notes for theoretical health physics
TRANSCRIPT
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Notes for Theoretical Health Physics
Tae Young Kong
1. Stochastic processesa. Independent events
Reference: James E. Turner, Darryl J. Downing, and James S. Bogard, Statistical
Methods in Radiation Physics, pp.2!"#
$n some cases, gi%en addi&ional informa&ion will cause no c'ange in &'e
pro(a(ili&y of &'e e%en& occurring. T'en, in sym(ols, )r*+B-)r*+-, and so &'e
occurrence of B 'as no e/ec& on &'e pro(a(ili&y of &'e occurrence of +. 0e
&'en say &'a& e%en& + is independen& of e%en& B.
Two e%en&s + and B are independen& if and only if )r*+B-)r*+-
and)r*B+-)r*B-.
$ndependence T'eorem Two e%en&s, + and B, in a sample space are independen& if and only if
)r*+ 1B-)r*+-)r*B-.
Eample Two p'o&ons of a gi%en energy are normally inciden& on a me&al foil. T'e
pro(a(ili&y &'a& a gi%en p'o&on will 'a%e an in&erac&ion in &'e foil is 3.2.
4&'erwise, i& passes &'roug' wi&'ou& in&erac&ing. 0'a& are &'e pro(a(ili&ies
&'a& nei&'er p'o&on, only one p'o&on, or (o&' p'o&ons will in&erac& in &'e foil5Solu&ion
T'e num(er of p'o&ons &'a& in&erac& in &'e foil is a random %aria(le 6, w'ic'
can &a7e on &'e possi(le %alues 3, 8, or 2. T'ere are four simple e%en&s for &'e
sample space for &'e &wo p'o&ons: *n, n-, *n, y-, *y, n-, *y, y-.9ere y means
yes, &'ere is an in&erac&ion; and n means no, &'ere is no&,; &'e pair of
sym(ols in paren&'eses deno&ing &'e respec&i%e fa&es of &'e &wo p'o&ons. T'e
pro(a(ili&y of in&erac&ion for eac' p'o&on is gi%en as 3.2, and so &'e
pro(a(ili&y for i&s 'a%ing no in&erac&ion is 3.
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Since &'e pro(a(ili&y of yes; for a p'o&on is 3.2 and &'a& for no; is 3.
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T'e resolu&ion of &'e &o&al!energy pea7,
09 3.3or anormal cur%e, wi&' s&andard de%ia&ion P, i&
can (e s'own &'a& >09 2.#P. T'e
resolu&ion of a spec&rome&er depends on
se%eral fac&ors. T'ese include noise in &'e
de&ec&or and associa&ed elec&ronic sys&ems
as well as Quc&ua&ions in &'e p'ysical
processes &'a& con%er& radia&ion energy
in&o a measured signal. +pplying )oisson
s&a&is&ics, we can epress &'e resolu&ion in&erms of &'e a%erage num(er of
p'o&oelec&rons *wi&' s&andard de%ia&ion P
-:
µ µ
σ
µ
35.235.2===
FWHM R
wi&' >09 now referring &o &'e num(er, ra&'er &'an energy, dis&ri(u&ion. 0i&'
R 3.3< for &'e scin&illa&or, i& follows &'a& &'e a%erage num(er of
p'o&oelec&rons collec&ed per pulse is or di/eren& &ypes of de&ec&ors, &'e p'ysical limi&a&ion on resolu&ion imposed
(y &'e in'eren& s&a&is&ical spread in &'e num(er of en&i&ies collec&ed can (e
compared in &erms of &'e a%erage energy needed &o produce a single en&i&y.
>or &'e al de&ec&or Uus& gi%en, since an e%en& is regis&ered wi&' &'e
ependi&ure of 2 7eO, &'is a%erage energy is 0; *2333 eO-V*
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Eample>or &'e scin&illa&or analyed in &'e eample gi%en af&er >ig. 83.3, i& was found
&'a& &'e a%erage energy needed &o produce a p'o&oelec&ron was 8## eO.*a- 0'a& is &'e resolu&ion for &'e &o&al!energy pea7 for "#3!7eO p'o&ons5*(- 0'a& is &'e wid&' of &'e &o&al!energy pea7 *>09- in 7eO5*c- 0'a& is &'e resolu&ion for 8.2!eO p'o&ons5
Solu&ion*a- T'e a%erage num(er of p'o&oelec&rons produced (y a(sorp&ion of a "#3!
7eO p'o&on is "#3,333V8## 233. T'e resolu&ion is &'erefore, R 2.#V
*233-8V2 3.3".*(- >or "#3!7eO p'o&ons, i& follows &'a& >09 3.3"A"#3 8. 7eO.*c- T'e resolu&ion decreases as &'e sHuare roo& of &'e p'o&on energy. T'us,
&'e resolu&ion for 8.2!eO p'o&ons is 3.3" *3."#3V8.2-8V2 3.32.
d. Deviation from Poisson statistics – ano factor
Reference: James E. Turner. Atoms, Radiation, and Radiation Protection,
pp.
T'e >ano fac&or 'as (een in&roduced as a measure of &'e depar&ure of
Quc&ua&ions from pure )oisson s&a&is&ics. $& is de=ned as &'e ra&io of &'e
o(ser%ed %ariance and &'e %ariance predic&ed (y &'e la&&er:
iance Poisson
ianceObserved F
var
var =
.Repor&ed %alues of >ano fac&ors for gas propor&ional coun&ers are in &'e range
from a(ou& 3.8 &o 3.2 and, for semiconduc&ors, from 3.3 &o 3.8#. >or
scin&illa&ion de&ec&ors, > is near uni&y, indica&ing a )oisson!limi&ed resolu&ion.
!. Nuclear physics basicsa. ield descriptions
Reference: Radia&ion )ro&ec&ion Lompe&ency 8.8 p.22!2#
Point source T'e in&ensi&y of &'e radia&ion =eld decreases as &'e dis&ance from &'e source
increases. T'erefore, increasing &'e dis&ance will reduce &'e amoun& of
eposure recei%ed. $n many cases, especially w'en wor7ing wi&' poin&
sources, increasing &'e dis&ance from &'e source is more e/ec&i%e &'an
decreasing &'e &ime spen& in &'e radia&ion =eld. T'eore&ically, a poin& source is an imaginary poin& in space from w'ic' all &'e
radia&ion is assumed &o (e emana&ing. 0'ile &'is 7ind of source is no& real *all
real sources 'a%e dimensions-, any geome&rically small source of radia&ion
(e'a%es as a poin& source w'en one is wi&'in &'ree &imes &'e larges&
dimension of &'e source. Radia&ion from a poin& source is emi&&ed eHually in all
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direc&ions. T'us, &'e p'o&ons spread ou& &o co%er a grea&er area as &'e
dis&ance from &'e poin& source increases. T'e e/ec& is analogous &o &'e way
lig'& spreads ou& as we mo%e away from a single source of lig'& suc' as a lig'&
(ul(. T'e radia&ion in&ensi&y for a poin& source decreases according &o &'e $n%erse
SHuare Zaw w'ic' s&a&es &'a& as &'e dis&ance from a poin& source decreases or
increases &'e dose ra&e increases or decreases (y &'e sHuare of &'e ra&io of
&'e dis&ances from &'e source. T'e in%erse sHuare law (ecomes inaccura&e
close &o &'e source *i.e., wi&'in &'ree &imes &'e larges& dimension of &'e
source-.+s pre%iously men&ioned, &'e eposure ra&e is in%ersely propor&ional &o &'e
sHuare of &'e dis&ance from &'e source. T'e ma&'ema&ical eHua&ion is:
T'is eHua&ion is assuming &'e a&&enua&ion of &'e radia&ion in &'e in&er%ening
space is negligi(le and &'e dimensions of &'e source and &'e de&ec&or are
small compared wi&' &'e dis&ance (e&ween &'em. T'e in%erse sHuare law 'olds &rue only for poin& sourcesX 'owe%er, i& gi%es a
good approima&ion w'en &'e source dimensions are smaller &'an &'e
dis&ance from &'e source &o &'e eposure poin&. Due &o dis&ance cons&rain&s,
eposures a& cer&ain dis&ances from some sources, suc' as for a pipe or &an7,
canno& (e &rea&ed as a poin& source. $n &'ese si&ua&ions, &'ese sources mus&
(e &rea&ed as line sources or large surface sources.
x p er
S µ
π φ −=
24
for calcula&ion of Qu from &'e poin&
source
"ine Sources+n eample of a line source would (e a pipe carrying con&amina&ed cooling
wa&er or liHuid was&e, a con&rol rod, a series of poin& sources w'ic' are close
&oge&'er, or a needle inUec&ing a radioiso&ope in&o &issue. 0i&' line sources, an
assump&ion mus& (e made &'a& &'e dis&ri(u&ion of radioac&i%i&y is uniform
&'roug'ou& &'e source. 0'en no a&&enua&or is presen&, &'e rela&ions'ip
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(e&ween &'e line source emission ra&e and &'e Qu a& &'e
recep&or *)- depends on &'e loca&ion of &'e recep&or wi&'
respec& &o &'e line source. 9owe%er, &'is rela&ions'ip is
more comple ma&'ema&ically &'an in &'e case of &'e
poin& source, and &'e use of calculus is reHuired. T'efollowing =gure and formula applies &o line sources.
x
p eh
Sl µ θ θ π
φ −
−= )(4
0
Plane Sources+n eample of a plane source would (e a spill of liHuid con&aining radioac&i%i&y
on &'e Qoor. +gain, w'en es&ima&ing &'e amoun& of
radioac&i%i&y emana&ing from an area source, an
assump&ion mus& (e made &'a& &'e dis&ri(u&ion of
radioac&i%i&y is uniform &'roug'ou& &'e source. >or an
area source wi&' an a&&enua&or presen&, &'e calcula&ions
(ecome %ery complica&ed. >or illus&ra&i%e purposes, an
eample of a circular area source wi&'ou& an a&&enua&or presen& is gi%en.
