Detection And Dosimetry Of Ionising Radiation

Detection And Dosimetry Of Ionising Radiation - Transcript

MSc-REP Regan Dosimetry 1
Detection and Dosimetry of
Ionising Radiation
MSc-REP Lecture Notes
Paddy Regan
p.regan@surrey.ac.uk
http://www.ph.surrey.ac.uk/~phs1pr/lecture_notes
MSc-REP Regan Dosimetry 2
Course text book,
Radiation Biophysics
by
E.L. Alpen, Academic Press
2nd Edition, (1990)
Important chapters for this course,
Chapter 1: Quantities and Units
Chapter 4: Radiation/Matter interactions.
Chapter 5: Energy Transfer Processes
Chapter 16: Dose, Dose Equivalent
Also, refer to Radiation Detection and
Measurement, G.F.Knoll, 2nd Edition.
Introduction to Health Physics, H. Cember and
T.E. Johnson, 4th Edition (McGraw Hill)
MSc-REP Regan Dosimetry 3
Some Useful Web Pages
Dosimetry definitions etc.
• http://www.physics.isu.edu/radinf/terms.htm
• http://www.hps.org/publicinformation/radfactsheets/
Also, good notes on basic dosimetry terms etc. can be found at
• http://www.physics.mtsu.edu/~phys2020/index.html (chapter 11)
•http://www.physics.isu.edu/radinf/index.html
International Commission in Radiation Protection (ICRP) web site
• http://www.icrp.org/
Stopping powers, attenuation coeffs of x-rays, e-s, ps & ?s
from the USA National Institute for Standards and Technology
• http://physics.nist.gov/PhysRefData/contents-radi.html
• http://physics.nist.gov/PhysRefData/XrayMassCoeff/
(see also Seltzer Radiation Research 136 (1993) p147)
• http://www.nist.gov/physlab/data/xcom/index.cfm
•http://www.srim.org/ (for charged particles)
MSc-REP Regan Dosimetry 4
Relationship Between Detectors
and Dosimetry
– Physical and Chemical Effects of Ionising
Radiation.
– General Concepts and Units.
– Radiation Quantities and Definitions
– Absolute Methods of Dosimetry
MSc-REP Regan Dosimetry 5
Physical and Chemical Effects of
Ionising Radiation
Incident ionising radiation can cause the following effects on matter
(which can, therefore conversely be used to measure the amount of
radiation imparted):
• Ionisation (i.e., electrons removed from atoms)
• Excitation (atoms/molecules raised to excited states)
• Chemical effects (changes in the structure of molecules which
can lead to molecular disassociation resulting in biological changes).
• Radiation damage to the crystalline structure in solids.
• Thermal effects (radiation causes increase in temperature)
• Nuclear excitations and/or transmutations.
MSc-REP Regan Dosimetry 6
Radiation Damage in Biological Systems
• In biological organisms, radiation damage occurs due to the
ionisation of atoms and molecules in cells.
• The production of ions can result in chemical reactions which break
molecular bonds in proteins and other important biological molecules.
• Typically 1-> 40 eV of energy is needed to ionize a molecule or
atom, thus radiations such as ?, ? and ?, which can have energies in
the 100keV to few MeV range, can individually result in the
ionisation of thousands of atoms or molecules.
• Biological damage can subsequently result either by cells being
killed or mutating (which can result in cancer). A large enough dose
will destroy sufficient numbers of cells to kill the organism.
MSc-REP Regan Dosimetry 7
There are 2 main types of radiation damage in biological systems:
Somatic Damage (also known as ‘radiation sickness’): This refers
to damage to cells which are not associated with reproduction.
The degree of somatic damage depends on the organ exposed and the
age of the individual (younger = more susceptible to somatic damage).
Effects of somatic damage include:
• reddening of the skin,
• hair loss,
• ulceration,
• reduction of white blood cells,
• cataracts in the eyes,
• fibrosis of the lungs.
Genetic Damage: This refers to damage to cells associated with
reproduction which can lead to genetic mutations in the offspring.
MSc-REP Regan Dosimetry 8
Some Terms Related to Dose
• Chronic Dose: dose received over an extended period of time.
• Acute Dose: dose received in a short period of time.
• Somatic Effects: effects seen in an individual exposed to the dose.
• Genetic Effects: effects in the offspring of the individual exposed
to the radiation due to a pre-conception exposure of the offspring.
• Teratogenic Effects: are effects in the offspring of the individual
who experienced the dose during gestation.
• Stochastic Effects: are effects which occur on a random basis.
Such effects have no effective threshold, but the chances of such
an effect are increased with dose. Cancer is a stochastic effect.
• Non-Stochastic Effects: can be directly related to the size of the
dose received. They often have a dose threshold below which the
effect does not occur. Skin burning from radiation is a non-
stochastic effect.
MSc-REP Regan Dosimetry 9
Basis of Detector/Dosimetry Systems
Dosimetry/radiation detection systems can then be designed and
operated using these effects. Basic systems include,
• Calorimetry, based of thermal effects and increases in temperature.
This provides the most basic and accurate ‘primary standard’.
• Chemical dosimeters, based on chemical effects and molecular
changes, a good and accurate, ‘secondary standard’
• Ionisation chambers - electronic ionisation.
• Proportional Counters/Geiger-Mueller detectors - electronic
ionisation and atomic/molecular excitation in a gas medium.
• Semiconductor detectors (silicon, germanium, CdTe) - ionisation
MSc-REP Regan Dosimetry 10
Basis of Detector/Dosimetry Systems (cont.)
• Scintillation counters (e.g., NaI(Tl), BaF2) - scintillation light emitted
following molecular excitations. (see Knoll p221, p231)
• Solid state integrating dosimeters - radiation damage in solids
• Photographic methods - radiation damage in solids
• Solid state track detectors - radiation damage in solids
• Activation detectors - nuclear transmutation (for neutrons usually
via (n,?), (n,p) or (n,?) reactions).
Slow (thermal) neutrons detection can use (see Knoll p483ff & 707 ff)
10B(n,?) 7Li (Q=2.310, 94%, E(7Li) = 0.84 MeV, E(?) = 1.47 MeV).
6Li(n,?)3H (Q=4.78 MeV, E(3H) = 2.73 MeV, E(?) = 2.05 MeV)
55Mn(n,?)56Mn T1/2=2.6h ; 59Co(n,?)60Co T1/2=10.4min & 5.3y ;
109Ag(n,?)110Ag, T1/2=24secs; 164Dy(n,?)165mDy, T1/2=1.3mins .
Threshold activation detectors (for fast neutrons) include
59Co(n,?)56Mn, T1/2=2.56h ; 23Na(n,?)20F (in a NaI(Tl) detector)
MSc-REP Regan Dosimetry 11
FromKnoll p707
MSc-REP Regan Dosimetry 12
From Knoll p708
MSc-REP Regan Dosimetry 13
From Knoll p709
MSc-REP Regan Dosimetry 14
Definitions, Quantities and Units (Alpen p5ff)
Exposure (X): The exposure is defined as the ratio of the charge
(of one sign) ?Q produced in a medium when all the electrons
liberated by photons in the volume element of the medium with mass
?m, are completely stopped in the volume. Thus
The (old) unit of exposure is the Roentgen (R) .
The natural SI unit for exposure would be C/Kg
but is never used. 1 Roentgen = 2.58x10-4 C/Kg (see later, ‘KERMA’)
m
QX
?
?
=
The Roentgen was originally defined at a 1928 conference as
‘ …the quantity of X-radiation which, when secondary electrons are
fully utilised and the wall effect of the chamber is avoided, produces
in 1cm3 of atmospheric air at 0oC and 76cm of mercury pressure
such a degree of conductivity that 1 electrostatic charge is measured
at saturation current’. (Air was chosen as a standard medium since
air/gold leaf ionisation chambers were standard equipment).
Exposure only applies to X- and ?-rays, not p, ?, n, e- etc.
MSc-REP Regan Dosimetry 15
The W-value for electrons in air (i.e., average incident energy required
to produce a single effect) is 33.7eV per ion pair, (= 33.7 J/C).
The absorbed dose in air at normal STP which is subjected to
an exposure of 1 roentgen is 87 erg per gram.
In soft tissue, 1 roentgen = 98 erg per gram i.e. approximately 1 rad
This is true for most low -Z (atomic number) materials such as
air, soft biological tissue, plastics etc.
The definition of exposure is only for X and ? rays. The more
general use of absorbed dose is a more useful concept.
Exposure measurements when used have units of ‘air-KERMA’
from Kinetic Energy Release in Medium (A), see later.
MSc-REP Regan Dosimetry 16
Dose and Absorbed Dose (D): is the energy deposited,
?ED by ionising radiation to a mass, ?m of matter
in a given volume element. m
ED D
?
?
=
The standard unit of absorbed dose was the rad (plural also is rad),
where 1 rad = 100 erg per gram.
The SI unit for absorbed dose is the gray (Gy) , 1 Gy = 1Joule / kg.

