000-2) quantity causing a m A For an atom or nucleus, this energy is
moment change to its energy (ISO 80000-5) ΔW in an external mag- quantized and can be written as:
netic field of field flux density B (IEC 80000-6):
W = g μ M B
x
ΔW = −μ · B
where
g is the appropriate g factor (item 10-
14.1 or item 10-14.2), μ is mostly the
x
Bohr magneton or nuclear magneton
(item 10-9.2 or item 10-9.3), M is mag-
netic quantum number (item 10-13.4),
and B is magnitude of the magnetic flux
density.
See also IEC 80000-6.
10-9.2 Bohr magneton μ magnitude of the magnetic moment of an electron in a m A
B
state with orbital angular momentum quantum number
l=1 (item 10-13.3) due to its orbital motion:
e
μ =
B
2m
e
where
e is the elementary charge (ISO 80000-1),
 is the reduced Planck constant (ISO 80000-1), and
m is the rest mass (item 10-2) of electron
e
6 © ISO 2019 – All rights reserved
Table 1 (continued)
Item No. Quantity Unit Remarks
Name Symbol Definition
10-9.3 nuclear magneton μ absolute value of the magnetic moment of a nucleus: m A Subscript N stands for nucleus. For the
N
neutron magnetic moment, subscript
e
n is used. The magnetic moments of
μ =
N
protons and neutrons differ from this
2m
p
quantity by their specific g factors (item
where
10-14.2).
e is the elementary charge (ISO 80000-1),
 is the reduced Planck constant (ISO 80000-1), and
m is the rest mass (item 10-2) of proton
p
2 −1
10-10 spin s vector (ISO 80000-2) quantity expressing the internal kg m s Spin is an additive vector quantity.
angular momentum (ISO 80000-4) of a particle or a par-
ticle system
10-11 total angular J vector (ISO 80000-2) quantity in a quantum system J s In atomic and nuclear physics, orbital
momentum composed of the vectorial sum of angular momentum L eV s angular momentum is usually denoted
(ISO 80000-4) and spin s (item 10-10) by l or L.
2 −1
kg m s
The magnitude of J is quantized so that:
J =+ jj()1
where j is the total angular momentum
quantum number (item 10-13.6).
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  .

Table 1 (continued)
Item No. Quantity Unit Remarks
Name Symbol Definition
2 −1 −1 2 −1 −1
10-12.1 gyromagnetic ratio, γ proportionality constant between the magnetic dipole A m J s 1 A·m /(J·s) = 1 A·s/kg = 1 T ·s
moment and the angular momentum:
magnetogyric ratio, A s/kg The systematic name is “gyromagnetic
μ = γ J coefficient”, but “gyromagnetic ratio” is
−1
gyromagnetic coef- kg s A
more usual.
ficient where
The gyromagnetic ratio of the proton is
μ is the magnetic dipole moment (item 10-9.1), and
denoted by γ .
p
J is the total angular momentum (item 10-11)
The gyromagnetic ratio of the neutron is
denoted by γ .
n
2 −1 −1 2 −1 −1
proportionality constant between the magnetic dipole A m J s 1 A·m /(J·s) = 1 A·s/kg = 1 T ·s
10-12.2 gyromagnetic ratio γ
e
moment and the angular momentum of the electron
of the electron,
A s/kg
magnetogyric ratio μ = γ J
e −1
kg s A
of the electron,
where
gyromagnetic coeffi-
μ is the magnetic dipole moment (item 10-9.1), and
cient of the electron
J is the total angular momentum (item 10-11)

