Radiation Chemistrypubs.acs.org/doi/pdf/10.1021/ba-1968-0081.ch038of 0, 1, 2, and 4 relaxation lengths from a point isot...
0 downloads
108 Views
2MB Size
38 A Significant Correction Factor in Gamma Ray Dosimetry
Downloaded by CORNELL UNIV on August 24, 2016 | http://pubs.acs.org Publication Date: January 1, 1968 | doi: 10.1021/ba-1968-0081.ch038
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
Downloaded by CORNELL UNIV on August 24, 2016 | http://pubs.acs.org Publication Date: January 1, 1968 | doi: 10.1021/ba-1968-0081.ch038
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
Downloaded by CORNELL UNIV on August 24, 2016 | http://pubs.acs.org Publication Date: January 1, 1968 | doi: 10.1021/ba-1968-0081.ch038
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 <
30.
B u t for samples c o n t a i n i n g h i g h a t o m i c number—e.g., eerie sulfate s o l u t i o n s — t h i s a p p r o x i m a t i o n i n the calculations leads to a n a b s o r b e d dose w h i c h is s l i g h t l y too h i g h . I n case of
6 0
C o r a d i a t i o n , the p a i r p r o d u c t i o n
is n e g l i g i b l e i n l i g h t elements, w h i l e i n c e r i u m , the heaviest c o n s i d e r e d here, it is
0.8%.
T h e values of the a b s o r p t i o n coefficients Downloaded by CORNELL UNIV on August 24, 2016 | http://pubs.acs.org Publication Date: January 1, 1968 | doi: 10.1021/ba-1968-0081.ch038
those r e p o r t e d b y S t o r m et al.
Energy F l u x Density Spectrum. point isotropic
6 0
Co
u s e d i n this r e p o r t
are
(10). ^(JP
has b e e n c a l c u l a t e d for a
source e m b e d d e d i n a large w a t e r c o n t a i n e r
Goldstein and Wilkins
(3).
(The
by
n o m e n c l a t u r e i n this p a p e r is that
r e c o m m e n d e d b y the I n t e r n a t i o n a l C o m m i s s i o n o n R a d i o l o g i c a l U n i t s a n d M e a s u r e m e n t s (6),
w h i c h differs f r o m that u s e d b y G o l d s t e i n a n d
W i l k i n s w h o u s e d I f o r the same q u a n t i t y as ^
i n this p a p e r . ) C o r r e
s p o n d i n g energy b u i l d u p factors i n w a t e r w e r e m e a s u r e d b y G . R . W h i t e (12),
V a n D i l l a a n d H i n e (2),
(8).
T h e s e e x p e r i m e n t a l b u i l d u p factors w e r e f o u n d to agree w i t h the
B i b e r g a l et al. (1 ), a n d b y Sehested et
al.
t h e o r e t i c a l l y c a l c u l a t e d ones w i t h i n e x p e r i m e n t a l a n d c a l c u l a t e d a c c u r a c y of 1 0 % .
W e i s s a n d B e r n s t e i n (11)
s t u d i e d the energy s p e c t r u m b e l o w
150 K e v . a n d f o u n d agreement w i t h Spencer's a n d Fano's
calculated
values ( 9 ) , w h o s e c a l c u l a t i o n s w e r e the basis for the r e p o r t b y G o l d s t e i n a n d W i l k i n s (3).
A l l this indicates that the intensity s p e c t r u m
reported b y Goldstein a n d W i l k i n s for a point isotropic
6 0
C o source i n
w a t e r is f a i r l y correct a n d it w i l l , therefore, be u s e d i n E q u a t i o n 1.
The
spectra are s h o w n i n F i g u r e 1. Calculation of Equation 1. G o l d s t e i n a n d W i l k i n s list o n l y a f e w points o n the spectral curves.
W e h a v e g r a p h i c a l l y i n t e r p o l a t e d these
points so that s m a l l intervals c o u l d b e u s e d i n the n u m e r i c a l i n t e g r a t i o n of E q u a t i o n 1. F u r t h e r , a n e x t r a p o l a t i o n of the s p e c t r a l values b e y o n d the lowest v a l u e r e p o r t e d b y G o l d s t e i n a n d W i l k i n s w a s d o n e b y assum i n g that at the l o w energies the s p e c t r a l d i s t r i b u t i o n is s i m i l a r to that for a p r i m a r y p h o t o n energy of 1 M e v . E q u a t i o n 1 was i n t e g r a t e d n u m e r i c a l l y , because neither ^ c a n be expressed a c c u r a t e l y w i t h s i m p l e f u n c t i o n s .
nor
^
T h e w i d t h s of the
energy intervals u s e d i n the i n t e g r a t i o n w e r e 0.01 M e v . f r o m 0.025 M e v . to 0.175 M e v . ; 0.0125 M e v . for photons of 0.1750 M e v . to 0.1875 M e v . ; 0.025 M e v . f o r photons of 0.1875 M e v . to 1.2125 M e v . ; a n d 0.0375 M e v .
