Applied Radiation and Isotopes 102 (2015) 15–28 Contents lists available at ScienceDirect Applied Radiation and Isotopes journal homepage: www.elsevier.com/locate/apradiso Precise measurements of the absolute γ-ray emission probabilities of 223 Ra and decay progeny in equilibrium S.M. Collins a,n, A.K. Pearce a, P.H. Regan a,b, J.D. Keightley a a b National Physical Laboratory, Hampton Road, Teddington, Middlesex TW11 0LW, United Kingdom Department of Physics, University of Surrey, Guildford, Surrey GU2 7XH, United Kingdom H I G H L I G H T S Discrepancies found within currently published γ-ray emission probabilities. Absolute γ-ray emission probabilities of decay series in equilibrium determined. Significant improvement in precision of measured values. Closer agreement between deduced and experimental α transition probabilities. Correlation coefficients presented for γ-emissions of 223Ra, 219Rn and 211Pb. art ic l e i nf o a b s t r a c t Article history: Received 25 September 2014 Received in revised form 3 March 2015 Accepted 14 April 2015 Available online 15 April 2015 Precise measurements of the absolute γ-ray emission probabilities have been made of radiochemically pure solutions of 223Ra in equilibrium with its decay progeny, which had been previously standardised by 4π(liquid scintillation)-γ digital coincidence counting techniques. Two high-purity germanium γ-ray spectrometers were used which had been accurately calibrated using a suite of primary and secondary radioactive standards. Comparison of the activity concentration determined by the primary technique against γ-ray spectrometry measurements using the nuclear data evaluations of the Decay Data Evaluation Project exhibited a range of 18% in the most intense γ-ray emissions ( 41% probability) of the 223 Ra decay series. Absolute γ-ray emission probabilities and standard uncertainties have been determined for the decay of 223Ra, 219Rn, 215Po, 211Pb, 211Bi and 207Tl in equilibrium. The standard uncertainties of the measured γ-ray emission probabilities quoted in this work show a significant improvement over previously reported γ-ray emission probabilities. Correlation coefficients for pairs of the measured γ-ray emission probabilities from the decays of the radionuclides 223Ra, 219Rn and 211Pb have been determined and are presented. The α-transition probabilities of the 223Ra have been deduced from P(γ þ ce) balance using the γ-ray emission probabilities determined in this work with some agreement observed with the published experimental values of the α-emission probabilities. Crown Copyright & 2015 Published by Elsevier Ltd. All rights reserved. Keywords: Nuclear data 223 Ra 219 Rn 215 Po 211 Pb 207 Tl Gamma-ray emission probabilities Gamma-ray spectrometry Correlation coefficients Radioactivity 1. Introduction Radium-223 is a naturally occurring radionuclide, occupying the later stages of the primordial decay series of 235U (see Fig. 1), that makes up approximately 0.7200(51)% of naturally occurring uranium (Rosman and Taylor, 1998). With a half-life of 11.4354 (17) d (Collins et al., 2015), 223Ra has undergone investigations for use as a radiopharmaceutical, with successful clinical trials for targeted radiotherapy of bone metastases and bone palliation that occur from late-stage castration resistant prostate cancer n Corresponding author. E-mail address: [email protected] (S.M. Collins). http://dx.doi.org/10.1016/j.apradiso.2015.04.008 0969-8043/Crown Copyright & 2015 Published by Elsevier Ltd. All rights reserved. (Michalski et al., 2013; Nilsson et al., 2007; Parker et al., 2013). As a group II element, radium shares many chemical properties with calcium and exhibits a high level of incorporation into metabolically active osteoblastic bone and tumour lesion sites (Bruland et al., 2008; Nilsson et al., 2007). Coupled with the relatively short dose deposition range of α-emissions this allows a highly targeted cytotoxic dose of ionising radiation to a specific cancer site with reduced damage to the bone marrow and other surrounding healthy tissue, giving this treatment obvious