- Email: [email protected]
Can the ZoMBieS method be used to characterise scintillator non-linearity?
Applied Radiation and Isotopes 87 (2014) 265–268
Contents lists available at ScienceDirect
Applied Radiation and Isotopes journal homepage: www.elsevier.com/locate/apradiso
Can the ZoMBieS method be used to characterise scintillator non-linearity? L.J. Bignell n Activity Standards Laboratory, Australian Nuclear Science and Technology Organisation, Lucas Heights, NSW 2234, Australia
H I G H L I G H T S
Liquid scintillation detection efficiency spectra measured using ZoMBieS method. Different Birks quenching parameter is obtained for each photomultiplier. ZoMBieS method currently appears unsuitable for non-linearity measurements.
art ic l e i nf o
a b s t r a c t
Article history: Received 20 April 2013 Accepted 4 November 2013 Available online 12 November 2013
Measurements of the detection efficiency as a function of deposited electron energy in a liquid scintillation cocktail between 4 keV and 49 keV are obtained using the ZoMBieS method. Comparison is made between the measured data and the Poisson–Birks detection efficiency model. Measurements of the Birks non-linearity parameter, kB, and the linearised scintillation response of each photomultiplier, ωi, were made using these data. However, the value of kB that best linearises the scintillator response is found to vary depending upon which photomultiplier is used in its determination, and the measured kB and ωi vary depending on the external source geometry. The cause of this behaviour is unknown. The triple-coincident detection efficiency appears to be unaffected by any systematic errors. Crown Copyright & 2013 Published by Elsevier Ltd. All rights reserved.
Keywords: Liquid scintillator ZoMBieS method Scintillator non-linearity Birks quenching
1. Introduction Liquid scintillators exhibit a non-linear light output as a function of energy deposit by ionising radiation. The most commonly used model to account for this non-linearity, which is also known as ionisation quenching, is due to Birks (1964). Birks’ model requires the calculation of the scintillator stopping power and the determination of a non-linearity parameter, kB. The characterisation of the scintillator non-linearity is important for precision liquid scintillation measurements in applications such as radionuclide metrology (Péron and Cassette, 1994; Broda et al., 2007) and neutrino detection (Aberle et al., 2011; Krosigk et al., 2013). The kB value is commonly evaluated in radionuclide metrology by choosing the value that gives a self-consistent measured activity for varied detection efficiency. One problem with this approach is that the uncertainties associated with the measurement of kB are often the greatest source of uncertainty in the activity measurement (Zimmerman et al., 2010; Nähle et al., 2010).
The Zero Model By using Coincidence Scintillation (ZoMBieS) method is a new liquid scintillation-based absolute radioactivity measurement technique (Bignell et al., 2013) that offers a direct means of characterising the scintillator response. The technique is based upon a modified Compton coincidence method (Péron and Cassette, 1994) and allows measurement of the detection efficiency as a function of energy deposited in the scintillator. In this paper, the potential for the ZoMBieS method to provide an alternative measurement of the kB value of scintillators is assessed.
2. Theory In a liquid scintillation detector, if the number of created photoelectrons at the ith photomultiplier tube (PMT) photocathode induced by some energy deposit E in the scintillator is assumed to obey Poisson statistics, the detection efficiency of a single PMT as a function of E may be written as:
εi ðEÞ ¼ 1 e Ωi ðEÞE n
Corresponding author. Tel.: þ 61 2 9717 9751. E-mail addresses: [email protected], [email protected]
ð1Þ
where Ωi(E) is the mean number of photoelectrons that are produced at the photocathode per unit energy deposit in the
0969-8043/$ - see front matter Crown Copyright & 2013 Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.apradiso.2013.11.006
266
L.J. Bignell / Applied Radiation and Isotopes 87 (2014) 265–268
scintillator, and is referred to here as the scintillation response. The energy dependence of the scintillation response may be written as: Z E dE Ωi ðEÞE ¼ ωi EQ ðEÞ ¼ ωi ð2Þ dE 0 1 þ kB dx where kB is a material-dependent parameter, ωi is the mean number of photoelectrons produced at the ith PMT photocathode per unit of linearised energy deposit in the scintillator, and is here referred to as the linearised scintillator response. Q(E) is the Birks correction for the scintillator non-linearity. Since Q(E) corrects the non-linear response of the scintillator to linearity ωi is expected to be a constant for each PMT in the detector. The ZoMBieS method allows the direct measurement of εi(E). By comparing the measured εi(E) with Eqs. (1) and (2) one can directly obtain the scintillator response of each PMT, theoretically correct for Birks quenching, and confirm whether a constant ωi may be obtained.
