Indi;1Il Journal of Pure & A ppli ed Ph ys ics
Vo l. 37 . September 1999. pp. ()99-70R
Attenuation and scattering of gamma ray through pink granite
H M Mahmoud
Ph ysics Depart ment. Facul ty of Sc ience. Qena. South Valley Uni vers ity. Egypt
Received: 22 Dece mher 1997: rev ised) Fehruary 1999: accepted 17 M ay 1999
Th e ahsorpt ion and side scallering of ga mmn ray~ nre eve nts thai have strong dependence on th e gra in diameter (ri) . sample~
densit y (I I). ph oton energy (C) and chemi cal co mposition of a sa mpl e. These parnmeters were sllldi ed for two different kind s of
pink ~ ranit e rocks (in two forms-co mpressed and natural rocks) w hi ch are investi gated to co nstru ct new shielding material s for
inl ense gamm;1 r;IYs. On one hand the study showed a direet proportionality between atte nu ation coefficicnts and the percent age
of hoth ferric and ferrous oxides in rock : on the other hand . an inverse relation was obta ined between th e previous ratio ~ and
side scallerin g coe llic ient s. AS;I result. increase in these ra ti os is follo wed by nn increase in the elli ciency o f screening nucl ear
radi at ion by th e rock. The determined va lues of hnlf- va lue layer X I12 ;Ire found to increase proporti onall y wi th tI. but th e rate of
ch;lI1ge of X II::! wit h rI is dependen t on photon energy.
I Introduction
Studi es were co ndu cted by th e auth or on th e interac tion o r g;lmma ra ys with some co mm onl y ava ilable
co mpressed powdered material s, with a vi ew to developing low cost shields to protect wo rkers from ga mma
rad iati ons, and to know th e e ffect of th e presence both
fe rri c and ferrous ox ide in th e material on both atte nu ati on and scatteri ng of ga mm a rays by t he samples so as
to co nstru ct a hi gh qualit y shi e ld for sc ree nin g rad iati on.
The qu antity wid e ly used in ca lculatin g ga mm a rays
pe netrati on and energy depos ition in bi ologica l shi e ldin g and othe r materia ls are th e mass atte nu ati on coeffi c ient " pip. A narrow beam or monoe nerge ti c photons is
atte nuat ed accordin g to the familiar ex ponenti al absorpt ion la w. Fo r more co mpl ica ted situat ions than narrow
beam , th e attenuati on is still basica ll y ex ponenti a l, but
is modi fi ed by two add iti o nal fac tors. T he fi rst of these.
sometimes call ed a geo metry racto r, depends esse nti a ll y
on th e so urce geo metry. The oth er fa ctor is ca ll ed the
buildup ractor, whi ch tak es into acco unt seco nd ary photons produced in th e absorber as the res u It of o ne or more
Co mpt o n scatte rs. For a thin shi e ld and narrow bea m,
th e buildup factor is unilY. Whe n the sa mpl e thi ckness,
I is small and th e detec tor sizL: can be neg lected. th e
garnma ra y flux de nsity at th e detecto r is give n b/
()) =
S
(, - It(IC )1
.. .( I )
R th e so urce-detec to r distan ce . As the thi ck ness o r the
shi e ld is in crease or as th e w idth of the bea m in crease,
th e flu x density is given by)
(1) =
S
(,- (l (/;') I
...
(2)
4
where 8 is the buildup fa ctor The buildup fa ctor is
defined as follows: in th e passage of radi at ion through
a medium , the rati o of th e total va lue of a specified
radi at ion quantity at any point to the co ntri buti on to th at
va lue from rad iati on reac hin g the point without ha vin g
und ergo ne a colli sion. The bui ldup fa ctor can he obtain ed, in princ ipl e, by ex periment , but si nce the attenuati on and scatterin g cross- sec ti ons are kn ow n with
reasonabl e acc uracy. buildup factors are custo maril y
obtained by soluti on of th e photon transport equati o n.
The total va lue of a spec ified rad iati on at so me poi nt in
space is predicted by the co rres po ndin g reason of so me
type of detector at a point in space, th at is the detecto r
res ponse R, which represented by a flux density, (Nr, E)
t1ll1itipi ied by the detector res po nse fun ct ion R( t ·). where
r is the di stance from a sou rce. The buildup fa ctor 13 is
give n by:
I:"
Rf dE R (E)<l) ( r. E)
13 =
_'--'-0_ __ _ _ _ __
4rr l? 2
whe re S is the so urce strength . ( ~I E) the linear atte nu ation coe rfi c ient (cm- I ). I th e shi e ld thickn ess (cm). and
8 1£,, - pl )
4 rr R 2
_
... (:l)
ROR ( E )" ) (J)" ( r )
o
0
where Rand c)) ( r ) correspond to th e respo nse and flu x
to uncollided photo ns at a di stance r from a point so urce
700
INDIAN JPURE APPL PI-IYS , VOL 37. SEPTEMBER 199<)
of monoenergeti c photons . Buildup factors are not constant , but vary wit h a num ber of parameters, as foll ows:
I. Bui Idup fac tor de pend s on th e type of th e detector
res ponse functi on R. Expos ure buildup factor is the
detector response fun cti on, whi ch depends on its abso rpti on in air. Some auth ors give the names of radiati on and
air kenna for thi s res ponse. Energy absorpti on building
fac tor is the detec tor res ponse fun cti on whi ch depends
on its ahsorpti on in the materia l. Some auth ors give th e
names of energy depos iti on, medium ke nna and absorbed dose.