8 © ISO 2019 – All rights reserved
Table 1 (continued)
Item No. Quantity Unit Remarks
Name Symbol Definition
10-13.1 quantum number N number describing a particular state of a quantum system 1 Electron states determine the binding
L energy E = E(n,l,m,j,s,f ) in an atom.
M
Upper case letters N, L, M, J, S, F are usu-
j
ally used for the whole system.
s
F
The spatial probability distribution of an
electron is given by │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:
m
ψ (rR,,ϑφ)(=⋅rY)(ϑφ,)
nl l
where
r ,,ϑφ are spherical coordinates
(ISO 80000-2) with respect to the
nucleus and to a given (quantization)
axis, Rr() is the radial distribution
nl
m
function, and Y (,ϑφ) are spherical
l
harmonics.
In the Bohr model of one-electron atoms,
n, l, and m define the possible orbits of
an electron about the nucleus.
10-13.2 principal quantum n atomic quantum number related to the number n−1 of 1 In the Bohr model, n = 1,2,…,∞ is related
number radial nodes of one-electron wave functions to the binding energy of an electron and
the radius of spherical orbits (principal
axis of the elliptic orbits).
For an electron in an H atom, the
semi-classical radius of its orbit is
r = a n and its binding energy is
n 0
E = E /n .
n H
Table 1 (continued)
Item No. Quantity Unit Remarks
Name Symbol Definition
10-13.3 orbital angular l atomic quantum number related to the orbital angular 1
momentum quantum momentum l of a one-electron state l =− ll()1 , ln=−01,,, 1
l
i
number
where
L
l is the orbital angular momentum and
 is the reduced Planck constant
(ISO 80000-1).
If reference is made to a specific particle
i, the symbol l is used instead of l;
i
if reference is made to the whole system,
the symbol L is used instead of l.
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.
10-13.4 magnetic quantum m atomic quantum number related to the z component l , j or 1
z z
lm=  , jm=  , and sm=  , with the
zl zj zs
number s , of the orbital, total, or spin angular momentum
z
m
i
ranges from −l to l, from −j to j, and ±1/2,
M
respectively.
m refers to a specific particle i. M is used
i
for the whole system.
Subscripts l, s, j, etc., as appropriate, in-
dicate the angular momentum involved.
 is the reduced Planck constant
(ISO 80000-1).
10-13.5 spin quantum s characteristic quantum number s of a particle, related to 1 Spin quantum numbers of fermions are
number its spin (item 10-10), s: odd multiples of 1/2, and those of bos-
ons are integers.
s =+ ss()1
where  is the reduced Planck constant (ISO 80000-1)

10 © ISO 2019 – All rights reserved
Table 1 (continued)
Item No. Quantity Unit Remarks
Name Symbol Definition
10-13.6 total angular j quantum number in an atom describing the magnitude of 1 j refers to a specific particle i; J is used
i
momentum quantum total angular momentum J (item 10-11) for the whole system.
j
i
number
The quantum number J and the magni-
J
tude of total angular momentum J (item
10-11) are different quantities.
The two values of j are l±1/2. (See item
10-13.3.)
10-13.7 nuclear spin I quantum number related to the total angular momentum 1 Nuclear spin is composed of spins of the
quantum number (item 10-11), J, of a nucleus in any specified state, normally nucleons (protons and neutrons) and
called nuclear spin: their (orbital) motions.
In principle there is no upper limit for
J =+ II()1
the nuclear spin quantum number. It has
possible values I = 0,1,2,… for even A and
where  is the reduced Planck constant (ISO 80000-1)
1 3
I= ,, for odd A.
2 2
In nuclear and particle physics, J is
often used.
10-13.8 hyperfine structure F quantum number of an atom describing the inclination of 1 The interval of F is │I−J│, │I−J│+1, ., I−J.
quantum number the nuclear spin with respect to a quantization axis given
This is related to the hyperfine splitting
by the magnetic field produced by the orbital electrons
of the atomic energy levels due to the
interaction between the electron and
nuclear magnetic moments.
10-14.1 Landé factor, g quotient of the magnetic dipole moment of an atom, and 1 These quantities are also called g values.
the product of the total angular momentum quantum num-
g factor of atom The Landé factor can be calculated from
ber and the Bohr magneton:
the expression:
μ
g= gL(),,SJ =+11()g −
e
J⋅μ
B
JJ+11++SS −+LL 1
() () ()
where ×
21JJ()+
μ is magnitude of magnetic dipole moment (item 10-9.1),
where g is the g factor of the electron.
e
J is total angular momentum quantum number (item
10-13.6), and
μ is the Bohr magneton (item 10-9.2)
B
Table 1 (continued)
Item No. Quantity Unit Remarks
Name Symbol Definition
10-14.2 g factor of nucleus or g quotient of the magnetic dipole moment of an atom, and 1 The g factors for nuclei or nucleons are
nuclear particle the product of the nuclear spin quantum number and the known from measurements.
nuclear magneton:
μ
g=
I⋅μ
N
where
μ is magnitude of magnetic dipole moment (item 10-9.1),
I is nuclear spin quantum number (item 10-13.7), and
μ is the nuclear magneton (item 10-9.3)
N
−1
10-15.1 Larmor angular ω angular frequency (ISO 80000-3) of the electron angular rad s
L
frequency momentum (ISO 80000-4) vector precession about the
−1
s
axis of an external magnetic field:
e
ω = B
L
2m
e
where
e is the elementary charge (ISO 80000-1),
m is the rest mass (item 10-2) of electron, and
e
B is magnetic flux density (IEC 80000-6)
−1
10-15.2 Larmor frequency ν quotient of Larmor angular frequency (ISO 80000-3) and 2π s
L
−1
10-15.3 nuclear precession ω frequency (ISO 80000-3) by which the nucleus angular rad s
N
angular frequency momentum vector (ISO 80000-4) precesses about the axis
−1
s
of an external magnetic field:
ω = γ B
N
where
γ is the gyromagnetic ratio (item 10-12.1), and
B is magnetic flux density (IEC 80000-6)