3. The ZoMBieS method The ZoMBieS detector is a liquid scintillation detector with three PMTs (Hamamatsu R331-05) operating in coincidence, and an additional High Purity Germanium (HPGe) detector that also operates in coincidence and as the trigger source. The PMTs are mounted at 120o intervals surrounding the liquid scintillator and are housed within a light-tight, temperature controlled chamber with the right angle-mounted HPGe detector also extending into the chamber volume from an external dewar. A collimated 51Cr source was used as the scintillation excitation source. The external source was mounted within the scintillation chamber and the lead collimation was wide enough to permit the source to irradiate the entirety of the scintillator volume. The constant fraction discriminated (Ortec 935) PMT signals were fed into fast 8-bit digitisers (NI PXI-5153) and the HPGe signal was amplified using a shaping amplifier (Canberra 2024) before being fed into a high resolution 12 bit digitiser (NI PXI-5124). The trigger signal was obtained from the HPGe via a timing filter amplifier (Ortec 474) and constant fraction discriminator (Ortec 935) before being acquired by a fast digitiser (NI PXI-5153). The acquisition of all digitisers was synchronised and controlled using a custom-written LabView program. The energy deposited in the scintillator was inferred based on the measured HPGe pulse height, which was evaluated by least-squares fitting of the incoming pulses with a Gaussian function. PMT coincidences were evaluated with a coincidence resolving time of 40 ns. This acquisition therefore allows the measurement of double and triple PMT coincidences as a function of HPGe energy. The basis of the ZoMBieS technique is the can be seen by considering the triple-to-double coincidence ratio (TDCR) as a function of energy deposit in the scintillator. For a monoenergetic energy deposit, the TDCR may be written as: TDCR ¼
ε123 ε1 ε2 ε3 ¼ ¼ ε1 ε23 ε2 ε3
ð3Þ
where ε123 is the triple coincidence detection efficiency, ε23 is double coincidence detection efficiency between PMT 2 and 3, and εi is the detection efficiency of the ith PMT. It can therefore be seen that in the ZoMBieS detector, the determination of the TDCR as a function of energy deposit E in the scintillator is tantamount to a measurement of εi(E). It should be noted that the TDCR as defined in Eq. (3) differs from the convention used by some other authors of dividing the triple coincidences by the logical sum of double coincidences. A detailed description of the ZoMBieS measurement hardware and analysis procedure is given elsewhere (Bignell et al., 2013).
4. Measurements All liquid scintillation measurements were performed using 10 mL of Insta-Gel dispensed into a glass vial. ZoMBieS measurements were taken using the external 51Cr source at a variety of Compton scattering angles, so as to sample the detection efficiency over a sufficient range of energies. The measurements were taken over the course of approximately 1 month so as to minimize the statistical component of the measurement uncertainty. Fig. 1 shows the εi associated with each PMT for one of these measurements, with the Compton-coincident HPGe energy spectrum overlaid. The detection efficiency diverges at low energies as the statistical noise and accidental coincidences with the full energy peak becomes significant, while at high energies photons which lose energy in the scintillator, HPGe detector, and a non-sensitive part of the detector geometry affect the measurement. The efficiency increases monotonically with energy deposit over the useable range, as expected. The useable energy ranges associated with the data sets acquired for this study are presented in Table 1. The triple detection efficiencies associated with all data collected are presented in Fig. 2. The results are consistent within the uncertainties of the measurement (omitted from the figure for clarity). The scintillation response and linearised scintillation response – calculated using Eqs. (1) and (2) – are presented in Fig. 3, for the measurement data presented in Fig. 1. The uncorrected scintillator response (when kB¼0) exhibits an energy dependence and each tube was able to be corrected to an approximately constant response by using the Birks correction and an appropriate value of kB. However, different values of kB were required to linearise the scintillation response (Table 1). Furthermore, different kB values were required to linearise the scintillation response between different measurements same PMT (Table 1). For some acquisitions, the kB value required to linearise the data is negative, which is unphysical.