2. It also depe nd s on the geo metri c confi guration of
th e so urce - a point isot ropic source, plane norma l bea m
or monodirecti ona l beam and plane isotop ic source.
}. Itdepends on the geometri c co nfi gurat ion of attenuatin g medi um-infinite or finite, homogeneous or
heterogeneous.
4. It de pends on th e ene rgy of th e source photons,
whi ch is take n to be monoe nergeti c.
:'i . It depend s on the depth of penetrati on through the
atte nu at in g medium .
2 Ex perimental Details
The chose n material s are two kind s of pink granite
rocks. The abso rpti on of ga mma ray radiati ons by these
maleri als is influe nced) by (i) the grain size of the
particles, (ii ) th e press ure app li ed on th e parti cles, (iii )
th e sam pl e de nsit y, (iv) the energy of radiati on source,
(v) th e elemental co mpos it ion, (v i) th e sa mpl e thi ckn ess,
and (v ii ) th e atollli c number Z or the medium :! . The
material s we re mec hani call y gro un d to rin e powde r,
th en sieved through standard set or sie ves (w ith diameters as 0. 18, 0. 16. O. 10. (l.O9, 0.08 , n .07 1 and n .056 mm
to obtain grain s with mea n diameters n. 17, O. I}, 0.095 ,
0.085 and O.06}5 mm) ror sepa rati on to proper grain
2
sizes . Se lec ted grain s we re pressed under 35 tonne/c m
ror all differe nt grain size powders in the fo rm of di scs
6 cm in diamete r, and or thi ckness ran gin g from 0.55 to
2.5 cm. Three so urces o r gamma- radiati on have bee n
L1sed in thi s ex periment: Cow in the form of cobaltous
chloride, whi ch e mits two gammas of energies 1.33 and
I. 17 Me V, Cs 1 \7 in the form or caes iu III ch loride whi ch
emits a 0.661 MeV gamma-ray and Ba l ' \ in th e form or
ba rium chl orid e whi ch emits 0.36 Me V gamma- rays .
Eac h so urce is housed in a lead co ntain er alone, radiatio n
is co nfin ed to a narro w beam by a lead co llimat or hav in g
a small ho le.
A sc intill ation counter was L1 sed in thi s ex periment (I S
~I detec tor a LII' co llimato r is a hole 8 c m in length and I
cm dia meter bored th ro ugh ~ I cubic lead block ha vin g an
edge of 8 cm. This is foll owed by a similar bl ock
contain ing a narrow bored hole 7 mm in diameter. The
two lead blocks are arranged such that th e two bored
holes are aligned wit h th e source to gi ve a narro w
co llimated bea m with reasonab le intensity. O n th e detector side th e collimator has a narro w ho le 1.5 mm in
diameter. The collimato r thi ck ness all ows for th e absorpti on of radi al ion scattered ou t of the bea m in side the
co il i matar, so th at th e scattered rad iati on does not
. emerge in the room. The sca ler used in thi s ex pe riment
is a BAIRO-ATOMIC scaler, model 966- 1' 0, Bedford
se ri es. The output vo ltage ran ges from zero to 10-1 V.
(see Fig. l, which is a sc he mati c diagram for good geometry abso rpti on and side scatteri ng arran ge ment).
Linear attenuat ion coefficient of ~L gamma-rays in
two pink granite rocks in co mpressed <1 ndnatural fo rm s
for the different sources ha ve been calculated. Linea r
atte nuation coefficient of two pink granite roc ks were
determin ed from the linea r relation betwee n log
';1and
X, from whi ch /l ca n be calcu latL:d by di viding the slope
of the strai ght line, res ultin g from th e last relat ion by
0.4343. The mass attenu ati on coefficient /lIp can be
calculated by div iding th e linea r attenu ati on coeffici e nt
p. by the density of th e absorbi ng material a~ foll ows:
- I
pip
= -cm--0 = cm-'1 g
gl cm '
The rela xa ti on le ngth (o r mean free path , mfp ) can be
ca lcul ated from the definitio n relaxati on le ngth = IIlin ear atte nuati on coefficient.
