CC BY
34
UDC 621.039.51
Badawi M.S., Gouda M.M., El-Khatib A.M., Nafee S.S., El-Mallah E.A.
Physics Department, Faculty of Science, Alexandria University, 21511 Alexandria, Egypt
NEW ANALYTICAL APPROACH TO CALIBRATE CYLINDRICAL HPGE DETECTOR INCLUDING CORRECTIONS FOR SELF ATTENUATION OF LARGE CYLINDRICAL SOURCES AND ATTENUATION OF ALL DETECTOR
HOUSING MATERIALS
HPGe semiconductor detectors are very useful for radioactivity measurement and to calculate the absolute activity, the full energy peak efficiency of the detector is needed. In this work, to calibrate the co-axial HPGe semiconductor detector, we introduce a new theoretical approach based on the Direct Statistical method proposed by Selim and Abbas to calculate the full-energy peak efficiency for cylindrical detectors. The present method depends on the accurate analytical calculation of the average path length covered by the photon inside the detector active volume and the geometrical solid angle, to obtain a simple formula for the efficiency. In addition, self attenuation of source matrix (with radius greater than the radius of the detector), the attenuation by the source container and the detector housing materials are also treated by calculating the average path length cross these materials. 152 Eu aqueous sources covering the energy range from 121 up to 1408 keV were used. Remarkable agreement between the measured and the calculated efficiencies is achieved with discrepancies less than 2%.
Keywords: HPGe detectors, large cylindrical sources, full-energy peak efficiency and self-attenuation.
1. Introduction
For low activity samples, using the extended sources in gamma ray spectrometry will improve the sensitivity of detection and in order to obtain correct results, the self attenuation of the sample must be taken into consideration. The calculation of full-energy peak efficiency and the self attenuation of source material using experimental, semi-empirical and Monte Carlo approaches have been treated by several authors (Lippert, 1983; Moens and Hoste, 1983; Nakamura, 1983; Haase et al., 1993; Mihaljevic et al., 1993; Wang et al., 1995; Sima and Arnold, 1996 and Wang et al., 1997). Recently, Selim and Abbas (1998, 2000); Abbas (2001a, 2001b, 2001c); Abbas and Selim (2002), using spherical coordinates system, derived direct analytical integrals of the detector efficiencies (total and full-energy peak) for any source-detector configuration and implemented these analytical expressions into a numerical integration computer program. Moreover, they introduced a new theoretical approach (Abbas, 2006; Abbas et al., 2006; Nafee and Abbas, 2008) based on that Direct Statistical method to determine the detector efficiency for an isotropic radiating point source at any arbitrary position from a cylindrical detector, as well as the extension of this approach to evaluate the volumetric sources.
In the present work, we will modify this simplified approach to determine the full-energy
peak efficiency of the co-axial detector with respect to point and volumetric sources, taking into account evaluating the attenuation fatt by the dead layer and the end-cap material of the detector, the self attenuation Sself by the source matrix and finally, the attenuation S by the source container material.
sc J
The arrangement of this paper is as follows. Section 2 presents direct mathematical formulae for the full-energy peak efficiency for the point source and the large cylindrical source, where the attenuation of photons through the dead layer, the detector end cap material, the source container material and through the source itself is also treated. Section 3 contains experimental setup used in our measurements. Section 4 contains comparisons between the calculated efficiency using the formulae derived in this work with the experimental measurements to show the validity of the present mathematical formulae. Conclusions are presented in Section 5.
2. Mathematical viewpoint
2.1. The case of a non-axial point source
Consider a right circular cylindrical (2R х L), detector and an arbitrarily positioned isotropic radiating point source located at a distance h from the detector top surface, and at a lateral distance p from its axis. The efficiency of the detector with respect to point source is given as follows (Abbas et al., 2006):
£ po int fatt £ g £i (1)
where e; and £g are the intrinsic and the geometrical efficiencies which were derived by Abbas et al., (2006) and it is very important to reintroduce in Section 2.1.1 because they are essential in the present work. fatt is the attenuation by the detector dead layer and end cap material and in Section 2.1.2, this factor will be calculated by a new method which is dependent on calculating the average path length cross these materials.