Fig. 1. The single PMT detection efficiency spectrum, εi(E), in PMT 1–3. A spectrum of the triple coincident counts is overlaid to illuminate the region of valid data.
Table 1 kB value and ωi, determined for each photomultiplier using the technique described in the text, for each acquisition. Valid energy (keV)
Parameter
PMT 1
PMT 2
PMT 3
29.8–49.3
kB (cm/MeV) ωi (keV 1) kB (cm/MeV) ωi (keV 1) kB (cm/MeV) ωi (keV 1) kB (cm/MeV) ωi (keV 1)
0.022 0.101 0.0011 0.0827 0.0060 0.0964 0.0013 0.0775
0.030 0.105 0.0010 0.0703 0.00071 0.0705 0.00099 0.0738
0.024 0.0576 0.0011 0.0922 0.00264 0.0930 0.00043 0.0903
13.3–34.8 3.8–21.8 4.8–28.3
L.J. Bignell / Applied Radiation and Isotopes 87 (2014) 265–268
5. Discussion As kB is a scintillator-dependent parameter, the same value of kB should be required to correct the PMTs to uniform response. The fact that the values of kB which were required to correct the scintillator response to a constant value are different for each of the PMTs suggests that there may be a systematic experimental error that affects the measured non-linearity of the scintillator. A possible source of systematic error is that of scattering of the 51 Cr gamma rays within the detector housing, PMTs, shielding, or mounting arrangement. Measurements have been performed with an empty glass vial to confirm that the direct irradiation of the PMTs has no effect upon the measurement. Some effects due to scattering are evident at energy deposits above 22 keV in Fig. 1. The measured efficiency spectrum appears to decrease, and not increase with energy above 25 keV which is physically implausible. Validation measurements of the activity of a 63Ni source by Bignell et al. (2013) confirm the ability of these data to accurately
Fig. 2. The triple coincident detection efficiency spectrum, εT(E), associated with the liquid scintillator, measured over various incident angles.
267
measure radioactivity, which suggests that any effects due to scattering are minor. That different values of kB and ωi are determined for the different measurements also suggests that there may be either some instability or geometry dependence of the measurement system. The εT spectra obtained agree within their statistical uncertainties, which indicates that the system is at least robust enough for activity measurements. Systematic effects due to source-detector geometry may be possible if the excitation of the scintillator volume is inhomogeneous. The collimator used in this study was deliberately chosen to be wide enough to cover the cross-section of the scintillator volume, so that any inhomogeneity must be due to photon attenuation within the scintillator. However, for the 320 keV 51Cr photons used, the attenuation through the scintillator is quite low. Photon attenuation calculations performed using the mass attenuation coefficient values of polyvinyltoluene (Hubbell and Seltzer, 1995) and a scintillator density of 0.9 g/cm3 suggest that a 320 keV photon beam that passes along the diameter of the liquid scintillator will exit the volume with 93.5% of its original intensity. This suggests that photon attenuation within the scintillator volume will not modify this distribution significantly. The scintillator light yield and PMT sensitivity are known to vary with ambient temperature. However, the temperature control of the detector is quite tight making temperature fluctuation an unlikely source of the observed instability. The PID-controlled thermoelectric modules provide heating and cooling to maintain a constant temperature to within 7 0.1 1C inside the detector housing. Gain instability in the HPGe shaping amplifier is another possible source of error. As the evaluation of the linearity data also involves dividing by the energy, even small changes in the gain may affect the measurement. Consider a true energy deposit x in the scintillator. This value is inferred by the detected HPGe energy. However, if there is some gain drift that has occurred since the energy calibration of the HPGe detector, then the measured energy deposit xmeas will differ from x by some small value δ. In order to solve Eq. (1) for Ωi, or Eq. (2) for ωi, one must divide by the energy. The relative error, Δ, associated with dividing by xmeas
Fig. 3. The scintillation response and ωi as measured in one of the external source geometries. The values of kB required to obtain a constant response (ωi) were not identical, and are given in Table 1.