advantages over the relatively long energy deposition range of β-emitting bone-targeting radiopharmaceuticals e.g. 89Sr, 166Ho and 153Sm, that have been used historically. Additionally, as a naturally occurring radionuclide it is of interest as a potential radiotoxic hazard from 16 S.M. Collins et al. / Applied Radiation and Isotopes 102 (2015) 15–28 Fig. 1. Decay series of naturally occurring radioactive material (NORM) and technologically enhanced NORM (TENORM) (Kathren, 1998). The 223Ra nucleus decays by 100% α-emission to excited states of 219Rn (Chechev, 2011c), the decay scheme of which is shown in Fig. 2, with a small branch (4.7 10 10 relative to the α-decay branch (Kutschera et al., 1985)) decaying via the spontaneous emission of a 14C nuclear cluster to 209Pb (Rose and Jones, 1984). The 219Rn further decays via a series of relatively short-lived (T1/ 2 o37 min) α- and β-emitting decay progeny each decaying via their respective excited states (Chechev, 2011a, 2011b, 2011c; Nichols, 2011; Kondev, 2013a, 2013b; Luca, 2010; Luca, 2011) with associated γ-ray emissions, with the series terminating at the stable nucleus of 207Pb. The 14C cluster decay mode of 223Ra has not been investigated in the scope of this work. In view of the growing importance of 223Ra in these applications the National Physical Laboratory (NPL) undertook a course of work to provide an absolute standardisation of 223Ra (Keightley et al., 2015) that would provide traceability to the SI unit of the Becquerel. Two solutions of 223Ra were independently standardised, henceforth referred to as S1 and S2, using liquid scintillation (LS) absolute standardisation techniques, the first performed in 2013 and the second in 2014. Initial measurements of the solutions were made by high purity germanium (HPGe) γ-ray spectrometry of the thirteen most intense γ-ray emissions (41%) of the 223Ra decay series, listed in Table.1. The activity of each selected γ-ray of the 223Ra decay series was determined using the nuclear data from the evaluations of the Decay Data Evaluation Project (DDEP) (Chechev, 2011c; Nichols, 2011; Kondev, 2013a; Luca, 2010). Whilst 235 U. the weighted mean activity of the individual γ-ray emissions were in good agreement with the activity determined by the LS standardisation techniques (see Fig. 3), the activity concentration calculated from the various γ-ray emissions had a range of 18%, as shown in Table 1 and Fig. 4. We considered this indicated a statistically significant discrepancy in the existing published γ-ray emission data, and that further measurements were required. This conclusion reflected the findings of Kellett and Nichols (Kellett and Nichols, 2013) who highlighted a disagreement between the αtransitions and values deduced from the P(γ þ ce) balance within the 219 Rn excited levels. A review of the currently published normalised γ-ray emission values (Blaton-Albicka et al., 1976; Briançon and Leang, 1968; Davidson and Connor, 1970a; Hesselink, 1972; Kossert et al., 2015; Krien et al., 1970; Sheline et al., 1998) for the decay of 223Ra was performed. In all cases, with the exception of Krien et al. (1970), no specific information was provided regarding the full-energy peak (FEP) efficiency calibration of the γ-ray spectrometers used. Such FEP efficiency calibrations are critical to the accuracy of γ-ray emission probability measurements. Comprehensive details of the methodology used and the resulting FEP efficiency calibration curve are therefore presented in detail in this article. Maintaining a chemical separation of the different radionuclides present in the decay series of 223Ra is problematic due to the short half-lives of the decay progeny and evolution of 219Rn; therefore the measurements were made of the decay series in equilibrium within an aqueous solution. Investigation of the γ-ray emissions from the decay of 223Ra and its decay progeny indicated S.M. Collins et al. / Applied Radiation and Isotopes 102 (2015) 15–28 Fig. 2. Decay scheme of 223 Ra to states in 17 219 Rn (Chechev, 2011c). Table 1. γ-ray nuclear data from the DDEP (Chechev, 2011a; Nichols, 2011; Kondev, 2013a; Luca, 2010) and determined activity per unit mass of the S1 solution by HPGe γ-ray spectrometry. Energy/keV Radionuclide Intensity /% Activity/kBq g 1 122.3 144.3 154.2 269.5 271.2 323.9 338.3 351.0 401.8 404.8 427.2 445.0 832.0 Final result 223 1.238(19) 3.36(8) 5.84(13) 14.23(32) 11.07(22) 4.06(8) 2.85(6) 13.00(19) 6.75(22) 3.83(6) 1.81(4) 1.28(4) 3.5(5) 55.4(9) 54.0(13) 53.9(12) 49.0(11) 50.9(10) 47.1(9) 48.0(10) 53.1(8) 50.8(17) 54.7(9) 54.1(12) 50.0(16) 52.1(8) 52.0(8) Ra Ra 223 Ra 223 Ra 219 Rn 223 Ra 223 Ra 211 Bi 219 Rn 211 Pb 211 Pb 223 Ra 211 Pb 223 Fig. 3. S1 activity per unit mass determined by various measurement techniques. the measurements of the primary γ-ray emission of each radionuclide would be essentially unaffected by interferences from the decay of the other radionuclides present, although some potential convolutions would be present in the energy range of the main γray emissions of 223Ra (269.5 keV) with 219Rn (271.3 keV) and 219 Rn (401.8 keV) with 211Pb (404.8 keV). A full uncertainty budget is detailed within this paper. All uncertainties are stated as standard uncertainties or combined standard uncertainties as defined in the Guide to the Expression of Uncertainty in Measurement (GUM) (BIPM, 2008). 2. Experimental method 2.1. Sample preparation Two separate active solutions were supplied by Algeta ASA (Norway) with a nominal activity of 50 MBq 223RaCl2 in a 10 mL sodium citrate pH buffer solution. Following previous experience at NPL with 223RaCl2 in this chemical format, the material was diluted with an aqueous solution of 1 M HCl to reduce the risk of hydrolysis and any associated loss of activity during transfer of the active solution between vessels. Solution S1 was diluted to a nominal activity concentration of 50 kBq g 1 in 1 M HCl, with 1 g 18 S.M. Collins et al. / Applied Radiation and Isotopes 102 (2015) 15–28 2.3. HPGe γ-ray spectrometry Fig. 4. Activity per unit mass of the individual γ-ray emissions of 223Ra and decay progeny in equilibrium compared to the absolute activity per unit mass determined for S1 (solid line) with the standard uncertainty (dashed lines). aliquots dispensed to three 2 mL ISO ampoules (ISO, 2010) for measurement by γ-ray spectrometry and dispensed to sixteen 34 mL Wheaton type liquid scintillation vials. Solution S2 was diluted to a nominal activity concentration of 330 kBq g 1 in 1 M HCl and dispensed to a further three 2 mL ISO ampoules (ISO, 2010) for γ-ray spectrometry and sixteen 22 ml Wheaton type liquid scintillation vials. In order to minimise the risks associated with emanation of 219Rn, the ampoules were flame sealed and the vial screw threads wrapped with PTFE tape. 2.2. Absolute standardisation The S1 solution was standardised using the CIEMAT/NIST efficiency tracing method (Broda et al., 2007) and the 4π(LS)-γ digital coincidence counting (DCC) technique (Keightley and Park, 2007; Keightley and Watt, 2002). The S2 solution was standardised using the 4π(LS)-γ DCC technique only. A description of the measurement methodology has been covered in-depth by Keightley et al. (2015). The results of these measurements can be found in Table 2. The activity per unit mass for the two solutions were determined as AS1 ¼ 52.35(17) kBq g 1 and AS2 ¼ 329.2(11) kBq g 1. Table 2 Activity per unit mass of techniques. 223 Two LN2 cooled HPGe γ-ray spectrometers, identified as BART and LORAX, were used to perform the measurements. BART is an n-type HPGe γ-spectrometer with a resolution (FWHM) of 1.79 keV at 1.3 MeV and a relative efficiency of 28%, LORAX is an n-type semi planar HPGe γ-spectrometer with a resolution of 0.6 keV at 0.122 MeV. Both detectors were contained in identical 1.5 m 1 m 1 m Pb shields comprised of 10 cm thick aged Pb walls covered with a 0.5 mm Cd and 0.7 mm Cu graded liner to reduce effects from background radiation and Pb fluorescence X-rays in the spectra. Aluminium optical bread boards were mounted along the horizontal axis of the coffin with a kinematic mounting plate holding a precision engineered sample holder