2.1.1. The intrinsic (£.) and the geometrical (eg) efficiencies
The intrinsic and geometrical efficiencies are represented by Eqs. (2) and (3) respectively.
£, = 1 - e
-¡d
h=
4p
(2)
(3)
where d is the average path length traveled by a photon through the detector, ffl, is the solid angle subtended by the source-detector and they are represented by Eqs. (4) and (5) respectively, and they will be discussed in details according to the source detector configuration as shown below, while m is the attenuation coefficient of the detector material.
detector active volume for both cases. The values of the polar and the azimuthal angles are shown in Table 2.
2.1.2. The attenuation factor (^tt)
The attenuation factor fatt is expressed as:
fatt flay fcap (6)
where flay is the attenuation by the detector dead layer and fcap is the attenuation by the detector end cap material and they are given by:
__lay lay
lay ~ ^
^ -¡ S
f = e cap cap J cap
(7)
where ¡ilay and Hcap are the attenuation coefficients of the detector dead layer and end cap material respectively. While 8lay and ôcap are the average path length traveled by a photon through the detector dead layer and end cap material respectively and they are represented as follow:
Slay =
n n ........
J/ff sinddddç JJft'j sin8dddç
m 8 í=1 m 8 J=1
Q
JJsin8d8dm
m 8
n n
JJXtJsin8d8dm JJXtJsin8d8dm
í=i
S __
cap~ JJsin8d8dm
í=i
Q
(8)
J djd Q) JJ( f^dj )sin 8dmd8
d -= 8m J=1 „-(4)
Qd Q
Q
where d1, d2, ..., dn are the possible path lengths traveled by the photon within the detector active volume.
Q = JJsin8d8dm.
(5)
8 m
There are two main cases to be considered for calculating the efficiency of the detector with respect to point source, the first is that the lateral displacement of the source is smaller than or equal the detector circular face's radius (p^R) and the second is that the lateral distance of the source is greater than the detector circular face's radius (p>R). The two cases have been treated by Abbas et al., (2006). Table 1 shows the geometrical efficiency, the possible path lengths and the average path length traveled by the photon within the
where, t',t'2,.....,t'n and t* f2,....., fn are the possible
path lengths traveled by the photon within the detector dead layer and end cap material respectively.
The case in which p<R
Consider the detector has dead layer with upper surface thickness tDF. Each photon enters the detector must pass through the face of dead layer, so that there is only one photon path length through the dead layer which is given by:
ti =
cos0
(9)
The average path length Slay traveled by a photon through the dead layer is given by:
- 7
S, =7
ay
(10)
where I2 is as identified before in Table 1 and Zx is given by:
t
DF
2
Table 1. The geometrical efficiency, the possible path lengths and the average path length traveled by the photon within the detector active volume for cases c <R and c>R (Abbas et al., 2006)
p>R
p < R
di =
cos 0
= pcosp + A^/R2 -p2 sin2 p h 1 sin 0 cos 0
= h + L pcosp+AR2 - p
' cos 0 sin 0
= 1y¡R2 - p2 sin2 p
1 ■ 2 sin p
sin0
A = f-11 00
I 1 000
(face ^ base) (face ^ side) (side ^ base) (side ^ side),
di =
cos0
pcosp+i/R2 — p2 sin2 p h
(face ^ base)
2 sin0
1 I 12
d =— ' £g = 1T
U 2n
cos0
(face ^ side)
I. g 2n
I3 = II d3sin0dpd0 + I I d1sin0dp+ | d3sin0dp
