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Effect on number albedo values for 662 keV photons from radiation shielding materials stratified with lead
Nuclear Instruments and Methods in Physics Research B34 (1988) 9-14 North-Holland, Amsterdam
9
EFFECT ON NUMBER ALBEDO VALUES FOR 662 keV PHOTONS FROM RADTATION SHIEL,DING MATERIALS STRATIFIED WITH LEAD
A. BHAnACHARJEE
and A.K. SINHA
Department of Physics, Regional Engineering Coilege, Sikhar-788 010, Assam, India
Received 28 August 1987 and in revised form 6 April 1988
Albedo measurements for backscattered gamma rays from semi-infinite scatterers have suitable applications in the design of gamma ray shields particularly in nuclear reactor and accelerator shields and in many other nuclear installations. The insertion of lead slabs into stratified combination with other shielding materials has been found to increase the shielding property appreciably. The stratified slabs of alternating heterogeneous layers have been found in this investigation to have a virtual homogeneous property with a definite effective atomic number. The purpose of the present investigation is to find out the extent to which the shielding property increases in binary configuration with lead and to investigate into the dependence of the saturation thickness of the shielding media on the effective atomic number of each configuration. The indigeneously designed Uniform Sensitivity Photon Counter used in this investigation has an edge over all previous methods of experimental measurements that it is independent of response correction. The number albedo values as well as angular distribution of backscattered photons for iron, aluminium and concrete stratified with lead slabs at 662 keV energy have been reported here.
1. Introduction Experimentally obtained albedo values for semi-infinite single layer scatterers have been used since the mid sixties as a parameter in designing gamma ray shields [l-6]. However the literature on albedo measurements for stratified layers is scarce. Hyodo [7] carried out measurements with stratified layers of aluminium and tin. Nakata [8] investigated the effect of lead sheet placed in front of semi-infinite concrete slabs, though the investigation was not exhaustive. It is observed in the present investigation that a suitable combination of stratified layers of different materials and thickness increases the shielding property. Because of high photoelectric absorption of lead, stratified layers of lead with slabs of other materials decreases the shielding thickness to an appreciable extent. The stratified slabs of alternating heterogeneous layers of different materials are found to have a virtual homogeneous property and the effective atomic number are computed on this assumption. The measured albedo values of stratified slabs are found to agree well with their computed effective atomic number. Albedo measurements for photons backscattered from various scatterers were carried out by Hyodo [l], Pozdneyev [2], and Nakata [8] using a phosphor detector coupled with a multichannel analyser. Since backscattered photons have mixed energies, the spectrum obtained by above method needed response correction. The indigeneously designed Uniform Sensitivity Photon Counter (USPC) has an advantage over previous mea0168-583X/8&/$03.50 0 Elsevier Science Publishers B.V. {North-Holland Physics Publishing Division)
surements since it is independent of response correction and the results are obtained in a straightforward manner. In the present investigation USPC has been used for the measurement of differential and total albedo values for backscattered 662 keV photons from stratified combination of iron, aluminium and concrete with lead. 2. Uniform sensitivity photon counter It has been shown by Ghose [9] that by using a filter of suitable material and thickness with a NaI(T1) crystal, 1.0
0.8
t 0.6 E: 0.4 0.2
0
I,
I
,j
0.6 1.0 t--+ Fig. 1. Efficiency vs fraction of time graph. 0
10
A. Bhattacharjee, AX
Sinha / Albedo values for 662 kevphotons Table 1 Size and thickness of scatterers used
0.4 r
a1 0
2.0 1.0 E in Mev Fig. 2. Variation of calculatedefficiency with energy forf = 0.8. the efficiency of the filter-crystal combination remains constant from 250 keV in the lower energy range and above. For paraxially incident gamma rays, the intrinsic efficiency of the filter-crystal comb~ation expressed in counts/photo~ is given by 2:= (I-
eFaP) eBb+,
where a and b are the thicknesses of the crystal and the filter and $I and n are total and noncoherent absorption coefficient of the filter and the crystal respectively. It was further shown that if the filter of suitable thickness and material was kept in front of the NaI(Tl) crystal for a certain period f and then removed for the period (1 -f), the efficiency of the combination under the condition would be E = (I-
e-“P)f(l
-f)
i-f ePb*].