268
L.J. Bignell / Applied Radiation and Isotopes 87 (2014) 265–268
measurements of the energy-dependent scintillator response using the Poisson–Birks model of detection efficiency. The scintillator non-linearity was able to be corrected to linearity by using the Birks equation and an appropriate value of kB. However, different values of kB were obtained for each of the three photomultipliers in the detector. The cause of this unexpected behaviour is unknown. Based on these measurements, the ZoMBieS method appears unsuitable as a means to characterise scintillator non-linearity until the source of this error can be located.
References Fig. 4. The relative error associated with gain drift (Eq. (4)), using the HPGe energy calibration checks carried out between the ZoMBieS measurements. The two traces indicate the error obtained as a function of energy for two different energy calibrations relative to a third.
rather than x is given by
Δ¼
xmeas x δ ¼ x x
ð4Þ
for measurements of the scintillator non-linearity, one is most interested in the limit of low energy; x-0. In this limit, Δ diverges, so that even small gain instabilities may affect the measured nonlinearity. The energy calibration of the HPGe detector was been checked three times using the same amplifier settings in the course of this study. Fig. 4 calculates Δ as a function of energy for two of these energy calibrations relative to the third. Although some differences are seen, they do not appear to be of sufficient magnitude at the relevant energy deposits to explain the observed discrepancies. 6. Conclusion Measurements of the detection efficiency spectrum of a liquid scintillator using the ZoMBieS method have been transformed to
Aberle, C., Buck, C., Hartmann, F.X., Schönert, S., Wagner, S., 2011. Light output of double chooz scintillators for low energy electrons. J. Instrum. 6 (11), P11006. Bignell, L.J., Mo, L., Steele, T., Hashemi-Nezhad, S-R, 2013. The zero model by using coincidence scintillation (ZoMBieS) method of absolute radioactivity measurement. IEEE Trans. Nucl. Sci. 60 (5), 4007–4014. Birks, J.B., 1964. The Theory and Practice of Liquid Scintillation Counting. Pergamon Press, Oxford, UK. Broda, R., Cassette, P., Kossert, K., 2007. Radionuclide metrology using liquid scintillation counting. Metrologia 44 (4), S36. Hubbell, J., Seltzer, M., 1995. Tables of X-ray Mass Attenuation Coefficients and Mass Energy-Absorption Coefficients. Tech. Report, NISTIR-5632, ver. 1.4. Nähle, O., Kossert, K., Cassette, P., 2010. Activity standardization of 3H with the new TDCR system at PTB. Appl. Radiat. Isot. 68, 1534–1536. Péron, M., Cassette, P., 1994. COCO, a Compton coincidence experiment to study liquid scintillator response in the 1–20 keV energy range. Nucl. Instrum. Methods Phys. Res., Sect. A 353, 41–45. Krosigk, B., Neumann, L., Nolte, R., Röttger, S., Zuber, K., 2013. Measurement of the proton light response of various LAB based scintillators and its implication for supernova neutrino detection via neutrino–proton scattering. Eur. Phys. J. C 73 (4), 2390. Zimmerman, B., Altzitzoglou, T., Rodrigues, D., Broda, R., Cassette, P., Mo, L., Ratel, G., Simpson, B., van Wyngaardt, W., Wätjen, C., 2010. Comparison of triple-todouble coincidence ratio (TDCR) efficiency calculations and uncertainty assessments for 99Tc. Appl. Radiat. Isot. 68, 1477–1481.