The conversion between grays and rad is 1 Gy = 100 rad
Thus, 1 rad =0.01Gy = 1cGy (‘centrigray’) which is also used.
10Gy would constitute a lethal whole body dose in a human.

MSc-REP Regan Dosimetry 17
Energy Imparted (?ED): is the difference between the sum of the
energies of all the directly and indirectly ionising particles which
have entered a volume element of mass ?m, given by ?EE and the
sum of the energies of all those which have left the volume (corrected
for any changes in rest mass, ?ER, which have taken place due to
nuclear reactions within the volume element).
RLED EEEE ?????=?
The SI unit for the energy imparted is the gray (Gy).
MSc-REP Regan Dosimetry 18
Equivalent Dose ( HT )
The human equivalent dose, HT measures the biological damage to a
human due to exposure to a particular type of radiation.
It is defined by HT = WR x DT , where T represents a specific tissue or
part of the body. H is also called the ‘radiation-weighted dose’
The SI unit for human-equivalent dose is the sievert (Sv).
1 Sv = 1 gray x WR
The traditional unit for human-equivalent dose is the rem, where
1 rem = ‘Roentgen Equivalent Man’ = dose in rad x Q = 0.01 Sv.
Typical values are (milli-rems and 10s of micro-sieverts.
Often the body can be exposed to different types and energies of
radiation at the same time. Then the human-dose equivalent is given
by
the weighted sum of absorbed doses of
radiation of type R, resulting in the
observed biological damage to tissue/organ, T.
RT
R
RT DWH ,×= ?
MSc-REP Regan Dosimetry 19
Quality/Weighting (‘Q/WR’) Radiation Factors,
ICRP radiation weighting (W) factors.
MSc-REP Regan Dosimetry 20
Example
A patient has a chest x-ray. The area of the chest exposed to the x-ray
beam is approximately 500 cm2 and the intensity of the x-ray beam is
0.3 W/m2. The patient is exposed for 0.2 seconds. Hospital regulations
state that the absorbed dose must be kept below 0.0020 Gy.
a) What is the power of the beam to which the patient is exposed ?
b) What is the maximum human-equivalent dose for the patient ?
( )
public). for the ICRP by thelimit annual drecommende the twice(i.e.
2mSv0.002Sv dose equivalenthuman max. thusrays,-for x 1Q (iii)
0.002Gykg0.003J/1.5 senergy/mas Dose (ii)
Kg5.10.002Gy
0.2s0.015W mass min. mass min.
s 0.2 W 0.15 0.002Gy
Gy 0.002 below dose absorbed keep to tissueof mass Minimum (i)
0.003JJ 0.2 x 0.015 mepower x ti beamby impartedEnergy b)
0.015W Power 0.0001mm)01.0(1cm
0.05m3.0cm5003.0 )area(m )W/mIntensity( (J/s)Power a)
2222
2222
===
===
=
×
=?
×
=
===
=?==
×=×=×=
MSc-REP Regan Dosimetry 21
Relative Biological Effectiveness (RBE): The RBE of a particular
radiation is the ratio of the absorbed dose of a reference radiation DR
(which is often taken to be gamma-rays from a 60Co source or 250kV
X-rays) to the absorbed dose of the particular radiation which is begin
examined, DX, in order to attain the same level of biological effect.
X
R
X D
DRBE =
RBE is related (but not identical) to the quality factor, Q (which is
equivalent in most cases to WR) in the measurement of dose equivalent.
MSc-REP Regan Dosimetry 22
Effective Dose (HE)
The same size of dose can cause different degrees of biological
damage depending on which part/organ of the body is exposed.

In order to account for this, the ICRP (publication number 60, 1990)
provided a list of Tissue Weighting Factors, (WT) for the organs and
tissues which are susceptible to the main biological radiation damage.
? ×=
T
TTE HWH
The Effective Dose (HE) is a way of determining the
whole-body biological damage due to radiation exposure of different
types to different types of the body. This is given by the weighted
sum of the equivalent dose for that type of radiation, multiplied by the
tissue weighting factors for that particular area of the body, HT.
Thus
Note HE and HT both have SI units of sieverts (Sv).
MSc-REP Regan Dosimetry 23
The total sum of weighting factors = 1.00
MSc-REP Regan Dosimetry 24
The weighting factor, WT
for an organ is given by
the risk to that organ
divided by the total risk.
The weighting factors are
given by the lifetime risk
coefficient divided by the
total risk.
Thus, the weighting factor for
fatal gonad cancer would
be 1.33/7.25 = 0.18 in the
general population and
0.80/5.53= 0.14 for
occupational radiation workers.
Alpen p430
MSc-REP Regan Dosimetry 25
ICRP Recommended Annual Dose Limits
Body Part Occupational General Public
Whole body
(HE)
20mSv 1mSv
Eye lens (HT) 150mSv 15mSv
Skin (HT) 500mSv 50mSv
Hands & Feet
(HT)
500mSv ---------
Note these recommended limits EXCLUDE any medical or natural
background radiation doses.
MSc-REP Regan Dosimetry 26
Some More Definitions…
Particle Fluence (? ): is the number of particles, ?N which enter a
sphere of cross-sectional area a, such that ?=?N/?a.
? has units of particles/m2.
Particle Fluence rate (?) : is the rate of particle fluence with respect
to time. ? = ?? / ?t and thus ? has units of particle/m2s.
Energy Fluence (? ): is related to the particle fluence. It is defined
by ? = ?Ef / ?a, where ?Ef is the sum of the particle energies
which enter a cross-sectional area, ?a. Units are Joules/m2
Energy Fluence Rate (?): is the quotient of the energy fluence with
respect to time, i.e., ?= ?? / ?t . Units are Joules/m2s.
MSc-REP Regan Dosimetry 27
KERMA (Alpen p8, p90)
Typically, when radiation (x-rays, ? rays and charged particles)
interact with their environment, they transfer kinetic energy to
the medium in which they are interacting.
It is possible however, that not all of the transferred kinetic energy
remains in the volume of interest. This can be due to radiative
losses (bremsstrahlung) and kinetic energy losses associated with
secondary particles produced.
KERMA is the Kinetic Energy Release in the Medium (A is added!)
Kerma, (K) accounts for the energy transferred to
the volume (without correcting for energy losses
after interaction). It is defined by the expression,
where ?EK is the sum of initial kinetic energies of all the charged
particles liberated by ionising particles or photons in a volume
element of a specific material. Kerma is thus reflects the energy
RELEASED in a medium. Kerma has the SI unit of the gray (Gy)
m
EK K
?
?
=
MSc-REP Regan Dosimetry 28
Charged Particle Equilibrium (CPE) : Charged particle equilibrium
is said to exist at a point p, centred in a volume V, if each charged
particle carrying out a certain energy from this volume is replaced
by another identical particle which carrying the same energy into the
volume.
If CPE exists at a point, the dose = kerma (D = K) at that point
(provided that the secondary radiation losses by the charged
particles such as bremsstrahlung are negligible).
Dose is the energy absorbed in the unit volume,
while
kerma is the energy transferred from the original particle (or photon)
in the same unit volume.
MSc-REP Regan Dosimetry 29
Absolute Methods of Dosimetry
Absolute methods of dosimetry can provide measurements for the
absorbed dose without the instrument (‘dosemeter’) being calibrated
in a known radiation field. (Most instruments give measurements
relative to calibrated primary or secondary standards).
It is however possible to calibrate certain detector media which
can then be placed inside the sensitive volume of specific dosemeters.
These instruments then posses an effective ‘internal calibration’ and
as such can be described as absolute dosemeters.
For any radiation phenomenon (e.g., gammas neutrons etc.) to be used
for radiation dosimetry, we need to know
1) the fraction (?) of the absorbed dose (D) which is channelled into
a given effect, and
2) the average energy (H) needed to produce a given effect (e.g.,
ionisation, chemical changes, nuclear reactions etc.)
MSc-REP Regan Dosimetry 30
Thus, the energy per unit mass going to any specific effect = ?D.
If this causes Ne subsequent effects per unit mass, and the average
energy required to produce the unit effect is H, then the total energy
required is the product of Ne and H, ie. Ne.H = ?D
Thus, since D = (H/?).Ne, ,, if (H / ?) is a constant and known, the
number of effects induced by the radiation (Ne) is proportional to the
absorbed dose. Thus the dose can be obtained by measuring Ne.
Consider a charged particle of energy E, coming rest inside a medium.
If a fraction ?i of the particle’s kinetic energy produces ionisation
in the medium, assuming that the energy required to cause ionisation
by radiation induced collisions is Hi, we have ?iE=Ni Hi and the
number of ions produced is Ni=(?i.E)/Hi .
Now, (E / Ni)=(Hi / ?I) is the average energy required to produce one
electron-ion pair, which is known as the W-value.
(NOTE, This is NOT the same as WR mentioned earlier).
MSc-REP Regan Dosimetry 31
Therefore, ii
i
i
i
i
i
NNHHN .WD W
E
=???
?
???
?
=?== ??
Thus, if we know W, we have the calibration factor (Hi / ?i) without
having to know Hi or ?i individually.
In the case of dosimetry based on calorimetry, Ht is the energy required
to raise the temperature of a unit mass of the radiation absorber by 1K,
which is also the definition of the specific heat, S of the material.
Here the ‘measured effect’ is the temperature rise in degrees kelvin
which is caused by the induced radiation.
( )
energy. absorbed theof 13% is energy) thermal
-(nonoutput light thesince 87.0 NaI(Tl)For .1 cases,most In
energy. thermalinto converted is which dose theoffraction
theis and massunit per input energy thermal theis where
D D and Thus,
tt =?
??
?×???
?
???
?
=???×=??=?=
??
?
??
t
t
te
mQ
TSTSmQTN
MSc-REP Regan Dosimetry 32
Radiation Equilibrium
C
V V’(?m)
A
B
C
P
d
Consider a volume, V, uniformly filled with radioactive material.
Inside this volume, V, is a smaller secondary volume, V’ (containing
mass, ?m) which surrounds the point P. The shortest distance between
the boundaries of V and V’ is given by d.
The radiation coming from points
in and around V’ must be in one
of three categories:
i) Type A tracks: spend all their
energy (their entire ‘life history’)
inside V’.
ii) Type B tracks: originate inside V’
but give up part of their energy outside; &
iii) Type C tracks: start outside V’ but give up some energy inside.
MSc-REP Regan Dosimetry 33
If the distance d, is
larger than the maximum range
of the ionising radiation being
considered (neutrinos are usually
neglected), then there is a
complete symmetry in the region V’.
This means, on average (i.e. for
large numbers of radiation tracks),
the tracks of type B and C will
balance out and the energy removed
from V’ by type B tracks will be
compensated by the energy deposited into V’ by tracks of type C.
In these conditions, RADIATION EQUILIBRIUM is said to exit in V’.
C
V V’(?m)
A
B
C
P
d
MSc-REP Regan Dosimetry 34
A more complete definition of absorbed dose is given in Radiation
Dosimetry volume 1 (1968) pp 32-33, edited by Attix and Roesch.
‘ The energy imparted to matter by ionising radiation per unit mass
is called the absorbed dose. By energy imparted to matter, we mean
that which appears as ionisation or excitation, increase in chemical
energy or crystal lattice energy etc. in the material. The energy that
goes into changes in rest mass of the material or in the radiation itself
(pair production) is excluded by definition; in some cases this energy
can be comparable with absorbed dose, but does not produce
important extra-nuclear effects .’
Thus, the energy absorbed can be split into 2 components, causing:
1) changes in atomic/molecular/lattice energy states and
2) changes in the rest mass.
MSc-REP Regan Dosimetry 35
Thus, by conservation of mass energy, the energy imparted to matter
in the volume element V’ is given by ?ED = ?EE - ?EL - ?ER
If there is RADIATION EQUILIBRIUM then ?EE = ?EL and
so,
?ED = - ?ER and thus the absorbed dose, D = ?ED / ?m
The dose imparted to V’ thus arises from the reduction in the rest mass
of the radionuclides within V’ following their decay to create the
ionising decay products. (The energy removed by neutrinos following
?-decay is excluded since their absorption is vanishingly small).
C
V V’(?m)
A
BC P
d
Consider the point, P, within the volume V’.
?EE is the sum of the total energies of all
the ionising radiations entering V’.
?EL is the sum of the total energies
of ionising radiations leaving V’; and
?ER is the increase in rest mass inside V’.
MSc-REP Regan Dosimetry 36
[ ] [ ]
[ ] [ ]intint
int
intintint
int
, thereforeand
then exists, mequilibriuradiation If