0 0 0 y 0 pmax
+ || d4 sin 0dpd0+ I I d1 sin 0dp+ | d2 sin 0dp
00 cmax 0T V o pmx
0 Pc 04 Pmax
+ I I d4 sin 0dpd0+ I I d2 sin 0dpd0
0T pmax 0 o
03 cm,x 03 p
I3 = I I d3 sin 0 dp d0+ I I d4 sin 0 dp d0 '""■:
01 o 00 p i
02 p I
+ ||d4 sin OdpM ^ (03 < g2 )
03 o i
0 p 04 Pon i
+ || d4sin0dpd0 + I I d2sin0dpd0 i
d0
d0
02 n
... (03 0 02 )
I1 = n Id1 sin 0d0+ IId2 sin 0dpd0
0 0 0 04 pnax
+ || d2sin0dpd0
1
Prn^disin0- I d2 sin 0 dp
d0
04
I2 = nj sinÛdÛ+ I pmaxsin0d0
L =
= Pax sin 0d0+ jp sin 0d0+ IPmax sin 0d0
L
L
0
0
9m>x °4
Zj = jjt[ sinddddç + j jt'sinddddç .(11) Z' = Jjt'sinddddç + J j t'sing dg dç.(14)
Also, if ta is the thickness of upper surface of end cap material, so, each photon to enter the detector must pass through the face of end cap, so that there is only one photon path length through the end cap which is given by:
t =
h
cos 6
(12)
The average path length Scap traveled by a photon through end cap is given by:
Z
8 =Z
cap j
12
(13)
where I2 is as identified before in Table 1 and Z' is given by:
The case in which p>R
For dead layer of the detector with upper surface thickness tDF and side surface thickness tDS, as shown in Fig. 1, there are two probabilities to be considered for the photon path length to pass through dead layer and enter the detector as follow: I. From the face of dead layer, so that the photon path length through dead layer is given by:
t =
cos6
(15)
II. From the side of dead layer, so that the photon path length through dead layer is given by:
' p cos ç + y
t2 =
(R + tDs )2-p2sm2ç pcosç + .JR
2 2 ♦ 2 p Sin2 ç
2
p2 2
1 + —r Sin2 ç 2 R Y
sin 6
sin 6
sin 6
(16)
The average path length 8lay traveled by a where I4 is as identified before in Table 1, while,
there are two sub cases for obtaining the value of Z3 according to the values of the polar angles 0i as (17) follow:
photon through the dead layer is given by:
- Z
lay
L
i. The case in which (62> 6' )
6'c ^^lax 62 (c 6c (c 64 (max
Z3 = J J ?2sin6d(d6+JJt'2sin6d(d6 + JJt'sin6d(d6 + J J t'sin6d(d6. (18)
6 0 6'c 0 62 0 6c 0
ii. The case in which (62< 6'c )
62 <„ 6'c (max 6c (c 64 (max Z3 = J J t2sin6d(d6 + J J t'sin6d(d6+JJt'sin6d(d6 +J J t'sin6d(d6. (19)
№l 0
S2 0
Table 2. The values of the polar and the azimuthal angles based on the source to detector configuration
(Abbas et al., 2006)
The azimuthal angles
The polar angles
S = tan
S4 = tan
dT = tan
lR -P
h + L
R +p' h
/
1p2 - R2
yjh(h + L)
02 = tan
e„ = tan
> -p h
h+L
03 = tan
e'„ = tan-1
R +ps
h + L
/
' Vçmax çmax
çmax = cos~
çmax = cos~
p2 - R2 + h2 tan2 g 2ph tan0
p2 - R2 + (h + L)2 tan2 g 2p(h + L)tan0
çc = sm
' R "
vp/
2
2
t
a
t
DF
DS
1
Consider end cap material of upper surface thickness t , side surface thickness t , and inner
a 7 w7
radius Ra, as shown in Fig. 1, there are two cases considered according to the relation between the lateral distance p, and the inner radius of the detector end cap as follow:
a) the case in which (R < p < Ra) In this case we can see that, each photon to enter the detector must pass through the face of end cap, so that there is only one photon path length through the end cap which is given by:
must be taken into consideration which is d , and
cap7
is given by:
= tan—1
fP-R A h — k
(21)
where k is the distance between the detector end cap and the detector upper surface.
