Detection and Dosimetry of Ionising Radiation

1
Detection and Dosimetry of Ionising Radiation

• MSc-REP Lecture Notes
• Dr. P.H.Regan
• p.regan_at_surrey.ac.uk
• http//www.ph.surrey.ac.uk/phs1pr/lecture_notes

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.
3
Some Useful Web Pages

• Dosimetry definitions etc.
• http//www.physics.isu.edu/radinf/terms.htm
• http//www.hps.org/publicinformation/radfactsheet
  s/
• 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 as
• 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)

4
Part 1 Relationship Between Detectors and
Dosimetry

• Physical and Chemical Effects of Ionising
  Radiation.
• General Concepts and Units.
• Radiation Quantities and Definitions
• Absolute Methods of 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.

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-gt 40 eV of energy is needed to
  ionize a molecule or
• atom, thus radiations such as a, b and g, 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.

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.

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.

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

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,g), (n,p) or (n,a) reactions).
• Slow (thermal) neutrons detection can use (see
  Knoll p483ff 707 ff)
• 10B(n,a) 7Li (Q2.310, 94, E(7Li) 0.84 MeV,
  E(a) 1.47 MeV).
• 6Li(n,a)3H (Q4.78 MeV, E(3H) 2.73 MeV, E(a)
  2.05 MeV)
• 55Mn(n,g)56Mn T1/22.6h 59Co(n,g)60Co
  T1/210.4min 5.3y
• 109Ag(n,g)110Ag, T1/224secs 164Dy(n,g)165mDy,
  T1/21.3mins .
• Threshold activation detectors (for fast
  neutrons) include
• 59Co(n,a)56Mn, T1/22.56h 23Na(n,a)20F (in a
  NaI(Tl) detector)

11
FromKnoll p707
12
From Knoll p708
13
From Knoll p709
14
Definitions, Quantities and Units (Alpen p5ff)
Exposure (X) The exposure is defined as the
ratio of the charge (of one sign) DQ produced in
a medium when all the electrons liberated by
photons in the volume element of the medium with
mass Dm, 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)
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 g-rays, not p, a,
n, e- etc.
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 g 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.
16

17
Energy Imparted (DED) 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 Dm, given by DEE and the
sum of the energies of all those which have left
the volume (corrected for any changes in rest
mass, DER, which have taken place due to nuclear
reactions within the volume element).
The SI unit for the energy imparted is the gray
(Gy).
18
Equivalent Dose ( HT ) (see Alpen p426) 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 Q 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 Q 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.
19
Quality/Weighting(Q/W) Radiation Factors, from
the U.S. Nuclear Regulatory Commission (NRC)
Note that sometimes the ICRP calls these Quality
(Q) factors while the ICRP calls them Weighting
(W) factors. They are equivalent.

• X-ray, g-rays, b, electrons, Q1
• Neutron (general) Q10, BUT specifically
• Elt10 keV, Q2-5
• E10 keV, Q2.5-10
• E100 keV, Q7.5-10
• E500 keV, Q10-20
• E1-2 MeV, Q20
• E2-20 MeV, Q5
• High energy protons, as, fission fragments,
  heavy-ions etc. Q20

20
FromAlpen p426
21
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 ?
22
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.
RBE is related (but not identical) to the quality
factor, Q in the measurement of dose equivalent.