To determin e the side scatterin g coefficie nts. the
detector was fix ed at a certain di stan ce from the samDET ECTO R
I SC INTIL LATION
i COl INT[ I(
CIRCU IT
Ph
--C,
8==}~ J)f;TI'CTOJ{
!- _L_I
A13S01(fI EI(
Ph
s
Pl,
Fi g. I - A schcmalic d iagram ror g()od gcolll ciry
,Ihsorplio n <Inti sid e sC< lllcrin g ,IIT;Jn ge lllcll l
-
701
MAHMOUD: GAMMA RAY THROUGH GRANITE
pi e's edge (2 cm) and directed perpendicular to the
direction of the incident beam . Then different measurements are taken along th e extension of the sa mple by
varyin g the thi ckn ess of absorber. In thi s ex periment two
different kinds of pink granite rocks were investigated,
as shi elding materials, the che mical co mpositi on for
which are presented in Table I .
~ll
X
o
r
pink granite No . 1
J...
24
(,0
0.078
fi 0,063
Co
'
Bal3J
. 18
x
E
u
'0
1:13
.,
3 Results and Discussion
8
3.1 Linear and mass attenuation cocflicicnts and J'claxation
Icngth
A narrow beam of monoenerget ic photons with a
incide nt intensity In penetratin g a layer of material with
thickness X and den sity p, emerges with intensity I give n
by the exponential attenuation law
I
-=ex p(-I..IX)
In
I
10
~l =)( /11 I
Eq. ( I ) or (2) ca n be rew ritte n as
10
log I = 0.4343pX
"o
bO·~
~ gO.048
u~
~~
0i::E
0.033
.. .(4)
0.0 18
.. .(5)
0.06
O.IX
0 .14
0. 10
d, mm
... (6)
From whi ch ca n be obta ined from measured va lues
I", I and X, and th en graphi ca ll y from attenuati on curves
by usin g th e last linear curve. Both the linear ()..I) and
mass attenuation coeffi cie nts (~l)/p) of both compressed
powdered and natural rock of two pink granite for the
three radi oactive so urces CO(lO, Cs l:17 and Ba m (where
its energy E varyin g from tU6 to 1.33 MeV) were
eva lu ated .
If a collimated beam of n photons pe r second passes
normall y through a fo il co ntainin g N atoms I cm-' , the
number £Ill of primary photons whi ch are removed from
th e co llimated beam per second is given by
d ll
-- = N ( 0 I + 0 , + 0 " ) d x =P d x
... (7 )
II
1"
Fig . 2 -
Variation or gra in diameter (d mill) or th e co mpressed
sampl es or pink granite rock No . 1 with hoth mass attenuat ion
2
coclli cient (fl i p. cm /g) and relaxation length (A. crn )
X I-' / P
Pink granite No.2
0.078
8
IR
0.063
I J 7_______
'"
C
~
"
c
.g
~
12
where 0,,11, 0 c and 0 "" are th e atomic cross-sections for
the photoel ec tri c effec t, COl11pton effec t and pair produ cti on processes, res pecti ve ly. T he attenuation of th e
photon bewll is desc ribed by a simple exponenti al la w
wi th a linear atte nuation coeffic ie nt )..I, as
II
- =exp(- )..IX)
'""
... (8)
n.01 8
II i)
Fig. :2 and 1 show the variation of )..lIp and th e re laxati on length, A, as a fun ction of th e gra in diameter (d) for
two kinds o f pillk grallit e rocks. It is possib le to see that
pi p vari es linea rl y with d acco rdin g to th e eq uati on
pip = - (/(/ + k for o ()63S :S; d :S; n.17 111m
... (9)
r~,O(,
Fig. :1 -
0.10
d.mm
Vari ,ltion or grain di :1Il1cte r (d.
III III )
silillpi es or pin k grani te rock N o.2 wit h hoth
2
n, I ~
0. 14
or the c ()J1lpres~ecl
J1lil S~
atl enLliit ioll
coelTi cic lll (pip. c lll lg) and rela xmion length (Ie. CIll )
7():2
IN I)I ;\N 11'1 11<1 - ;\ 1'1'1. PI I Y'). \ O l. :n. SF I'TFivl lll ': I, I ')')')
\v he re a re present s th e rate o r c han ge or pip with tI, a nd
k is a co nstant w hi c h depe nds o n the ki nd or
ab ~o rbe r.
The fi g ures also s how that the re la xa ti o n le ng th . A,
in c reases lin early w ith d acco rdin g to th e followin g
e illpiri ca l forilluia ( 10)
A== lid + k fo r O.OG35 $ d $ n.17 mill
variation of ~l/p a nd A we re studi ed with th e variation of
p . T he o btained va lu es of f,l/p and A ve rs us p, a re plotted
In Fi gs.4 and5 for two pin k g ranite rocks. It is see n th a t
p i p in c reases linearl y w ith p in the e ne rgy range o f
inle res t accordin g to the fo ll ow in g e mpiri cal fo rmu laS,
== hp + C
1'0 1'
nen ti a ll y w ith p acco rdin g to th e fo ll ow ing e illpiri cal
ro rmula .
... ( I 0)
whe re A re prese nt s the rate of c han ge of A w ith d, and k
is a co nstant w h ic h de pe nds o n th e kind of absorbe r, the
~l/ p
w he re h re prese nts th e ra te o f c han ge of p i p w ith p , a nd
(. is ; t co ns tant w hi c h de pe nd s o n the kine! of abso rbe r.