Since the above equation is linear with f, the E vs f lines for a particular set of a and b and for different values of gamma ray energies will ideally intersect at a point. For this value of f the ideal response photon counter will have equal efficiency for the same energy range under wnsideration. In practice the value of f has a spread over a smal1 range the centre of which may be taken as the optimum value of f as shown in fig. 1. If e is calculated for the photon energies under consideration using the optimum value of f, the efficiency of the combination is found to remain constant as shown in fig. 2. In the present inv~tigation the material of the filter is ~~~~ of thickness 35 g/cm’, the crystal is a 2 x 2 in. NaI(Tl) scintillator and the optimum value of f is 0.8.
Scatterer
Thickness of each plate (cm)
Dimensions or latera (cm’ )
Symbol in a configuration
Aluminium Iron Concrete Lead
0.3 0.3 2 0.1
40x40 40x40 40x40
A I C L
40X40
men&on and symmetry in a configuration which are given in table 1. The semi-infinite dimension of each slab has been considered by making the source-to-slab distance much smaller than the surface dimension of the slab. This will minimise the escape of photons from the edge of the slab. The isotropic 137Cs source of 30 PCi strength is placed at the point of intersection of the centre of the first layer and the axis of the detector as shown in fig. 3. The front face of the first layer is kept at a distance of 100 cm from the detector. The different scatterer slabs are placed on a goniometer calibrated in degrees. The angle B between the normal to the surface of the scatterer and the detector axis is measured at intervals A0 equal to 10 o from 0 o to 90 O. To eliminate forward scattered radiation at the 90* position, the goniometer is placed close to 90 O. The whole assembly was placed on a foam bed at an appreciable distance from the floor to avoid scattering from there. Moreover foam has a negligible scattering effect and the walls and ceilings being at a distance from the detecting assembly have little to contribute. The total and d~ferenti~ albedo values for single layer of individual scatterer and their stratified composition in different configurations for 662 keV photon energy have been measured. The subscript in a configuration shows the total number of plate(s) of the material present in each configuration. For example in the L,Ai wn~gmation one plate of lead is followed by one plate of sunburn and the arrangement has been repeated. Similarly in the L&Z, configuration two plates of lead have been placed in front of one plate of concrete and
3. Experimental arrangement and method 3.1. Experimental
arrangement
In the present investigation composite layers of aluminium, iron, concrete and lead have been used. Concrete slabs have been made by mixing 25% cement of quoted composition with 25% gravel and 50% sand. Each concrete slab is supplied with an iron net inside, The size and thickness of each scatterer used in this measurement for full emergence of backscattered photons has been decided considering semi-infinite di-
GmiMnocer J.-L i I I II II FOAM L
BE@
Fig. 3. Experimental arrangement.
A. Bhattacharjee, A.K. Sinha / Albedo values for 662 keVphotons
the arrangement is repeated. The same arrangement has been followed in all other configurations. The conventional electronic circuitry comprising of a pulse amplifier, a single channel analyser and a decade scaler has been used.
11
coefficient (?) to the total attenuation coefficient ($‘j. The total attenuation coefficient (&) and the scattering coefficient (&) of the two constituent materials in the heterogeneous mixture at the energy (Ei) are obtained using the formmae given below when the strati-
fied composition is assumed as a homogeneous entity. 3.2. Experimental
method
The differential number albedo Nd(@, X) for a particular angle f3 and slab thickness x is expressed by the fraction of photons emerging at the angle B per steradian and for one primary photon incident on the scatterer. The total number albedo for a particular thickness is obtained by integrating the differential values over angular coordinates. The total number albedo N(x) for a particular thickness x is calculated using the following equation: k=9
where the solid angle Qnk= /Ae/z2~
sin t? d0
where two materials are Ml and M2 and their weight fractions are whll and wM2 respectively. Following the above procedure the ratios of &.J&, are calculated at various energies. The ratio of $//J,’ for various pure elements with atomic number close to the composite materials are then computed. By interpolation the effective atomic number Z,,, of the composite layer is determined- It has also been observed that Zen depends slightly on energy. By the above method the computed value of effective atomic number of concrete slabs used in the present investigation was found to be 12.71 for 662 keV photon energy.
for k=O,
0 +
f
(k++)Ae2~
s (k-
kA8 f (k-t)
sin i3
;) de
de
211 sin f? df?
for I< k<8,
for k=9,
A@
and where 48 = 10 O. The integral counts were noted with anafyser bias well below the backscattered peak for a time to have good counting statistics. The differential number albedo value N,(B, x) for a definite thickness x measured in angular steps of 10” were calculated by subtracting integral counts without the scatterer from that with the scatterer for a counting time 100 s considering the value of f= 0.8. The total number albedo N(x) for a particular thickness x was obtained by integration over angular coordinates as shown in the equation. The total albedo values were obtained for three different bias settings of the pulse height analyser. The bias were set at 1, 2 and 3 V to include backscattered radiation and to avoid noise at zero bias of the anafyser. Readings were then extrapolated to zero bias and the extrapolated value was considered as the total number albedo value.