dose, totalThe
R
ext
RE
L
ext
L
ext
E
RLE
ext
R
ext
L
ext
E
D
ext
D
EEED
EEE
EEEEEED
EED
?+???=
?+?=?
???????????=?
?+?=
True radiation equilibrium only occurs in the
highly symmetric case (as described above), but
it can be useful to consider some approximations.
If we consider flows of radiation energy into
and out of a unit mass from both internal
and external radiation sources, then
i.e the Dose (D) is the
energy from the loss in rest mass following radioactive decay minus
any increase in rest mass from external & internal radiation interactions,
or put another way
Dose = [decrease in rest mass] - [Increase in rest mass]
ext
EE?
ext
LE?
ext
DE?extRE?
int
EE?
int
RE?
int
DE?
ext
LE?
MSc-REP Regan Dosimetry 37
[ ] [ ]
[ ]
achieved.not is mequilibriuradiation perfect and absorbed isradiation
incident theofpart only since positive bemust where


ext
L
ext
E
ext
R
ext
L
ext
E
EE
EEED
?+?
???+?=
Therefore, the absorbed dose equals the net reduction in rest mass
(neglecting neutrino energy) per unit mass of material.

If there are no internal sources of energy, (for example, if the material
is only irradiated by external sources), then
Note that for photon energies less than 1.022 MeV (the e+e- production
threshold), there are essentially NO CHANGES in REST MASS and
thus .
In this case, the absorbed dose arises from the difference between the
energy entering the volume and that leaving it.
0=? extRE
MSc-REP Regan Dosimetry 38
Charged Particle Equilibrium
X-ray and ?-ray photons, and neutrons are uncharged. As such, they
are described as INDIRECTLY IONISING RADIATIONS since
they deposit their absorbed dose in matter by a 2-step process:
1) Kinetic energy is transferred to charged particles (e.g., via recoil
electrons for photons or nuclear reactions products for neutrons).
2) These charged particles subsequently deposit energy in the medium.
If each charged particle carrying energy out of V’ is balanced by
an identical particle carrying the same amount of energy into the
same volume element, CHARGED PARTICLE EQUILIBRIUM
is said to exist inside V’.
MSc-REP Regan Dosimetry 39
( ) ( )[ ] ( ) ( ) ( )[ ]uRuLuEcLcED EEEEEE ?????+???=?
( ) ( ) ( ) ( )[ ]
( ) ( ) ( )[ ]uRuLuED
c
L
c
E
c
L
c
E
EEEE
EEEE
?????=?
=????=?