There are two probabilities to be considered for the photon path length to pass through end cap and enter the detector as follow:
I. From the face of end cap, so that the photon path length through end cap is given by:
ti = -
(20)
cosO
b) the case in which (p > Ra)
In this case there is very important polar angle
t=-
cosO
(22)
II. From the side of end cap, so that the photon path length through end cap is given by:
h =■
»cosç + ^R + tw )2 — p2 sin2 ç pcosy + ^y/^)
2 2 • 2 p Sin2 ç
p2 2
1 + T Sin2 ç 2R2
sinO
sinO
sinO
.(23)
The average path length 8cap traveled by a photon through end cap is given by:
_ 7'
S = ^
cap j 14
(24)
where I4 is as identified before in Table 1, while Z'3 is varied according to the possible relations between the polar angles for two main previous cases. Table 3 shows the values of Z3'.
2.2. The case of a co-axial cylindrical source
The efficiency of a cylindrical detector with radius R and height L arising from a cylindrical source with radius S (S>R) and height H, as shown in Fig. 2, is given by:
Fig. 1. A diagram of a cylindrical - type detector with a non-axial point source (p >R)
£cyl
Sself Ssc fait £g
V
(25)
where V is the volume of the cylindrical source (V=pS2H), Ssdf is the self attenuation by the source matrix and S is the attenuation by the
sc
source container material. The intrinsic and geometrical efficiencies are as identified before in Eqs. (2) and (3) respectively, but the average path length d traveled by the photon through the detector active volume and the solid angle will have new forms due to the geometry of the volumetric source, as shown in Fig. 2. The average path length is expressed as:
H +ho 2n R
J J (JI1 pdp + j 13 p dp) dadh
d =
H +ho 2n R
(26)
J J (JI2 pdp + JI4 pdp)dadh
ho 0 0 R
where a is the angle between the lateral dis-
t
t
a
a
tance p and the detector's major axis. The geometrical efficiency £ is given by:
H +ho 2n gR
J J (J I2 pdp + J I4 pdp) dadh
£g =■
2n
(27)
where I1, I2, I3 and I4 are as identified before in Table 1.
The new forms of the average path length traveled by the photon through the detector dead layer and the detector end cap material are given by Eqs. (28) and (29) respectively.
H+ho 2n R S
J J(JZ1 pdp + JZ3pdp)dadh
S=
ho 0 0
lay H+ho 2n R
(28)
J J (JI2 pdp + JI4 pdp)dadh
ho 0 0 R
where Z1 is as identified before in Eq. (11),while Z3 represented by Eqs. (18) or (19) according to the values of the polar angles 0i.
H+ho 2n R S
J J (JZ'pdp + JZ'3 pdp)dadh
S=
ho 0 0
cap H +ho 2n R
(29)
J J (J12 pdp + JI4 pdp)dadh
where Z' is as identified before in Eq. (11),while Z3 is as identified before in Table 3.
In the case of a co-axial cylindrical source with radius is greater than the radius of the detector, there are two probabilities to be considered; the probability that the lateral distance of the source is smaller than the detector circular face radius, i.e. p <R and the lateral distance of the source is greater than the detector circular face radius, i.e. p >R and in the two cases, there is only one path to the photon that way out from the source which is exit from the base and is given by:
t1=
h - ho
cos 8
(30)
where h is the distance between the source active
o
volume and the detector upper surface. The source matrix self attenuation S f is given by:
seij
-¡ t
S = e s self e
(31)
where m is the attenuation coefficient of the source
s -
matrix and t is the average path length traveled by a photon inside the source and is given by:
where:
ho + H n R
ho + H n S
J JJg1 pdpdadh + J JJg2 pdpdadh
t = t (ti) =
h„ 0 0
ho 0 R
ho +H n R
ho + H n S
J JJ I2 pd pdadh + J JJ I4 pd pdadh
h0 0 0 ho 0 R
82 84
g1 = n J t1 sin 8 d8 + J^max t1 sin 8 d8
(32)
(33)
8'c mma
8c mc
84 mm
J J t1sin8dmd8 +J Jt1sin8dmd8 + J J t1sin8d^d8
80 e'c 0 8c o
8'c 8c 84
J múx ti sin 8 d8+J m ti sin 8 d8+J mmaxti sin 8 d8
(34)
0
8
2
If tB is the source container bottom thickness, so, there is only one path to the photon that way out from the source container which is exit from the base and is given by:
ti =
cos6
The attenuation S by the source container
sc J
material is given by:
-¡ tc
S = e c sc
(36)
(35) where mc is the attenuation coefficient of the source
t
B
Table 3. The different integration terms for Z^ according to the possible relations between the polar angles
for cases R < c < Ra and c > Ra
Z
ec qc
в 4 <Pm
öl >3
cap
вс > öcap
в >в'
^ cap — uc
в4 > всар > вс
всар > в4
J J* ifsin edqde + J J tf sin edqde + J J if sin edqxde
в о в с о вс о
в с 9с в4<Ртгх
J J tf sin edqde + J J tf sin edqde + J J if sin edqxie
e1 о в'с о в,, о
вс PÎoax в'с q'max вс 9с .......