Hart; Radiation Chemistry Advances in Chemistry; American Chemical Society: Washington, DC, 1968.
38.
B R N j OLFSSON
Gamma
Ray
555
Dosimetry
f o r p h o t o n s of 1.2125 M e v . t o 1.2500 M e v . F o r t h e p r i m a r y p h o t o n s f r o m 6 0
C o 1.17 M e v . a n d 1.33 M e v . , a n average energy of 1.25 M e v . w a s u s e d . G o l d s t e i n a n d W i l k i n s (3) d o n o t list t h e p h o t o n i n t e n s i t y s p e c t r u m d i r e c t l y b u t t h e v a l u e of A
dI (E)
9
,
B
x
where / X t
0.0632 c m . " is t h e t o t a l a b s o r p t i o n coefficient i n w a t e r a t the p r i m a r y p h o t o n energy E
=
1
Downloaded by CORNELL UNIV on August 24, 2016 | http://pubs.acs.org Publication Date: January 1, 1968 | doi: 10.1021/ba-1968-0081.ch038
0
W e h a v e , therefore, first c a l c u l a t e d t h e v a l u e d • · 4ΤΓΓ · β χ ρ ί ^ · r) = 2
1.602
· ΙΟ" · 3.7 · 1 0 C · 8
10
/ \ Γ 2 . 5 β χ ρ ( - ^ · r ) · /%(Ε ) 4*r* · e x p U * 0 · [ Λ
2
0
+
m
( ) 7
T h e first t e r m i n t h e b r a c k e t is t h e c o n t r i b u t i o n f r o m t h e p r i m a r y g a m m a rays (1.17 a n d 1.33 M e v . ) at t h e p o i n t P, r c m . f r o m t h e p o i n t source a n d t h e last t e r m is t h e c o n t r i b u t i o n f r o m t h e scattered
gamma
rays at t h e p o i n t P . d is the dose rate i n rads p e r s e c ; r is t h e distance i n water f r o m the point isotropic
6 0
C o source of C curies; p = 0.0632 c m . t
- 1
is t h e t o t a l l i n e a r a b s o r p t i o n coefficient i n w a t e r f o r 1.25 M e v . p h o t o n s ; is t h e scattered g a m m a r a y i n t e n s i t y s p e c t r u m ; a n d
is the
energy transfer coefficient i n t h e dosimeter. I t is a s s u m e d that t h e d o s i m e ter is s m a l l e n o u g h n o t to c h a n g e t h e energy i n t e n s i t y s p e c t r u m i n t h e w a t e r at t h e p o i n t P, a n d that i t is large e n o u g h to m a k e t h e effect of g a m m a electron n o n e q u i l i b r i u m negligible. Definition of Absorbed Dose Buildup Factor. I n t h e analysis of t h e dose v a r i a t i o n , t h e c o n c e p t of dose b u i l d u p f a c t o r is u s e f u l . T h e u s u a l d e f i n i t i o n of dose b u i l d u p factor (3, 5,7) dosimeter.
l i m i t s its use to dose i n a n a i r
T h e present d e f i n i t i o n of a b s o r b e d dose m e a s u r e d i n rads,
b y w h i c h dose i n a n y m a t e r i a l o r i n a n y dosimeter is d e f i n e d ( 6 ) makes t h e p r e v i o u s d e f i n i t i o n of dose b u i l d u p factor t o o restrictive. W e w i l l , therefore, r e p l a c e t h e dose b u i l d u p factor b y d e f i n i n g t h e a b s o r b e d dose b u i l d u p f a c t o r B(r) f o r a g i v e n d o s i m e t e r i n a g i v e n m e d i u m as t h e r a t i o of t h e a c t u a l a b s o r b e d dose i n t h e d o s i m e t e r to t h e a b s o r b e d dose that w o u l d b e m e a s u r e d i n t h e d o s i m e t e r i f there w a s n o scattered r a d i a t i o n . T h e v a l u e o f E q u a t i o n 7 w a s , therefore, d i v i d e d b y t h e a b s o r b e d dose
Hart; Radiation Chemistry Advances in Chemistry; American Chemical Society: Washington, DC, 1968.
556
RADIATION CHEMISTRY
1
rate f r o m t h e u n s c a t t e r e d p h o t o n s , t h e first t e r m o n t h e r i g h t side i n E q u a t i o n 7. T h i s q u o t i e n t v a l u e w e c a l l B(r),
J ^ e x p U - r ) . dE ^^^-^
/%(Εθ)
B(f)
where J
0
(8)
μ*(Εο)
=
2.5 M e v . p e r o n e d i s i n t e g r a t i o n of ι—ι
Downloaded by CORNELL UNIV on August 24, 2016 | http://pubs.acs.org Publication Date: January 1, 1968 | doi: 10.1021/ba-1968-0081.ch038
i.e.,
6 0
Co.