)1ln(4 2
2
h
aS a p +=φ
b. Interaction of radiation #ith matter and interaction ratesi. Production of annihilation radiation$ %remsstrahlung$ and
&uger electrons
Reference: James E. Turner. Atoms, Radiation, and Radiation Protection,
pp., #
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producing &'e radia&ion (ecause &'e deQec&ions are
s&ronger. + single elec&ron can emi& an 6!ray p'o&on
'a%ing any energy up &o i&s own 7ine&ic energy. +s a resul&,
a monoenerge&ic (eam of elec&rons produces a con&inuous
spec&rum of 6 rays wi&' p'o&on energies up &o &'e %alue of &'e (eam energy. T'ese con&inuous 6 rays are called
(remss&ra'lung, or (ra7ing radia&ion.;
&uger electrons>ollowing eUec&ion of &'e p'o&oelec&ron, &'e inner!s'ell %acancy in &'e
a&om is immedia&ely =lled (y an elec&ron from an upper le%el resul&ing
in a release of energy. +l&'oug' mos& of &'e &ime &'is energy is
released in &'e form of an emi&&ed p'o&on, &'e energy can also (e
&ransferred &o ano&'er elec&ron, w'ic' is eUec&ed from &'e a&om. T'is
second eUec&ed elec&ron is called an +uger elec&ron.
c. 'adioactive decayi. Half(life$ mean life$ decay constant$ activity
Reference: 9erman Lem(er. Health Physics. 4th edition, p.<
Half(life T'e &ime reHuired for any gi%en radionuclide &o decrease &o one!'alf of
i&s original Huan&i&y is a measure of &'e speed wi&' w'ic' i& undergoes
radioac&i%e &ransforma&ion. T'is period of &ime is called &'e 'alf!life and
is c'arac&eris&ic of &'e par&icular radionuclide. Eac' radionuclide 'as i&s
own uniHue ra&e of &ransforma&ion, and no opera&ion, ei&'er c'emical
or p'ysical, is 7nown &'a& will c'ange &'e &ransforma&ion ra&eX &'e
decay ra&e of a radionuclide is an unal&era(le proper&y of &'a& nuclide.
E6+)ZE ".8Lo(al&!3, a gamma!emi&&ing iso&ope of co(al& w'ose 'alf!life is #.
years, is used as a radia&ion source for radiograp'ing pipe welds.
Because of &'e decrease in radioac&i%i&y wi&' increasing &ime, &'e
eposure &ime for a radiograp' will (e increased annually. Lalcula&e &'e
correc&ion fac&or &o (e applied &o &'e eposure &ime in order &o accoun&for &'e decrease in &'e s&reng&' of &'e source.
Solu&ionEHua&ion can (e wri&&en as
n
A
A20 = *since n A
A
2
1
0
=-
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By &a7ing &'e logari&'m of eac' side of &'e eHua&ion, we 'a%e
2loglog 0 n A
A=
w'ere n, &'e num(er of 3Lo 'alf!li%es in 8 year, is 8V*#.- 3.8
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T'e uni& of ac&i%i&y is &'e BecHuerel *BH-, de=ned as one disin&egra&ion
per second: 8 BH 8 s\8. T'e &radi&ional uni& of ac&i%i&y is &'e curie *Li-,
w'ic' was originally &'e ac&i%i&y ascri(ed &o 8 g of 22Ra. T'e curie is
de=ned as 8 Li .A8383 BH, eac&ly.
ii. Simple decay
Reference: James E. Turner. Atoms, Radiation, and Radiation Protection,
pp.
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111 N
dt
dN λ −=
^
t
oe N N 1
11
λ −=
221122112 1 N e N N N
dt
dN t o λ λ λ λ
λ −=−= −
ul&iply (y
t e 2λ
for (o&' sides
dt e N dt N edN e t t t )(
1012221222 λ λ λ λ λ λ
−=+
dt e N e N d t t )(
1012122 ][
λ λ λ λ −=
$n&egra&e (o&' sides
t d e N dt e N t
t t
t
∫ ∫ −= 0)(
1010
2122 λ λ λ λ
t
t t e
N e N
0
)(
12
1012
122
−
= −λ λ λ λ λ
λ
]1[ )(
12
1012
122 −−
= − t t e N
e N λ λ λ
λ λ
λ
][ 21
12
1012
t t ee
N N λ λ
λ λ
λ −− −
−
=
iv. Serial decay
Reference: James E. Turner. Atoms, Radiation, and Radiation Protection,
pp.
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of daug'&er a&oms 2 per uni& &ime is eHual &o &'e ra&e a& w'ic' &'ey
are produced, +8, minus &'eir ra&e of decay, ]22:
2212 N A
dt
dN λ −=
dt N A
dN =− 2212
λ
w'ere +8 can (e regarded as cons&an&. $n&roducing &'e %aria(le u +8
\ ]22, we 'a%e du \]2d2 and,
dt u
du2λ −=
$n&egra&ion gi%es
ct N A +−=− 2221 )ln( λ λ
w'ere c is an ar(i&rary cons&an&. $f 23 represen&s &'e num(er of a&omsof nuclide *2- presen& a& & 3, &'en we 'a%e c ln*+8 \ ]223-.
t N A
N A2
2021
221ln λ λ
λ −=
−−
or
t e N A N A 2)( 2021221
λ λ λ −−=−
Since ]22 +2, &'e ac&i%i&y of nuclide *2-, and ]223 +23 is i&s ini&ial
ac&i%i&y,t t
e Ae A A 22 2012 )1( λ λ −− +−=
$n many prac&ical
ins&ances one s&ar&s wi&' a
pure sample of nuclide *8-
a& & 3, so &'a& +23 3,
w'ic' we now assume.
T'e ac&i%i&y +2 &'en (uilds
up as s'own in >ig. ".".
+f&er a(ou& se%en
daug'&er 'alf!li%es *&_
T2-, e\]2& G8 and EH.
reduces &o &'e condi&ion +8
+2, a& w'ic' &ime &'e
daug'&er ac&i%i&y is eHual
&o &'a& of &'e paren&. T'is condi&ion is called secular eHuili(rium. T'e
&o&al ac&i%i&y is 2+8. $n &erms of &'e num(ers of a&oms, 8 and 2, of &'e
paren& and daug'&er, secular eHuili(rium can (e also epressed (y
wri&ing
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2211 N N λ λ =
Transient ,-uilibrium T1 T!0
w'en 23 3 and &'e 'alf!life of &'e paren& is grea&er &'an &'a& of &'e
daug'&er, (u& no& grea&ly so
)( 21
12
101222
t t ee N
N λ λ
λ λ
λ λ λ −− −
−=
0i&' &'e con&inued passage of &ime, e \]2& e%en&ually (ecomes negligi(le
wi&' respec& &o e\]8&, since ]2 ` ]8. $n addi&ion since +8 ]88 ]883e\
]8& is &'e ac&i%i&y of &'e paren& as a func&ion of &ime, &'is rela&ion says
&'a&
12
122
λ λ
λ
−=
A A
T'e &ime a& w'ic' &'e daug'&er ac&i%i&y is larges&
1
2
12
ln1
λ
λ
λ λ −=t
for maimum +2 T'e &o&al ac&i%i&y is larges& a& &'e earlier &ime
2
121
2
2
12 2ln
1
λ λ λ
λ
λ λ −−=t
for maimum +8 +2
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v. &ctivation 2decay relations
Reference: James E. Turner. Atoms, Radiation, and Radiation Protection,
p.22
Reference: Llass 3", Zec&ure 28
delayirr t t ee N A 22 )1(112
λ λ φ σ −−−=
d. Nuclear decay schemes
Reference: James E. Turner. Atoms, Radiation, and Radiation Protection, pp.2!
Refer &o +ppendi D and deduce &'e decay sc'eme of 28+l.28+l b: \82.288 eO,
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e. Shielding and radiation attenuation
Reference: Radia&ion )ro&ec&ion Lompe&ency 8.8 p.8
+lp'a par&icles are rela&i%ely massi%e, slow mo%ing par&icles &'a& in&erac& (y
ionia&ion and eci&a&ion. T'erefore, alp'a radia&ion is no& %ery pene&ra&ing.
+lp'a radia&ion is no& an e&ernal 'aard and can (e s'ielded (y:+ few inc'es of air.
+ s'ee& of paper.+ dead layer of s7in.
Be&a par&icles are rela&i%ely lig'&, fas& mo%ing par&icles &'a& in&erac& (y
ionia&ion and eci&a&ion. Bea& radia&ion is modera&ely pene&ra&ing dependen&
on &'e energy or %eloci&y of &'e (e&a par&icle, and can (e an e&ernal 'aard if
i& can pene&ra&e &'e dead layer of s7in. Be&a radia&ion s'ould (e s'ielded (y
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low a&omic num(er ma&erials *i.e., - &o pre%en& &'e produc&ion of
(remss&ra'lung radia&ion. T'ese ma&erials include:)las&ic.0ood.+luminum.
eu&ron s'ielding in%ol%es slowing down fas& neu&rons and a(sor(ing &'ermal
neu&rons. >or eample, con&rol rods in nuclear reac&ors can (e fa(rica&ed from
(oron, w'ic' is a good ma&erial &o a(sor( &'ermal neu&rons. eu&ron s'ielding
is 'ig'ly dependen& on &'e energy of &'e neu&ron. T'e goal in neu&ron
s'ielding is &o genera&e a c'arged par&icle %ia an in&erac&ion. T'e (es&
in&erac&ion for s'ielding neu&rons would (e an elas&ic collision wi&' a lig'&
nucleus suc' as a 'ydrogen a&om. + 'ydrogen nucleus consis&s of a single
pro&on and allows a signi=can& &ransfer of energy &o a pro&on (ecause &'e
masses of &'e pro&on and neu&ron are almos& &'e same. T'e neu&ron collides
wi&' &'e pro&on, &ransferring energy and recoils &'e pro&on away from i&s
elec&ron cloud. T'e li(era&ed pro&ons range is &'en %ery s'or&, causing
ionia&ions and eci&a&ions along &'e recoiled pro&ons pa&'. eu&rons can (e
s'ielded (y ma&erials wi&' a 'ig' 'ydrogen con&en& suc' as:0a&er.Loncre&e.)las&ic.>uel 4il.)araMn.