O n th e o th e r ha nd the re lax ati o n le ng th decreases ex po-
0.0635 $ d $ 0.1 7 mm
... ( I I )
A == B P + C fo r 0.0635 $ d $ 0.1 7 mill
... ( 12)
where B re prese nts the rate o f c ha nge o f A w ith p, and
C is a co nstant w hi c h de pe nd s o n th e kind of absorber.
As the powde r gets fin e r ( i.e. d gets s mall e r) the
de ns ity, p, inc reases, thi s in c reas in g th e num be r of scalte rin g centres ca us in g e nh a nced e lilllin ation of ph o to ns
frollllhe inc ide nt bealll, leadin g to in c reased a tte nuati o n.
Th e cO lllpari so ns be tween t he m ass attenu a t io n coe ffic ie nts and re la xa ti o n le ng th fo r two kind s of pink g ra nite
rocks a re s how n in Tables 2 and 3.
pink grani te No.1
0 I' I P
x )..
X
24
0.078
0.078
---1"
Pink grnnilc No.2
)..
Co w ,
~
i'-. ___
0.063
..... ......
,
0.063
;;
c:
'0
"
!l3
'"
'u
E
"
"
"
i'!'g 0048
..:: c:"
o
12
u,g
§" 0.048
"
Cs 137 ,
"
el)'C
~
~/
;;- :1
s
"
; ]'"
i
E
~'
---
---
0
~
., I,
r·'
"-
/~
u
. ~-
-"
12
<=
...
t=
. '"
~
0.'"
Co
01::>: 0.033
.-r-
___c-u-- ~
O _--<'f-" "-
O.O IX
2.20
<=
cY-,
~
"
~
:1 ..".
'"'
~
.g
".-
~
~
GQ
.
·6
+
---------
0.0 18
---------'-_ _ _
2.30
~
_ __
~_....J
2.20
2.10
2.50
2.40
2.'10
2. 30
p,g/CIll'
Fi ~. -I -
V; lri;Hio n or dCllsity (p . g/e IlY\) o r Ihe co mprcsscd sa m·
ri g.. 5 -
t
Vari:l tion or dcnsit y (p. g/C lll ) or thc compressc d sa lll-
pies o j plilk grallit e rock ,\lo. 1 \V ilh hOlh mas s ;llI cll ua tioll
plcs o r pink granitc rock No.1 wi th bot h mas, allcnll at ic>ll
cnclTiClCll t (pip . c m"/g) ;lIld rc l;l xatio ll ICllgth (A. CIIl )
coc lTicicll 1 (pip. cill e/g) alld rcla xali(l n Icngth ( A.
Tabl c I (,h clll COlllp.
Pink (; r;lIli tc
Th c chcmical cOlllposilioll
I'DI'
e lll )
t\Vo pink g r;lIlilc rocks
SiO!
;\l 2()\
FC20 ,
FcO
NgO
CIO
7().')5
14.57
1.56
I.X5
o 91
O.X 7
74.]4
1-1.44
0 11
1.00
(l.45
0.(,1
K20
TiO!
1120 ,
L .O .I.
4 .()1l
:l.50
010
OOX
I).X5
4 .XX
] .00
0 1]0
(J.() I
1.03
;leO
'0. 1
Pill k gr;lllilc
i\o.2
703
MAHMOUD: GAMMA RAY THROUGH GRANITE
Table 2 - Measured values or mass attenuation coefficients and relaxation length for pink granite rock No. 1 with different
radiation source energies
Grain diameter d
mm
Density p
g/cm
C0
60
1.33 & 1.17 MeV
Co 137 0.661 MeV
Bal33 0.36 MeV
3
2
~I cm 2g
Acm
wpcm g
Acm
J.l/p cm l g
Acm
D. 17
2.258
0.01996
22. 19
0.03356
13.19
0.04453
9.95
0.13
2.3D6
0.02204
19.68
0.03708
11.69
0.04922
8.81
0.095
2.327
D.D2362
18.20
(1.03973
10.82
0 .05272
!U5
0.085
2.368
0.02525
16.73
0.04246
9.95
0.05637
7.49
0.n63
2.490
0 .0282R
14.20
0.04762
8.42
0.06321
6.35
Natural rock
2.631
0.02829
13.44
0.04761
7.98
0.06319
6.01
Table 3 - Measured values of mass attenuation coefficients and relaxation length for pink granite rock No.2 with different
radiation source energics
Grain diameter d
mill
Density p
g/cm
Coc..., 1.33 & 1.17 MeV
Com 0.661 MeV
m1p cm 2g
Acm
J.I/p cm g
Acm
J.I/p cm"g
Acm
Bam 0.36 MeV
3
2
n.17
2.1 32
0.01<)96
23.50
(Hl3356
13 .97
0.04453
10.53
n. 13
2.179
n.02204
20.83
0.03708
12.38
0.04922
9.32
0.095
2.198
0.02362
19.26
0.03973
11.45
0.05272
8.63
n.OR5
2.236
0.02525
17.71
0.04246
10.53
0.05637
7.93
n.063
2.352
0.02828
15.03
0.04762
8.93
0.06321
6.73
Natural rock
2.485
0.02829
14.23
0.04761
8.45
0 .06319
6.37
3.2 Half value layer
If a beam of gamma-rays impinges on a sheet of
absorbing material, some of the radiation will pass on
through, while some will be absorbed or scattered . As
the thickness of the absorber is increased, the fraction of
the radiation passing through will decrease. When exactly half the radiation passes through the absorber (the
other half being absorbed or scattered), the thickness of
the absorber is called the half value layer (HVL) or the
ha lf thickness X 1I2 . Since the intensity of radiation is
reduced by 50% by passing through one HVL, then it
wi 1/ be reduced by another SO% of the original intensity
in passin g through ~I second HVL of the absorber').