giving 0 , thus
If a volume element is irradiated by an external source, considering the
energy carried in to and out of V’ by
(i) charged (c) (e.g., electrons, positrons, alphas, fission fragments; and
(ii) uncharged (u) particles (mainly photons and neutrons), then:
Note that there is no ‘rest mass’ term (?ER) in the first square bracket
about since electrons and photons cause virtually no rest mass changes
in the normal expected energy ranges for these radiations.
If CHARGED PARTICLE EQUILIBRIUM (CPE) exists, then
Thus, in effect, for CPE, the dose is delivered by the
UNCHARGED FLUX, and is equal to the net energy left inside
in the absorber, minus any changes in the rest mass.
MSc-REP Regan Dosimetry 40
If the mass of the material encompassed by the volume element V’ is
given by ?m, then D = (?ED / ?m) = (?EK / ?m) = K,
where K = KERMA, the energy released per unit mass.
Thus, in CPE, D=K, i.e. DOSE = KERMA
It is now common practice to refer to kinetic energy transfer to charged
particles and to replace ?EK with ?Etr .
CPE is always present when radiation equilibrium occurs, but in
many practical cases, CPE is closely attained, even though radiation
equilibrium is not. For electrons we speak of ‘electronic equilibrium’.
Then under Charged Particle Equilibrium (CPE) conditions, ?ED=?EK
( ) ( ) ( )[ ]uRuLuED EEEE ?????=?
( ) ( ) ( ) ( ) ( ) ( )uRuLuEKuRKuLuE EEEEEEEE ?+???=?????=???
This result can be interpreted alternatively as:
The net energy brought into the medium by uncharged radiations
supplies kinetic energy (?EK) to charged interaction products, and
also any accompanying rest mass changes. Thus we can write,
Recalling (p40) that
MSc-REP Regan Dosimetry 41
Consider the case of a broad,
parallel beam of photons
which travel through vacuum,
perpendicular to the surface of
an ‘infinite’ absorptive medium.
As the photons interact in
successively deeper layers of
the absorptive medium
progressively further from the
surface, the overlapping tracks of the recoil electrons will deliver an
increasing dose to the material.
This dose build up continues to a depth that can just be reached by
those electrons which are emitted from the surface radiation
interactions and thus the width of this ‘build-up region’ is equal to the
maximum range of the recoil electrons in the medium.
MSc-REP Regan Dosimetry 42
The absorbed dose falls off slowly with depth from
the surface as the photon flux is absorbed in the
medium. There is also a finite dose from recoil
electrons and backscattered photons originating
from inside the medium.
The primary flux transferred to kinetic energy
of recoil electrons is maximised at the SURFACE,
thus the KERMA is also maximised at this point.
• Beyond the build-up region, the KERMA and DOSE curves lie close together since
electronic equilibrium can be closely approximated in this region.
• The D (dose) curve is shifted slightly ‘downstream’ relative to the K (kerma)
curve by about the average recoil electron range, since their kinetic energy delivers
dose to the medium along their tracks as they slow down.
• There is an opposing effect due to the emission of bremsstrahlung by the electrons as
they slow down in the medium (in low-Z stoppers, this is a small effect). However, the
longer range of the bremsstrahlung photons compared to the e- s means that they often
escape the region of interest and do not contribute to the local dose. Bremsstrahlung
effects are usually neglected in the detailed definition of exposure in air.
• The contemporary replacement for ‘exposure’ is ‘air-kerma’ which is almost equal
to the dose in air under CPE conditions. The air dose can be measured directly from
the output of an air-walled ion chamber.
MSc-REP Regan Dosimetry 43
( ) ( )
event.n interactioper nsferredenergy tra average theis
andevent n interactioper absorbedenergy average theis
material.absorber theofdensity theis andt coefficienn attenuatio total theis
fluence, particle theis where, and
trav
abav
travabav
E
E
a
NEKED
?µ
?
µ
?
µ
?
?
=??=?=
(from Alpen p 91)
For fast electrons, D and K can also be defined in terms of the incident fluence
MSc-REP Regan Dosimetry 44
A radiation energy fluence E, (in units of Jm-2) of photons passing
through an absorber falls off exponentially with increasing depth,
(after build-up to CPE). That is E(x)=Eoexp(-µenx) - (1), where
µen is the linear energy absorption coefficient, and x is the depth
(or linear distance through the medium).
( )
absorber. theof surface thefrom Similarly,
maximum. buildup dose thebeyondregion CPE in the
,mass
energy
length
1
length
Joules
mass
length of dimensions has 1
.1 gives, density massabsorber by the gMultiplyin
1- exp (1), atingDifferenti
2
3
0
EK
ED
Ddosedx
dE
E
dx
dE
Edx
dEExEdx
dE
tr
en
en
enenenen
?=
?=?
?=????
???
?
=??
???
?
?
?=??=??=
?
µ
?
µ
?
?
µ
?
?
µµµµ
Mass Energy Absorption Coefficients
MSc-REP Regan Dosimetry 45
( ) ( )xIxIIdx
dI µµ ?=???= exp 1 0
Note µen/? = mass energy absorption coefficient [units of cm2.g-1]
and µtr/? = mass energy transfer coefficient [units of m2.kg-1]
The two coefficients can be
obtained from the slopes of the
dose-depth and kerma-depth
curves respectively, and are both
very closely related (but not
identical!) to the underlying mass
attenuation coefficient.
For a photon fluence I, which enters a small absorber element of
thickness dx in which the fluence is reduced by an amount dI, the
LINEAR ATTENUATION COEFFICIENT (µ) is given by
The mass attenuation coefficient is defined by (µ /? ) ,
where ? is the density of the absorber material
MSc-REP Regan Dosimetry 46
Edx
dE?Idx
dI?
I
dI
E
dEE
EdIdEEIE
?
1 n,subsitutioby 1 Since
. ,for ngsubstituti Thus,
ating,differenti ,
??=??=
?=?
×=×= ??
The energy fluence carried by the photon beam given by the photon
fluence multiplied by the photon energy, ie.
This look very similar to the definition of the linear energy absorption
coefficient µen (see p45), but while µ describes photons (and the
energy which they carry) which are removed from the primary photon
beam, µen describes the energy absorbed in the medium.
µen is always smaller than µ since there are other effects which can
remove photons in the beam which do not necessarily impart energy
(e.g., bremsstrahlung, fluorescence, X-rays, Compton scattered photons
and pair production/ annihilation radiation.).
MSc-REP Regan Dosimetry 47
( )
( ) ( )gg
(g)
E
cm
f
E
cm?-f?E
???
tr
tr
?
s
?
ppsc
?
petr
ppc
?=?=
=
=
???
?
???
?
?++???
?
???
?
?=
++=
+
1 and 1 thus,
further coeff. absorptionenergy thereduces This dose. local the tocontribute
not does and lungbremsstrah of form in the radiated-re is electrons recoil
toed transferrisch energy whi kinetic theof fraction, small) (typicallyA
radiation. eeby en energy takincident theoffraction )MeV022.1(2
photons scattered by the taken collisionsCompton in fraction energy theis
; rays-X sticcharacteri theofenergy mean theis where
2111 t,coefficiennsfer energy tralinear
theeach term, torelatedradiation secondary escapefor allow weIf
by given ist coefficienn attenuatiolinear The
en
en
-
2
0
2
0
pe
?
µ
?
µµµ
?
µµµµ
The linear attenuation coefficient can be reduced to allow for the escape
processes to give an expression for the LINEAR ENERGY TRANSFER
MSc-REP Regan Dosimetry 48
Mass energy absorption
coefficients
µen < µ
511keV
Pair-Production
e-
e+
brem
brem
511keV
brem
Compton scattering
e-
Compton scatter
Photo-electric effect
e-
brem
K? etc
brem = bremsstrahlung
MSc-REP Regan Dosimetry 49
Mass attenuation coefficients for (A) Lead and (B) Water.
Taken from Alpen, p81-82.
MSc-REP Regan Dosimetry 50
Relationship between air-kerma, exposure & absorbed dose in air
Consider an electron of K.E. Te, induced in air by photon interactions, which is
brought to rest inside unit mass of air. A fraction, g, of this energy escapes from the
sample in the form of bremsstrahlung radiation.
Hence the energy absorbed in unit mass of air, (i.e. absorbed dose) is given by:
Dair = (1 - g)Te.
This produces Ni ion pairs in this unit mass and an additional gNi ion pairs externally due to
absorption of the escaping bremsstrahlung, giving a total of (1 + g)Ni ion pairs at a total
energy cost of Te.
Therefore, from the definition of W-value, we can write We = Te/(1 + g)Ni and thus:
Te = WeNi(1 + g).
Substituting for Te in the expression for the dose given above:
 