)'o&on s'ielding is also 'ig'ly dependen& on &'e energy of &'e p'o&on and &'e
a&omic num(er of &'e s'ielding ma&erial. +s in neu&ron s'ielding, &'e goal is
&o produce a c'arged par&icle %ia an in&erac&ion, prefera(ly &'e p'o&oelec&rice/ec&, in w'ic' all of &'e p'o&on energy is &ransferred &o &'e elec&ron. T'e
p'o&oelec&rons range in ma&&er is %ery s'or&, causing ionia&ions and
eci&a&ions in &'e s'ielding ma&erial. T'e energy of &'e p'o&on is &'en
&ransferred &o &'e s'ield (y p'o&oelec&rons. Since p'o&ons in&erac& wi&'
elec&rons, p'o&ons can (e s'ielded (y any ma&erial w'ic' pro%ides an
adeHua&e num(er of elec&rons. T'is can (e done (y use of 'ig' a&omic
num(er *'ig' -, suc' as lead or uranium. $f space is no& limi&ed, wa&er or
concre&e may (e a prac&ical s'ielding ma&erial.
Reference: James E. Turner. Atoms, Radiation, and Radiation Protection,
pp.83!88
0'a& &'ic7ness of concre&e and of lead is needed &o reduce &'e num(er of
#33! 7eO p'o&ons in a narrow (eam &o one!four&' &'e inciden& num(er5
Lompare &'e &'ic7nesses in cm and in g cm\2. Repea& for 8.#!eO p'o&ons.Sol"tion
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0e use EH. *or lead,3.2# e\3.3#8$# ,
and so $# 28.2 g cm\2 and # 2. cm. +& &'is energy &'e Lomp&on e/ec& is
&'e principal in&erac&ion &'a& a&&enua&es &'e (eam, and &'erefore all ma&erials
*ecep& 'ydrogen- gi%e compara(le a&&enua&ion per g cm \2. Zead is almos&
uni%ersally used w'en low!energy p'o&on s'ielding is reHuired.
3. Ioni4ing radiationa. Types and sources
Reference: >ran7 9. +&&i. $n&roduc&ion &o Radiological )'ysics and Radia&ion
Dosime&ry, pp.2!
T'e impor&an& &ypes of ioniing radia&ions &o (e considered are:i. r!rays5 Elec&romagne&ic radia&ion emi&&ed from a nucleus or in
anni'ila&ion reac&ions (e&ween ma&&er and an&ima&&er.ii. 6!rays: Elec&romagne&ic radia&ion emi&&ed (y c'arged par&icles *usually
elec&rons- in c'anging a&omic energy le%els *called c'arac&eris&ic orQuorescence !rays- or in slowing down in a Loulom( force =eld
*con&inuous or (remss&ra'lung !rays-. o&e &'a& an !ray and a y!ray
p'o&on of a gi%en Huan&um energy 'a%e iden&ical proper&ies, di/ering
only in mode of origin. Iamma rays origina&e in &'e nucleus. 6!rays
origina&e in &'e elec&ron =elds surrounding &'e nucleus or are mac'ine!
produced.
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iii. >as& elec&rons: $f posi&i%e in c'arge, &'ey are called posi&rons. $f &'ey
are emi&&ed from a nucleus &'ey are usually referred &o as !rays
*posi&i%e or nega&i%e-. $f &'ey resul& from a c'arged!par&icle collision
&'ey are referred &o as h rays.i%. 9ea%y c'arged par&icles: Csually o(&ained from accelera&ion (y a
Loulom( force =eld in a Oan de Iraa/, cyclo&ron, or 'ea%y!par&icle
linear accelera&or. +lp'a par&icles are also emi&&ed (y some radioac&i%e
nuclei. Types include: )ro&on ! &'e 'ydrogen nucleus. Deu&eron ! &'e deu&erium nucleus, consis&ing of a pro&on and
neu&ron (ound &oge&'er (y nuclear force. Tri&on ! a pro&on and &wo neu&rons similarly (ound. +lp'a par&icle ! &'e 'elium nucleus, i.e., &wo pro&ons and &wo
neu&rons. 4&'er 'ea%y c'arged par&icles consis&ing of &'e nuclei of
'ea%ier a&oms, ei&'er fully s&ripped of elec&rons or in any case
'a%ing a di/eren& num(er of elec&rons &'an necessary &o
produce a neu&ral a&om. )ions ! nega&i%e !mesons produced (y in&erac&ion of fas&
elec&rons or pro&ons wi&' &arge& nuclei.%. eu&rons: eu&ral par&icles o(&ained from nuclear reac&ions ?e.g., *p, n-
or =ssion@, since &'ey canno& &'emsel%es (e accelera&ed
elec&ros&a&ically.
T'e $LRC *$n&erna&ional Lommission on Radia&ion Cni&s and easuremen&s,
88- 'as recommended cer&ain &erminology in referring &o ioniing radia&ions
w'ic' emp'asies &'e gross di/erences (e&ween &'e in&erac&ions of c'arged
and unc'arged radia&ions wi&' ma&&er:i. Direc&ly $oniing Radia&ion. >as& c'arged par&icles, w'ic' deli%er &'eir
energy &o ma&&er direc&ly, &'roug' many small Loulom(!force
in&erac&ions along &'e par&icles &rac7.ii. $ndirec&ly $oniing Radia&ion. 6! or r!ray p'o&ons or neu&rons *i.e.,
unc'arged par&icles-, w'ic' =rs& &ransfer &'eir energy &o c'arged
par&icles in &'e ma&&er &'roug' w'ic' &'ey pass in a rela&i%ely few large
in&erac&ions. T'e resul&ing fas& c'arged par&icles &'en in &urn deli%er&'e energy &o &'e ma&&er as a(o%e.
b. *haracteristics
S&a&ed a(o%e Types and sources6
c. ield -uantities
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Reference: >ran7 9. +&&i. $n&roduc&ion &o Radiological )'ysics and Radia&ion
Dosime&ry, pp.
i. >ZCELEReferring &o >ig. 8.8, Ze& , (e &'e epec&a&ion %alue of &'e num(er of
rays s&ri7ing a =ni&e sp'ere surrounding poin& ) during a &ime in&er%ale&ending from an ar(i&rary s&ar&ing &ime t o &o a la&er &ime t . $f &'e
sp'ere is reduced &o an in=ni&esimal a& P wi&' a grea&!circle area of da,
we may de=ne a Huan&i&y called &'e Quence, j, as &'e Huo&ien& of &'e
di/eren&ial of Ne, (y da:
da
dN e=Φ
w'ic' is usually epressed in uni&s of m!2 or cm!2.ii. >ZC6 DES$TY *4R >ZCELE R+TE-
j may (e de=ned a(o%e for all %alues of t &'roug' &'e in&er%al from t =
t o *for w'ic' j jma-. T'en a& any &ime t wi&'in &'e in&er%al we may
de=ne &'e Qu densi&y or Quence ra&e a& ) as
=
Φ=
da
dN
dt
d
dt
d eϕ
w'ere dj is &'e incremen& of Quence during &'e in=ni&esimal &ime
in&er%al dt a& &ime t , and &'e usual uni&s of Qu densi&y are m!2 s!8 or cm!
2 s!8.iii. EERIY >ZCELE
T'e simples& =eld!descrip&i%e Huan&i&y w'ic' &a7es in&o accoun& &'e
energies of &'e indi%idual rays is &'e energy Quence k, for w'ic' &'e
energies of all &'e rays are summed. Ze& R (e &'e epec&a&ion %alue of
&'e &o&al energy *eclusi%e of res&!mass energy- carried (y all &'e ,
rays s&ri7ing a =ni&e sp'ere surrounding poin& ) during a &ime in&er%al
e&ending from an ar(i&rary s&ar&ing &ime t o &o a la&er &ime t . $f &'e
sp'ere is reduced &o an in=ni&esimal a& ) wi&' a grea&!circle area of da,
we may de=ne a Huan&i&y called &'e energy Quence, k, as &'e Huo&ien&
of &'e di/eren&ial of R (y da:
da
dR=Ψ
w'ic' is usually epressed in uni&s of J m!2 or erg cm!2.
>or &'e special case w'ere only a single energy E of rays is presen&, &'e
a(o%e eHua&ions are rela&ed (y
e EN R =
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and
Φ=Ψ E
i%. EERIY >ZC6 DES$TY *4R EERIY >ZCELE R+TE- may (e de=ned a(o%e eHua&ion for all %alues of t &'roug'ou& &'e
in&er%al from & &o *for w'ic' k 3- &o & &ma *for w'ic' k kma-.
T'en a& any &ime & wi&'in &'e in&er%al we may de=ne &'e energy Qu
densi&y or energy Quence ra&e a& ) as:
=
Ψ=Ψ
da
dR
dt
d
dt
d
w'ere dk is &'e incremen& of energy Quence during &'e in=ni&esimal
&ime in&er%al d& a& &ime & , and &'e usual uni&s of energy Qu densi&y are J
m!2 s!8 or erg cm!2 s!8.
8 eO 8.32 A 83! erg 8.32 A 83!8 J
d. Interaction #ith matter
i. Ioni4ation$ e7citation$ 8(value
Reference: Radia&ion )ro&ec&ion Lompe&ency 8.8 p.#Reference: >ran7 9. +&&i. $n&roduc&ion &o Radiological )'ysics and
Radia&ion Dosime&ry, p.
L'arged par&icle radia&ions, suc' as alp'a par&icles or elec&rons, will
con&inuously in&erac& wi&' &'e elec&rons presen& in any medium
&'roug' w'ic' &'ey pass (ecause of &'eir elec&ric c'arge. T'ese
par&icles mus& undergo an in&erac&ion resul&ing in a full or par&ial
&ransfer of energy of &'e inciden& radia&ion &o &'e elec&ron or nuclei of
&'e cons&i&uen& a&om. $f &'e energy &ransferred &o &'e elec&ron is
grea&er &'an &'e energy 'olding &'e elec&ron &o &'e a&om, &'e elec&ron
will lea%e &'e a&om and crea&e ionia&ion. $onia&ion is &'e process of
&urning an elec&rically neu&ral a&om in&o an ion pair consis&ing of a
nega&i%ely c'arged elec&ron un(ound &o an a&om, and an a&om missing
one elec&ron crea&ing a ne& posi&i%e c'arge. $f insuMcien& energy is
&ransferred &o &'e elec&ron &o lea%e &'e a&om, &'e elec&ron is said &o (e
eci&ed. Eci&a&ion does no& crea&e ionia&ion or ion pairs, (u& does
impar& some energy &o &'e a&om. 0!%alue is &'e mean energy *in eO-
spen& (y a c'arged par&icle of ini&ial energy % o in producing eac' ion
pair:
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N
T W o≅
w'ere N is &'e epec&a&ion %alue of &'e num(er of ion pairs produced
(y suc' a par&icle s&opping in &'e medium *usually a gas- &o w'ic' 0
refers. T'e %alue for elec&rons, & ". eO ip\8.
ii. 'ange$ *SD& range$ density thic9ness$ mean(free path
Reference: Radia&ion )ro&ec&ion Lompe&ency 8.8 p.8<
L'arged par&icles 'a%e a de=ni&e range in ma&&er. T'e range of a
c'arged par&icle in an a(sor(er is &'e a%erage dep&' of pene&ra&ion of
&'e c'arged par&icle in&o &'e a(sor(er (efore i& loses all of i&s 7ine&ic
energy and s&ops. T'e energy of &'e par&icle, w'ic' is a func&ion of &'e
mass of &'e par&icle and i&s %eloci&y, and &'e elec&rical c'arge of &'e
par&icle a/ec& &'e range of &'e c'arged par&icle in a ma&erial. T'e
a&omic densi&y *num(er of a&oms per cu(ic cen&ime&er- and &'e a&omic
num(er *- of &'e s'ielding ma&erial also a/ec& range.