Contents lists available at ScienceDirect
Applied Radiation and Isotopes journal homepage: www.elsevier.com/locate/apradiso
Can the ZoMBieS method be used to characterise scintillator non-linearity? L.J. Bignell n Activity Standards Laboratory, Australian Nuclear Science and Technology Organisation, Lucas Heights, NSW 2234, Australia
H I G H L I G H T S
Liquid scintillation detection efficiency spectra measured using ZoMBieS method. Different Birks quenching parameter is obtained for each photomultiplier. ZoMBieS method currently appears unsuitable for non-linearity measurements.
art ic l e i nf o
a b s t r a c t
Article history: Received 20 April 2013 Accepted 4 November 2013 Available online 12 November 2013
Measurements of the detection efficiency as a function of deposited electron energy in a liquid scintillation cocktail between 4 keV and 49 keV are obtained using the ZoMBieS method. Comparison is made between the measured data and the Poisson–Birks detection efficiency model. Measurements of the Birks non-linearity parameter, kB, and the linearised scintillation response of each photomultiplier, ωi, were made using these data. However, the value of kB that best linearises the scintillator response is found to vary depending upon which photomultiplier is used in its determination, and the measured kB and ωi vary depending on the external source geometry. The cause of this behaviour is unknown. The triple-coincident detection efficiency appears to be unaffected by any systematic errors. Crown Copyright & 2013 Published by Elsevier Ltd. All rights reserved.
Keywords: Liquid scintillator ZoMBieS method Scintillator non-linearity Birks quenching
1. Introduction Liquid scintillators exhibit a non-linear light output as a function of energy deposit by ionising radiation. The most commonly used model to account for this non-linearity, which is also known as ionisation quenching, is due to Birks (1964). Birks’ model requires the calculation of the scintillator stopping power and the determination of a non-linearity parameter, kB. The characterisation of the scintillator non-linearity is important for precision liquid scintillation measurements in applications such as radionuclide metrology (Péron and Cassette, 1994; Broda et al., 2007) and neutrino detection (Aberle et al., 2011; Krosigk et al., 2013). The kB value is commonly evaluated in radionuclide metrology by choosing the value that gives a self-consistent measured activity for varied detection efficiency. One problem with this approach is that the uncertainties associated with the measurement of kB are often the greatest source of uncertainty in the activity measurement (Zimmerman et al., 2010; Nähle et al., 2010).
The Zero Model By using Coincidence Scintillation (ZoMBieS) method is a new liquid scintillation-based absolute radioactivity measurement technique (Bignell et al., 2013) that offers a direct means of characterising the scintillator response. The technique is based upon a modified Compton coincidence method (Péron and Cassette, 1994) and allows measurement of the detection efficiency as a function of energy deposited in the scintillator. In this paper, the potential for the ZoMBieS method to provide an alternative measurement of the kB value of scintillators is assessed.
2. Theory In a liquid scintillation detector, if the number of created photoelectrons at the ith photomultiplier tube (PMT) photocathode induced by some energy deposit E in the scintillator is assumed to obey Poisson statistics, the detection efficiency of a single PMT as a function of E may be written as:
εi ðEÞ ¼ 1 e Ωi ðEÞE n
Corresponding author. Tel.: þ 61 2 9717 9751. E-mail addresses: [email protected], [email protected]
ð1Þ
where Ωi(E) is the mean number of photoelectrons that are produced at the photocathode per unit energy deposit in the
0969-8043/$ - see front matter Crown Copyright & 2013 Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.apradiso.2013.11.006
266
L.J. Bignell / Applied Radiation and Isotopes 87 (2014) 265–268
scintillator, and is referred to here as the scintillation response. The energy dependence of the scintillation response may be written as: Z E dE Ωi ðEÞE ¼ ωi EQ ðEÞ ¼ ωi ð2Þ dE 0 1 þ kB dx where kB is a material-dependent parameter, ωi is the mean number of photoelectrons produced at the ith PMT photocathode per unit of linearised energy deposit in the scintillator, and is here referred to as the linearised scintillator response. Q(E) is the Birks correction for the scintillator non-linearity. Since Q(E) corrects the non-linear response of the scintillator to linearity ωi is expected to be a constant for each PMT in the detector. The ZoMBieS method allows the direct measurement of εi(E). By comparing the measured εi(E) with Eqs. (1) and (2) one can directly obtain the scintillator response of each PMT, theoretically correct for Birks quenching, and confirm whether a constant ωi may be obtained.