12 © ISO 2019 – All rights reserved
Table 1 (continued)
Item No. Quantity Unit Remarks
Name Symbol Definition
−1
10-16 cyclotron angular ω quotient of the product of the electric charge of a particle rad s The quantity v = ω /2π is called the
c c c
frequency and the magnitude of the magnetic flux density of the mag- cyclotron frequency.
−1
s
netic field, and the particle mass:
q
ω = B
c
m
where
q is the electric charge (IEC 80000-6) of the particle,
m is the mass (ISO 80000-4) of the particle, and
B is the absolute value of the magnetic flux density
(IEC 80000-6)
10-17 gyroradius, r radius (ISO 80000-3) of circular movement of a particle m
g
with mass (ISO 80000-4), velocity v (ISO 80000-3), and
Larmor radius r
L
electric charge q (IEC 80000-6), moving in a magnetic field
with magnetic flux density B (IEC 80000-6):
mvB×
r =
g
qB
10-18 nuclear quadrupole Q z component of the diagonalized tensor of nuclear quadru- m The electric nuclear quadrupole mo-
moment pole moment: ment is eQ.
This value is equal to the z component
Q= ()3zr− ρ(,xy ,)zV d
()
∫ of the diagonalized tensor of quadru-
e
pole moment.
in the quantum state with the nuclear spin in the field
direction (z), where
e is the elementary charge (ISO 80000-1),
2 2 2 2
r = x + y + z ,
ρ(x,y,z) is the nuclear electric charge density
(IEC 80000-6), and
dV is the volume element dx dy dz