Dair = (1 - g).WeNi(1 + g) = WeNi(1 - g2)
Since Te = WeNi(1 + g) and remembering that air-kerma, Kair, is defined as the initial kinetic
energy transferred per unit mass of air then
Kair = Te = WeNi(1 + g) and thus Kair = Dair/(1 - g).
MSc-REP Regan Dosimetry 51
The relative importance of the three major types of gamma-ray
interaction. The lines show regions of gamma-ray energy and the Z
(atomic number) of the absorber material for which the two
neighbouring effects are equal. Taken from Knoll p. 54
MSc-REP Regan Dosimetry 52
Worked Example:
A 8 MeV photon penetrates into a 200g mass of tissue and
undergoes a single, pair production interaction.
Both the e+ and e- particles created in this interaction dissipate all
their kinetic energy within the mass through secondary ionisation
and bremsstrahlung production.
Two bremsstrahlung photons of energy 1.1 and 2 MeV
respectively are produced and escape from the mass without further
interaction.
The positron, after expending all its kinetic energy
interacts with an ambient electron within the mass and they mutually
annihilate.
Both photons created in the annihilation radiation escape the mass
before further interaction.
Calculate
(i) the kerma and
(ii) absorbed dose the tissue receives from these interactions.
MSc-REP Regan Dosimetry 53
ANSWER:
Kerma is the sum of initial kinetic energies per unit mass of all charged
particles produced by the radiation.
In this case, this is the kinetic energy of the e+e- pair released, which is 6.978
MeV
(i.e. 8MeV- the rest masses of the electron and positron created (1.022 MeV)).
This is split evenly between the two particles such that they each have 3.489
MeV.
This is the sum of the initial kinetic energies.
The Kerma = KE released / mass of the tissue volume, and thus
GykgJkgg
J
dm
KEreleasedKerma 1212
13
106.5/106.52.0200
106.1978.6
??
?
×=×=
=
××
==
MSc-REP Regan Dosimetry 54
Absorbed Dose is defined as the energy absorbed per unit mass.
In this case, from the 8 MeV photon, an initial 6.978MeV of Kinetic Energy is
released
in the medium by the initial pair production interaction.
This is followed by losses from the material of 1.1+2=3.1 MeV from the
bremsstrahlung interactions of the electron formed in the pair production
interaction.
and 2 annihilation photons (1.022 MeV), all which escaped from the mass.
Thus of the initial energy interacting with the mass of 8 MeV, 4.122 MeV is not
absorbed in this tissue volume and thus, including the change in rest mass of the
tissue
volume (from the creation of the e+e- pair = 1.022 MeV), the absorbed dose is
given by ( ) Gykg
J
kg
MeVMeV
dm
dEDose 12
13
101.32.0
106.1878.3
2.0
122.48
?
?
×=
××
=
?
==
Answer (cont).
MSc-REP Regan Dosimetry 55
Mass energy absorption
coefficients
A photon source placed between two semi-infinite
absorbers
S
1 2
CPECPE
MSc-REP Regan Dosimetry 56
Mass energy absorption
coefficients
The energy fluence, E, passing through both absorbers is the
same ( ) ED en ?= 11 / ?µ ( ) ED en ?= 22 / ?µ
( )
( ) 11
22 /
/ DD
en
en
?=
?µ
?µ
( )
( ) 1
221 /
/
?µ
?µ
en
enS =? D2 = 1S2.D1 where
MSc-REP Regan Dosimetry 57
1
22
11
2
11
1
2
2
2
2
1
1
where , thereforeand
and regions, CPE In the
???
????
?
???
????
?
==?
???
????
?
???
????
?
=
????
????
?
=????
????
?
=
?
µ
?
µ
?
µ
?
µ
?
µ
?
µ
en
en
en
en
enen
SDSDD
EDED
PConsider a photon source placed
midway between 2 ‘infinite’ absorbers.
The energy fluence E (in Jm -2), passing
through both absorbers must be the same, and thus we can write,
Thus, in a given radiation field, the dose in one medium (such as
biological tissue) can be derived from measurement in a second, more
practical medium (e.g., air), if the ratio of their mass energy
absorption coefficients is known (and if CPE is attained in both).
D1
(µen /? )1
D2
(µen /? )2
MSc-REP Regan Dosimetry 58
• A special case if an air-filled ion chamber is used.
• The W-value in air is 33.7eV/ion pair.
• Using this the absorbed dose in air corresponding to an exposure of
X = 1 roentgen can be calculated to be 87erg.g-1 (= 0.87 rad).
Thus, the relation to dose in ANY MEDIUM of type m, situated at
a point where the exposure is 1 roentgen can be found using the relation:
Dm = airSm.Dair
Thus, Dair=0.87.airSm rad.
More generally, for an exposure of X roentgens, the dose in rads is given
by Dm=0.87.airSm.X rad
or written another way, Dm=f.X rad where f = 0.87.airSm
f is called the ‘rad per roentgen factor’.
For photons of E?=10 keV -> 3 MeV in soft tissues (made of H,C,O
and other low-Z elements), f = 0.92-0.97. Water has f = 0.90-0.96.
Bone (calcium, Z=20) has f = 3.6 for 10 keV and 0.92 @ 1MeV
MSc-REP Regan Dosimetry 59
The dose in higher Z materials is much larger than in air (and other low-Z materials)
for lower X-ray energies due to the strong Z-dependence of the photoelectric effect
cross-section (?pe~Zn/E?4-5)
The photon attenuation coefficients, and the related energy absorption coefficients
are complex functions of E? and atomic no.(Z), but over a RESTRICTED RANGE
of these two parameters, it is possible to represent the dosimetric behaviour of a
mixture of elements (such as in biological tissue) with the use of a single
parameter, called the EFFECTIVE ATOMIC NUMBER, Zeff.
For soft tissues over the range of diagnostic X-rays ( E=10-250 keV, Zeff=7.8).
This concept can be useful for estimating the degree of equivalence (or ‘matching’)
between real biological tissue and possible dosimetric media.
Although PERFECT MATCHING (i.e., 1S2=1.0) is only true for identical atomic
compositions, approximate matching is often good enough for radiation protection
purposes.
For example, tissue-equivalent gas mixtures can be used inside tissue-equivalent and
used inside natural body apertures to accurate dose measurements in radiotherapy.
Effective Atomic Numbers and’ Matching’
MSc-REP Regan Dosimetry 60
Cavity Detectors
Consider a volume of gas contained in a cavity inside a solid material which
itself is surrounded by a third material. When CPE is attained in the cavity gas
and in the medium surrounding the ion chamber:
Dm = gSm Dg
If the absorbed dose gives rise to Jg (C.kg-1) of ionisation in the gas then the
dose in the gas is:
Dg (J.kg-1) = Jg (C.kg-1) x wg (J.C-1)
 
? Dm = gSm Jg wg (Gy)
 
In this way the dose rate in the medium of interest can be derived from the
ion chamber current.
If the cavity wall, the cavity gas and the surrounding medium are all well
matched we have the homogeneous ion chamber case and gSm = 1.0.
MSc-REP Regan Dosimetry 61
Relationship between air-kerma, exposure and
absorbed dose in air
Air-dose, Dair, is derived directly from the output of an air-walled ion chamber by
collecting all of the ionisation in the sensitive volume, dividing by the mass of air
it contains and multiplying by We. The ionisation per unit mass is simply the
exposure, X, so we can also write:
 
Dair = X . We .
 
However in SI units we express exposure not in ion pairs per unit mass but in
coulombs per kilogram. (recall, The energy needed to produce an ion pair in air is
33.7eV ? 33.7JC-1 (1eV = 1J * 1.6x10-19C-1)
Thus air-dose is related to exposure by air-dose (J.kg-1) = exposure (C.kg-1) x
We/e(J.C-1) where We is expressed in joules per ion pair and e, the electronic
charge, is in coulombs.
 
? and
 
so again kerma is slightly larger than absorbed dose in this case.
/eWXD eair ?= ( )g
e
?
?
= 1
/WXK eair
MSc-REP Regan Dosimetry 62
The Bragg-Gray principle says that the amount of ionization
produced in a small gas-filled volume cavity surrounded by
a larger, solid absorbing medium is directly proportional to
the radiation energy absorbed by the solid.
The gas cavity must be small enough relative to the mass of the
solid absorber to leave the angular and velocity distributions of
the primary electrons unchanged.
The cavity must be surrounded of a solid with sufficient thickness to
achieve electronic equilibrium.
MSc-REP Regan Dosimetry 63
Bragg-Gray Cavity Relation
Consider a cavity of unit area and width ?x; and let the energy lost inside the
cavity medium by an electron crossing it at right angles to the long side be ?E.
?xdx
dT?E
c
g
???
???
?
=
electron track
gas
?E
?xunit area ( ) xxm gg ?=?=? ??.1
c
gg
g dx
dT
?
1
?m
?ED ??
???
?
==
c
gg dx
dT
?
1 ??
???
? is the mass stopping
power for electrons.
MSc-REP Regan Dosimetry 64
By taking the ratio of these two expressions we find that,
where gsm is the ratio of mass stopping powers of the medium and the cavity
gas respectively. By measuring the ionisation per unit mass in the cavity, Jg:
Bragg-Gray Cavity Relation
Dg ? mass stopping power, and for the same electron fluence in the
surrounding medium we have. c
mm
m dx
dT
?
1D ??
???
?
?
 