J j2 sin edqde + J JJ if sin Qdqde + JJtfsin edqxie + J Jtf sinedqde
в1 о всар о в'с о вс о
^PÎnax всар 9с вс 9с в4 9max
J J ti sinedqde + J J ti sinedqde + J J" tf sin edqde + J J tf sin edqde
ei о (ос о ecap о ec о
e'c q'max ec qc ecap qmax ö4 qmax
J J t2 sin edqde + J Jt2 sin edqde + J J ti sinedqde + J Jtisinedqxie
ef о e'c о ec о ecap о
ec qmax ec qc emap qmax ö4 qmax
J Jti sinedqde + J J*i sin edqde+ J J ti sinedqde + J J tf sinedqde
R<P < Ra
P> Ra
e4 q m
ec о
Fig. 2. The possible cases of the photon path lengths through source - detector system
Badawi ms and others
container material and tc is the average path length traveled by a photon inside the source container and is expressed as:
~c = t (C). (37)
3. Experimental setup
The full-energy peak efficiency was measured for a p-types Canberra HPGe cylindrical detector (Model GC1520) with relative efficiency 15 %. Table 4 shows the manufacturer parameters in millimeter and the setup values for the detector. The sources are Polypropylene (PP) plastic vials of volumes 200 and 400 mL filled with an aqueous solution contains 152Eu radionuclide which emits y-ray in the energy range from 121 up to 1408 keV, Table 5 shows sources dimensions. Efficiency measurements were generated by positioning the sources over the end cap of the detector. In order to prevent dead time,
the activity of the sources was kept low (5048 ± 49.98 Bq). Measurements were carried out using multichannel analyzers (MCA) to obtain statistically significant main peaks in the spectra that were recorded and processed by ISO 9001 Genie 2000 data acquisition and analysis software made by Canberra.
The acquisition time was high enough to make the statistical uncertainties less than 1%. The peaks were fitted using Gaussians with low-energy tails appropriate for germanium detector. Spectra acquired with gamma vision were analyzed with the program using its automatic peak search and peak area calculations, along with changes in the peak fit using the interactive peak fit interface when necessary to reduce the residuals and error in the peak area values. The peak areas, the live time, the run time and the start time for each spectrum were entered in the spreadsheets that were used to perform the calculations necessary to generate the efficiency curves.
