38 A Significant Correction Factor in Gamma Ray Dosimetry
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ARI BRNJOLFSSON U. S. Army Natick Laboratories, Natick, Mass. 01760
Softening of the gamma rays as they penetrate light mate rials may cause very large differences in the radiation doses absorbed in the samples and in the dosimeters. This is illustrated in the present paper by calculating the dose in 14 dosimeters and several other materials placed at distances of 0, 1, 2, and 4 relaxation lengths from a point isotropic Co source embedded in a large water container. These calcu lations show for instance, that the doses in water, Lucite, Fricke dosimeter, lithium fluoride, poly(vinyl chloride) and 0.4M ceric sulfate solution at zero distance from the source are in the ratios: 100: 96: 100: 83: 92: 99; at a distance cor responding to µ · r = 1 the dose ratios are 100: 95: 100: 85: 124: 169; and at a distance corresponding to µ ∙ r = 4 the similar ratios are: 100: 93: 101: 87: 162: 251. 60
t
t
A b s o r b e d dose i n a s a m p l e i r r a d i a t e d b y g a m m a rays is u s u a l l y determ i n e d b y m e a s u r i n g t h e a b s o r b e d dose i n a d o s i m e t e r ; f o r instance, a F r i c k e d o s i m e t e r p l a c e d i n the p o s i t i o n of t h e s a m p l e . T h i s a b s o r b e d dose i n the dosimeter is, h o w e v e r , g e n e r a l l y different f r o m that i n t h e sample. T o a r r i v e at t h e a b s o r b e d dose i n the s a m p l e , corrections m u s t b e m a d e f o r t h e difference.
T h e s e corrections are p a r t l y c a u s e d b y
g a m m a electron n o n - e q u i l i b r i u m at the b o u n d a r y , transfer of energy of e x c i t e d states across t h e b o u n d a r y , a n d p a r t l y c a u s e d b y differences i n mass energy transfer coefficients w h i c h are f u n c t i o n s of t h e a t o m i c n u m b e r a n d t h e g a m m a r a y energy. T h e corrections c a u s e d b y b o u n d a r i e s w i l l n o t b e c o n s i d e r e d i n this p a p e r , b u t o n l y t h e corrections c a u s e d b y mass e n e r g y transfer coefficients. I n r a d i a t i o n d o s i m e t r y t h e energy a b s o r b e d p e r ml. of s a m p l e is u s u a l l y the q u a n t i t y of interest. T o a r r i v e at t h e energy a b s o r b e d p e r m l . 550 Hart; Radiation Chemistry Advances in Chemistry; American Chemical Society: Washington, DC, 1968.
38.
BRNJOLFSSON
Gamma
of the sample, the dose D
d
Ray
551
Dosimetry
i n the dosimeter—i.e.,
the F r i e k e dosimeter,
is first m u l t i p l i e d b y the r a t i o — , i.e., the ratio of d e n s i t y p of the s a m p l e Pd s o l u t i o n to the d e n s i t y p of the dosimeter s o l u t i o n . S e c o n d l y , the dose D is m u l t i p l i e d b y the ratio — · — , i.e., the ratio of the mass energy Pb μα s
d
d
transfer coefficients.
T h e s e t w o corrections factors are u s u a l l y a p p l i e d .
T h e t h i r d c o r r e c t i o n factor, w h i c h is the r a t i o of the a d s o r b e d dose b u i l d u p factors i n the s a m p l e a n d the dosimeter, is u s u a l l y i g n o r e d , b u t is s h o w n i n this p a p e r to be v e r y i m p o r t a n t . T h e a b s o r b e d dose b u i l d u p Downloaded by CORNELL UNIV on August 24, 2016 | http://pubs.acs.org Publication Date: January 1, 1968 | doi: 10.1021/ba-1968-0081.ch038
factor is d e f i n e d i n this p a p e r analogous to the dose b u i l d u p factor, a n o t a t i o n u s e d w h e n the u n i t r o e n t g e n was s t i l l the u n i t of r a d i a t i o n dose. T h i s p a p e r shows the m a g n i t u d e of this t h i r d c o r r e c t i o n factor, w h i c h is c a u s e d b y differences i n g a m m a - r a y a t t e n u a t i o n coefficients a n d s o f t e n i n g of the g a m m a - r a y s p e c t r u m . A s a n i l l u s t r a t i v e e x a m p l e , the dose i n d i f ferent dosimeters is c a l c u l a t e d as a f u n c t i o n of the distance f r o m a p o i n t i s o t r o p i c cobalt-60 source i n w a t e r .