23
Effective Human-Equivalent 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.
The Effect Human-Equivalent 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).
24
From Alpen p427
Remainder (adrenals, brain, upper large
intestine, small intestine, kidney, muscle,
pancreas, spleen, thymus and uterus) 0.05 The
total sum of weighting factors 1.00
25
Alpen p430
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.
26
ICRP Recommended Annual Dose Limits
Note these recommended limits EXCLUDE any medical
or natural background radiation doses.
27
Some More Definitions Particle Fluence (F )
is the number of particles, DN which enter a
sphere of cross-sectional area a, such that
FDN/Da. F has units of particles/m2. Particle
Fluence rate (f) is the rate of particle
fluence with respect to time. f DF / Dt and
thus f has units of particle/m2s. Energy Fluence
(y ) is related to the particle fluence. It is
defined by y DEf / Da, where DEf is the sum
of the particle energies which enter a
cross-sectional area, Da. Units are
Joules/m2 Energy Fluence Rate (Y) is the
quotient of the energy fluence with respect to
time, i.e., Y Dy / Dt .
Units are Joules/m2s.
28
KERMA (Alpen p8, p90) Typically, when radiation
(x-rays, g 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 DEK 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)
29
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.
30
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 (f) 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.)
31
Thus, the energy per unit mass going to any
specific effect fD. 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 fD Thus, since D
(H/f).Ne, ,, if (H / f) 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 fi of the
particles kinetic energy produces ionisation in
the medium, assuming that the energy required to
cause ionisation by radiation induced collisions
is Hi, we have fiENi Hi and the number of ions
produced is Ni(fi.E)/Hi . Now, (E / Ni)(Hi /
fI) is the average energy required to produce one
electron-ion pair, which is known as the W-value.
32
Therefore,
Thus, if we know W, we have the calibration
factor (Hi / fi) without having to know Hi or fi
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.
33
Radiation Equilibrium
Consider a volume, V, uniformly filled with
radioactive material. Inside this volume, V, is a
smaller secondary volume, V (containing mass,
Dm) 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.
34
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.
35
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.
36
Consider the point, P, within the volume V. DEE
is the sum of the total energies of all the
ionising radiations entering V. DEL is the sum
of the total energies of ionising radiations
leaving V and DER is the increase in rest
mass inside V.
Thus, by conservation of mass energy, the energy
imparted to matter in the volume element V is
given by DED DEE - DEL - DER If there is
RADIATION EQUILIBRIUM then DEE DEL and so,
DED - DER and thus the absorbed dose, D
DED / Dm 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 b-decay is
excluded since their absorption is vanishingly
small).
37
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
38
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 ee- 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.
39
Charged Particle Equilibrium
X-ray and g-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.
40
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 (DER) 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.
41
This result can be interpreted alternatively
as The net energy brought into the medium by
uncharged radiations supplies kinetic energy
(DEK) to charged interaction products, and also
any accompanying rest mass changes. Thus we can
write,
Recalling (p40) that
Then under Charged Particle Equilibrium (CPE)
conditions, DEDDEK
If the mass of the material encompassed by the
volume element V is given by Dm, then
D (DED / Dm) (DEK / Dm) K, where K
KERMA, the energy released per unit mass. Thus,
in CPE, DK, i.e. DOSE KERMA It is now common
practice to refer to kinetic energy transfer to
charged particles and to replace DEK with DEtr
. 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.
42
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.
43

• 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

44
(from Alpen p 91) For fast electrons, D and K can
also be defined in terms of the incident fluence
45
Mass Energy Absorption Coefficients
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(-menx) -
(1), where men is the linear energy absorption
coefficient, and x is the depth (or linear
distance through the medium).
46
Note men/r mass energy absorption coefficient
units of cm2.g-1 and mtr/r 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 (m) is given by
The mass attenuation coefficient is defined by (m
/r ) , where r is the density of the absorber
material
47
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 men (see
p45), but while m describes photons (and the
energy which they carry) which are removed from
the primary photon beam, men describes the energy
absorbed in the medium. men is always smaller
than m 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.).
48
The linear attenuation coefficient can be reduced
to allow for the escape processes to give an
expression for the LINEAR ENERGY TRANSFER
49
Mass attenuation coefficients for (A) Lead and
(B) Water. Taken from Alpen, p81-82.
50
Consider 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,
D2 (men /r )2
D1 (men /r )1
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).
51

• A special case if when 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
• 1roentgen can be calculated to be 87erg.g-1 (
  0.87 rad).
• Thus, using the relation shown on p51, 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, Dair0.87.airSm rad.
• More generally, for an exposure of X roentgens,
  Dm0.87.airSm.X rad
• or written another way, Dmf.X rad where f
  0.87.airSm
• f is called the rad per roentgen factor.
• For photons of Eg10 keV -gt 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, Z20) has f 3.6 for 10 keV and
  0.92 _at_ 1MeV

52
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
53
Effective Atomic Numbers and Matching
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 (speZn/Eg4-5) The photon
attenuation coefficients, and the related energy
absorption coefficients are complex functions of
Eg 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 ( E10-250
keV, Zeff7.8). 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., 1S21.0) 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.