Reference: James E. Turner. Atoms, Radiation, and Radiation Protection,
p. 88,
*SD& is &'e contin"o"s'slo(in)'do(n appro#imation. $& ignores
Quc&ua&ions of energy loss in collisions and assumes &'a& a c'arged
par&icle loses energy con&inuously along i&s pa&' a& &'e linear ra&egi%en (y &'e ins&an&aneous s&opping power.
Reference: Radia&ion )ro&ec&ion Lompe&ency 8.8 p.8<
T'e fac&or &'a& a/ec&s &'e range of a c'arged par&icle in any ma&erial
is a uni& called densi&y!&'ic7ness. Density(thic9ness can (e
calcula&ed (y mul&iplying &'e densi&y of a ma&erial in grams per cu(ic
cen&ime&er *gVcm- (y &'e dis&ance &'e par&icle &ra%eled in &'a&
ma&erial in cen&ime&ers. T'e produc& is densi&y!&'ic7ness in uni&s of
grams per sHuare cen&ime&er *gVcm2
-. Densi&y!&'ic7ness can (econsidered a cross!sec&ional &arge& for a c'arged par&icle as i& &ra%els
&'roug' &'e ma&erial. T'e concep& of densi&y!&'ic7ness is impor&an& &o
discussions of (e&a radia&ion a&&enua&ion (y 'uman &issue, de&ec&or
s'ieldingVwindows, and dosime&ry =l&ers. +l&'oug' ma&erials may 'a%e
di/eren& densi&ies and &'ic7nesses, if &'eir densi&y!&'ic7ness %alues are
&'e same, &'ey will a&&enua&e (e&a radia&ion in a similar manner. >or
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eample, a piece of ylar used as a de&ec&or window wi&' a densi&y of
mgVcm2 will a&&enua&e (e&a radia&ion similar &o &'e ou&er layer of
dead s7in of &'e 'uman (ody w'ic' 'as a densi&y!&'ic7ness of
mgVcm2.
Reference: James E. Turner. Atoms, Radiation, and Radiation Protection,
p. 88
T'e mean free path is &'e mean dis&ance of &ra%el of a c'arged
par&icle (e&ween collisions. $& is &'e reciprocal of μ &'a& is &'e
macroscopic cross sec&ion, &'e pro(a(ili&y per uni& dis&ance of &ra%el
&'a& an elec&ronic collision &a7es place. *8V μ*
iii. Stopping po#er$ linear energy transfer$ linear energy transfer
Reference: James E. Turner. Atoms, Radiation, and Radiation Protection,
pp. 88#, 82Reference:
'&&p:VVwww.med.'ar%ard.eduVUpnmVp'ysicsVnml&dVradprinVsec&V.2V2.
.'&ml
S&opping power is &'e a%erage linear ra&e of energy loss of a 'ea%y
c'arged par&icle in a medium, designa&ed \d+Vd # , in eO cm\8. T'e
linear energy &ransfer *ZET- is &'e ra&e of energy &ransfer per uni&
dis&ance along a c'arged!par&icle &rac7 as &'e Huo&ien& \d+ZVd # . T'e
ZET is similar &o &'e s&opping power ecep& &'a& i& does no& include &'e
e/ec&s of radia&i%e energy loss *i.e., Bremss&ra'lung- or del&a!rays. T'e
di/erence (e&ween ZET and s&opping power is &'a& ZET is local energy
deposi&ion only and s&opping power is concerned wi&' &'e &o&al energy
los& (y &'e par&icle. T'e s&opping power and ZET are nearly eHual for
'ea%y c'arged par&iclesX for (e&as ZET does no& include del&a!rays nor
Bremss&ra'lung. T'e ZET is rela&ed &o Biological Damage. T'e se%eri&y
and permanence of (iological c'anges are direc&ly rela&ed &o &'e local
ra&e of energy deposi&ion along &'e par&icle &rac7. T'e 'ig'er &'e ZET,
&'e 'ig'er &'e Huali&y fac&or in de&ermining dose eHui%alen&.
iv. *ompton e:ect$ photoelectric e:ect$ pair production
Reference: Radia&ion )ro&ec&ion Lompe&ency 8.8 p.8<
Photoelectric ,:ect$n &'e p'o&oelec&ric e/ec& &'e p'o&on impar&s all of i&s energy &o an
or(i&al elec&ron of some a&om. T'e p'o&on, since i& consis&ed only of
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energy in &'e =rs& place,
simply %anis'es. T'e
energy is impar&ed &o
&'e or(i&al elec&ron in
&'e form of 7ine&icenergy of mo&ion,
o%ercoming &'e
a&&rac&i%e force of &'e
nucleus for &'e elec&ron
*&'e (inding energy- and
usually causing &'e
elec&ron &o Qy from i&s
or(i& wi&' considera(le %eloci&y. T'us, an ion pair resul&s. T'e
pro(a(ili&y of p'o&oelec&ric e/ec& a& i&s maimum, occurs w'en &'eenergy of &'e p'o&on is eHual &o &'e (inding energy of &'e elec&ron.
T'e &ig'&er an elec&ron is (ound &o &'e nucleus, &'e 'ig'er &'e
pro(a(ili&y of p'o&oelec&ric e/ec&, so mos& p'o&oelec&rons are inner
s'ell elec&rons. T'e p'o&oelec&ric e/ec& is seen primarily as an e/ec& of
low energy p'o&ons wi&' energies near &'e elec&ron (inding energies of
ma&erials and 'ig' ma&erials w'ose inner!s'ell elec&rons 'a%e 'ig'
(inding energies.
*ompton Scattering
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$n Lomp&on
sca&&ering &'ere is a
par&ial energy loss
for &'e incoming
p'o&on. T'e p'o&onin&erac&s wi&' an
or(i&al elec&ron of
some a&om and only
par& of &'e p'o&on
energy is &ransferred
&o &'e elec&ron. +f&er
&'e collision, &'e
p'o&on is deQec&ed in a di/eren& direc&ion a& a reduced energy. T'e
recoil elec&ron, now referred &o as a Lomp&on elec&ron, producessecondary ionia&ion in &'e same manner as does &'e p'o&oelec&ron,
and &'e sca&&ered p'o&on con&inues on un&il i& loses more energy in
ano&'er p'o&on in&erac&ion. T'e pro(a(ili&y of a Lomp&on in&erac&ion
increases for loosely (ound elec&rons and, &'erefore, increases
propor&ionally &o &'e of &'e ma&erial. Lomp&on sca&&ering is primarily
seen as an e/ec& of medium energy p'o&ons and i&s pro(a(ili&y
decreases wi&' increasing energy.
)'o&on energy af&er Lomp&on sca&&ering
)cos1(12
0
'
θ −+=
cm E
E E
r
r r
$ncoming p'o&on energy
)cos1(12
0
'
'
θ −−=
cm
E
E E
r
r r
+ngle of &'e p'o&on sca&&er
ϕ θ
tan12
cot2
0
+=
cm
E
* recoiled elec&rons angle-
Pair Production)air produc&ion occurs w'en &'e p'o&on is con%er&ed &o mass. $n pair
produc&ion a p'o&on simply disappears in &'e %icini&y of a nucleus and
in i&s place appears a pair of elec&rons: one nega&i%ely and one
posi&i%ely c'arged *an&i!par&icles are also called elec&ron and posi&ron
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respec&i%ely-. )air produc&ion is impossi(le unless &'e p'o&on
possesses grea&er &'an 8.322 eO of energy &o ma7e up &'e res& mass
of &'e par&icles. +ny ecess energy in &'e p'o&on a(o%e &'e 8.322 eO
reHuired &o crea&e &'e &wo elec&ron masses is simply s'ared (e&ween
&'e &wo elec&rons as 7ine&ic energy of mo&ion, and &'ey Qy ou& of &'ea&om wi&' grea& %eloci&y. T'e pro(a(ili&y increases for 'ig' ma&erials
and 'ig' energies. T'e pair produc&ion elec&ron &ra%els &'roug' ma&&er,
causing ionia&ions and eci&a&ions, un&il i& loses all of i&s 7ine&ic energy
and is Uoined wi&' an a&om. T'e posi&i%e elec&ron *7nown as a posi&ron-
also produces ionia&ions and eci&a&ions un&il i& comes &o res&. 0'ile a&
res&, &'e posi&ron a&&rac&s a free elec&ron, w'ic' &'en resul&s in
anni'ila&ion of &'e pair, con%er&ing (o&' in&o elec&romagne&ic energy.
T'us, &wo p'o&ons of #88 7eO eac' arise a& &'e si&e of &'e anni'ila&ion
*accoun&ing for &'e res& mass of &'e par&icles-. T'e ul&ima&e fa&e of &'eanni'ila&ion p'o&ons is ei&'er p'o&oelec&ric a(sorp&ion or Lomp&on
sca&&ering followed (y p'o&oelec&ric a(sorp&ion.