4. Effective atomic number The effective atomic number of the heterogeneous layer of two materials has been calculated on the procedure followed by Berger and Raso [LOI. The quantity which distinguishes the backscattering from one material from that of another is the ratio of the scattering
5. Results and discussion The total albedo values for stratified combinations of lead and ahnnininm in two configurations and lead and concrete in three configurations at 662 keV energy are shown in fig. 4. The two lead/duminium configurations are the stratified combinations A,L, and ItAt with aluminium and lead as first layer, respectively. It is seen in table 2 that the total albedo value is higher when a scatterer of lower atomic number is used as the first layer in a configuration. From table 2 we observe that the effect of backscattering from the first layer is significant and the backscattering of gamma rays mostly arises in the region near the front surface of the slab. The dimensions of individual scatterers, weight fractions, their atomic number and effective atomic number of stratified layers are shown in table 3. It is observed from table 3 that the effective atomic number of stratified composition lies between the atomic number of constituent elements. The minimum thickness of a scattering surface for which the backscattering effect is maximum is considered as the saturation thickness. The total number albedo values as well as saturation thickness of aluminium, iron, concrete, lead and their stratified configurations are shown in table 4. The experimentally obtained values of saturation thickness for 662 keV photons as shown in table 4 when plotted decreases
exponentially with the increase of atomic number (fig. 5). This observation agrees well with that of Paramesh et al. 1111. It is further observed from the same table that the saturation thickness reduces to an appreciable extent when lead scatterers are inserted inside scattering
12
A. Bhattacharjee, A.K. Sinha / Albedo values for 662 keYphotons
r
662 keV
E ”
L, A,____A___. 0 -cl
1
Q
1
1
1
1
1.0
1
’
1
2.0
.-= * z
8-
; .E
6-
i-1cl A L2 q-w L3 q-o-0
0
1
I 1 1 1 I 2 4 6 Thickness incm
’
1
8
’
69.11
LI*I Ilk1 Llfl
57.92
ClJ-1
46.78
LlCl
Total albedo value
Percentage of difference
0.185 0.145 0.245 0.130 0.3175 0.145
21.62
+ 0.01 f 0.01 f 0.01 f 0.01 f 0.01 +0.01
1
1
0
I
IO
Table 2 Total albedo values showing dependence on front layer material
AILI
-
01
Fig. 4. Total number albedo values as a function of thickness for stratified configurations of aluminium, lead and concrete for 662 keV photons.
Symbol of the configuration
-
I
I
I
30 Atomic
-_ ---__
I
J-7
60
I 90
Number
Fig. 5. Saturation thickness as a function of atomic number. Present investigation -; Paramesh et al., - - -.
slabs of aluminium, iron and concrete. The angular distributions of backscattered 662 keV photons are shown in fig. 6. The total albedo values of individual elements and the average values of the stratified combination of &I-,, Ii&). (IiLi, L,IJ and GLi, L,CJ as a function of atomic number are shown in fig. 7. The results obtained in the present investigation are in good agreement with the values obtained by Hyodo for single layer elements. It is observed in the present investigation both from the table and the graph that the number albedo values decrease with increasing atomic number. This is because the cross-section for photoelectric ab-
46.93 54.33
Table 3 Thickness, number of plates and weight fraction of constituent scatterer(s) and effective atomic number of each configuration Configuration
Thickness of constituent scatterer(s) (cm)
No. of plates of constituent scatterers
Weight fraction
f-r*, f-a*, f&r &I, &I, w, LIC, w, w,
L = 0.1 L=O.2 L = 0.3 L = 0.1 L = 0.2 L = 0.3 L = 0.1 L = 0.2 L=O.3
L=l L=2 L=3 L=l L=2 L=3 L=l L=2 L=3
W, W, W, W, w, w, W, W, W,
A = 0.3 ‘4=0.3 A = 0.3 z = 0.3 z = 0.3 z = 0.3 c = 2.0 c= 2.0 c=2.0
A=1 A=1 A=1 I=1 Z=l Z=l C=l C=l C=l
= = = = = = = = =
0.583 0.737 0.802 0.325 0.490 0.591 0.171 0.292 0.382
W, = W, = W, = W, = w, = w, = WC = WC= WC=
Computed Z 0.417 0.263 0.192 0.675 0.510 0.409 0.829 0.708 0.618
57.92 65.72 70.00 46.78 54.85 59.43
13
A, Bhattacharjee, A. K. Sinha / Albedo values for 662 ke Vphotons Table 4 Total rmmber aibedo values and saturation thickness of scatterers and their stratified combination Element or configuration
Z or 2 err
Saturation thickness
Total munber albedo value Present work
Sinha et al.