 
g
m
gm DsD =
gg
m
gm wJsD =
MSc-REP Regan Dosimetry 65
If a cavity ionization chamber is built with a wall material
whose radiation absorption properties are similar to those
of tissue, then the energy absorbed per unit mass of the wall
material, dEm/dMm is related to the energy absorbed per
unit mass of gas in the cavity gas, dEg/dMg by the relation:
JwdM
dE
S
S
dM
dE
m
m
g
g
m
m
m ××=×= ?
where Sm is the mass stopping power of the wall material and Sg is the
mass stopping power of the cavity gas and their ratio can be written by
m
g
m
S
S ?=
w is the mean energy dissipated in the production of the ion-pair in the gas
and J = number of ions pairs created per unit mass in the gas.
MSc-REP Regan Dosimetry 66
Example Question:
Calculate the absorbed dose measured in a tissue-equivalent chamber
with a 1cm3 air filled cavity within the chamber which is exposed to a
source of 60Co gamma rays for 10 minutes.
A total of 2.25x109 electrons are collected from the chamber as a result
of ionization events in this period and the average mass stopping
power ratio of tissue to air is given by:
137.1=
g
m
S
S for 60Co gamma rays
USEFUL INFORMATION:
Average energy required to form an e--ion pair in air at STP = 34eV.
1eV = 1.6x10-19J ; the density of air at STP,
?air = 1.293x10-6kg/cm3
( ) ( ) ( ) Gycmcmkg
ionseVJeVJwdM
dE
m
m
m 0108.01/293.1
1025.2/106.134137.1 33
9
19
=
×
×
××××=××= ??
SOLUTION:
MSc-REP Regan Dosimetry 67
Calorimetry
1. Temperature rise ?T in a mass ?m of a material (whose
specific heat S is known) is measured ? ?Q = ?m.S.?T
(?m.S is the heat capacity)
2. Null method: a measured amount of electrical energy is
supplied to an identical "dummy" absorber to maintain it at the
same temperature as the irradiated sample; this obviates the
need for differential heating/cooling corrections.
3. Latent heat method; the mass of a substance undergoing a
change of state at constant temperature due to absorption of
radiation energy is measured (e.g. melting of ice).
MSc-REP Regan Dosimetry 68
Calorimetry
Low Temperature Calorimetry
Calorimetry can be used for absolute calibration of the
disintegration rate of radioactive sources. For a monoenergetic
alpha emitter it is easy to ensure all the disintegration energy is
contained inside the calorimeter. The rate of heat input to the
calorimeter is equal to the energy output rate from the source.
?Q/?t = ?N/?t x Eav
where ?N/?t is the disintegration rate and Eav is the average energy
per disintegration of charged reaction products.
MSc-REP Regan Dosimetry 69
Calorimetry
Example Question
310.5 kBq of Ra-226 in 30 ml of water gave a
temperature increase of 0.076 mK in 11 hours;
assuming no heat losses and ignoring escaping gamma
radiation show this corresponds to a mean
disintegration energy of approximately 4.87 MeV, given
the specific heat capacity of water is 4.18 kJkg-1K-1.
MSc-REP Regan Dosimetry 70
Example Answer
310.5 kBq of Ra-226 emits an alpha 100% of ?N times in 11 hours:
?N = 310.5 x 103 x 11 x 60 x 60
= 1.23x1010
The total energy released is:
?Q = ?m S ?T
= 0.03kg x 4.18x103Jkg-1K-1 x 7.6x10-5K
= 0.00958J
The energy of each emission is therefore:

E = ?Q / ?N
= 0.00958 / 1.23x1010
= 7.79x10-13J
= 7.79x10-13J / 1.6x10-19 eVJ-1
= 4.87 MeV
MSc-REP Regan Dosimetry 71
Calorimetry
Thermometry
Semiconductors (thermistors) have temperature coefficients of
resistance of ~ -2 to -4 % per K.
Platinum resistance thermometers are more stable and
reproducible but are less sensitive (~ +0.4 % per degree).
Using thermistors, in order to measure ?T ? 10-3 K to ~ 1 % we
need to measure resistance changes of ~ 100 parts per billion
using a sensitive Wheatstone bridge.
Alternatively thermocouples such as copper/constantan with ?V =
50 µV per K can be employed and the output voltage measured
with a potentiometer; several thermocouples in series generate a
larger potential difference.
MSc-REP Regan Dosimetry 72
Calorimetry
Low Temperature Calorimetry
(1) Heat transfer by radiation (?T4) is reduced so that thermal
isolation of the calorimeter from its surroundings is easier to attain.
 
(2) Specific heat capacity decreases to give a much larger
temperature change for a given radiation dose.
 
(3) Thermistor sensitivity increases to ~ 10 % per K.
In combination these improvements in sensitivity enable dose rates
as low as ~30 mGy per minute to be measured to an accuracy
of ?25 % in a one hour run.
MSc-REP Regan Dosimetry 73
Solid State Integrating Detectors
In alkali halides, such as LiF, NaI, etc (which form simple cubic lattices) the
outer shell electron in the alkali is donated to the halide to produce an inert
gas like in both atoms, and produces an insulator.
In the lattice F-centres and H-centres are regions of positive and negative
charge which can bind to wandering electrons and holes respectively.
Impurity (activator) atoms can be added to the lattice in interstitial positions
to create trapping centres.
Ionising radiation can damage the lattice if they are very energetic (recoil
energy of ~10-20 eV is needed) or may give rise to free charges which can
become semi-permanently trapped.
The number of trapped charges represents some measure of the absorbed
dose, this phenomenon is used in (a) RadioPhotoLuminescence and (b)
ThermoLuminescence.
MSc-REP Regan Dosimetry 74
Radiophotoluminescence Dosimetry
Unirradiated radiophotoluminescence (RPL) solids are not luminecence
until they absorb ionising radiation.
The trapped charges in RPL devices are detected and quantified by
irradiating the dosemeter with UV light. This excites the trapped electrons
into higher quantum states, as they fall back to the ground state they emit
visible light. This light can then be measured with a PMT and standardised
by calibration in a known radiation field.
Valence band
Conduction band
Electron
Trap
Hole
Trap
UV light
Visible light
Formation Readout
MSc-REP Regan Dosimetry 75
Radiophotoluminescence Dosimetry
Typical optical absorption/emission curves for an RPL glass is shown
below.
MSc-REP Regan Dosimetry 76
Radiophotoluminescence Dosimetry
The apparatus used to readout RPL glasses which are used for
intermediate doses (10?Gy to 104Gy) is shown below.
There are two types of RPL glass (1) high-Z barium [enhances low energy
photon response (2) low-Z lithium or aluminium phosphate which is more
tissue equivalent.
RPL dosemeters are easily read-out and can be read out many times.
RPL Glass
PMT
Optical filter
(removes visible)
UV lampUV
Luminscence
and UV scatter
UV filter (removes
scattered UV)
MSc-REP Regan Dosimetry 77
Thermoluminescence Dosimetry
Thermoluminescence Dosemeters (TLD) are similar to RPLs in the way
electrons are created and trapped. They differ in the way they are readout.
Electron
Trap
Hole
Trap
Conduction band
Valence band
Formation Readout
Mg
Ti
TLD
photons
The trapped electrons and holes (Mg sites) in TLDs are
recombined by heating the material promoting the electrons back
into the conduction band before recombination (Ti sites).
MSc-REP Regan Dosimetry 78
Thermoluminescence Dosimetry
TLDs are readout by systems which essentially consists of a heating and
light measurement system.
MCS
Current
Integrator
DC
amp PM
T
HV
supply
Optical
IR } filters
N2 flushing gas
Heater
MSc-REP Regan Dosimetry 79
Thermoluminescence Dosimetry
As the TLD material is heated light is emitted as a series of “glow-peaks”
A) CaSO4:Mn ;B) LiF:Mg,Ti ;C) CaF2 ;and D) CaF2:Mn. As the temperature
rises above 200°C “black body” radiation increases. Peaks about 200°C
are favoured.
MSc-REP Regan Dosimetry 80
Thermoluminescence Dosimetry
Randall-Wilkins theory of glow curves: The probablity per unit time of an
electron being detrapped (i.e. freed) by thermal energy is (this is the
probablity the electron energy is in the Maxwell-Boltzman tail above the
trap depth Et), ??
???
? ?
= kT
ESyprobabilit texp, ?
??
???
? ?
=? kT
EnSdt
dnrate texp,
where Et = depth of energy trap, S = constant, k = Boltzmann’s constant
and T = temperature.
The rate at which electrons escape from a trap of energy Et is,
where n = number of electrons in a trap. Et and S can be determined
experimentally. For example LiF:Mg,Ti has several dominant traps
ranging from 1 to 2eV, with S values of 1012 to 1020 s-1. This implies the
mean lifetime in shallow traps will be a few minutes, whilst in deeper traps
the mean lifetime is around 80 years. This results in a natural “fading” of
TL signal with time.
MSc-REP Regan Dosimetry 81
Additional revision slides,examples
and additional material
MSc-REP Regan Dosimetry 82
Internal Dosimetry and Effective Half-Life
The effective elimination rate constant is the sum of the probability of
radioactive
decay, ?R and the biological elimination constant, ?B, such that ?E=?R+?B.
The effective half-life is the time for the quantity of radioactive material in
an organ to fall to a half of its original value, i.e for Q0 to decay to Q0/2.
TE=ln2/?E=0.693/?E.
For 1st order kinetics
( ) ( ) [ ]( ) ( ) ???
?
???
?
?=?=+?=???=
E
EBRBR T
tQtQtQttQtQ 693.0expexpexpexpexp)( 0000 ?????
MSc-REP Regan Dosimetry 83
From the general expression for the activity, ANdt
dN
=?= ?
we can solve and substitiute to get:
( ) { } ( )tdt
dNtAtAdt
dN ?? ?=?== expexp 00
( )dttdt
dNdN ??= exp0
The expression for imparted dose rate will have a similar form since the dose rate
is directly proportional to the activity of the sample. Thus we have the initial
expression
( )dttdt
dDdD E??×= exp0
Since dD0/dt = a constant (i.e. initial dose rate at time t=0),
then
( ) ( )dttdt
dDdttdt
dDdD ttt E
tt
t E ??? ==== ?=?×= 000 0 expexp ??
MSc-REP Regan Dosimetry 84
( ) ( )
tt
t
E
E
tdt
dDtD
=
=
??
???
?
??=?
0
0 exp1 ?
?
( ) ( ) ( ) ??
???
?
???
?
???
?
+??=??
???
?
???
?
???
?
????=?
E
E
EE
E
E
tdt
dDtdt
dDtD
?
?
??
?
?
1exp11exp1 00
( ) ( ) ??
???
?
???=? tdt
dDtD E
E
?
?
exp110
Integrating gives the total imparted dose time t after the initial internal
contamination D(t)
MSc-REP Regan Dosimetry 85
Worked Example Question
MSc-REP Regan Dosimetry 86
Worked Example
MSc-REP Regan Dosimetry 87
Example examination question (2009):
MSc-REP Regan Dosimetry 88
(2009)
Exam
question
MSc-REP Regan Dosimetry 89
Example exam question (2009)
MSc-REP Regan Dosimetry 90
Example exam question (2009)
MSc-REP Regan Dosimetry 91
Example exam question (2009)
MSc-REP Regan Dosimetry 92
Exposure Rate Constants
Example Question
 Using the expression dX/dt = ?? A/d2, where dX/dt is the
exposure rate, A the activity and d the distance,
Show that ?? = 3.2 R.cm2.hr-1.mCi-1 for Caesium-137 given the
following information:
The gamma-ray branching ratio for the 662 keV decay
following the 137Cs decay is 85%.
 