Table 1 (continued)
Item No. Quantity Unit Remarks
Name Symbol Definition
10-19.1 nuclear radius R conventional radius (ISO 80000-3) of sphere in which the m This quantity is not exactly defined. It is
nuclear matter is included given approximately for nuclei in their
ground state by:
13/
Rr= A
where
−15
r ≈×12, 10 m, and A is the nucleon
number (item 10-1.3).
Nuclear radius is usually expressed in
−15
femtometres, 1 fm = 10 m.
radius of a sphere such that the relativistic electron energy m This quantity corresponds to the
10-19.2 electron radius r
e
is distributed uniformly: electrostatic energy E of a charge
distributed inside a sphere of radius r
e
e as if all the rest energy (item 10-3) of the
r =
e
2 electron were attributed to the energy
4πε mc
00e
of electromagnetic origin, using the
where
relation Em= c .
e0
e is the elementary charge (ISO 80000-1),
ε is the electric constant (IEC 80000-6),
m is the rest mass (item 10-2) of electron, and
e
c is the speed of light in vacuum (ISO 80000-1)
10-20 Compton wavelength λ quotient of the Planck constant and the product of the m The wavelength of electromagnetic
C
mass of the particle and the speed of light in vacuum: radiation scattered from free electrons
(Compton scattering) is larger than
h
that of the incident radiation by a maxi-
λ =
C
mum of 2λ .
mc
C
where
h is the Planck constant (ISO 80000-1),
m is the rest mass (item 10-2) of a particle, and
c is the speed of light in vacuum (ISO 80000-1)
o
14 © ISO 2019 – All rights reserved
Table 1 (continued)
Item No. Quantity Unit Remarks
Name Symbol Definition
10-21.1 mass excess Δ difference between the mass of an atom, and the product kg The mass excess is usually expressed in
of its mass number and the unified mass constant: daltons, 1 Da = 1 u.
Da
Δ = m − A · m See item 10-2.
a u
u
where
m is the rest mass (item 10-2) of the atom,
a
A is its nucleon number (item 10-1.3), and
m is the unified atomic mass constant (item 10-4.3)
u
10-21.2 mass defect B sum of the product of the proton number and the hydrogen kg The mass excess is usually expressed in
atomic mass, and the neutron rest mass, minus the rest daltons, 1 Da = 1 u.
Da
mass of the atom:
If the binding energy of the orbital
u
B = Z m( H) + N m − m
n a
electrons is neglected, Bc is equal to
o
where
the binding energy of the nucleus.
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),
m is the rest mass (item 10-2) of the neutron, and
n
m is the rest mass (item 10-2) of the atom
a
10-22.1 relative mass excess Δ quotient of mass excess and the unified atomic mass 1
r
constant:
Δ = Δ/m
r u
where
Δ is mass excess (item 10-21.1), and
m is the unified atomic mass constant (item 10-4.3)
u
Table 1 (continued)
Item No. Quantity Unit Remarks
Name Symbol Definition
10-22.2 relative mass defect B quotient of mass defect and the unified atomic mass 1
r
constant:
B = B/m
r u
where
B is mass defect (item 10-21.2), and
m is the unified atomic mass constant (item 10-4.3)
u
10-23.1 packing fraction f quotient of relative mass excess and the nucleon number: 1
f = Δ /A
r
where
Δ is relative mass excess (item 10-22.1), and
r
A is the nucleon number (item 10-1.3)
10-23.2 binding fraction b quotient of relative mass defect and the nucleon number: 1
b = B /A
r
where
B is relative mass defect (item 10-22.2), and
r
A is the nucleon number (item 10-1.3)
-1
10-24 decay constant, λ quotient of –dN/N and dt, where dN/N is the mean s For exponential decay, this quantity is
fractional change in the number of nuclei in a particular constant.
disintegration
energy state due to spontaneous transformations in a time
constant For more than one decay channel,
interval of duration (ISO 80000-3) dt:
λλ=
∑ a
1 dN
λ=−
where λ denotes the decay constant
a
N dt
for a specified final state and the sum is
taken over all final states.
10-25 mean duration of life, τ reciprocal of the decay constant λ (item 10-24): s Mean duration of life is the expected
value of the duration of life of an unsta-
mean life time
ble particle or an excited state of a par-
τ=
λ
physics> in a short time interval follows a Poisson
distribution.
16 © ISO 2019 – All rights reserved
Table 1 (continued)
Item No. Quantity Unit Remarks
Name Symbol Definition
10-26 level width Γ quotient of the reduced Planck constant and the mean life: eV Level width is the uncertainty of the en-
ergy of an unstable particle or an excited
J