Hvodo et al.
Monte Carlo
A
13.00 69.11 74.99 77.00 82.00 57.92 65.72 70.00 26.00 46.78 54.85 59.43 12.71
7.8 1.2 I.0 0.9 0.4 I.2 1.0 0.9 3.3 4.2 2.4 2.3 12.0
0.565 k 0.009 0.145 * 0.009 0.120+0.009 0.095 + 0.009 0.082 -I_0.009
0.545 It 0.006
0.59iO.02
-
LA L2A1 L,A,
L LlIl Wl L3Il
I L,Cr L2Cl L3Cl
C
0.105 _t 0.002
0.09 + 0.02
0.07
0.130 0.105 0.100 0.395
+ 0.009 * 0.009 -i_0.009 i 0.009
0.35 tro.01
0.42 * 0.02
0.32
0.145 0.115 0.096 0.45
* 0.009 i: 0.009 f 0.009 *to.01
0.405 *0.01
-
0.43
sorption for incident photons increases with the increase of atomic number. For the same reasons the total number albedo values for the stratified layers lie between albedo values of component layers. This also
662 Kev
L,Tl .......A .._ L2Il ____.D_____ L3II ---o--
40
col~f~rms appr~able reduction of satm~tion thickness when plates of higher atomic number are alternately placed between slabs of lower atomic number. The sharp decrease of backscattering of gamma rays occurs with the increase of atomic number for the same reason. A comparative study of total albedo values with other available data both with experimental and theoretical Monte car10 values particularly in case of single layer elements confirms the successful application of USPC in the measurement of number albedo [12,13].
2
X. ul ?$ $
L, A, ..
40
&A4
t
A I.....
..-_-n____
L3_At--O--
Heterogeneous Angle
Q
in degree
Fig. 6. Angular distribution of backscattered 662 keV Photons for stratified configurations of alum.inium, iron, lead and concrete.
Layer
Atomic
Number
Z
Pig. 7. Total albedo as a function of atomic number.
14
A. Bhattacharjee, A.K. Sinha / Albedo values for 662 kevphotons
The authors are grateful to the Department of Atomic Energy, Government of India for financing the work. One of the authors (A.B.) expresses his gratitude to the Principal, Regional Engineering College, Silchar for the kind permission accorded to him to undertake the work.
References [l] T. Hyodo, Nucl. Sci. Eng. 12 (1962) 178. [2] D.B. Pozdneyev, J. Nucl. Eng. 21 (1967) 197. [3] J.J. Steyn and D.G. Andrews, Nucl. Sci. Eng. 27 (1967) 318. [4] M. Biswas, A.K. Sinha and S.C. Roy, Nucl. Instr. and Meth. 159 (1980) 157.
[A M. Biswas, A.K. Sinha and S.C. Roy, J. Nucl. Sci. Tech. 17 (1980) 559. [61A.K. Sinha, A. Chatterjee and A.M. Ghose, Proc. 2nd. Int. Symp. Rad. Phys. Penang (May 25-29, 1982) p. 918. 171 T. Hyodo, J. Nucl. Sci. Tech. 5 (1968) 458. PI M. Nakata, J. Nucl. Sci. Tech. 10 (1961) 263. 191A.M. Ghose, Nucl. Instr. and Meth. 34 (1965) 45. [W M.J. Berger and D.J. Raso, Radiat. Res. 12 (1960) 20. [111 L. Paramesh, P. Venkatramaiah, K. Gopala and H. Sanjecviah, Nucl. Instr. and Meth. 206 (1983) 327. 1121A.K. Sinha and A. Bhattacharjee, Proc. IEEE 9th Conf. Engineering Med. Bio. Sot. Boston (Nov 13-16, 1987) p. 1967. 1131A.K. Sinha and A. Bhattacharjee, Ind. J. Phys. 62A (1988) 31.