3. The ZoMBieS method The ZoMBieS detector is a liquid scintillation detector with three PMTs (Hamamatsu R331-05) operating in coincidence, and an additional High Purity Germanium (HPGe) detector that also operates in coincidence and as the trigger source. The PMTs are mounted at 120o intervals surrounding the liquid scintillator and are housed within a light-tight, temperature controlled chamber with the right angle-mounted HPGe detector also extending into the chamber volume from an external dewar. A collimated 51Cr source was used as the scintillation excitation source. The external source was mounted within the scintillation chamber and the lead collimation was wide enough to permit the source to irradiate the entirety of the scintillator volume. The constant fraction discriminated (Ortec 935) PMT signals were fed into fast 8-bit digitisers (NI PXI-5153) and the HPGe signal was amplified using a shaping amplifier (Canberra 2024) before being fed into a high resolution 12 bit digitiser (NI PXI-5124). The trigger signal was obtained from the HPGe via a timing filter amplifier (Ortec 474) and constant fraction discriminator (Ortec 935) before being acquired by a fast digitiser (NI PXI-5153). The acquisition of all digitisers was synchronised and controlled using a custom-written LabView program. The energy deposited in the scintillator was inferred based on the measured HPGe pulse height, which was evaluated by least-squares fitting of the incoming pulses with a Gaussian function. PMT coincidences were evaluated with a coincidence resolving time of 40 ns. This acquisition therefore allows the measurement of double and triple PMT coincidences as a function of HPGe energy. The basis of the ZoMBieS technique is the can be seen by considering the triple-to-double coincidence ratio (TDCR) as a function of energy deposit in the scintillator. For a monoenergetic energy deposit, the TDCR may be written as: TDCR ¼
ε123 ε1 ε2 ε3 ¼ ¼ ε1 ε23 ε2 ε3
ð3Þ
where ε123 is the triple coincidence detection efficiency, ε23 is double coincidence detection efficiency between PMT 2 and 3, and εi is the detection efficiency of the ith PMT. It can therefore be seen that in the ZoMBieS detector, the determination of the TDCR as a function of energy deposit E in the scintillator is tantamount to a measurement of εi(E). It should be noted that the TDCR as defined in Eq. (3) differs from the convention used by some other authors of dividing the triple coincidences by the logical sum of double coincidences. A detailed description of the ZoMBieS measurement hardware and analysis procedure is given elsewhere (Bignell et al., 2013).
4. Measurements All liquid scintillation measurements were performed using 10 mL of Insta-Gel dispensed into a glass vial. ZoMBieS measurements were taken using the external 51Cr source at a variety of Compton scattering angles, so as to sample the detection efficiency over a sufficient range of energies. The measurements were taken over the course of approximately 1 month so as to minimize the statistical component of the measurement uncertainty. Fig. 1 shows the εi associated with each PMT for one of these measurements, with the Compton-coincident HPGe energy spectrum overlaid. The detection efficiency diverges at low energies as the statistical noise and accidental coincidences with the full energy peak becomes significant, while at high energies photons which lose energy in the scintillator, HPGe detector, and a non-sensitive part of the detector geometry affect the measurement. The efficiency increases monotonically with energy deposit over the useable range, as expected. The useable energy ranges associated with the data sets acquired for this study are presented in Table 1. The triple detection efficiencies associated with all data collected are presented in Fig. 2. The results are consistent within the uncertainties of the measurement (omitted from the figure for clarity). The scintillation response and linearised scintillation response – calculated using Eqs. (1) and (2) – are presented in Fig. 3, for the measurement data presented in Fig. 1. The uncorrected scintillator response (when kB¼0) exhibits an energy dependence and each tube was able to be corrected to an approximately constant response by using the Birks correction and an appropriate value of kB. However, different values of kB were required to linearise the scintillation response (Table 1). Furthermore, different kB values were required to linearise the scintillation response between different measurements same PMT (Table 1). For some acquisitions, the kB value required to linearise the data is negative, which is unphysical.