Table 4. The manufacturer parameters and the setup values
Manufacturer
Canberra Industries
Drawing
Serial Number 06089367
Detector Model GC1520
Geometry Closed end
Coaxial
Relative Efficiency (%) 15
Photopeak - Compton ratio 40
Voltage bias (V) (+) 4500
Crystal Model 7500SL
Resolution (FWHM) at 133 keV 2.0 keV
Shaping time (ms) 4
Preamplifier Model 2002CSL
Amplifier Model 2026
MCA Multi port II
VPS Model 3106D
Detector type HPGe (P- type)
Shaping Model Gaussian
Mounting Vertical
Outer Electrode Thickness (mm) 0.5
Inner Electrode Thickness (mm) 0.3x10-3
Window Electrode Thickness (mm) 0.5
Crystal Diameter (mm) 48
Crystal Length (mm) 54.5
Core hole Diameter (mm) 7.5
Core hole Depth (mm) 37.5
Detector Model 6 C IS ¿C
Cryostat Model Detector S/N
2£j2
ÔtCY^ib 1
rf-.NOOv EcEC-WDC
91H tlf -v» C J« «4 'rp<»l. 2 pi«C*«
№>vMi M;' 'C jcacc
-CI'OJ'AT v]*tcv -!* WINDOW
G« CB»ST*L DLTTEB ELECTRODE
!«*<» ELCCrscec
COPE fSlOtM.) CO«TACI C&'STM. OLXB 803 «0 H «Ol VAClAjW SP »CE
ÍHK*f
91« <32 r-o TEFLON ¡HSIXAT0R HIGH VOLUME COKTfcCf
0 06 (13
Table 5 Parameters of the sources
Source Volume mL Items
400 200
113.89 113.89 Outer diameter (mm)
42.25 21.13 Height (mm)
2.03 2.03 Wall thickness (mm)
5048 ± 49.98 5048 ± 49.98 Activity (Bq)
4. Results and discussion
The full-energy peak efficiency values for the p-type HPGe cylindrical type detector were measured as a function of the photon energy using the following equation
e (E )= N(E) nCi (38) V ' TAsP(E)AA 1 y '
where N(E) is the number of counts in the full-
energy peak which can be obtained using Genie
2000 software, T is the measuring time (in second),
P(E) is the photon emission probability at energy
E, AS is the radionuclide activity and C are the
correction factors due to dead time and radionuclide
decay. In these measurements of low activity sources,
the dead time always less than 3%, so the
corresponding factor was obtained simply using
ADC live time. The acquisition time was long
enough to get statistical uncertainties of the net
peak areas smaller than 1%. The background
subtraction was done. The decay correction Cd for
the calibration source from the reference time to
the run time was given by:
Cd = (39)
where X is the decay constant and AT is the time interval over which the source decays corresponding to the run time. The main source of uncertainty in the efficiency calculations was the uncertainties of the activities of the standard source solutions. Once the efficiencies have been fixed by applying the correction factors; the overall efficiency curve is obtained by fitting the experimental points to a polynomial logarithmic function of the fifth order using a non linear least square fit. In this way, the correlation between data points from the same calibrated source has been included to avoid the over-estimation of the uncertainty in the measured efficiency. The uncertainty in the full-energy peak efficiency c£ was given by:
If de Y 2 f de Y 2 fde Y 2
ye = J y" +[dP J IS J yN (40)
where cA, cP and cN are the uncertainties associated with the quantities AS, P(E) and N(E) respectively. Figs. 3 and 4 show the full-energy peak efficiencies of a co-axial HPGe detector; measured, calculated with S „and calculated without S „ for
self self
cylindrical sources (200 mL and 400 mL) as functions of the photon energy. Obviously, the neglected of the self attenuation factor in the calculations caused the increasing in the full energy peak effi-
ciency values, so to get correct results; the self attenuation factor must be taken into consideration. The percentage deviations between the calculated (with and without Sf and the measured full-energy peak efficiency values were calculated by:
A % = e" Ssef -e— x100 (41) e
cal-with Sseif
% = ecal-w1thout S-lf -emeas x100 (42) e
cal-without Sseif
where ,f, £ , ,f and £ are the calcu-
cal-with Sseir cal-without Sselt meas
lated with self attenuation factor, calculated without self attenuation factor and experimentally measured efficiencies, respectively. Figs. 5 and 6 show the percentage deviations A1% and A2% for cylindrical sources (200 mL and 400 mL respectively), placed at the end cap of p-type HPGe cylindrical detector.