9
EFFECT ON NUMBER ALBEDO VALUES FOR 662 keV PHOTONS FROM RADTATION SHIEL,DING MATERIALS STRATIFIED WITH LEAD
A. BHAnACHARJEE
and A.K. SINHA
Department of Physics, Regional Engineering Coilege, Sikhar-788 010, Assam, India
Received 28 August 1987 and in revised form 6 April 1988
Albedo measurements for backscattered gamma rays from semi-infinite scatterers have suitable applications in the design of gamma ray shields particularly in nuclear reactor and accelerator shields and in many other nuclear installations. The insertion of lead slabs into stratified combination with other shielding materials has been found to increase the shielding property appreciably. The stratified slabs of alternating heterogeneous layers have been found in this investigation to have a virtual homogeneous property with a definite effective atomic number. The purpose of the present investigation is to find out the extent to which the shielding property increases in binary configuration with lead and to investigate into the dependence of the saturation thickness of the shielding media on the effective atomic number of each configuration. The indigeneously designed Uniform Sensitivity Photon Counter used in this investigation has an edge over all previous methods of experimental measurements that it is independent of response correction. The number albedo values as well as angular distribution of backscattered photons for iron, aluminium and concrete stratified with lead slabs at 662 keV energy have been reported here.
1. Introduction Experimentally obtained albedo values for semi-infinite single layer scatterers have been used since the mid sixties as a parameter in designing gamma ray shields [l-6]. However the literature on albedo measurements for stratified layers is scarce. Hyodo [7] carried out measurements with stratified layers of aluminium and tin. Nakata [8] investigated the effect of lead sheet placed in front of semi-infinite concrete slabs, though the investigation was not exhaustive. It is observed in the present investigation that a suitable combination of stratified layers of different materials and thickness increases the shielding property. Because of high photoelectric absorption of lead, stratified layers of lead with slabs of other materials decreases the shielding thickness to an appreciable extent. The stratified slabs of alternating heterogeneous layers of different materials are found to have a virtual homogeneous property and the effective atomic number are computed on this assumption. The measured albedo values of stratified slabs are found to agree well with their computed effective atomic number. Albedo measurements for photons backscattered from various scatterers were carried out by Hyodo [l], Pozdneyev [2], and Nakata [8] using a phosphor detector coupled with a multichannel analyser. Since backscattered photons have mixed energies, the spectrum obtained by above method needed response correction. The indigeneously designed Uniform Sensitivity Photon Counter (USPC) has an advantage over previous mea0168-583X/8&/$03.50 0 Elsevier Science Publishers B.V. {North-Holland Physics Publishing Division)
surements since it is independent of response correction and the results are obtained in a straightforward manner. In the present investigation USPC has been used for the measurement of differential and total albedo values for backscattered 662 keV photons from stratified combination of iron, aluminium and concrete with lead. 2. Uniform sensitivity photon counter It has been shown by Ghose [9] that by using a filter of suitable material and thickness with a NaI(T1) crystal, 1.0
0.8
t 0.6 E: 0.4 0.2
0
I,
I
,j
0.6 1.0 t--+ Fig. 1. Efficiency vs fraction of time graph. 0
10
A. Bhattacharjee, AX
Sinha / Albedo values for 662 kevphotons Table 1 Size and thickness of scatterers used
0.4 r
a1 0
2.0 1.0 E in Mev Fig. 2. Variation of calculatedefficiency with energy forf = 0.8. the efficiency of the filter-crystal combination remains constant from 250 keV in the lower energy range and above. For paraxially incident gamma rays, the intrinsic efficiency of the filter-crystal comb~ation expressed in counts/photo~ is given by 2:= (I-
eFaP) eBb+,
where a and b are the thicknesses of the crystal and the filter and $I and n are total and noncoherent absorption coefficient of the filter and the crystal respectively. It was further shown that if the filter of suitable thickness and material was kept in front of the NaI(Tl) crystal for a certain period f and then removed for the period (1 -f), the efficiency of the combination under the condition would be E = (I-
e-“P)f(l
-f)
i-f ePb*].