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v. &ttenuation coe;cients
Reference: Radia&ion )ro&ec&ion Lompe&ency 8.8 p.23
0'en s'ielding agains& !rays and gamma rays, i& is impor&an& &o
realie &'a& p'o&ons are remo%ed from &'e incoming (eam on &'e (asis
of &'e pro(a(ili&y of an in&erac&ion *p'o&oelec&ric, Lomp&on, or pair
produc&ion-. T'is process is called a&&enua&ion and can (e descri(ed
using &'e linear a&&enua&ion coefficien&, , w'ic' is &'e pro(a(ili&y of
an in&erac&ion per pa&' leng&' &'roug' a ma&erial. T'e linear
a&&enua&ion coeMcien& %aries wi&' p'o&on energy and &ype of ma&erial.
a&'ema&ically, &'e a&&enua&ion of a narrow (eam of monoenerge&icp'o&ons is gi%en (y:
xe x
µ −= 0)(
w'ere:$*- Radia&ion in&ensi&y ei&ing a ma&erial of &'ic7ness $o Radia&ion in&ensi&y en&ering a ma&eriale Base of na&ural logari&'ms *2.8"......- Zinear a&&enua&ion coefficien& T'ic7ness of ma&erial.
T'is eHua&ion s'ows &'a& &'e in&ensi&y is reduced eponen&ially wi&'
&'ic7ness. $*- ne%er ac&ually eHuals ero (ecause !rays and gamma
rays in&erac& (ased on pro(a(ili&y and &'ere is a =ni&e *al(ei& small-
pro(a(ili&y &'a& a gamma could pene&ra&e &'roug' a &'ic7 s'ield
wi&'ou& in&erac&ing. S'ielding for !rays and gamma rays &'en
(ecomes an +Z+R+ issue and no& an issue of s'ielding &o ero
in&ensi&ies.
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T'e formula a(o%e is used &o calcula&e &'e radia&ion in&ensi&y from a
narrow (eam (e'ind a s'ield of &'ic7ness , or &o calcula&e &'e
&'ic7ness of a(sor(er necessary &o reduce radia&ion in&ensi&y &o a
desired le%el. Ta(les and grap's are a%aila(le w'ic' gi%e %alues of
de&ermined eperimen&ally for di/eren& radia&ion energies and manya(sor(ing ma&erials. T'e larger &'e %alue of &'e grea&er &'e
reduc&ion in in&ensi&y for a gi%en &'ic7ness of ma&erial. T'e fac& &'a&
lead 'as a 'ig' for ! and gamma radia&ion is par&ially responsi(le for
i&s wide use as a s'ielding ma&erial.
vi. 'ayleigh scattering *oherent scattering0
Reference: >ran7 9. +&&i. $n&roduc&ion &o Radiological )'ysics and
Radia&ion Dosime&ry, p.8#
Rayleig' sca&&ering is called co'eren&; (ecause &'e p'o&on issca&&ered (y &'e com(ined ac&ion of &'e w'ole a&om. T'e e%en& is
elas&ic in &'e sense &'a& &'e p'o&on loses essen&ially none of i&s
energyX &'e a&om mo%es Uus& enoug' &o conser%e momen&um. T'e
p'o&on is usually redirec&ed &'roug' only a small angle. T'erefore &'e
e/ec& on a p'o&on (eam can only (e de&ec&ed in narrow!(eam
geome&ry. Rayleig' sca&&ering con&ri(u&es no&'ing &o 7erma or dose,
since no energy is gi%en &o any c'arged par&icle, nor is any ionia&ion
or eci&a&ion produced.
Reference: James E. Turner. Atoms, Radiation, and Radiation Protection,
pp. 8
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coeMcien&. $& follows &'a& e\ μ# is Uus& &'e pro(a(ili&y *i.e., NVN3- &'a& a
normally inciden& p'o&on will &ra%erse a sla( of &'ic7ness # wi&'ou&
in&erac&ing. T'e fac&or e\ μ# &'us generally descri(es &'e frac&ion of
uncollided p'o&ons; &'a& go &'roug' a s'ield.
+& low p'o&on energies &'e (inding of &'e a&omic elec&rons is impor&an&
and &'e p'o&oelec&ric e/ec& is &'e dominan& in&erac&ion. 9ig'!
ma&erials pro%ide grea&er a&&enua&ion and a(sorp&ion, w'ic' decrease
rapidly wi&' increasing p'o&on energy. T'e coeMcien&s for )( and C
rise a(rup&ly w'en &'e p'o&on energy is suMcien& &o eUec& a
p'o&oelec&ron from &'e K s'ell of &'e a&om. 0'en &'e p'o&on energy is
se%eral 'undred 7eO or grea&er, &'e (inding of &'e a&omic elec&rons
(ecomes rela&i%ely unimpor&an& and &'e dominan& in&erac&ion is
Lomp&on sca&&ering. Since &'e elemen&s *ecep& 'ydrogen- con&ain
a(ou& &'e same num(er of elec&rons per uni& mass, &'ere is no& a large
di/erence (e&ween &'e %alues of &'e mass a&&enua&ion coeMcien&s for
&'e di/eren& ma&erials.
T'ere are s'arp increases in &'e a&&enua&ion coeMcien& for &'e
p'o&oelec&ric e/ec& w'en &'e p'o&on energy Uus& eceeds &'e (inding
energy of &'e elec&ron s'ell *K s'ell- of a&om.
+#ample0'a& &'ic7ness of concre&e and of lead are needed &o reduce &'e
num(er of #33!
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7eO p'o&ons in a narrow (eam &o one!four&' &'e inciden& num(er5
Lompare &'e&'ic7nesses in cm and in g cm\2.Sol"tion0e use EH. *
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+n eample is gamma!ray cap&ure (y a 23)( nucleus wi&' emission of
a neu&ron: 23or &'ese reasons,
p'o&onuclear reac&ions can (e impor&an& around 'ig'!energy elec&ron
accelera&ors &'a& produce energe&ic p'o&ons.
T'e &'res'olds for *, p- reac&ions are of&en 'ig'er &'an &'ose for *, n-
reac&ions (ecause of &'e repulsi%e Loulom( (arrier &'a& a pro&on mus&
o%ercome &o escape from &'e nucleus. +l&'oug' &'e pro(a(ili&y for
ei&'er reac&ion is a(ou& &'e same in &'e lig'&es& elemen&s, &'e *, n-
reac&ion is many &imes more pro(a(le &'an *, p- in 'ea%y elemen&s.
+#ampleLompu&e &'e &'res'old energy for &'e *,n- p'o&odisin&egra&ion of
23
)(. 0'a& is &'e energy of a neu&ron produced (y a(sorp&ion of a 83!eO p'o&on5Sol"tion
T'e mass di/erences, -, from +ppendi D, are \2. eO for 23)(, \
2. eO for 23#)(, and
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Kerma is de=ned as &'e &o&al ini&ial 7ine&ic energy of all c'arged
par&icles li(era&ed (y unc'arged radia&ion *or indirec&ly ioniing
radia&ion: p'o&ons and neu&rons- per uni& mass of mass. T'is Huan&i&y,
w'ic' 'as &'e dimensions of a(sor(ed dose, is called &'e erma
*Kine&ic Energy Released per uni& +ss-. By de=ni&ion, 7erma includes
energy &'a& may su(seHuen&ly appear as (remss&ra'lung and i& also
includes +uger!elec&ron energies. T'e 7erma decreases s&eadily
(ecause of &'e a&&enua&ion of &'e primary radia&ion wi&' increasing
dep&'. Speci=cally, 7erma and a(sor(ed dose a& a poin& in an irradia&ed
&arge& are eHual w'en c'arged!par&icle eHuili(rium eis&s &'ere and
(remss&ra'lung losses are negligi(le.
dm
dE " tr =
L'arged par&icle eHuili(rium *L)E- eis&s for &'e %olume O if eac'
c'arged par&icle of a gi%en &ype and energy lea%ing O is replaced (y an
iden&ical par&icle of &'e same energy en&ering in &erms of epec&a&ion
%alues.
ii. &bsorbed dose
Reference: James E. Turner. Atoms, Radiation, and Radiation Protection,
pp. 2!
T'e primary p'ysical Huan&i&y used in dosime&ry is &'e a(sor(ed dose.
$& is de=ned as &'e energy a(sor(ed per uni& mass from any 7ind of
ioniing radia&ion in any &arge&. T'e uni& of a(sor(ed dose, J 7g\8, is
called &'e gray *Iy-. T'e older uni&, &'e rad, is de=ned as 833 erg g \8.
*8Iy833rad-.)'o&ons produce secondary elec&rons in air, for w'ic' &'e a%erage
energy needed &o ma7e an ion pair is & " eO ip\8 " JL\8.
#! $ %
$
#!
% R /1076.8
341058.21
34
−−
×=××
=
T'us, an eposure of 8 R gi%es a dose in air of
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iii. ,7posure
Reference: James E. Turner. Atoms, Radiation, and Radiation Protection,
p. 2
Eposure is de=ned for gamma and 6 rays in &erms of &'e amoun& of
ionia&ion &'ey produce in air. T'e uni& of eposure is called &'e
roen&gen *R-. T'e roen&gen is de=ned as &'e amoun& of energy
reHuired &o li(era&e 2.#< A 83!" L of c'arge from 8 7g of air a& s&andard
&empera&ure *2 K- and pressure *3 mm9g-. *8R 2.#
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M
NaW
T N A
⋅==
2/1
693.0λ
s
%i
mole !
moleatoms !
s086.0
/107.3
1
/137
/1002.610
36002436517.30
693.010
233
=×⋅××⋅×××=
−
Eposure ra&e a& dis&ance r 8m from a poin& source of ac&i%i&y
3.3or eample, &'e de&ec&or ma&erial of
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scin&illa&ion de&ec&or emi&s %isi(le lig'&. T'e lig'& s&ri7es &'e p'o&o ca&'ode
crea&ing elec&ron in &'e )*p'o&omul&iplier- &u(e.Some of &'e p'ysical and c'emical radia&ion e/ec&s &'a& apply &o radia&ion
de&ec&ion and measuremen& for 'eal&' p'ysics purposes are lis&ed in Ta(le
(elow.
b. +as(>lled detectors
Reference: a&ional uclear Securi&y +dminis&ra&ion. uali=ca&ion S&andard
Reference Iuide \ Radia&ion )ro&ec&ion, pp."