From the curves plotted between radiation intensity
and absorber thickness, the half value layer X I/l is deter-
-I = e .
2
In 2 = JlXYz
- II'>\-.
In 2
Xy,=--
-
Jl
0.693
Xy, = - - c m
Jl
Tables 4 and 5 present the half value layer for two
pink granite rocks .
(a) Dependence ofX'f2 011 grain size and photon energy
The half value layer X II2 for all samples were calcll-
0.693
·
Iate d f rom t he re Iatlon
( X 112 = -em ), and
-
I I _ I ' - ll ·r,
11 -
2
( , (;
~l
was
11
determined froni the curves between log
mined . The relationship between the hal f value layer and
the linear attenuation coefficient when
X = X I12 and 1= 1/2 In is g iven by
... (13)
~
I,
and X. the
obtained values of X II2 were plotted versus the grai n
diameter (d) for all samples under in vestigation as
shown in Fi g. 6 .
704
INDIA N J PURE APPL PHYS. VOL 37. SEPTEMBER
It was show n that XI /~ increased linearly as the pm1icle
diamete r d increase. T his re lati on could he represented
( c)
16
Il)l)l)
Pink
gr"nit~
' --c~o-I
No. 1
-- ~;:...~---
--'
hy th e empirical formuh t
X II2 = Ad + C
0 .0635 ::; d ::; 0 . 17 cm ... ( 14)
where C is a constant and A represents the rate of
change of X I /~ with d. The variati on of X II!. w ith d can be
exp lained by th e fact th at as the grain diameter (d )
i n c rease ~ the boundary surface area decreases, and th e
Illulti pi e scatterin g dec reases. This dec reases the att enuation of the inc ide nt radiation inside the absorber and
co nseque ntl y the half va lu e layer increases . Fig. 6 shows
a direct proportionality between ha lf va lue layer X I12 and
photon energy .
g
,..
12
X
- -- - .,.---'
0.14
O. IS
0.14
0 .1 '
(0)
16
5
12
3.3 Stlld~' of side scattering and determination of its
coeflicients
The radiation fi e ld at a point in space remote from th e
source ca n be divided into two co mponent s. The first
compo ne nt is th e unco llided (or as th ey are sometimes
called th e unscarte red) photons that arrive at the point
wit hou t hav in g undergo ne any inte racti o ns with th e
transported med iul1l . The second component is composed of the co llided or sc att ered photon s. These ha ve
und ergone one or more interacti ons resultin g in chan ges
of directi on or energy , or both.
To meas ure the scattered radiation, the detector was
placed perpendi cular to th e in c ident radiati o n at a dista nce 01':2 cm from edge of th e samples. The detector
was moved parallel to th e extension of the sa mpl e.
Measure ment s were tak en at equal steps I cm apart.
th e detector was mo ved in a c ircular plane around th e
.\ ampl e di scs at 45 ° inte rvals. the n th e average value o r
the Illeas ured side sca tteri ng was tak en. Three different
pa rameters were investi gated ( I ) The effec t of photon
energy on side scatterin g usin g three different sources
Cow, Cs l17 and Ba l .n
( 2) The density of the absorber
0 ) The effec t o f grain size of sa mpl e materi a l. As in
th e case or co mpressed powdered gabro andtrickto lite 5,
the scattered to primary radiati on rati o (Ii I,,) was found
to decre;lse exponen ti a ll y along th e exte nsion of the
absorber. He nee the empiri cal formula for sid e scatterin g. is give n by
/, = 10 exp (-e(\1)
...( 15)
where 10 is the intensit y or initial radiati on when th ere is
no th ickness, I , th e intensit y of radi ati on after cross in g I
Clll thi ck ness o r the abso rhe r, I the thi ck ness of the
<lbso rber and el\ the side scatte ring coeffic ient , by usin g
I incar equat ion
0. 10
0.06
d J lll11
Fi g. 6 - Var iati on or hall' va lli e 1:lye r (X 112. cm ) and grain
diameler (d. mm) or Ihe comJ1 re~~ ecl ~amples for bOl h pink granite
rock ~ all1J1l e s (a) No . 1 and (b) N o.2
I
log -'.'. = 0.4343eI)s t
I,
<lnd
.
drawlll~
L
.
the re lat io n betwee n
...( 16)
l o~
L
I
I,
-'.'. and I c m. one
can calculate th e sid e scatt ering coeffi c ien ts
e(),
for all
sam ples, where slope of straight line is eq ual 0.4343 cI\.