According to Eq. (31), the self attenuation factor is depending on two important factors which are the attenuation coefficient of the source matrix and the average path length through the source itself. The effect of these factors can be shown in Fig. 7 which represents the variation of a self attenuation factor obtained from Eq. (31) with the photon energy. The self attenuation factor for 200 mL is greater than that of 400 mL when the two sources are placed at the same position with respect to the same detector; this is because the average path length calculated for 200 mL is smaller than that for 400 mL. So as the cylindrical source volume is increasing, the importance of the self attenuation factor becomes interesting and can't be neglected when calibrating the detector, but must be calculated with more accuracy to get good results. Also, the self attenuation is increasing as the energy is increasing and that is related to the effect of the source matrix attenuation coefficient.
5. Conclusions
In this work, the authors have derived direct mathematical expression for the calculation of the full-energy peak efficiency of a co-axial HPGe detector using a cylindrical source. The measurements were carried out by using 152Eu aqueous radioactive source placed in large cylindrical beakers. Figs. 3-6 show there is a good agreement between the measured and the calculated values. The percentage deviations of the results are less than 2% when the self attenuation factor is taken into consideration.
22.03.2013
s
Photon energy (keV)
Fig. 3. The full-energy peak efficiencies of a co-axial HPGe detector; measured (squares and intervals), calculated with Ssdf (circles with solid line) and calculated without Sselj: (triangles with solid line) for cylindrical source (200 mL) as functions of the photon energy
s
400 mL
Measured
- Calculated ™th Sse|f
- Calculated ™thout S
Photon energy (keV)
Fig. 4. The full-energy peak efficiencies of a co-axial HPGe detector; measured (squares and intervals), calculated with Sstif (circles with solid line) and calculated without Sstif (triangles with solid line) for cylindrical source (400 mL) as functions of the photon energy
Photon energy (keV)
Fig. 5. The percentage deviations and for cylindrical source (200 mL) placed at the end cap of p-type HPGe cylindrical detector
■ A1 30 • " A1
• • 25 • A2
• •
• • 20 •
• • • <1 15. 10. • • • •
■ ■ ■ 5
Photon energy (keV)
Fig. 6. The percentage deviations and for cylindrical source (400 mL) placed at the end cap of p-type HPGe cylindrical detector
0.01
J.0'
IE -3
1E-3
1000
0
300
600
900
0
300
600
900
35
20
5
0
0
0 600 1200
Photon energy (keV)
Fig. 7. Variation of self attenuation factor with the photon energy for different source volumes placed at the end cap of the detector
Acknowledgment
The authors would like to express their sincere thanks to Prof. Dr. Mahmoud. I. Abbas, Faculty of Science, Alexandria University, for the very valuable professional guidance in the area of radiation physics and for his fruitful scientific collaborations on this topic.
Dr. Mohamed. S. Badawi would like to introduce a special thanks to The Physikalisch-Technische Bundesanstalt (PTB) in Braunschweig, Berlin, Germany for fruitful help in preparing the homemade volumetric sources.
References:
1. Abbas, M.I., 2001a. A direct mathematical method to calculate the efficiencies of a parallelepiped detector for an arbitrarily positioned point source. Radiat. Phys. Chem. 60, 3.
2. Abbas, M.I., 2001b. Analytical formulae for well-type NaI(Tl) and HPGe detectors efficiency computation. Appl. Radiat. Isot. 55, 245.
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M. S. Badawi, Physics Department, Faculty of Science, Alexandria University, 21511 Alexandria, Egypt.
[Doctor], e-mail: [email protected], Tel:+201005154976. M. M. Goud, Physics Department, Faculty of Science, Alexandria University, 21511 Alexandria, Egypt. [Doctor], e-mail: [email protected], Tel:+201142911711. A. M. El-Khatib, Physics Department, Faculty of Science, Alexandria University, 21511 Alexandria, Egypt. [Professor. Doctor], e-mail: [email protected], Tel:+201000230122. S. S. Nafee, Physics Department, Faculty of Science, Alexandria University, 21511 Alexandria, Egypt. [Doctor], e-mail: [email protected], Tel:+201010058780. E. A. El-Mallah, Physics Department, Faculty of Science, Alexandria University, 21511 Alexandria, Egypt. [Doctor], e-mail: [email protected], Tel:+201005154976.