Methods in Radiation Physics, pp.2"8!38
Reference: 9erman Lem(er. Health Physics. 4th edition, p."2
Eac' &ype of radia&ion 'as a speci=c pro(a(ili&y of in&erac&ion wi&' &'e
de&ec&or media. T'is pro(a(ili&y %aries wi&' &'e energy of &'e inciden&
radia&ion and &'e c'arac&eris&ics of &'e de&ec&or gas. T'e pro(a(ili&y of
in&erac&ion is epressed in &erms of speci=c ionia&ion wi&' uni&s of ion pairs
per cen&ime&er. + radia&ion wi&' a 'ig' speci=c ionia&ion, suc' as alp'a, will
produce more ion pairs in eac' cen&ime&er &'a& i& &ra%els &'an will a radia&ion
wi&' a low speci=c ionia&ion suc' as gamma.
Ienerally, &'e pro(a(ili&y of in&erac&ion (e&ween &'e inciden& par&icle radia&ion
and &'e de&ec&or gas *and &'erefore &'e produc&ion of ions- decreases wi&'
increasing radia&ion energy. $n p'o&on in&erac&ions, &'e o%erall pro(a(ili&y of
in&erac&ion increases (ecause of &'e increasing con&ri(u&ion of &'e pair
produc&ion reac&ions. +s &'e energy of &'e par&icle radia&ion decreases, &'e
pro(a(ili&y of in&erac&ion increases, no& only in &'e gas, (u& also in &'e
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ma&erials of cons&ruc&ion. Zow energy radia&ions may (e a&&enua&ed (y &'e
walls of &'e de&ec&or and no& reac' &'e gas %olume. +s &'e num(er of
radia&ion e%en&s s&ri7ing a de&ec&or increases, &'e o%erall pro(a(ili&y of an
in&erac&ion occurring wi&' &'e forma&ion of an ion pair increases. $n addi&ion,
&'e num(er of ion pairs crea&ed increases and &'erefore de&ec&or responseincreases.
T'e pro(a(ili&y of an in&erac&ion occurring (e&ween &'e inciden& radia&ion and
a gas a&om increases as &'e num(er of a&oms presen& increases. + larger
de&ec&or %olume o/ers more &arge&s; for &'e inciden& radia&ion, resul&ing in a
larger num(er of ion pairs. Since, eac' radia&ion 'as a speci=c ionia&ion in
&erms of ion pairs per cen&ime&er, increasing &'e de&ec&or sie also increases
&'e leng&' of &'e pa&' &'a& &'e radia&ion &ra%erses &'roug' &'e de&ec&or. T'e
longer &'e pa&', &'e larger &'e num(er of ion pairs.
onoenerge&ic (eam of par&icles s&opping in parallel!pla&e ionia&ion c'am(er
wi&' %aria(le po&en&ial di/erence / applied across pla&es )8 and )2
T'e amoun& of energy epended in &'e crea&ion of an ion pair is a func&ion of
&'e &ype of radia&ion, &'e energy of &'e radia&ion, and &'e c'arac&eris&ics of
&'e a(sor(er *in &'is case, &'e gas-. T'is energy is referred &o as &'e ionia&ion
po&en&ial, or 0!Oalue, and is epressed in uni&s of elec&ron %ol&s *eO- per ion
pair. Typical gases 'a%e 0!Oalues of 2#!#3 eO, wi&' an a%erage of a(ou& " eO
per ion pair.
$n &'e sec&ion on de&ec&or sie, i& was s'own &'e pro(a(ili&y of in&erac&ion
increases wi&' de&ec&or sie. $n many cases, &'ere is a prac&ical limi& &o
de&ec&or sie. $ns&ead of increasing de&ec&or sie &o increase &'e num(er of
&arge&; a&oms, increasing &'e pressure of &'e gas will accomplis' &'e same
goal. Ias under pressure 'as a 'ig'er densi&y *more a&oms per cm - &'an a
gas no& under pressure, and &'erefore o/ers more &arge&s, a 'ig'er pro(a(ili&y
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of in&erac&ion, and grea&er ion pair produc&ion. >or eample, increasing &'e
pressure of a &ypical gas &o 833 psig increases &'e densi&y (y a(ou& &imes.
4nce &'e ion pair is crea&ed, i& mus& (e collec&ed in order &o produce an ou&pu&
pulse or curren& Qow from &'e de&ec&or. $f lef& undis&ur(ed, &'e ion pairs will
recom(ine, and no& (e collec&ed. $f a %ol&age po&en&ial is applied across &'e
elec&rodes, a =eld is crea&ed in &'e de&ec&ors, and &'e ion pairs will (e
accelera&ed &owards &'e elec&rodes. T'e s&ronger &'e =eld, &'e s&ronger &'e
accelera&ion. +s &'e %eloci&y of &'e elec&ron increases, &'e elec&ron may cause
one or more ionia&ions on i&s own. T'is process is 7nown as secondary
ionia&ion. T'e secondary ion pairs are accelera&ed &owards &'e elec&rode and
collec&ed, resul&ing in a s&ronger pulse &'an would 'a%e (een crea&ed (y &'e
ions from primary ionia&ion.
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$f &'e applied %ol&age po&en&ial is %aried from 3 &o a 'ig' %alue, and &'e pulse
sie recorded, a response cur%e will (e o(ser%ed. >or &'e purposes of
discussion, &'is cur%e is (ro7en in&o si regions. T'e ion c'am(er region, &'e
propor&ional region, and &'e Ieiger!tller region are useful for de&ec&or
designs used in radiological con&rol. 4&'er regions are no& useful. $n &'erecom(ina&ion region, &'e applied %ol&age is insuMcien& &o collec& all of &'e ion
pairs (efore some of &'em recom(ine.
+s &'e %ol&age &o &'e de&ec&or is increased, a poin& is reac'ed a& w'ic'
essen&ially all of &'e ions are collec&ed (efore &'ey can recom(ine. o
secondary ionia&ion or gas ampli=ca&ion occurs. +& &'is poin&, &'e ou&pu&
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curren& of &'e de&ec&or will (e a& a maimum for a gi%en radia&ion in&ensi&y
and will (e propor&ional &o &'a& inciden& radia&ion in&ensi&y. +lso, &'e ou&pu&
curren& will (e rela&i%ely independen& of small Quc&ua&ions in &'e power supply.
T'e ou&pu& of a gas!=lled de&ec&or w'en 833N of &'e primary ion pairs are
collec&ed is called &'e sa&ura&ion curren&.
$f &'e applied %ol&age po&en&ial is %aried from 3 &o a 'ig' %alue, and &'e pulse
sie recorded, a response cur%e will (e o(ser%ed. >or &'e purposes of
discussion, &'is cur%e is (ro7en in&o si regions.
%he %hree Re)ions 0se1"l 1or Radiation 2etection and Meas"rement T'e ion c'am(er region, &'e propor&ional region, and &'e Ieiger!tller region
are useful for de&ec&or designs used in radiological con&rol. 4&'er regions are
no& useful. $n &'e recom(ina&ion region, &'e applied %ol&age is insuMcien& &o
collec& all of &'e ion pairs (efore some of &'em recom(ine. $n &'e limi&ed
propor&ional region, nei&'er &'e ou&pu& curren& nor &'e num(er of ou&pu&
pulses are propor&ional &o &'e radia&ion le%el. Lali(ra&ion is impossi(le. $n &'e
con&inuous disc'arge region, &'e %ol&age is suMcien& &o cause arcing and
(rea7down of &'e de&ec&or gas.
%he Se"ence o1 +ents that 5cc"r 6ollo(in) an nitial oni8in) +ent in an
oni8ation 9ham:er, a Proportional 9o"nter and a ;ei)er'M
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%o(nsend aalanche. 0'en &'is 'appens, &'e end of &'e propor&ional region is
reac'ed and &'e Ieiger region (egins. +& &'is poin&, &'e sie of all pulses !
regardless of &'e na&ure of &'e primary ioniing par&icle ! is &'e same. 0'en
opera&ed in &'e Ieiger region, &'erefore, a coun&er canno& dis&inguis' among
&'e se%eral &ypes of radia&ions. 9owe%er, &'e %ery large ou&pu& pulses *`3.2#O- &'a& resul& from &'e 'ig' gas ampli=ca&ion in a Ieiger!uller *I- coun&er
means ei&'er &'e comple&e elimina&ion of a pulse ampli=er or use of an
ampli=er &'a& does no& 'a%e &o mee& &'e eac&ing reHuiremen&s of 'ig' pulse
ampli=ca&ion. Since all &'e pulses in a I coun&er are a(ou& &'e same 'eig'&,
&'e pulse 'eig'& is independen& of energy deposi&ion in &'e gas.
c. Scintillation detectors
Reference: a&ional uclear Securi&y +dminis&ra&ion. uali=ca&ion S&andard
Reference Iuide \ Radia&ion )ro&ec&ion, p.#2
Reference: 9erman Lem(er. Health Physics. 4th edition, pp."!"<
Scin&illa&ion de&ec&ors measure radia&ion (y analying &'e e/ec&s of &'e
eci&a&ion of &'e de&ec&or ma&erial (y &'e inciden& radia&ion. Scin&illa&ion is &'e
process (y w'ic' a ma&erial emi&s lig'& w'en eci&ed. $n a scin&illa&ion
de&ec&or, &'is emi&&ed lig'& is collec&ed and measured &o pro%ide an indica&ion
of &'e amoun& of inciden& radia&ion. umerous ma&erials scin&illa&e ! liHuids,
solids, and gases. + common eample is a &ele%ision pic&ure ma&erial w'ic'
scin&illa&es is commonly called a p'osp'or or a Quor. T'e scin&illa&ions are
commonly de&ec&ed (y a p'o&omul&iplier &u(e.
+ scin&illa&ion de&ec&or is a &ransducer &'a& c'anges &'e 7ine&ic energy of an
ioniing par&icle in&o a Qas' of lig'&. Scin&illa&ion coun&ers are widely used &o
coun& gamma rays and low!energy (e&a par&icles.