Air has a mass energy absorption coefficient at this
gamma-ray energy of 0.0293 cm2.g-1;

The activity is 1mCi, and the source distance is 1cm.
MSc-REP Regan Dosimetry 93
Example Answer
 
If activity A is 1mCi and the distance is 1cm. Therefore ?? = dX/dt. The Dose per second is given by
energy photon fluence multiplied by the mass energy absorption coefficient. [remember 1Ci = 3.7x1010
Bq]

Dose per second =
 0.85 x 3.7x107 mCi–1 x (0.662)x106 eV x 1.6x10-19 J.eV-1 x 0.0293 cm2.g-1
4pi x 1s

= 7.77x10-9 J.s-1.g-1.cm2.mCi-1
 
in 1 hour (1hr = 3600s)
 
= 2.80x10-5 J.g-1.cm2.hr-1.mCi-1
 
for 1 kg (1kg = 1000g)
 
= 2.80x10-2 J.kg-1.cm2.hr-1.mCi-1 (or in units Gy.cm2.hr-1.mCi-1)
 
in rads (1Gy = 100rad)
 
= 2.80 rad.cm2.hr-1.mCi-1
 
in Roentgen (1R = 0.87 rad)
 
= 3.2 R.cm2.hr-1.mCi-1
MSc-REP Regan Dosimetry 94
Radiation Equilibrium
P.V’
A B
d
C V
?EE = ionising radiation energy entering V'
?EL = ionising radiation energy leaving V'
?ER = increase in rest mass energy within V'
C.of.E ? energy imparted to matter in V',
?ED = ?EE - ?EL - ?ER
 
Under conditions of
radiation equilibrium
?EE = ?EL ? ?ED = -?ER
 
? Dose = ?ED/?m = - ?ER/?m
MSc-REP Regan Dosimetry 95
Radiation Equilibrium
?EEext
?EEint
?ELext
?EDext?ERext
?ERint
?EDint
?ELint
MSc-REP Regan Dosimetry 96
Total Dose,
D = ?EDext + ?EDint
? D = [?EEext-?ELext-?ERext]+[?EEint-?ELint-?ERint]

Radiation Equilibrium??EEext = ?ELext + ?Elint
? D = [?EEint] - [?ERext + ?ERint]
? D = [Decrease in rest mass] - [Increase in rest
mass]
If there are no internal sources,
? D = [?EEext - ?ELext] - ?ERext
Radiation Equilibrium
MSc-REP Regan Dosimetry 97
Charged Particle Equilibrium
Uncharged particles impart dose via two-
steps
1. Kinetic energy is transferred to
charged particles
2. These charged particles deposit
energy in the medium.
MSc-REP Regan Dosimetry 98
Charged Particle Equilibrium
Uncharged particles impart dose via two-
steps
1. Kinetic energy is transferred to
charged particles
2. These charged particles deposit
energy in the medium.
MSc-REP Regan Dosimetry 99
Charged Particle Equilibrium
If each charged particle carrying energy out of
V' is balanced by an identical particle carrying
the same amount of energy in, then charged
particle equilibrium (CPE) is said to exist inside
V'.
MSc-REP Regan Dosimetry 100
Charged Particle Equilibrium
If a volume is irradiated by an external source,
the energy carried in and out by charged (c) and
uncharged particles (u) is,
? ?ED = [(?EE)c-(?EL)c]+[(?EE)u-(?EL)u- (?ER)u]
If CPE exists,
(?EE)c = (?EL)c
? ?ED = [(?EE)u-(?EL)u- (?ER)u]
MSc-REP Regan Dosimetry 101
Charged Particle Equilibrium
Energy from uncharged radiation supplies ?EK to charged particles + rest mass changes,
(?EE)u - (?EL)u = ?EK + (?ER)u
? ?EK = (?EE)u - (?EL)u - (?ER)u
c.f. ?ED = [(?EE)u-(?EL)u- (?ER)u] from before
? ?ED = ?EK
MSc-REP Regan Dosimetry 102
Charged Particle Equilibrium
If the mass of material in the volume is ?m,
Dose = ?ED /?m
= ?EK /?m
= K, kerma
? C.P.E. ? D = K
CPE is always present when radiation equilibrium
occurs, but in many cases of practical interest CPE is
closely attained even though complete radiation
equilibrium is not.
MSc-REP Regan Dosimetry 103
Charged Particle Equilibrium
Vacuum Medium
Build up
Region
Relectron
Absorbed Dose
Kerma
e-
MSc-REP Regan Dosimetry 104
Mass energy absorption
coefficients
For an air filled ion chamber, the absorbed dose for an
exposure of 1R = 0.87rad.
air
m
airm DSD ?=
Hence for an exposure of X roentgen, the dose in rads is,
XSD mairm ??= 87.0
This can be written Dm = f.X where f = 0.87.airSm
which is called the rad per roentgen factor
X.D air ?= 870
MSc-REP Regan Dosimetry 105
Mass energy absorption coefficients
As radiation energy fluence passes through an
abosorber it decreases exponentially,
E = E0exp(-µenx)
Differentiating gives:
dE/dx = -µenE0exp(-µenx) = -µenE
Multiply by 1/?, (? is absorber mass density) to give
which has units of energy/mass ? dose
E?
?
dx
dE
?
1 en
?=??
???
?
?
MSc-REP Regan Dosimetry 106
Mass energy absorption coefficients
µen/? = mass energy absorption coefficient
E?
?D dose, en ?=
E?
?K kerma, tr ?=
µtr/? = mass energy transfer coefficient
MSc-REP Regan Dosimetry 107
Mass energy absorption coefficients
The linear attenuation coefficient is,
Allowing for escaping radiation,
Additionally bremsstrahlung reduces this again,
( ) ( ) ( )?2oppsc?petr Ec2m1?f1?E?1?? ?+?+?=
pppe ???? c ++=
g)(1?
?
?
? and g)(1?? trentren ?=?=?
MSc-REP Regan Dosimetry 108
Exposure Rate Constants
Consider a point source of photons in air of activity A mCi
situated at distance d from the point of interest where the
exposure rate is dX/dt R.h-1.
The exposure rate depends only on the activity of the
source and the inverse square of the distance from the
source.
Hence dX/dt = ??.A/d2 where ?? is called the exposure rate
constant. Using the above units ?? has units
R.cm2.h-1.mCi-1.
MSc-REP Regan Dosimetry 109
Additional Information on
Personal Dosimetry / TLDs
MSc-REP Regan Dosimetry 110
Thermoluminescence Dosimetry
Real TLD materials have a dose range of about 0.1?Gy to in excess of
10Gy. As well as specifically made TLD materials, suitable environmental
samples (such as the roof tiles in Hiroshima) can also be used.
TLD measurements though are subject to two types of spurious
luminescence (1) triboluminescence – arising from trapping of charges
generated by friction between loose grains, reduced by encapsulating the
TL crystals in a PFTE binder (2) chemiluminescence – arising from oxygen
induced surface reactions, reduced by N2 flushing.
In addition UV light can cause the TLD to prematurely fade and can be
reduced by keeping the TLD in light-tight packaging.
There are also two related techniques, Thermally Stimulated Electron
Emission (TSEE) and Thermally Stimulated Conductivity (TSC) which are
alternative readout methods.
MSc-REP Regan Dosimetry 111
Photographic Emulsion Dosimetry
The photographic emulsion is a suspension of silver halide crystals in a
gelatin matrix. The film badge has an emulsion coating on both sides
but of differing sensitivities, one for a high dose range, and the other for
low dose ranges.
When the film is exposed to X-rays, secondary ionisation makes one or
more of the silver halide ions latent. When developed this produces
metallic silver which varies spatially according to the amount of dose
absorbed within the matrix, this forms the photographic negative.
20µm
200µm
protective coating
base material
silver halide
grains in a
gelatin matrix
MSc-REP Regan Dosimetry 112
Photographic Emulsion Dosimetry
A typical film density versus exposure curve is shown below,
MSc-REP Regan Dosimetry 113
Photographic Emulsion Dosimetry
Despite some of the drawbacks described above photographic
dosimetry still has some advantages over alternatives like TLD.
(a) In fine grain emulsions individual particle tracks can be recognised
under a microscope and the nature and energy of the incident radiation
can be deduced. In radiation protection this has been used to record
proton recoil tracks arising in the surrounding gelatin matrix as result of
fast neutrons passing through the film badge.
(b) The technique produces a permanent visible record so that
exposures can be readily rechecked. For example radioactive
contamination of a film badge can be distinguished from a "normal"
uniform exposure to more distant radiation sources. The self-indicating
feature is advantageous if required as legal evidence.
(c) The technique is relatively "low-tech" compared with TLD for
example and needs less costly equipment which may make it
more practicable in some cases. Although it is not as readily
automated as a TLD system this may not be important if the
workforce being monitored is fairly small.
MSc-REP Regan Dosimetry 114
Personal Dosemeters
Film Badges and TLDs
MSc-REP Regan Dosimetry 115
Personal Dosemeter Badges
Thermoluminescent dosemeter (a.k.a. “TLD”)