(0) Relalion he fween side scorrering and hOlh rnalerio /
densily and pholon energy
.
Re lation between side scatterin g coeffi c ien t and ha th
the absorbe r density and the photon e nergy is-studi ed
from Figs.7 and 8, and Tables 6 and7, whic h summari se
the va riati on of" w ith both absorber density. p and
photon energy, E. It is noti ced that
I . T he side scatteri ng coeffi c ient decreases I inea rl y
as the abso rber density increases and thi s can be ex plained as fo ll ows:
Th ere is a change in the sa mpl e density du e to difference in grain size. This increase in the densit y-inc reases
the att enuat ion coeffici ent. which leads to a decrease in
side scatterin g coefficient acco rdin g to the e mpiri cal
fort11ula
Q), = Ap + IJ
1'01' 0.0635 ::; t! ::; 0 . 17 C lll
70)
MAHMOUD: GAMMA RAY THROUGH GRAN ITE
whe re A re presents the rat e of c han ge of (ll, with p. and
(b ) Dependence a/ the side scutrering coefficicnt on
/J is a con stant that depe nds on both the kind of abso rbe r
Rroill diam erer
Side scattering coeffic ients depe nd o n the grain di -
;lIld ph oto n e ne rgy of source .
amete r of th e ;lbsorbe r. This ca n be seen in F igs. 9 and
2 Th e s id e sca tte rin g coeffici e nt (]), increases as th e
10. and Ta bl es 6 and 7. which show the re lati o n between
ph oton e ne rgy in c reases in the e ne rgy ran ge of interest
the g ra in diameter and s id e scatte rin g coeffic ie nt fo r two
(0. 36-1. 33 MeV) . This can be attributed to Compto n
kinds of pink g ranite rocks. It is found that as the gralll
sca tte rin g. he nce th e scattered inte nsi ty is ex pected to
diame ter dec reases, th e s id e scatte rin g coe ffi c ie nt de-
in crease alon g the ex te nsion o f th e absorbe r. whe re th e
scatterin g angle dec reases. Howeve r, it was found that
crease linearl y.
It has been s hown that the s ide sc atte rin g coe ffi c ie nl
th e scatte red inte nsity decreases along the absorber ex-
varies with grain diameter according to the followin g
te nsion. This paradox find s an e xplanation in comparin g
e mpirical formula
(\\ = ed + F
ph oton e ne rgy with side sca tte ring coefficients.
Tahl e 4 -
for OJl635 ::; d ::; 0 . 17 mm ... ( 18)
Hal f vallie layers for pi llk granite rock No . 1
IIVL. l ' m
G I'ain diameter
111111
Co(,()( U 3& 1. 17 M eV)
Cs i:17 (Ol,61 Me V )
l3aI 1~(O .3 (, M eV )
0. 17
I.'d:-l
0. 14
(,. <)0
0. 1:>
13J,4
:-I . 10
(,. I I
1l()'JS
I U, I
7.50
5.(,5
O. OXS
II .Y)
O.O(l.1
'J .X4
5.X4
4.4 0
5. 1<)
Na tural rock
<) .31
5.5 ]
4 . 1(,
Tah le 5 -
Half va lue layers for rink gran ite rock No 1
G rai n diameter
H VL.
C ill
111 III
Cc/'()( 1.3 3 & I . 17 M eV )
Csi:17( OJ,61 M eV)
l3a " \0.](, M eV)
ll. 17
16.2<)
'J .6X
7.30
0. 1,\
14.44
X.W
6.46
o.ms
13. I S
7.93
S.'JX
(). OXS
12.27
7.30
S.60
0.063
10.42
6. 1<)
4.(,6
Natu ra l rock
'J .X(,
.'i.X(,
4.4 1
TOIh ie (, -
Measured v.liues of side sc'lll erin g coe ffi c ients for pi nk grn llite rock
G r;l illdi ;lIl1eter tl.
Densit y r
111111
g/C lly1
Cow 1. 33& 1.1 7M eV
<I', c m
-I
<If'-,
C lll
0 . 1 wit h cli llc rellt radiation source ellergies
l
Col ~7 0. 66 1 M eV
l3a ·\'\ O. 3(,M eV
<II,
Cill
-I
<1,-1,
Cill
<I,s Cill - I
<\>-I ,cm
11 . 17
2.2 5X
O.OS('](,
17.74
O.OSO(, 6
19.74
O.042() I
D. 'O
Il
2.3 0(,
().OSS I 'J
I H. 12
0 .04%0
20.16
tlO41 1:>
14 . J~
2:'27
o ()S46
I H.2X
O.04'J! .'i
20. ] S
004076
2-+.53
2.:1fl:-l
O.OS 374
I RJ,I
(J.()4X 39
20. M
o 04 ()()(,
2-L %
2.4')()
O.O.'i I I I
1'J .S(,
O.04S'J3
21 .77
0.03 x0')
2(' .2)
'2 .fl' I
()()dX 3X
2{)(,7
0 .04347
noo
ll.tnWS
27.74
(j
f) .01))
\l:l lur;JI met..