Fig. 1. The single PMT detection efficiency spectrum, εi(E), in PMT 1–3. A spectrum of the triple coincident counts is overlaid to illuminate the region of valid data.
Table 1 kB value and ωi, determined for each photomultiplier using the technique described in the text, for each acquisition. Valid energy (keV)
Parameter
PMT 1
PMT 2
PMT 3
29.8–49.3
kB (cm/MeV) ωi (keV 1) kB (cm/MeV) ωi (keV 1) kB (cm/MeV) ωi (keV 1) kB (cm/MeV) ωi (keV 1)
0.022 0.101 0.0011 0.0827 0.0060 0.0964 0.0013 0.0775
0.030 0.105 0.0010 0.0703 0.00071 0.0705 0.00099 0.0738
0.024 0.0576 0.0011 0.0922 0.00264 0.0930 0.00043 0.0903
13.3–34.8 3.8–21.8 4.8–28.3
L.J. Bignell / Applied Radiation and Isotopes 87 (2014) 265–268
5. Discussion As kB is a scintillator-dependent parameter, the same value of kB should be required to correct the PMTs to uniform response. The fact that the values of kB which were required to correct the scintillator response to a constant value are different for each of the PMTs suggests that there may be a systematic experimental error that affects the measured non-linearity of the scintillator. A possible source of systematic error is that of scattering of the 51 Cr gamma rays within the detector housing, PMTs, shielding, or mounting arrangement. Measurements have been performed with an empty glass vial to confirm that the direct irradiation of the PMTs has no effect upon the measurement. Some effects due to scattering are evident at energy deposits above 22 keV in Fig. 1. The measured efficiency spectrum appears to decrease, and not increase with energy above 25 keV which is physically implausible. Validation measurements of the activity of a 63Ni source by Bignell et al. (2013) confirm the ability of these data to accurately
Fig. 2. The triple coincident detection efficiency spectrum, εT(E), associated with the liquid scintillator, measured over various incident angles.
267
measure radioactivity, which suggests that any effects due to scattering are minor. That different values of kB and ωi are determined for the different measurements also suggests that there may be either some instability or geometry dependence of the measurement system. The εT spectra obtained agree within their statistical uncertainties, which indicates that the system is at least robust enough for activity measurements. Systematic effects due to source-detector geometry may be possible if the excitation of the scintillator volume is inhomogeneous. The collimator used in this study was deliberately chosen to be wide enough to cover the cross-section of the scintillator volume, so that any inhomogeneity must be due to photon attenuation within the scintillator. However, for the 320 keV 51Cr photons used, the attenuation through the scintillator is quite low. Photon attenuation calculations performed using the mass attenuation coefficient values of polyvinyltoluene (Hubbell and Seltzer, 1995) and a scintillator density of 0.9 g/cm3 suggest that a 320 keV photon beam that passes along the diameter of the liquid scintillator will exit the volume with 93.5% of its original intensity. This suggests that photon attenuation within the scintillator volume will not modify this distribution significantly. The scintillator light yield and PMT sensitivity are known to vary with ambient temperature. However, the temperature control of the detector is quite tight making temperature fluctuation an unlikely source of the observed instability. The PID-controlled thermoelectric modules provide heating and cooling to maintain a constant temperature to within 7 0.1 1C inside the detector housing. Gain instability in the HPGe shaping amplifier is another possible source of error. As the evaluation of the linearity data also involves dividing by the energy, even small changes in the gain may affect the measurement. Consider a true energy deposit x in the scintillator. This value is inferred by the detected HPGe energy. However, if there is some gain drift that has occurred since the energy calibration of the HPGe detector, then the measured energy deposit xmeas will differ from x by some small value δ. In order to solve Eq. (1) for Ωi, or Eq. (2) for ωi, one must divide by the energy. The relative error, Δ, associated with dividing by xmeas
Fig. 3. The scintillation response and ωi as measured in one of the external source geometries. The values of kB required to obtain a constant response (ωi) were not identical, and are given in Table 1.