                               
       
This is a reusable dosemeter which uses lithium fluoride to
measure radiation dose. It stores dose information until heated to
over 250°C when it gives out light the amount of which is
proportional to the dose received. It is environmentally robust and
excellent for use in all working environments.
Photographic film dosemeter (a.k.a. “film badge”)

                              
       
Film is worn in a holder containing several different filters. When
developed the film darkens in proportion to the amount of radiation
energy received. Due to the differing amounts of filtration we can
gain information on the energy of radiation causing the dose.
Radioactive contamination of the film can be readily identified.
Extremity dosemeter (a.k.a. “finger TLD”)

                                
                       
This is a miniature TLD which can be supplied in
different forms to suit your needs (stalls, straps or
rings). The finger stall is most commonly used and
is worn like the finger of a glove.
MSc-REP Regan Dosimetry 116
A dosemeter often measures two quantities. The first is the personal
dose equivalent Hp(10), which is often referred to as the “whole body”
dose which results from penetrating radiation. The second quantity is
the personal dose equivalent Hp(0.07) which is an assessment of the
dose equivalent to the skin from both weakly and strongly penetrating
radiations.
The “H” of Hp is used generally to signify the Equivalent Dose and is
in units of Sieverts. The “p” is used to signify it is personal equivalent
dose.
The definition of Hp(10) is the dose equivalent at a depth of 10 mm
into a human body. Similarly Hp(0.07) is 0.07mm into the body.
Other measurements of equivalent dose may not give accurate values
of the Hp equivalent dose as it is the absorption and scattering effects
of the human body throughout the different response to the energy of
the radiation which give true Hp readings.
Hp (0.07) and Hp (10)
MSc-REP Regan Dosimetry 117
Film Badge Dosemeters
For many decades the standard method personal dosimetry involved the
use of photographic emulsions in the form of film badge dosemeters.
Although they are increasingly being replaced by other methods, they are
still in use as dosemeters for X-, beta and gamma radiation.
To cover the required dose range the film incorporates two emulsions, of
different sensitivities. Additionally the film badge holder has a number of
different filters to sort out the various components of radiation exposure.
Detection Gamma rays X-rays Beta particles
Dose range
measured
0.1 mSv to 10 Sv 0.1 mSv to 400
mSv
0.1 mSv to 10 Sv
Energy range
detected
10 keV to 7 MeV
for Hp (0.07)
20 keV to 7 MeV
for Hp (10)
10 keV to 7 MeV
for Hp (0.07)
20 keV to 7 MeV
for Hp (10)
700 keV to 3.5
MeV (Emax) for
Hp (0.07)
MSc-REP Regan Dosimetry 118
The variation of response with energy and angle of incidence (mean
between 0° and 60°) for the quantities Hp(10) [red] and Hp (0.07) [blue]
is shown for photons in the graph below. This is for the combined film
emulsions and is normalised to caesium-137 with a value of 0.9.
The film badge is still found in hospitals and other medical
establishments where X-rays are used. It is the use of a technology
with is familiar to the user, that adds an important element of
confidence that the personal dosemeter is performing its required
use.
MSc-REP Regan Dosimetry 119
Thermoluminescent Dosemeters
Currently the most common used personal dosemeter. The dosemeter
consists of two thermoluminescent detectors containing the radiation-
sensitive material lithium fluoride (LiF). The detectors are located in a plate
which is identified uniquely by means of an array of holes. The lithium
fluoride stores the energy it receives from ionising radiations until it is
heated during processing (in this case to about 250°C) when the energy is
released as light. The amount of light released is proportional to the
radiation dose. The plate is supplied to the wearer in a plastic wrapper
which protects the detectors from light and contaminants.
LiF inserts
Current NRPB
TLD and new
Harshaw TLD
MSc-REP Regan Dosimetry 120
Detection X-rays and Gamma rays Beta particles
Dose range
measured
0.05 mSv to 10 Sv 0.05 mSv to 10 Sv
Energy range
detected
10 keV to 10 MeV for Hp (0.07)
15 keV to 10 MeV for Hp (10)
700 keV to 3.5 MeV
(Emax) for Hp (0.07)
The Hp(10), “whole body” dose is measured by the detector behind the
domed part of the holder. The Hp(0.07), “dose equivalent to the skin
from both weakly and strongly penetrating radiations” is measured by
the detector behind the circular window.
MSc-REP Regan Dosimetry 121
Optically Stimulated
Luminesence Dosemeters
Optically Stimulated Luminesence Dosemeters (OSLDs) measures
radiation through a thin layer of aluminum oxide. During analysis, the
aluminum oxide is stimulated with selected frequencies of laser light
causing it to become luminescent in proportion to the amount of
radiation exposure.
OSLDs gives accurate readings down to 1 µSv. This degree of
sensitivity is ideal for employees working in low-radiation environments
and for pregnant employees.
The Al203 (aluminum oxide) detector can be restimulated  numerous
times to confirm the accuracy of a radiation dose measurement. 
OSLDs be used for up to one year. They are unaffected by heat,
moisture, and pressure when the clear blister packaging is
uncompromised.
OSLD readers do not require heaters or gas flow.
MSc-REP Regan Dosimetry 122
Optically Stimulated
Luminesence Dosemeters
Measurements Photon
(X-Ray and Gamma Ray)
Beta Particle Neutron
(Optional Neutrak® 144 Detector Inside
Dosemeter)
Detector Al203 (Aluminum Oxide) Al203 (Aluminum Oxide) Neutrak 144 allyl diglycol carbonate solid state nuclear track detector
Analysis
Method
Optically Stimulated
Luminescence (OSL)
Optically Stimulated
Luminescence (OSL)
Chemical etching followed by track
counting
Energies
Detected
5 keV to in excess of 40
MeV
150 keV to in excess of 10
MeV
Fast: 40 keV to in excess of 35 MeV
Thermal: under 0.5 eV
Dose
Measurement
Range
10 uSv to 0.1 Sv 0.1 mSv to 10 Sv Fast: 0.2 mSv to 0.25 Sv
Thermal: 0.1 mSv to 50 mSv
Accreditation Accredited by NVLAP in all categories including VIII when neutron component is added, NVLAP
Lab Code 100518-0.
Landauer Luxel® Dosemeter
MSc-REP Regan Dosimetry 123
Neutron Dosemeters
The poly-allyl diglycol carbonate (PADC) neutron dosemeter is designed to
measure doses from neutron radiation in terms of the radiation quantities
specified by the Health and Safety Executive (HSE). The PADC neutron
service is approved by the HSE under Regulation 35 of the Ionising
Radiations Regulations 1999. The dosemeter is a passive device for the
detection of thermal, epithermal and fast neutrons. It is insensitive to other
radiations (gamma, X- and beta), is relatively unaffected by environmental
factors such as heat and humidity and has a very low radon sensitivity.
Detection Neutron radiation
Dose range
measured
0.2 mSv to 250 mSv
Energy range
detected
Thermal, epithermal and fast
(144 keV to 15 MeV)
neutrons for Hp (10)