state of a system due to the Heisenberg
Γ =
2 −2
principle.
kg m s
τ
where
The term energy level refers to the con-
figuration of the distribution function of
 is the reduced Planck constant (ISO 80000-1), and
the density of states. Energy levels may
be considered as discrete, like those in
τ is mean duration of life (item 10-25)
an atom, or may have a 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.
10-27 activity A differential quotient of N with respect to time, where N is Bq For exponential decay, A = λN, where λ is
the mean change in the number of nuclei in a particular the decay constant (item 10-24).
−1
s
energy state due to spontaneous nuclear transformations
The becquerel (Bq) is a special name for
in a time interval of duration (ISO 80000-3) dt:
second to the power minus one, to be
used as the coherent SI unit of activity.
dN
A=−
In report 85a of the ICRU a definition
dt
with an equivalent meaning is given
as: The activity, A, of an amount of a
radionuclide in a particular energy state
at a given time is the quotient of -dN by
dt, where dN is the mean change in the
number of nuclei in that energy state
due to spontaneous nuclear transforma-
tions in the time interval dt:
dN
A=− .
dt
See also section 0.3.
10-28 specific activity, a quotient of the activity A (item 10-27) of a sample and the Bq/kg
mass m (ISO 80000-4) of that sample:
−1 −1
massic activity kg s
a = A/m
Table 1 (continued)
Item No. Quantity Unit Remarks
Name Symbol Definition
10-29 activity density, c quotient of the activity A (item 10-27) of a sample and the Bq/m
A
volume V (ISO 80000-3) of that sample:
−3 −1
volumic activity, m s
c = A/V
A
activity concentration
10-30 surface-activity a quotient of the activity A (item 10-27) of a sample and the Bq/m This value is usually defined for flat
S
density total area S (ISO 80000-3) of the surface of that sample: sources, where S corresponds to the total
−2 −1
m s
area of surface of one side of the source.
a = A/S
S
10-31 half life T mean duration (ISO 80000-3) required for the decay of one s For exponential decay, T = (ln2)/λ,
1/2 1/2
half of the atoms or nuclei where λ is the decay constant (item 10-
24).
10-32 alpha disintegration Q sum of the kinetic energy (ISO 80000-4) of the α-parti- eV The ground-state alpha disintegration
α
energy cle produced in the disintegration process and the recoil energy, Q , also includes the energy of
α,0
J
energy (ISO 80000-5) of the product atom in a reference any nuclear transitions that take place
2 −2
frame in which the emitting nucleus is at rest before its kg m s in the daughter produced.
disintegration
10-33 maximum beta- E maximum kinetic energy (ISO 80000-4) of the emitted beta eV The maximum kinetic energy corre-
β
particle energy particle produced in the nuclear disintegration process sponds to the highest energy of the beta
J
spectrum.
2 −2
kg m s
10-34 beta disintegration Q sum of the maximum beta-particle kinetic energy (item eV For positron emitters, the energy for the
β
energy 10-33) and the recoil energy (ISO 80000-5) of the atom production of the annihilation radiation
J
produced in a reference frame in which the emitting nucle- created in the combination of an elec-
2 −2
us is at rest before its disintegration kg m s tron with the positron is part of the beta
disintegration energy.
The ground-state beta disintegration
energy, Q , also includes the energy of
β,0
any nuclear transitions that take place
in the daughter product.
10-35 internal conversion α quotient of the number of internal conversion electrons 1 The quantity α/(α+1) is also used and
factor and the number of gamma quanta emitted by the radi- called the internal-conversion fraction.
oactive atom in a given transition, where a conversion
Partial conversion fractions referring
electron represents an orbital electron emitted through
to the various electron shells K, L, . are
the radioactive decay
indicated by α , α , ….
K L
α /α is called the K-to-L internal con-
K L
version ratio.
18 © ISO 2019 – All rights reserved
Table 1 (continued)
Item No. Quantity Unit Remarks
Name Symbol Definition
10-36 particle emission differential quotient of N with respect to time, where N 1 Usually the kind of particles is specified,

N
rate is the number of particles being emitted from an infin- e.g. neutron emission rate or alpha par-
itesimally small volume element in the time interval of ticle emission rate.
duration dt (ISO 80000-3), and dt:
dN