Since the above equation is linear with f, the E vs f lines for a particular set of a and b and for different values of gamma ray energies will ideally intersect at a point. For this value of f the ideal response photon counter will have equal efficiency for the same energy range under wnsideration. In practice the value of f has a spread over a smal1 range the centre of which may be taken as the optimum value of f as shown in fig. 1. If e is calculated for the photon energies under consideration using the optimum value of f, the efficiency of the combination is found to remain constant as shown in fig. 2. In the present inv~tigation the material of the filter is ~~~~ of thickness 35 g/cm’, the crystal is a 2 x 2 in. NaI(Tl) scintillator and the optimum value of f is 0.8.
Scatterer
Thickness of each plate (cm)
Dimensions or latera (cm’ )
Symbol in a configuration
Aluminium Iron Concrete Lead
0.3 0.3 2 0.1
40x40 40x40 40x40
A I C L
40X40
men&on and symmetry in a configuration which are given in table 1. The semi-infinite dimension of each slab has been considered by making the source-to-slab distance much smaller than the surface dimension of the slab. This will minimise the escape of photons from the edge of the slab. The isotropic 137Cs source of 30 PCi strength is placed at the point of intersection of the centre of the first layer and the axis of the detector as shown in fig. 3. The front face of the first layer is kept at a distance of 100 cm from the detector. The different scatterer slabs are placed on a goniometer calibrated in degrees. The angle B between the normal to the surface of the scatterer and the detector axis is measured at intervals A0 equal to 10 o from 0 o to 90 O. To eliminate forward scattered radiation at the 90* position, the goniometer is placed close to 90 O. The whole assembly was placed on a foam bed at an appreciable distance from the floor to avoid scattering from there. Moreover foam has a negligible scattering effect and the walls and ceilings being at a distance from the detecting assembly have little to contribute. The total and d~ferenti~ albedo values for single layer of individual scatterer and their stratified composition in different configurations for 662 keV photon energy have been measured. The subscript in a configuration shows the total number of plate(s) of the material present in each configuration. For example in the L,Ai wn~gmation one plate of lead is followed by one plate of sunburn and the arrangement has been repeated. Similarly in the L&Z, configuration two plates of lead have been placed in front of one plate of concrete and
3. Experimental arrangement and method 3.1. Experimental
arrangement
In the present investigation composite layers of aluminium, iron, concrete and lead have been used. Concrete slabs have been made by mixing 25% cement of quoted composition with 25% gravel and 50% sand. Each concrete slab is supplied with an iron net inside, The size and thickness of each scatterer used in this measurement for full emergence of backscattered photons has been decided considering semi-infinite di-
GmiMnocer J.-L i I I II II FOAM L
BE@
Fig. 3. Experimental arrangement.
A. Bhattacharjee, A.K. Sinha / Albedo values for 662 keVphotons
the arrangement is repeated. The same arrangement has been followed in all other configurations. The conventional electronic circuitry comprising of a pulse amplifier, a single channel analyser and a decade scaler has been used.
11
coefficient (?) to the total attenuation coefficient ($‘j. The total attenuation coefficient (&) and the scattering coefficient (&) of the two constituent materials in the heterogeneous mixture at the energy (Ei) are obtained using the formmae given below when the strati-
fied composition is assumed as a homogeneous entity. 3.2. Experimental
method
The differential number albedo Nd(@, X) for a particular angle f3 and slab thickness x is expressed by the fraction of photons emerging at the angle B per steradian and for one primary photon incident on the scatterer. The total number albedo for a particular thickness is obtained by integrating the differential values over angular coordinates. The total number albedo N(x) for a particular thickness x is calculated using the following equation: k=9
where the solid angle Qnk= /Ae/z2~
sin t? d0
where two materials are Ml and M2 and their weight fractions are whll and wM2 respectively. Following the above procedure the ratios of &.J&, are calculated at various energies. The ratio of $//J,’ for various pure elements with atomic number close to the composite materials are then computed. By interpolation the effective atomic number Z,,, of the composite layer is determined- It has also been observed that Zen depends slightly on energy. By the above method the computed value of effective atomic number of concrete slabs used in the present investigation was found to be 12.71 for 662 keV photon energy.
for k=O,
0 +
f
(k++)Ae2~
s (k-
kA8 f (k-t)
sin i3
;) de
de
211 sin f? df?
for I< k<8,
for k=9,
A@
and where 48 = 10 O. The integral counts were noted with anafyser bias well below the backscattered peak for a time to have good counting statistics. The differential number albedo value N,(B, x) for a definite thickness x measured in angular steps of 10” were calculated by subtracting integral counts without the scatterer from that with the scatterer for a counting time 100 s considering the value of f= 0.8. The total number albedo N(x) for a particular thickness x was obtained by integration over angular coordinates as shown in the equation. The total albedo values were obtained for three different bias settings of the pulse height analyser. The bias were set at 1, 2 and 3 V to include backscattered radiation and to avoid noise at zero bias of the anafyser. Readings were then extrapolated to zero bias and the extrapolated value was considered as the total number albedo value.