1)
INDIAN J PURE APPL PHYS. VOL 37. SEPTEMBER 1999
706
pink granite No. J
pink granite No.1
0.058
0.052
I
s
I
I
,.
§ 0046
,
~
<.)
~
i
0.040
o
15
~
~.20
:0
2 .40
I
,~____~~______~i '5
0.034
2.50
0.06
0.1 0
0. 14
O. IS
d.mm
3
Fi!!. 7 -- V, lri al io n o f Jen, ily (p . g/cll1 )
or th e co mpressed
Fi g. 9 -- V ari ati o n or grain di amcler (d. Ill m ) of the co mpressed
,:unp ,l'S of pin, ' grani te roc-k No. I w ith bo th side scallering
sa mples or pink granite rock No. 1 w ith I1mh side scaltering
[ flelfll·l\.:n!s t tl), cm~ ' ) ;mJ I/tl). cm
coefri cicnts (tl) . [ m ~ I ) and I/CI). CI11
0.058 c.
y~'---
~'----~~~25
.~
0.052
I
•
I
I
e
<.)
e
~
;.----
/'"
<.)
0.046
4-
2- -
' 5, 0.046 L
"
~
L'l
'. DJ 1."
20
Sa
;;---~-,
.
20
0.1
-~~ J )
_/~ -
0.040
0.040
0.034 ·
IS
2 .10
2.20
2.30
~IS
0.034
--~------ - ~
0.t 4
0.10
2.40
0.18
d,mm
p,g /cm'
3
Fig. ~ -- Vari ati oo of dcnsity (p . glcm ) or the compressed
Fig. 10 -- V ariation of grai n di ameter (d. 111 111) or thc co mpressed
sampics or pink granit e rock No.2 wi th both side scaltering
sJ l11ples or pink granite rock No.2 with bOlh sidc scat terin!!
coeffic ients (eI>. c m ~ I) and I/CI). cm
coellicients ( ..
I
CI11- )
and II ..
CI11
'
707
MAm OUD: GAMMA RAY TH ROUGH GRANITE
T able 7 -
Measured va lues or side scattering coefTicienls for pink granite rock No.2 w ith dirferent radiation source energies
Grai n diameter d.
fllm
Den sity p .
Co
60
1.33 & 1.17 MeV
Com 0.661 MeV
Ba m 0.36 MeV
g/cm'
<1.\ em
-I
<1>-1, CI11
<I>, cm
-I
<I)-I, em
<1.\ em
-I
<I>-I,el11
() 17
2.1 :1:2
O.OSl)6<)
16.7S
O.OS3R5
IR.61
O.0444lJ
21.4H
0.13
2.1 70
O.OS84 1
17. 12
0.OS240
10.0S
O.ll43S2
22.lJH
O.1l9S
2. ll)H
0.OS7t)I
17.27
O.OS 204
19.22
0.043 i 6
23 . 17
(J.OHS
2.2:\6
(l.()S692
17 .S7
0.05 11S
1<) .55
0.04243
23.57
(l.()63
2.352
O.OS413
18.47
0.04864
20.56
O.()4034
24.70
Natural roek
2.4R5
0.05 123
1<).52
0.04604
2 1.72
0.038 19
26.19
-f'
where <I>, is the side scattering coefficient for the absorbe r, d, is the gra in di a meter, e re presents th e rate of
change of <I>, with d, F is a co nstant \vhich depe nds o n
both the kind of the absorbe r and photon e nergy of
so urce .
The variation of th e scattering coeffici e nts with grain
diamete r ca n be ex plained as follows:
( I) As the powder gets fi ner, the boundary surface
area in crease givin g ri se to multipl e sc attering. This
in creases the path o f inc id e nt radi ation in si de the abso rber. Hence the probabi lity that a photon will be
re moved from the beam in c reases lo . Co nsequ e ntl y th e
side scatterin g coeffic ie nt decreases.
('2) The compressed powdered abs orbe r ca n be con side red as a material containing small random vo ids
betwee n the grain s. As th e rando m void s between th e
grain s increase, the side scattering coefficient increases .
The random voids between grai ns become bi gger as
grain diameter increases so that th e side scattering coefficient is directly proporti o nal to th e grain diamete r.
3.4 Comparative study on two different kinds of pink granite
rocks
From Tabl es 2,3 ,6, 7 it is noticed that va lues of mass
atte nuat ion coefficient (pip ) are equal fo r two pink
gran ite rock samples at th e same gra in size. Th is is true
by defin ition. for two sa mpl es of the same kind. The n
from Tab les 6 and 7 it is noti ced that very small differences in attenuation and side scatteri ng coefficients
(~l,
cD,) are noticeable for two kind s of pink granite rock s .