N=
dt
10-37.1 reaction energy Q in a nuclear reaction, sum of the kinetic energies eV For exothermic nuclear reactions, Q>0.
(ISO 80000-4) and photon energies (ISO 80000-5) of the
J For endothermic nuclear reactions, Q<0.
reaction products minus the sum of the kinetic and photon
2 −2
energies of the reactants kg m s
10-37.2 resonance energy E kinetic energy (ISO 80000-4) of an incident particle, in the eV The energy of the resonance corre-
r
reference frame of the target, corresponding to a reso- sponds to the difference of the energy
E J
res
nance in a nuclear reaction levels involved of the nucleus.
2 −2
kg m s
10-38.1 cross section σ for a specified target entity and for a specified reaction m The type of process is indicated by sub-
or process produced by incident charged or uncharged scripts, e.g. absorption cross section σ ,
a
b
particles of a given type and energy, the quotient of the scattering cross section σ , fission cross
s
mean number of such reactions or processes and the inci- section σ .
f
dent-particle fluence (item 10-43)
−28 2
1 barn (b) = 10 m
10-38.2 total cross section σ sum of all cross sections (item 10-38.1) corresponding to m In the case of a narrow unidirectional
tot
the various reactions or processes between an incident beam of incident particles, this is the
σ b
T
particle of specified type and energy (ISO 80000-5) and a effective cross section for the removal of
target entity an incident particle from the beam. See
the Remarks for item 10-52.
−28 2
1 barn (b) = 10 m
2 −1
10-39 direction distribu- σ differential quotient of σ with respect to Ω, where σ is the m sr Quantities listed under items 10-39,
Ω
tion of cross section cross section (item 10-38.1) for ejecting or scattering a 10-40 and 10-41 are sometimes called
m
particle into a specified direction, and Ω is the solid angle differential cross sections.
(ISO 80000-3) around that direction:
The type of interaction needs to be
σ = dσ/dΩ specified.
Ω
Table 1 (continued)
Item No. Quantity Unit Remarks
Name Symbol Definition
10-40 energy distribution σ differential quotient of σ with respect to energy, where σ is m /J
E
of cross section the cross section (item 10-38.1) for a process in which the
−1 2
kg s
energy E (ISO 80000-5) of the ejected or scattered particle
is between E and E+dE:
σ = dσ/dE
E
10-41 direction and energy σ partial differential quotient of σ with respect to solid angle m /(J sr)
Ω,E
distribution of and energy, where σ is the cross section (item 10-38.1)
−1 2
kg s
cross section for ejecting or scattering a particle into a solid angle dΩ
around a specified direction and with an energy between
E and E+dE:
∂ σ
σ =
Ω ,E
∂∂Ω E
−1
10-42.1 volumic cross section, Σ product of the number density n of the atoms and of the m When the target particles of the medium
a
cross section (item 10-38.1) σ for a given type of atoms: are at rest, Σ = 1/l, where l is the mean
a
macroscopic
free path (item 10-71).
cross section Σ = n σ
a a

−1
10-42.2 volumic total Σ product of the number density n of the atoms and the m See the Remarks for item 10-49.
tot a
cross section, cross section (item 10-38.1) σ for a given type of atoms:
tot
Σ
T
macroscopic total Σ = n σ
tot a tot
cross section

−2
10-43 particle fluence differential quotient of N with respect to a, where N is the m The word “particle” is usually replaced
Φ
number of particles incident on a sphere of cross-sectional by the name of a specific particle, for
area a (item 10-38.1): example proton fluence.
If a flat area of size dA is passed
dN
Φ=
perpendicularly by a number of dN
da
particles, the corresponding particle
dN
fluence is:Φ=
dA
20 © ISO 2019 – All rights reserved
Table 1 (continued)
Item No. Quantity Unit Remarks
Name Symbol Definition
10-43   A plane area of size dA crossed at an
(cont.) angle α with respect to the surface nor-
mal by a number of dN particles results
in the particle fluence:
dN
Φ=
cos(α)dA
In report 85a of the ICRU a definition
with an equivalent meaning is given as:
The fluence, Φ , is the quotient of dN and
da, where dN is the number of particles
incident on a sphere of cross-sectional
area da:
dN
Φ= .
da
See also section 0.3.
−2 −1
10-44 particle fluence rate m s The word “particle” is usually replaced
 differential quotient of fluence Φ (item 10-43) with
Φ
by the name of a specific particle, for
respect to time (ISO 80000-3):
example proton fluence rate.
dΦ
The distribution function expressed in

