

ORIGINAL ARTICLE 

Year : 2018  Volume
: 41
 Issue : 3  Page : 110114 


Efficiency of highpurity germanium detector at characteristic gamma energies of ^{198}Au and ^{58}Co and covariance analysis
Imran Pasha^{1}, B Rudraswamy^{1}, E Radha^{2}, V Sathiamoorthy^{2}
^{1} Department of Physics, Bangalore University, Bengaluru, Karnataka, India ^{2} Indira Gandhi Center for Atomic Research, Kalpakkam, Tamil Nadu, India
Date of Submission  20Jun2018 
Date of Decision  20Jul2018 
Date of Acceptance  23Aug2018 
Date of Web Publication  19Nov2018 
Correspondence Address: Dr. B Rudraswamy Department of Physics, Bangalore University, Bengaluru  560 056, Karnataka India
Source of Support: None, Conflict of Interest: None  Check 
DOI: 10.4103/rpe.RPE_38_18
Naturally occurring ^{197}Au and ^{58}Ni foils were subjected to the neutron irradiation by placing them in a dry tubeI of Kalpakkam Mini reactor to produce gamma emitting ^{198}Au and ^{58}Co nuclear reaction products. The efficiency study of highpurity germanium detector corresponding to characteristic gamma energies 0.4118 and 0.8107 MeV of ^{198}Au and ^{58}Co was carried out by the methods of calibration of ^{152}Eu and covariance.
Keywords: Covariance, efficiency, highpurity germanium, Kalpakkam mini reactor
How to cite this article: Pasha I, Rudraswamy B, Radha E, Sathiamoorthy V. Efficiency of highpurity germanium detector at characteristic gamma energies of ^{198}Au and ^{58}Co and covariance analysis. Radiat Prot Environ 2018;41:1104 
How to cite this URL: Pasha I, Rudraswamy B, Radha E, Sathiamoorthy V. Efficiency of highpurity germanium detector at characteristic gamma energies of ^{198}Au and ^{58}Co and covariance analysis. Radiat Prot Environ [serial online] 2018 [cited 2019 Aug 23];41:1104. Available from: http://www.rpe.org.in/text.asp?2018/41/3/110/245796 
Introduction   
The calibration source ^{152}Eu consists of many characteristic gamma lines. It can be used for the efficiency calibration of highpurity germanium (HPGe) detector as its activity is known. It is not possible to measure directly the efficiency of HPGe detector for known energies of characteristic gamma lines of nuclear reaction products as their activities are unknown. However, it can be known using the methods of calibration of ^{152}Eu and covariance. This finds an application in knowing the nuclear reaction cross section of ^{198}Au and ^{58}Co.
Geraldo and Smith^{[1]} carried out work on least square methods and covariance matrix applied to the relative efficiency calibration of a Ge (Li) detector. Geraldo and Smith^{[2]}, carried out work on covariance analysis and fitting of germanium gammaray detector efficiency calibration data. Vidmar^{[3]} carried out work on EFFTRANA monte carlo efficiency transfer code for gammaray spectrometry. Jose et al.,^{[4]} carried out work on the estimation of radioactive nobal gas activity in Fast Breeder Test Reactor (FBTR)A simple method of calibration of HPGe detector. Shivashankar^{[5]}et al. carried out work on measurement and covariance analysis or reaction cross section for ^{58}Ni(n, p) ^{58} Co relative to cross section for the formation of ^{97}Zr fission product in neutroninduced fission of ^{232}Th and ^{238}U at effective neutron energies E_{n} = 5.89, 10.11 and 15.87 MeV. Sheela^{[6]}et al., carried out work on the efficiency of HPGe detector at characteristic gamma energies of ^{58}Co and^{115m} In in the reactions ^{59}Co(n, 2n) ^{58}Co and ^{115}In(n, n^{I})^{115m} In respectively. Further, they carried out the covariance analysis.
In the present study, the efficiency study of HPGe detector corresponding to characteristic gamma energies 0.4118 and 0.8107 MeV of ^{198}Au and ^{58}Co was carried out by the methods of calibration of ^{152}Eu and covariance.