It is fo und that pink granite rock No . 1 has attenuation
coefficient greater by very small values than that in pink
granite rock No .2, but at the sa me time va lues of th e side
scattering coefficient of pink granite rock No.1 are
sli ghtly smaller than that in pink granite rock No.2 . Th e
small differences in (p, cD,) for two diffe rent ki nds of
pink granite roc ks can be attributed to the fo ll ow in g:
( I ) The pink granite rock No. 1 has de ns ity greater
than that of pink gran ite rock N o.2.
(2) The perc entage conte nt of both ferric and ferrous
ox ide (Fe20 " FeO) in th e pink gra nite roc k No . 1 are
g reater than those of pink g ranite rock No.2.
It is noticed th at both attenuation and side scatteri ng
coefficients (p, <1\) depe nd on the perce ntage co nte nt of
iron compounds, parti c ularl y fe rric ox ide w hi c h contains two atoms of iro n a nd thu s a g reater atomic numbe r
(2) .
4 Conclusion
Th e a im of th e present work is to ide ntify indi geno us
and inex pensive materials to act as a shi e ld , capab le or
minimizing the nuclear radiatio n haza rd s to be low the
permissible dose, as also to study the effect of ferri c and
ferro us oxide on the gamma ray screening pro pe rti es for
materials under in vesti gati o n.
Two pink granite rock samples in natural form as
sheets and ground samp les with diffe re nt grain sizes by
usin g standard sieves with diamete rs ran g in g betvveen
0. 18,0. 16, 0.10, CJ.(19, 0 .08 , (J.071 and OJ)56 mm we re
used . All around roc k sa mpl es were pressed unde r ])
2
ton/cm , to form Tablets 6 c m in diame ter and thi c kness
ranging between 0 .55 and 2.5 cm, be fore bo mbardme nt
with gamma sources of e ne rgies ran g in g betwee n 0.36
60
1,7
I.n
and I. 33 MeV (C0 .Cs and Ba ).
Experimentally both th e linear, mass attenuati on coe fficient s, and side scattering coefficients for the two
pink granite rock samples were determined, usi ng three
different radiation source e ne rg ies. Res ults of th e present work showed that as the percentage c onte nt of both
ferric and ferrous ox ide in crease, the attc nuat ion coeffi-
70X
INDIAN.J PURE APPL PHYS . VOL 37. SEPTEMBER IlJlJ()
li onal Standard Refcrcncc Data systcm . ~~al i o n al Bureau of
standards. (US) Rcport NS RDS-N 352a. ( 1969).
cients increase, whereas the side scatte rin g coefficients
dec rease. The observed small diffe re nces in both and
~l
and <I>, for the two pink g ranite rock sa mples were
attributed to hi gher co ntent of M gO and both ferric and
ferro us oxide, which ha ve hi g h atollli c numbe r and
density .
It is co ncluded that gamma-ray screening properti es
of any mate rial inc rease as the pe rce ntage co ntent of
both ferric and fe rro us ox id e in the material increase.
The two pink granite roc k samples studied could be used
e ffecti ve ly, for gamma-ray shi e lding.
References
1
:2
.
Ferna lldez J E ('{ £I I.• Nlu/ial P/irs
. Cltl'lli. 4 1 ( 1993) 579-630.
3
( IlJ54).
4
Na-
Harima Y. Rat/illl Plt.'"s Clt l'l/l . 4 1 ( 1993 ) 63 1-Cl72 .
Gam lllci Y H (' I al .. !l1/1/ Fa!" Sci Assi ll{ Ulli l'. 2 (I'JXX ) 23 -:1X.
Kapoor S S & Ramalllurlh y V S. Nllcll'o" mlii(l{ i OIl de/I'("{o,..,.
Chaptcr 2. (Wilcy Easlcrn. 130111 ha y). 1')lJ .\ .
7
Ga illeel Y H & Eialtcr A L. /11111 Fw Sci, AssiLII Ullil '. ( i (176 )
X
Hu sscin MM . MSc Thesi s. Assiul Univers ity . Egy pl (I'J X4).
9
Chase. Rilupcr & Sulcoski. £.r/l('l"illl l'lI /.1 ;11 IlUclell,. \"(';ell c('
(A lpha Edili ons. Burgess. USA) . 1971.
10
Ahd-EI-Basel. MSc Thesis. Assiut Universil Y. Egypt. ( llJR3) .
H uhhel J H. PItO/()II CI"IISS .1"l'CliOIlS a ll('II{((lIiOIl coell/cit'll Is allli
('liNg.'" a/J.WI"/I!iOIl c(w/li"c il'lIls/iwl/ 10 kt'V 10 I(}O CeV.
Goldstein H & Wilkins .I E. USAEC REPORT NYO-3075
(NDA- 15C- 4 / ). Nuc lcar Dcvelopmen t Assoc ialcs. Ill c .