Φ=
dt  
terms of speed and energy, Φ andΦ ,
v E
are related to by:
 
ΦΦ==ddvEΦ .
vE
∫ ∫
Table 1 (continued)
Item No. Quantity Unit Remarks
Name Symbol Definition
10-44   This quantity has also been termed
(cont.) 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 item 10-43.
In report 85a of the ICRU a definition
with an equivalent meaning is given as:

The fluence rate, Φ , is the quotient of
dΦ and dt, where dΦ is the increment
of the fluence in the time interval dt:
dΦ

Φ= .
dt
See also section 0.3.
10-45 radiant energy R mean energy (ISO 80000-5), excluding rest energy (item eV For particles of energy E (excluding rest
10-3), of the particles that are emitted, transferred, or energy), the radiant energy, R, is equal to
J
received the product N·E where N is the number
2 −2
of the particles that are emitted, trans-
kg m s
ferred, or received
The distributions, N and R , of the
E E
particle number and the radiant energy
with respect to energy are given by
N = dN/dE and
E
R = dR/dE, respectively, where dN is
E
the number of particles with energy
between E and E+dE, and dR is their ra-
diant energy. The two distributions are
related by R = E·N .
E E
22 © ISO 2019 – All rights reserved
Table 1 (continued)
Item No. Quantity Unit Remarks
Name Symbol Definition
10-46 energy fluence differential quotient of radiant energy R (item 10-45) eV/m In report 85a of the ICRU a definition
Ψ
incident on a sphere of cross-sectional area (item 10-38.1) with an equivalent meaning is given as:
J/m
a with respect to that area:
The energy fluence, Ψ , is the quotient of
−2
kg s
dR
dR and da, where dR is the radiant
Ψ =
energy incident on a sphere of cross-sec-
da
tional area da:
dR
Ψ = .
da
See also section 0.3.
10-47 energy fluence rate W/m In report 85a of the ICRU a definition

differential quotient of the energy fluence Ψ (item 10-46)
Ψ
with an equivalent meaning is given as:
−3
kg s
with respect to time (ISO 80000-3):

The energy-fluence rate, Ψ , is the
dΨ

Ψ =
quotient of dΨ by dt, where dΨ is the
dt
increment of the energy fluence in the
time interval dt:
dΨ

Ψ = .
dt
See also section 0.3.
Table 1 (continued)
Item No. Quantity Unit Remarks
Name Symbol Definition
−2 −1
10-48 particle current J vector whose component in direction of an area normal is m s Usually the word “particle” is replaced
density given by: by the name of a specific particle, for
S
example proton current.
J = ΦΩ(,θα )cos()θ d
n ∫ Ω
Symbol S is recommended when there
is a possibility of confusion with the
where
symbol J for electric current density. For
neutron current, the symbol J is gen-
Φ ()θα, is the directional distribution of the particle
Ω
erally used. The distribution functions
fluence rate (item 10-44), and
expressed in terms of speed and energy,
J and J , are related to J by:
θ and α   are polar and azimuthal angles, respectively
v E
JJ==ddvEJ .
vE
∫∫
The directional distribution of the
particle fluence rate is also denoted as
particle radiance.
−1
10-49 linear attenuation μ for uncharged particles of a given type and energy the dif- m μ is equal to the macroscopic total cross
coefficient ferential quotient n with respect to l, where n is the frac- section Σ for the removal of particles
tot
μ
l
tion of N incoming particles that experience interactions in from the beam.
traversing a distance (ISO 80000-3) l in a given material:
Using the relation μ = μ/ρ between the
m
linear attenuation coefficient μ, the mass
dn 1 dN
μ==
attenuation coefficient μ (item 10-50)
m
dlN dl
and the density ρ, the defini
...