Experimental details
Naturally occurring foils ^{197}Au and ^{58}Ni with 99.85% purity procured from Alfa Aesar, USA, have been irradiated with neutrons consisting of spectrum of energies each with 3 h time by placing in dry TubeI location of Kalpakkam Mini reactor to obtain nuclear reactions ^{197}Au(n,γ) ^{198}Au and ^{58}Ni(n, p) ^{58}Co. The obtained products ^{198}Au and ^{58}Co are capable to emit gamma with characteristic energies 0.4118 and 0.8107 MeV respectively. Their gamma spectra have been measured using ptype coaxial vertical HPGe detector of Dounreay Stakeholder Group make available at FBTR laboratory, IGCAR. The resolution of the detector is 1.8 keV at 1332.5 keV. The measured spectra are shown in [Figure 1] and [Figure 2]. The measured spectrum of calibration source ^{152}Eu is shown in [Figure 3]. The point source ^{152}Eu capsulated in a thin disc of araldite. The analysis of the spectral data has been done both with softwares of APTEC Engineering Ltd., Canada and GENIE2000 Canberra Industries Inc., Meriden, USA.
Results and Discussion   
Efficiency calibration of highpurity germanium for ^{152}Eu
The full energy peak efficiency of HPGe detector was measured by considering nine gammaray energies (E_{i}, 1≤i ≤9) of ^{152}Eu source. The source in our experiment was placed 8 cm from the detector. Hence, the correction factor k_{c} due to coincidence summing effect was estimated using Monte Carlo simulation code EFFTRAN.^{[3],[4]} The source was procured on March 1, 1999 with initial activity A_{0} was 45500 Bq. The efficiency ε(E_{γ}) of detector is given by.
Where E_{γ} is γ energy, C is counts obtained from the measured ^{152}Eu gamma spectrum, I_{γ} is γ abundance, T_{½} is halflife (13.517 ± 0.014y), t is time elapsed between source and detector calibrations (17.92y). The decay data I_{γ} at each of the mentioned energies and T_{½} are retrieved from ENSDF data sets maintained by National Nuclear Data Center.^{[7]} The input data and the obtained detector efficiency ε(E_{γ}) at each of the gamma ray energy of ^{152}Eu are listed in [Table 1]. The comparison of the detector efficiencies with and without correction factor due to coincidence summing effect is shown in [Figure 4].  Figure 4: Detector efficiency with and without coincidence summing correction
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Covariance analysis for ^{152}Eu
The uncertainty^{[1]} (Δε_{i} in efficiency ε_{i} ranging from ε_{1}(E_{γ1}) to ε^{9} (E_{γ9}) is obtained using the following relation.
where ΔC_{i}, ΔI_{γi} ΔA_{0i} and Δλ_{i} are partial uncertainties (e_{kr}) in C_{i}, I_{i}, A_{Oi} and λ_{i} respectively.
e_{kr} is obtained with the following relation.
Where k = 1, 2,….9 corresponds to γ energies of ^{152}Eu and r is attribute with 1≤r≤4.
The obtained values of Δε_{i} and e_{kr} are shown in [Table 2].
The microcorrelation matrix Sij is shown in [Table 3].
The covariance matrix^{[2]} V_{εij} is obtained with the following relation and the obtained values are shown in [Table 4].
Where δε_{k}or Δε_{i} and δx_{r} are partial uncertainties in efficiency ε_{k} and partial uncertainty in x_{r}(C, I_{γ}, A_{o} and T_{1/2}), respectively.
The macrocorrelation matrix C_{εij} due to Δε_{i} and Δε_{j} is obtained with the following relation and its values are shown in [Table 5].
Efficiency of highpurity germanium for^{198}Au and^{58}Co
The covariance matrix V_{zij} is obtained with the following relation^{[5]} and its values are shown in [Table 6].
The linear parametric matrix Z, design matrix A and fitting parameter matrix P are related by
Matrices Z, A and P can be obtained with the following relations.
Where 1 ≤ i ≤ 9, 1 ≤ k ≤ m, m = 2, 3.8.