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d. Semiconduc&or de&ec&ors
Reference: a&ional uclear Securi&y +dminis&ra&ion. uali=ca&ion S&andard
Reference Iuide \ Radia&ion )ro&ec&ion, pp.#2!#
o&e: Solid!s&a&e de&ec&ors are more commonly referred &o as semiconduc&or
de&ec&ors *for eample, germanium \ a common semiconduc&or used in
radia&ion de&ec&ion-.$f a s&rong elec&ric =eld is applied &o &'e crys&al, &'e elec&ron in &'e conduc&ion
(and mo%es in accordance wi&' &'e applied =eld. Similarly, in &'e group of
=lled (ands, an elec&ron from a lower energy (and mo%es up &o =ll &'e 'ole
*%acancy- in &'e %alence (and. T'e 'ole i& lea%es (e'ind is =lled (y an
elec&ron from ye& a lower energy (and. T'is process con&inues, so &'e ne&
e/ec& is &'a& &'e 'ole appears &o mo%e down &'roug' &'e energy (ands in &'e
=lled group. T'us, &'e elec&ron mo%es in one direc&ion in &'e un=lled group of
(ands, w'ile &'e 'ole mo%es in &'e opposi&e direc&ion in &'e =lled group of (ands. T'is can (e li7ened &o a line of cars awai&ing a &oll (oo&', &'e &oll (oo&'
(eing &'e for(idden (and. +s a car lea%es &'e =lled %alence (and for &'e
un=lled conduc&ance (and, a 'ole is formed. T'e ne& car in line =lls &'is 'ole,
and crea&es a 'ole, and so on. LonseHuen&ly, &'e 'ole appears &o mo%e (ac7
&'roug' &'e line of cars.
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+ny impuri&ies in &'e crys&alline s&ruc&ure can a/ec& &'e conduc&ing a(ili&y of
&'e crys&alline solid. T'ere are always some impuri&ies in a semiconduc&or, no
ma&&er 'ow pure; i& is. 9owe%er, in &'e fa(rica&ion of semiconduc&ors,
impuri&ies are in&en&ionally added under con&rolled condi&ions. $f &'e impuri&y
added 'as an ecess of ou&er elec&rons, i& is 7nown as a donor impuri&y,(ecause &'e e&ra; elec&ron can easily (e raided or dona&ed &o &'e
conduc&ion (and. $n e/ec& &'e presence of &'is donor impuri&y decreases &'e
gap; (e&ween &'e group of =lled (ands and &'e group of un=lled (ands. Since
conduc&ion occurs (y &'e mo%emen& of a nega&i%e c'arge, &'e su(s&ance is
7nown as an n!&ype ma&erial. Similarly, if &'e impuri&y does no& con&ain
enoug' ou&er elec&rons, a %acancy or 'ole eis&s. T'is 'ole can easily accep&
elec&rons from o&'er energy le%els in &'e group of =lled (ands, and is called an
accep&or su(s&ance. +l&'oug' elec&rons mo%e &o =ll 'oles, as descri(ed a(o%e,
&'e appearance is &'a& &'e 'oles mo%e in &'e opposi&e direc&ion. Since &'isimpuri&y gi%es &'e appearance of posi&i%e 'oles mo%ing, i& is 7nown as a p!
&ype ma&erial. Since any crys&alline ma&erial 'as some impuri&ies in i&, a gi%en semiconduc&or
will (e an n!&ype or a p!&ype depending on w'ic' concen&ra&ion of impuri&y is
'ig'er. $f &'e num(er of n!&ype impuri&ies is eac&ly eHual &o &'e num(er of p!
&ype impuri&ies, &'e crys&alline ma&erial is referred &o as an in&rinsic
semiconduc&or.;
+ semiconduc&or &'a& 'as (een doped; wi&' &'e proper amoun& of &'e correc&&ype of impuri&y &o ma7e &'e energy gap (e&ween &'e &wo groups of (ands
Uus& rig'& ma7es a good radia&ion de&ec&or. + c'arged par&icle loses energy (y
crea&ing elec&ron!'ole pairs.
$f &'e semiconduc&or is connec&ed &o an e&ernal elec&rical =eld, &'e collec&ion
of elec&ron!'ole pairs can lead &o an induced c'arge in &'e e&ernal circui&
muc' as &'e collec& of elec&ron!posi&i%e a&om pairs *ion pairs- is used &o
measure radia&ion in an ion c'am(er. T'erefore, &'e semi!conduc&or de&ec&or
relies on &'e collec&ion of elec&ron!'ole pairs &o produce a usa(le elec&rical
signal.
4ne disad%an&age of &'e semiconduc&or de&ec∨ is &'a& &'e impuri&ies, in
addi&ion &o con&rolling &'e sie of &'e energy gap also ac& as &raps. +s
elec&rons *or 'oles- mo%e &'roug' &'e crys&alline ma&erial, &'ey are a&&rac&ed
&o &'e impuri&y areas or cen&ers (ecause &'ese impuri&y cen&ers usually 'a%e
a ne& c'arge. T'e carrier *elec&ron or 'ole- may (e &rapped for a w'ile a& &'e
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impuri&y cen&er and &'en released. +s i& (egins &o mo%e again, i& may (e
&rapped a& ano&'er impuri&y cen&er and &'en released again. $f &'e elec&ron or
'ole is delayed long enoug' during &ransi& &'roug' &'e crys&al, i& may no& add
&o &'e elec&rical ou&pu&.
T'us, al&'oug' &'e carrier is no& ac&ually los&, &'e ne& e/ec& on readou& is &'a&
i& is los&. +no&'er disad%an&age of &'e semiconduc&or de&ec&or is &'a& &'e
presence of impuri&ies in &'e crys&al is 'ard &o con&rol &o 7eep &'e energy gap
w'ere i& is desired. + newer &ec'niHue, &'e Uunc&ion coun&er, 'as (een
de%eloped &o o%ercome &'ese disad%an&ages.
$n a semiconduc&or Uunc&ion coun&er, an n!&ype su(s&ance is uni&ed wi&' a p!
&ype su(s&ance. 0'en &'e &wo are
di/used &oge&'er &o ma7e a
di/used Uunc&ion, a deple&ion layer
is crea&ed (e&ween &'e &wo
ma&erials. *T'is deple&ion layer is
formed (y &'e di/usion of elec&rons
from &'e n!&ype ma&erial in&o &'e p!
&ype ma&erial and &'e di/usion of
'oles from &'e p!&ype ma&erial in&o
&'e n!&ype ma&erial.-
T'is resul&s in a narrow region w'ic' is deple&ed of carriers and w'ic' (e'a%es
li7e an insula&or (ounded (y conduc&ing elec&rodes. T'a& is, a ne& c'arge on
eac' side of &'e deple&ion region impedes &'e fur&'er &ransfer of c'arge. T'is
c'arge is posi&i%e in &'e n!region and nega&i%e in &'e p!region. T'is (arrier can
(e (ro7en if we apply an e&ernal %ol&age &o &'e sys&em and apply i& wi&' &'e
proper (ias. + forward (ias; is applied w'en we connec& &'e posi&i%e
elec&rode &o &'e p!region. $n &'is case, &'e (arrier (rea7s down and elec&rons
Qow across &'e Uunc&ion. 9owe%er, if we apply a re%erse (ias; *nega&i%e
elec&rode connec&ed &o &'e p!region-, &'e (arrier 'eig'& is increased and &'e
deple&ed region is e&ended.
+ fur&'er ad%ancemen& in Uunc&ion coun&ers is &'e p!n &ype. T'is coun&er 'as
an in&rinsic region (e&ween &'e n and p surface layers. *+n in&rinsic
semiconduc&or was discussed earlier and is e/ec&i%ely a pure semiconduc&or.-
T'e presence of an in&rinsic region e/ec&i%ely crea&es a &'ic7er deple&ion area.
+ germanium!li&'ium Ie*Zi- de&ec&or is an eample of &'is &ype of de&ec&or.
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Zi&'ium *an n!&ype ma&erial- is di/used in&o p!&ype germanium. T'e n!p
Uunc&ion &'a& resul&s is pu& under re%erse (ias, and &'e &empera&ure of &'e
ma&erial is raised. Cnder &'ese condi&ions, &'e li&'ium ions drif& &'roug' &'e
germanium, (alancing n and p ma&erial and forming an in&rinsic region.
T'e 'ea& and (ias are remo%ed and &'e crys&al cooled Huic7ly &o liHuid
ni&rogen &empera&ures. T'is in&rinsic region ser%es as &'e region in w'ic'
in&erac&ions can &a7e place. T'e in&rinsic region can (e &'oug'& of as a (uil&!in
deple&ion region.
Due &o &'e large sie of &'e deple&ion region and &'e reduced mo(ili&y of &'e
elec&rons and 'oles due &o &'e depressed &empera&ure, a 'ig' c'arge is
necessary &o cause conduc&ion. T'e c'arge is c'osen 'ig' enoug' &o collec&
ion pairs, (u& low enoug' &o pre%en& noise.
Due &o &'e increased s&opping power of germanium o%er air a& !28o> &'eenergy reHuired &o crea&e an ion pair is only 2. eO compared &o . eO for
air. T'is means &'a& (y &'eory, a germanium de&ec&or will respond &o any
radia&ion &'a& will crea&e ion pairs. $n ac&uali&y, 'owe%er, &'e response &o
radia&ions o&'er &'an gamma is limi&ed (y &'e ma&erials surrounding &'e
de&ec&or, ma&erial necessary &o main&ain &empera&ure. +no&'er considera&ion
limi&ing response is &'e geome&ry of &'e crys&al. T'e mos& eMcien& response
occurs w'en &'e in&erac&ion &a7es place in &'e cen&er of &'e in&rinsic region,
&'is can only occur for gamma.
Radia&ion in&erac&s wi&' a&oms in &'e in&rinsic region &o produce elec&ron 'olepairs. T'e presence of ion pairs in &'e deple&ion region causes curren& Qow.
T'is is similar &o a &ransis&or, in &'a& ins&ead of inducing c'arges in &'e cen&er
sec&ion *&'e (ase in a &ransis&or- (y a (a&&ery or ano&'er source, &'e c'arge is
induced (y &'e crea&ion of ion pairs. Since i& is no& necessary for &'e ion
produced &o reac' &'e p and n region &o (e collec&ed, as in a gas =lled
c'am(er, &'e response is fas&er.