268
L.J. Bignell / Applied Radiation and Isotopes 87 (2014) 265–268
measurements of the energy-dependent scintillator response using the Poisson–Birks model of detection efficiency. The scintillator non-linearity was able to be corrected to linearity by using the Birks equation and an appropriate value of kB. However, different values of kB were obtained for each of the three photomultipliers in the detector. The cause of this unexpected behaviour is unknown. Based on these measurements, the ZoMBieS method appears unsuitable as a means to characterise scintillator non-linearity until the source of this error can be located.
References Fig. 4. The relative error associated with gain drift (Eq. (4)), using the HPGe energy calibration checks carried out between the ZoMBieS measurements. The two traces indicate the error obtained as a function of energy for two different energy calibrations relative to a third.
rather than x is given by
Δ¼
xmeas x δ ¼ x x
ð4Þ
for measurements of the scintillator non-linearity, one is most interested in the limit of low energy; x-0. In this limit, Δ diverges, so that even small gain instabilities may affect the measured nonlinearity. The energy calibration of the HPGe detector was been checked three times using the same amplifier settings in the course of this study. Fig. 4 calculates Δ as a function of energy for two of these energy calibrations relative to the third. Although some differences are seen, they do not appear to be of sufficient magnitude at the relevant energy deposits to explain the observed discrepancies. 6. Conclusion Measurements of the detection efficiency spectrum of a liquid scintillator using the ZoMBieS method have been transformed to
Aberle, C., Buck, C., Hartmann, F.X., Schönert, S., Wagner, S., 2011. Light output of double chooz scintillators for low energy electrons. J. Instrum. 6 (11), P11006. Bignell, L.J., Mo, L., Steele, T., Hashemi-Nezhad, S-R, 2013. The zero model by using coincidence scintillation (ZoMBieS) method of absolute radioactivity measurement. IEEE Trans. Nucl. Sci. 60 (5), 4007–4014. Birks, J.B., 1964. The Theory and Practice of Liquid Scintillation Counting. Pergamon Press, Oxford, UK. Broda, R., Cassette, P., Kossert, K., 2007. Radionuclide metrology using liquid scintillation counting. Metrologia 44 (4), S36. Hubbell, J., Seltzer, M., 1995. Tables of X-ray Mass Attenuation Coefficients and Mass Energy-Absorption Coefficients. Tech. Report, NISTIR-5632, ver. 1.4. Nähle, O., Kossert, K., Cassette, P., 2010. Activity standardization of 3H with the new TDCR system at PTB. Appl. Radiat. Isot. 68, 1534–1536. Péron, M., Cassette, P., 1994. COCO, a Compton coincidence experiment to study liquid scintillator response in the 1–20 keV energy range. Nucl. Instrum. Methods Phys. Res., Sect. A 353, 41–45. Krosigk, B., Neumann, L., Nolte, R., Röttger, S., Zuber, K., 2013. Measurement of the proton light response of various LAB based scintillators and its implication for supernova neutrino detection via neutrino–proton scattering. Eur. Phys. J. C 73 (4), 2390. Zimmerman, B., Altzitzoglou, T., Rodrigues, D., Broda, R., Cassette, P., Mo, L., Ratel, G., Simpson, B., van Wyngaardt, W., Wätjen, C., 2010. Comparison of triple-todouble coincidence ratio (TDCR) efficiency calculations and uncertainty assessments for 99Tc. Appl. Radiat. Isot. 68, 1477–1481.