ι ιM1I
DIFFERENTIAL ENERGY SPECTRA IN WATER C 0 POINT ISOTROPIC SOURCE 60
Figure
1.
Energy
dl spectra -j= in water at a
alii
distance r corresponding to μ · r — 1; μ · r = 2; and ^ · r = 4 from a point isotropic Co source. The ordinate shows and 4-rrr exp (μ - r) - - J ^ ; the abscissa the photon energy in Mev. ί
χ
60
t
2
ΐ
T h e a b s o r b e d dose b u i l d u p factor B ( r ) i n E q u a t i o n 8 is t h e r a t i o of the a c t u a l dose i n t h e d o s i m e t e r at a p o i n t P , r c m . f r o m a p o i n t iso tropic
6 0
C o source i m b e d d e d i n large w a t e r container, to t h e dose that
w o u l d b e m e a s u r e d at t h e same p o i n t i f there w e r e n o scattered r a d i a t i o n . I n this e q u a t i o n 7 is t h e energy e m i t t e d b y the source; I is t h e scattered 0
s
r a d i a t i o n flux at Ρ ; μι is t h e t o t a l a b s o r p t i o n coefficient of w a t e r (0.0632 cm." ); 1
and —
is t h e energy transfer
coefficient i n c m . / g r a m i n t h e 2
dosimeter. T h e i n t e g r a l i n E q u a t i o n 8 w a s c a l c u l a t e d f o r t e n elements c o m m o n i n a p p l i e d dosimeters. T h e s e t e n elements w e r e H , C , O , A l , S i , S, C I , F e ,
Hart; Radiation Chemistry Advances in Chemistry; American Chemical Society: Washington, DC, 1968.
38.
BRNJOLFSSON
Gamma
Ray
557
Dosimetry
C u , a n d C e . T h e c o r r e s p o n d i n g b u i l d u p factors c a l c u l a t e d a c c o r d i n g to E q u a t i o n 8 are l i s t e d i n T a b l e I I . Table II.
Dose Buildup Factors in Elements at Different Distances in Water from a Point Isotropic C o G 0
Downloaded by CORNELL UNIV on August 24, 2016 | http://pubs.acs.org Publication Date: January 1, 1968 | doi: 10.1021/ba-1968-0081.ch038
Element
He Li Be Β *C Ν *0 F Ne Na Mg *A1 *Si Ρ *s *C1 A
Element
Buildup Factors at μ · r = ΐ
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
1
2
4
1.958 1.96 1.96 1.97 1.98 1.995 2.02 2.051 2.10 2.17 2.25 2.36 2.494 2.665 2.86 3.106 3.38 3.61
3.101 3.10 3.11 3.13 3.16 3.201 3.27 3.363 3.50 3.69 3.92 4.25 4.627 5.115 5.65 6.367 7.14 7.90
5.618 5.62 5.64 5.68 5.74 5.850 6.01 6.228 6.59 7.20 7.62 8.32 9.179 10.32 11.50 13.24 15.04 17.00
Κ Ca Sc Ti V Cr Mn *Fe Co Ni *Cu Zn Br Zr Rh Sn I *Ce
Buildup Factors at ^ · r = t
19 20 21 22 23 24 25 26 27 28 29 30 35 40 45 50 53 58
I
2
4
3.94 4.31 4.71 5.19 5.75 6.17 7.00 7.66 8.2 9.0 9.86 10.8 16 23 31 40 45 38.5
8.8 9.9 11.2 12.5 14.0 15.6 17.3 19.24 21.2 23.2 25.43 28 43 62 85 112 130 103.6
19.1 21.5 24.4 27.5 31.0 34.7 39.0 43.29 48.0 52.8 57.7 64 97 138 190 252 295 241.1
Interpolation of the Values of B. T h e energy a b s o r p t i o n coefficient can be approximated b y :
J± = ρ
a
(
£
)
A
(£)
b
z +
-( ) f
z
( 9 )
A
where Ζ =
atomic number
A =
atomic weight
— —^ Λ
a(E) b(E)
=
== a f u n c t i o n of t h e p h o t o n energy E, b u t i n d e p e n d e n t of Ζ and A .
· f(Z) = b(E)
C o m p t o n absorption
photoelectric absorption
=
a f u n c t i o n of the p h o t o n energy Ε b u t i n d e p e n d e n t of Ζ and A .
f(Z) =
a f u n c t i o n of t h e a t o m i c n u m b e r b u t i n d e p e n d e n t of Ε
Hart; Radiation Chemistry Advances in Chemistry; American Chemical Society: Washington, DC, 1968.
558
RADIATION CHEMISTRY
1
I 1 -Π1 !
1
"""ΤI ΤΓ
200
-
-
o «oo Ο