Since &'e num(er of ion pairs produced is a func&ion of &'e inciden& energy,
and &'e resul&ing curren& is a func&ion of &'e amoun& of ion pairs, Ie*Zi-
response is in &erms of energy.
e. Special detectors
Reference: a&ional uclear Securi&y +dminis&ra&ion. uali=ca&ion S&andard
Reference Iuide \ Radia&ion )ro&ec&ion, pp.2!#
Thermoluminescent Dosimeter
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T'ermoluminescence *TZ- is &'e a(ili&y of some ma&erials &o con%er& &'e
energy from radia&ion &o a radia&ion of a di/eren& wa%eleng&', normally in &'e
%isi(le lig'& range. T'ere are &wo ca&egories of &'ermoluminescence:
Quorescence and p'osp'orescence.>luorescence
T'is is emission of lig'& during or immedia&ely af&er irradia&ion of &'e
p'osp'or. T'is is no& a par&icularly useful reac&ion for &'ermoluminescen&
dosime&ry *TZD- use.)'osp'orescence
T'is is &'e emission of lig'& af&er &'e irradia&ion period. T'e delay &ime can (e
from a few seconds &o wee7s or mon&'s. T'is is &'e principle of opera&ion used
for TZD. T'e proper&y of &'ermoluminescence of some ma&erials is &'e main
me&'od used for personnel dosime&ers a& D4E facili&ies. TZDs use p'osp'orescence as &'eir means of de&ec&ion of radia&ion. Elec&rons
in some solids can eis& in &wo energy s&a&es, called &'e %alence (and and &'e
conduc&ion (and. T'e di/erence (e&ween &'e &wo (ands is called &'e (and
gap. Elec&rons in &'e conduc&ion (and or in &'e (and gap 'a%e more energy
&'an &'e %alence (and elec&rons. ormally in a solid, no elec&rons eis& in
energy s&a&es con&ained in &'e (and gap. T'is is a for(idden region.;$n some ma&erials, defec&s in &'e ma&erial eis& or impuri&ies are added &'a&
can &rap elec&rons in &'e (and gap and 'old &'em &'ere. T'ese &rapped
elec&rons represen& s&ored energy for &'e &ime &'a& &'e elec&rons are 'eld, as
s'own (elow in =gure
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$n mos& ma&erials, &'is energy is gi%en up as 'ea& in &'e surrounding ma&erial,
'owe%er, in some ma&erials a por&ion of energy is emi&&ed as lig'& p'o&ons.
T'is proper&y is called luminescence. 9ea&ing of &'e TZ ma&erial causes &'e
&rapped elec&rons &o re&urn &o &'e %alence (and. 0'en &'is 'appens, energy is
emi&&ed in &'e form of %isi(le lig'&. T'e lig'& ou&pu& is de&ec&ed and measured
(y a p'o&omul&iplier &u(e and a dose eHui%alen& is &'en calcula&ed. + &ypical
(asic TZD reader con&ains &'e following componen&s:• 9ea&er ! raises &'e p'osp'or &empera&ure• )'o&omul&iplier &u(e ! measures &'e lig'& ou&pu&• e&erVRecorder ! display and record da&a
+ glow cur%e can (e o(&ained from &'e 'ea&ing process. T'e lig'& ou&pu& from
TZ ma&erial is no& easily in&erpre&ed. ul&iple pea7s resul& as &'e ma&erial is
'ea&ed and elec&rons &rapped in s'allow; &raps are released. T'is resul&s in a
pea7 as &'ese &raps are emp&ied. T'e lig'& ou&pu& drops o/ as &'ese &raps are
deple&ed. +s 'ea&ing con&inues, &'e elec&rons in deeper &raps are released.
T'is resul&s in addi&ional pea7s. Csually &'e 'ig'es& pea7 is used &o calcula&e
&'e dose eHui%alen&. T'e area under &'e cur%e represen&s &'e radia&ion energy
deposi&ed on &'e TZD.
Albedo DosimeterReference: Radia&ion )ro&ec&ion Lompe&ency 8.. p.R) 8.!8
TZDs used &o de&ec& neu&rons incorpora&e &wo iso&opes of li&'ium, Zi! and Zi!
, (o&' of w'ic' are eHually sensi&i%e &o gamma radia&ion. 9owe%er, Zi! 'as a
large cross sec&ion for &'e &'ermal neu&ron *n, - reac&ion. )roduc&ion of &'e
alp'a par&icle ini&ia&es &'e &'ermoluminescence process &'a& ul&ima&ely resul&sin a measure of &'e dose due &o &'ermal neu&ronsX w'ereas, Zi! is rela&i%ely
insensi&i%e &o &'ermal neu&rons. T'e Zi! p'osp'or will read (o&' neu&ron and
gamma radia&ion in&erac&ionsX w'ereas, &'e Zi! p'osp'or will read only
gamma in&erac&ions. eu&ron dose is de&ermined (y su(&rac&ing &'e Zi!
reading *r- from &'e Zi! reading *nr- and applying a con%ersion fac&or &o &'e
di/erence.
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T'e &erm al(edo s&ands for reQec&ing. Some of &'e &'ermal neu&rons de&ec&ed
(y &'e Zi! are originally fas& neu&rons &'a& in&erac& wi&' 'ydrogen in &'e (ody,
are &'ermalied, reQec&ed or sca&&ered o/ &'e (ody and de&ec&ed. T'is ma7es
&'e al(edo dosime&er posi&ion sensi&i%eX &'erefore, i& mus& (e properly
orien&a&ed. Because &'e neu&rons can (e modera&ed &o &'ermal energies, &'ey
are reQec&ed from &'e (ody &'roug' &'e (ac7 of &'e (adge in&o &'e al(edo
dosime&er. T'erefore, i& is impor&an& &o wear &'e dosime&er e&remely close &o
&'e (ody *on &'e Qes'- &o o(&ain accura&e measuremen&s. T'e fron& of &'e
(adge is s'ielded wi&' cadmium &o reUec& e&ernal &'ermal neu&rons.
Pocket Dosimeter)oc7e& dosime&ers are compac&, easy!&o!carry de%ices &'a& indica&e an
indi%iduals accumula&ed dose &o radia&ion a& any&ime, &'us elimina&ing &'e
delay of =lm (adgeVTZD processing. 9owe%er, (ecause of &'e possi(ili&y of
faul&y readings due &o roug' &rea&men&, &'e dosime&er reading does no&
cons&i&u&e a permanen& legal record of dose recei%ed. + poc7e& dosime&er can
(e self!reading or no&. $n &'e self!reading &ype, a small compound microscope
is used &o o(ser%e &'e response. T'e &ype w'ic' is no& self!reading, called &'e
poc7e& c'am(er, is similar in cons&ruc&ion &o &'e self!reading &ype, (u& ano&'er
ins&rumen& called &'e c'arger reader mus& (e used &o read i&. T'e self!reading
&ype is normally preferred since i& can (e read anyw'ere and a& any &ime.+ self!reading poc7e& dosime&er consis&s of a small air!=lled c'am(er in w'ic'
a Huar& =(er elec&rome&er, a small microscope and a gradua&ed scope across
w'ic' &'e s'adow of &'e Huar& =(er mo%es &o indica&e &'e applied dose, is
suspended. T'e design and opera&ion of a self!reading poc7e& dosime&er u&ilies &'e
principle of disc'arging a pair of opposi&e c'arged surfaces w'en &'e air
(e&ween &'em is eposed &o ioniing radia&ion. T'e elec&ric c'arge reHuired &o
a&&rac& &'e ionied gas par&icles is impressed on &'e elec&rome&er and &'e
c'am(er wall (y means of a sui&a(le c'arging uni&. $oniing radia&ion
pene&ra&ing &'e c'am(er forms posi&i%ely and nega&i%ely c'arged gas
par&icles. T'ese c'arged par&icles are a&&rac&ed &o &'e opposi&ely c'arged
surfaceX i.e., &'e nega&i%e par&icles are a&&rac&ed &o &'e elec&rome&er and &'e
posi&i%e par&icles are a&&rac&ed &o &'e c'am(er wall. T'e migra&ion of &'e
nega&i%e par&icles &o &'e elec&rome&er permi&s &'e =(er &o mo%e closer &o &'e
frame, w'ic' in &urn causes &'e s'adow of &'e =(er &o mo%e across &'e
cali(ra&ed scale.
Film Badge
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Reference: James E. Turner. Atoms, Radiation, and Radiation Protection, pp.
2#!2.
>ilm emulsions con&ain small crys&als of a sil%er 'alide *e.g., +gBr-, suspended
in a gela&ine layer spread o%er a plas&ic or glass surface, wrapped in lig'&!&ig'&
pac7aging. Cnder &'e ac&ion of ioniing radia&ion, some secondary elec&rons
released in &'e emulsion (ecome &rapped in &'e crys&alline la&&ice, reducing
sil%er ions &o a&omic sil%er. Lon&inued &rapping leads &o &'e forma&ion of
microscopic aggrega&es of sil%er a&oms, w'ic' comprise &'e la&en& image.
0'en de%eloped, &'e la&en& images are con%er&ed in&o me&allic sil%er, w'ic'
appears &o &'e eye as dar7ening of &'e =lm. T'e degree of dar7ening, called
&'e op&ical densi&y, increases wi&' &'e amoun& of radia&ion a(sor(ed. +n
op&ical densi&ome&er can (e used &o measure lig'& &ransmission &'roug' &'e
de%eloped =lm.
Doses from gamma and (e&a radia&ion can (e inferred (y comparingdensi&ome&er readings from eposed =lm (adges wi&' readings from a
cali(ra&ed se& of =lms gi%en di/eren&, 7nown doses under &'e same
condi&ions. T'e dar7ening response of =lm &o neu&rons, on &'e o&'er 'and, is
&oo wea7 &o (e used in &'is way for neu&ron personnel moni&oring.>ilm cali(ra&ion and &'e use of densi&ome&er readings &o o(&ain dose would
appear, in principle, &o (e s&raig'&forward. $n prac&ice, 'owe%er, &'e procedure
is complica&ed (y a num(er of fac&ors. >irs&, &'e densi&y produced in =lm from
a gi%en dose of radia&ion depends on &'e emulsion &ype and &'e par&icular lo&
of &'e manufac&urer. Second, =rm is a/ec&ed (y en%ironmen&al condi&ions,suc' as eposure &o mois&ure, and (y general aging. Ele%a&ed &empera&ures
con&ri(u&e &o (ase fog in an emulsion (efore de%elopmen&. T'ird, signi=can&
%aria&ions in densi&y are in&roduced (y &'e s&eps in'eren& in &'e =lm!
de%elopmen& process i&self. + serious pro(lem of a di/eren& na&ure for dose
de&ermina&ion is presen&ed (y &'e s&rong response of =lm &o low!energy
p'o&a