Calculations
of Absorbed Dose
T h e g a m m a - r a y energy i n rads p e r second a b s o r b e d i n a n i n f i n i t e s i m a l v o l u m e d x d y d z at the p o i n t P ( x , y , z ) is g i v e n b y d = 1.60209 · 10-8 f J ο
E
= 1.60209 · 10-8 Γ Jo
m
Ε
a
—
x
E
.
. J^l
dE
^(E) ρ
dl(E) dE
.
p
d
E
(
1
)
.
where d = Ε = φ(Ε) =
dose rate i n rads/sec. = 100 e r g / g r a m sec. p h o t o n energy i n M e v . p h o t o n flux d e n s i t y = the t o t a l n u m b e r of photons of energy less t h a n Ε w h i c h enter a sphere of cross-sectional area 1 c m . p e r sec. at the c o n s i d e r e d p o i n t P . φ ( Ε ) is i n units of c m . " sec." ( t o t a l n u m b e r of p h o t o n s p e r c m . per s e c ) . 2
2
=
1
2
p h o t o n flux d e n s i t y s p e c t r u m = n u m b e r of photons i n the energy i n t e r v a l Ε to Ε + dE w h i c h enter a sphere of cross-sectional area 1 c m . p e r sec. at t h e c o n s i d e r e d point P. 2
^/IF~ d
* * * °^ M e v - c m . " sec." ( n u m b e r of p h o t o n s p e r M e v . p e r c m . p e r sec. ). s
n
u n
t s
1
2
1
2
( E) —- = p
mass energy transfer coefficient i n c m . / g r a m of the d o s i m eter at Ρ f o r p h o t o n s i n the e n e r g y i n t e r v a l Ε to Ε + d E . ρ is the d e n s i t y i n g r a m / c c . 2
Hart; Radiation Chemistry Advances in Chemistry; American Chemical Society: Washington, DC, 1968.
552
RADIATION CHEMISTRY
7(E)
=
1
the energy flux d e n s i t y or intensity—i.e., the total energy of a l l the photons w i t h energy less t h a n Ε that cross a sphere of cross-sectional area of 1 c m . p e r sec. at the p o i n t P. 1(E) is i n units of M e v . · c m . " · sec." ( e n e r g y i n M e v . per c m . per s e c ) . 2
2
1
2
dl(E)
the energy flux d e n s i t y s p e c t r u m or i n t e n s i t y s p e c t r u m — i.e., t o t a l energy of the p h o t o n s i n the energy i n t e r v a l Ε to Ε + dE that cross a sphere of cross-sectional area of 1
dE
c m . p e r sec. at the c o n s i d e r e d p o i n t Ρ · = do a£ ^ · Ε is i n units of c m . " sec." ( e n e r g y i n M e v . p e r M e v . per c m . " per s e c ) . 2
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2
1
2
T h e A b s o r p t i o n Coefficient. I n E q u a t i o n 1 the mass energy transfer coefficient — Ρ
should be
used
a n d not
the
mass
energy
absorption
coefficient — g i v e n b y Ρ tl Ρ
=
L- + ^£ + — Ρ Ρ Ρ
(2)
where τ = Ρ σ &
=
p h o t o e l e c t r i c mass a t t e n u a t i o n coefficient i n c m . / g r a m . 2
1.