4. Effective atomic number The effective atomic number of the heterogeneous layer of two materials has been calculated on the procedure followed by Berger and Raso [LOI. The quantity which distinguishes the backscattering from one material from that of another is the ratio of the scattering
5. Results and discussion The total albedo values for stratified combinations of lead and ahnnininm in two configurations and lead and concrete in three configurations at 662 keV energy are shown in fig. 4. The two lead/duminium configurations are the stratified combinations A,L, and ItAt with aluminium and lead as first layer, respectively. It is seen in table 2 that the total albedo value is higher when a scatterer of lower atomic number is used as the first layer in a configuration. From table 2 we observe that the effect of backscattering from the first layer is significant and the backscattering of gamma rays mostly arises in the region near the front surface of the slab. The dimensions of individual scatterers, weight fractions, their atomic number and effective atomic number of stratified layers are shown in table 3. It is observed from table 3 that the effective atomic number of stratified composition lies between the atomic number of constituent elements. The minimum thickness of a scattering surface for which the backscattering effect is maximum is considered as the saturation thickness. The total number albedo values as well as saturation thickness of aluminium, iron, concrete, lead and their stratified configurations are shown in table 4. The experimentally obtained values of saturation thickness for 662 keV photons as shown in table 4 when plotted decreases
exponentially with the increase of atomic number (fig. 5). This observation agrees well with that of Paramesh et al. 1111. It is further observed from the same table that the saturation thickness reduces to an appreciable extent when lead scatterers are inserted inside scattering
12
A. Bhattacharjee, A.K. Sinha / Albedo values for 662 keYphotons
r
662 keV
E ”
L, A,____A___. 0 -cl
1
Q
1
1
1
1
1.0
1
’
1
2.0
.-= * z
8-
; .E
6-
i-1cl A L2 q-w L3 q-o-0
0
1
I 1 1 1 I 2 4 6 Thickness incm
’
1
8
’
69.11
LI*I Ilk1 Llfl
57.92
ClJ-1
46.78
LlCl
Total albedo value
Percentage of difference
0.185 0.145 0.245 0.130 0.3175 0.145
21.62
+ 0.01 f 0.01 f 0.01 f 0.01 f 0.01 +0.01
1
1
0
I
IO
Table 2 Total albedo values showing dependence on front layer material
AILI
-
01
Fig. 4. Total number albedo values as a function of thickness for stratified configurations of aluminium, lead and concrete for 662 keV photons.
Symbol of the configuration
-
I
I
I
30 Atomic
-_ ---__
I
J-7
60
I 90
Number
Fig. 5. Saturation thickness as a function of atomic number. Present investigation -; Paramesh et al., - - -.
slabs of aluminium, iron and concrete. The angular distributions of backscattered 662 keV photons are shown in fig. 6. The total albedo values of individual elements and the average values of the stratified combination of &I-,, Ii&). (IiLi, L,IJ and GLi, L,CJ as a function of atomic number are shown in fig. 7. The results obtained in the present investigation are in good agreement with the values obtained by Hyodo for single layer elements. It is observed in the present investigation both from the table and the graph that the number albedo values decrease with increasing atomic number. This is because the cross-section for photoelectric ab-
46.93 54.33
Table 3 Thickness, number of plates and weight fraction of constituent scatterer(s) and effective atomic number of each configuration Configuration
Thickness of constituent scatterer(s) (cm)
No. of plates of constituent scatterers
Weight fraction
f-r*, f-a*, f&r &I, &I, w, LIC, w, w,
L = 0.1 L=O.2 L = 0.3 L = 0.1 L = 0.2 L = 0.3 L = 0.1 L = 0.2 L=O.3
L=l L=2 L=3 L=l L=2 L=3 L=l L=2 L=3
W, W, W, W, w, w, W, W, W,
A = 0.3 ‘4=0.3 A = 0.3 z = 0.3 z = 0.3 z = 0.3 c = 2.0 c= 2.0 c=2.0
A=1 A=1 A=1 I=1 Z=l Z=l C=l C=l C=l
= = = = = = = = =
0.583 0.737 0.802 0.325 0.490 0.591 0.171 0.292 0.382
W, = W, = W, = W, = w, = w, = WC = WC= WC=
Computed Z 0.417 0.263 0.192 0.675 0.510 0.409 0.829 0.708 0.618
57.92 65.72 70.00 46.78 54.85 59.43
13
A, Bhattacharjee, A. K. Sinha / Albedo values for 662 ke Vphotons Table 4 Total rmmber aibedo values and saturation thickness of scatterers and their stratified combination Element or configuration
Z or 2 err
Saturation thickness
Total munber albedo value Present work
Sinha et al.