The covariance matrix V_{p} can be obtained with the following relation.
A and V_{p} matrices can be generated for various m values lying between 2 and 8. In the present case, m = 5 is considered. Their values are shown in [Table 7] and [Table 8], respectively.
Fitting parameter matrix P is obtained with the following relation and its values are shown in [Table 9].
The least square condition states that the best estimate for parameter vector in the model is the one which minimizes the Chisquare statistics given by
The obtained x^{2} and values are 5.93 and 1.48 for m = 5, respectively.
The obtained values for m = 2, 3, 4, 6, 7 are 63.4, 18.6, 3.8, 1.45, 0.29, and 0.568, respectively. The two values for m = 5 and 6 are closer to one. m = 5 was considered for further calculation as this was less than the other.
The design A_{c}, linear parametric Z_{c}, covariance V_{Zc}, efficiency covariance V_{εc}, and correlation C_{εc} matrices.^{[6]} For ^{198}Au (0.411802 MeV) and ^{58}Co (0.810759 MeV) were obtained with the following relations.
The obtained values of ε_{c}, V_{εc} and C_{εc} are shown in the [Table 10].  Table 10: Estimated parameters at two gamma energies of the activated foils
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Conclusions   
The energy depended efficiency calibration of HPGe detector corresponding to characteristic gamma energies of ^{152}Eu has been carried out. The fitting parameters have been estimated by Chisquare test. The efficiency corresponding to characteristic gamma energies 0.4118 and 0.8107 MeV of ^{198}Au and ^{58}Co nuclear reaction products of unknown activity has been estimated by the knowledge of fitting parameters and the corresponding covariance study has also been carried out.
Financial support and sponsorship
The research work was supported by DAE BRNS, Mumbai through a major research project (sanctioned No. 36 (6)/14/92/2014 BRNS/2727).
Conflicts of interest
There are no conflicts of interest.
References   
1.  Geraldo LP, Smith DL. Least square methods and covariance matrix applied to the relative efficiency calibration of a Ge (Li) detector. Instit Pesqui Energeticas Nucl 1989;243:116. 
2.  Geraldo LP, Smith DL. Covariance analysis and fitting of germanium gammaray detector efficiency calibration data. Nucl Instrum Methods Phys Res A 1990;290:499508. 
3.  Vidmar T. EFFTRANA Monte Carlo efficiency transfer code for gammaray spectrometry. Nucl Instrum Methods Phys Res A 2005;550:6038. 
4.  Jose MT, Baskar S, Meenakshisundaram V. Estimation of radioactive nobal gas activity in FBTR A simple method of calibration of HPGe detector. Conference IRPA12, 3; 2008. 
5.  Shivashankar BS, Ganesan S, Naik H, Suryanarayana SV, Nair NS, Prasad KM. Measurement and covariance analysis or reaction cross section for ^{58}Ni (n, p) ^{58} Co relative to cross section for formation of ^{97}Zr fission product in neutroninduced fission of ^{232}Th and ^{238}U at effective neutron energies E _{n}=5.89, 10.11 and 15.87 MeV. Nucl Sci Eng 2014;179:42333. 
6.  Sheela YS, Naik H, Prasad KM, Ganesan S, Nair NS, Suryanarayana SV. The efficiency and error covariance matrix of HPGe detector at characteristic gamma energies of reaction products ^{58}Co and ^{115}mIn in the Measurement of ^{59}Co (n, 2n) ^{58} Co Reaction Cross Section Relative to ^{15}In (n, n') ^{115}mIn. Internal Report, No.MU/Statistics/DAEBRNS/2017/2; 12 March, 2017. 
7.  NuDat 2.7, Nudat 2.7 National Nuclear Data Center, Brookhaven National Laboratory; 2016. Available from: http://www.nndc.bnl.gov/nudat2/. [Last accessed on 2018 May 04]. 
[Figure 1], [Figure 2], [Figure 3], [Figure 4]
[Table 1], [Table 2], [Table 3], [Table 4], [Table 5], [Table 6], [Table 7], [Table 8], [Table 9], [Table 10]
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