σ
the a b s o r p t i o n c o m p o n e n t of the total C o m p t o n
cross section i n c m . / g r a m , E is the average e n e r g y g i v e n to the electrons i n the C o m p t o n process w i t h t o t a l cross 2
e
section — i n c m . " / g r a m f o r i n c o m i n g photons of energy 2
h
— = Ρ
,
p
the cross section for the p a i r p r o d u c t i o n i n c m . / g r a m . 2
T h e mass e n e r g y transfer coefficient is s i m i l a r l y g i v e n b y P'k
Ρ
_j_ Ç[a _|_
Ρ
Ρ
K
&
Ρ
(3)
where Ta
Ρ
ρ
( 0 Χ
(4)
(5)
Hart; Radiation Chemistry Advances in Chemistry; American Chemical Society: Washington, DC, 1968.
38.
BRNJOLFSSON
Gamma
Ray
553
Dosimetry
where δ =
average e n e r g y e m i t t e d as fluorescent r a d i a t i o n p e r p h o t o n a b s o r b e d i n the p h o t o e l e c t r i c process.
=
is the c o r r e c t i o n f o r e s c a p i n g r a d i a t i o n f r o m the a n n i h i l a t i o n of t h e p o s i t r o n .
v
δ is m a i n l y d e t e r m i n e d b y t h e fluorescence y i e l d a> i n the K - s h e l l . a> is, a c c o r d i n g to H a g e d o o r n a n d W a p s t r a (4) g i v e n b y k
k
W k
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1
— ( - 6 . 4 · ΙΟ" + 3.4 · ΙΟ" · Ζ - 1.03 · 1 0 " Z ) ; 2
0>
2
6
3
(6)
4
k
where Ζ =
atomic number n u m b e r K - s h e l l vacancies n u m b e r K - s h e l l x-rays
W k
o> as a f u n c t i o n of the a t o m i c n u m b e r ( Ζ ) is s h o w n i n T a b l e I. k
T a b l e I.
Fluorescent
Fluorescent Yield ωκ '100K ·100 r
Atomic Number 2 Element 10 14 16 20 26 29 30 40 50 56 58 60
Ο Ne Si S Ca Fe Cu Zn Zr Sn Ba Ce Nd
K» + K in %
Au
0.18 0.57 2.7 4.9 12 29 39 43 70 83 88 89 90
Yield
Absorptions Coefficient Electron Binding in cm. /gram in Energy in Kev. _ Water at the Gamma Energy K-Shell L-Shell 2
.532 .867 1.839 2.472 4.038 7.112 8.972 9.659 17.998 29.200 37.441 40.444 43.568
33,000 7,200 800 320 72 13.5 6.8 5.4 0.76 0.157 0.075 0.062 0.053
.019 .118 .193 .400 .842 1.100 1.196 2.532 4.465 5.987 6.549 7.126
I n l i g h t elements δ is a l w a y s s m a l l , because most of t h e energy is t a k e n u p b y the A u g e r electrons a n d — c a n t h e n b e r e p l a c e d b v —. A s Ρ ' Ρ the a t o m i c n u m b e r increases, t h e fluorescent r a d i a t i o n increases. A p o r t i o n of the fluorescent r a d i a t i o n , e s p e c i a l l y f r o m the L - s h e l l or the h i g h e r shells, is often a b s o r b e d w i t h i n t h e dosimeter; f o r instance, t h e 1,000 e.v. x-rays f r o m the L - s h e l l i n c o p p e r penetrate o n l y 2 · 10~ c m . of w a t e r . 4
Hart; Radiation Chemistry Advances in Chemistry; American Chemical Society: Washington, DC, 1968.
554
RADIATION CHEMISTRY
1
T h e r e f o r e , i n these calculations w e h a v e n e g l e c t e d this fluorescent r a d i a t i o n a n d u s e d — i n s t e a d of — i n E q u a t i o n 3. T h i s a p p r o x i m a t i o n is Ρ ρ a d e q u a t e f o r samples a n d dosimeters c o n t a i n i n g a t o m i c n u m b e r Ζ