Hvodo et al.
Monte Carlo
A
13.00 69.11 74.99 77.00 82.00 57.92 65.72 70.00 26.00 46.78 54.85 59.43 12.71
7.8 1.2 I.0 0.9 0.4 I.2 1.0 0.9 3.3 4.2 2.4 2.3 12.0
0.565 k 0.009 0.145 * 0.009 0.120+0.009 0.095 + 0.009 0.082 -I_0.009
0.545 It 0.006
0.59iO.02
-
LA L2A1 L,A,
L LlIl Wl L3Il
I L,Cr L2Cl L3Cl
C
0.105 _t 0.002
0.09 + 0.02
0.07
0.130 0.105 0.100 0.395
+ 0.009 * 0.009 -i_0.009 i 0.009
0.35 tro.01
0.42 * 0.02
0.32
0.145 0.115 0.096 0.45
* 0.009 i: 0.009 f 0.009 *to.01
0.405 *0.01
-
0.43
sorption for incident photons increases with the increase of atomic number. For the same reasons the total number albedo values for the stratified layers lie between albedo values of component layers. This also
662 Kev
L,Tl .......A .._ L2Il ____.D_____ L3II ---o--
40
col~f~rms appr~able reduction of satm~tion thickness when plates of higher atomic number are alternately placed between slabs of lower atomic number. The sharp decrease of backscattering of gamma rays occurs with the increase of atomic number for the same reason. A comparative study of total albedo values with other available data both with experimental and theoretical Monte car10 values particularly in case of single layer elements confirms the successful application of USPC in the measurement of number albedo [12,13].
2
X. ul ?$ $
L, A, ..
40
&A4
t
A I.....
..-_-n____
L3_At--O--
Heterogeneous Angle
Q
in degree
Fig. 6. Angular distribution of backscattered 662 keV Photons for stratified configurations of alum.inium, iron, lead and concrete.
Layer
Atomic
Number
Z
Pig. 7. Total albedo as a function of atomic number.
14
A. Bhattacharjee, A.K. Sinha / Albedo values for 662 kevphotons
The authors are grateful to the Department of Atomic Energy, Government of India for financing the work. One of the authors (A.B.) expresses his gratitude to the Principal, Regional Engineering College, Silchar for the kind permission accorded to him to undertake the work.
References [l] T. Hyodo, Nucl. Sci. Eng. 12 (1962) 178. [2] D.B. Pozdneyev, J. Nucl. Eng. 21 (1967) 197. [3] J.J. Steyn and D.G. Andrews, Nucl. Sci. Eng. 27 (1967) 318. [4] M. Biswas, A.K. Sinha and S.C. Roy, Nucl. Instr. and Meth. 159 (1980) 157.
[A M. Biswas, A.K. Sinha and S.C. Roy, J. Nucl. Sci. Tech. 17 (1980) 559. [61A.K. Sinha, A. Chatterjee and A.M. Ghose, Proc. 2nd. Int. Symp. Rad. Phys. Penang (May 25-29, 1982) p. 918. 171 T. Hyodo, J. Nucl. Sci. Tech. 5 (1968) 458. PI M. Nakata, J. Nucl. Sci. Tech. 10 (1961) 263. 191A.M. Ghose, Nucl. Instr. and Meth. 34 (1965) 45. [W M.J. Berger and D.J. Raso, Radiat. Res. 12 (1960) 20. [111 L. Paramesh, P. Venkatramaiah, K. Gopala and H. Sanjecviah, Nucl. Instr. and Meth. 206 (1983) 327. 1121A.K. Sinha and A. Bhattacharjee, Proc. IEEE 9th Conf. Engineering Med. Bio. Sot. Boston (Nov 13-16, 1987) p. 1967. 1131A.K. Sinha and A. Bhattacharjee, Ind. J. Phys. 62A (1988) 31.