attached to enable highly reproducible geometric source positioning in front of the detector window. The energy calibration of both detectors was performed using the most intense γ-rays ( 41%) of 152Eu, covering an energy region from 121.8 keV to 1408.0 keV. The energy calibration resulted in peak centroids within 0.05 keV of the 152Eu γ-ray energies evaluated by the DDEP (Vanin et al., 2004). The spectra were collected using a chain of CANBERRA analogue electronics (AFT Research amplifier 2025, Analogue-to-Digital Converter 8715, AIM) connected to a PC running the CANBERRA GENIE 2000 v2.1c software. The net peak area losses due to dead time were corrected for by the electronics using the integrated pile-up rejection (PUR)/live-time correction (LTC) circuit. An additional correction was required for pulse pile-up occurring from random coincidence summing events which had not been captured by the integrated PUR/LTC circuit of the analogue electronics (Rajput, 2010). This was determined empirically for each detector using the decay corrected counts of a 99mTc source. All spectra were analysed using CANBERRA GENIE 2000 v2.1c. The fit to each peak was manually reviewed and adjusted where necessary using the CANBERRA GENIE Interactive Peak Fit application. The photopeak areas were corrected for background and integrated decay (Harms and Jerome, 2004) during the counting period. 2.3.1. Full-energy peak (FEP) efficiency calibration The FEP detection efficiencies were determined using a suite of traceable primary and secondary standards of γ-ray emitting radionuclides to cover the photon energy range from 14 keV to 1836 keV. The calibration geometry was 1 g aqueous solution in a 2 mL ISO ampoule at perpendicular distances from the detector window of 30 cm and 16.5 cm for detectors BART and LORAX respectively. Each calibration point was measured with multiple sources, collecting at least 105 counts in the photopeaks of interest. Using the evaluated nuclear data from the DDEP (BIPM, 2004) for each radionuclide, the FEP efficiency was estimated using the equation: ε keV = N × Ct × Cd × Cp × Cc t × m × A 0 × Iγ where, Ra solutions S1 and S2 determined by multiple εkeV Measurement technique S1 activity/ kBq g 1 S2 activity/kBq g 1 CIEMAT/NIST efficiency tracing 4π(LS)-γ DCC HPGe γ-ray spectrometry 4π APPC (α)-γ coincidence counting 4π APPC (α þβ)-γ coincidence counting Final result 52.4(4) 52.34(18) 52.0(8) 52.4(4) 52.5(10) – 329.2(11) 325(5) 52.35(17) 329.2(11) – N Ct Cd Cp Cc t m A0 Iγ photopeak efficiency total counts collected in photopeak Integrated decay correction Self-absorption correction to H20 Pulse pile-up correction True coincidence summing correction Live time of measurement Mass of active material Activity per unit mass of radioactive material γ-ray emission probability per decay (1) S.M. Collins et al. / Applied Radiation and Isotopes 102 (2015) 15–28 Table 3 Full-energy peak efficiency calibration points for the HPGe γ-ray spectrometers BART and LORAX. Energy/keV Radionuclide 14.41 26.24 35.49 46.54 59.54 88.03 122.06 136.47 165.86 320.08 391.70 514.00 661.66 834.84 898.04 1115.54 1173.23 1332.49 1836.05 57 Full-energy peak efficiency /% BART Co Am 125 I 210 Pb 241 Am 109 Cd 57 Co 57 Co 139 Ce 51 Cr 113 Sn 85 Sr 137 Cs 54 Mn 88 Y 65 Zn 60 Co 60 Co 88 Y 241 LORAX 2 2.96(10) 10 1.29(5) 10 1 1.52(4) 10 1 1.647(23) 10 1 1.674(10) 10 1 1.67(4) 10 1 1.601(11) 10 1 1.537(24) 10 1 1.416(12) 10 1 8.54(6) 10 2 7.16(6) 10 2 5.61(5) 10 2 4.53(4) 10 2 3.716(14) 10 2 3.499(20) 10 2 2.929(22) 10 2 2.822(8) 10 2 2.534(14) 10 2 1.93(9) 10 2 9.0(3) 10 2 3.44(12) 10 1 – 4.26(6) 10 1 4.33(3) 10 1 4.29(8) 10 1 3.88(3) 10 1 3.54(6) 10 1 2.893(25) 10 1 1.107(10) 10 1 8.23(7) 10 2 5.63(5) 10 2 4.06(3) 10 2 3.038(12) 10 2 2.793(13) 10 2 2.162(16) 10 2 2.045(6) 10 2 1.770(5) 10 2 1.218(5) 10 2 As the chemical composition of the aqueous calibration standards varied, as is necessary to obtain a stable solution of the various elements, corrections were calculated for each data point to compensate for the difference in expected self-absorption compared to H20. The corrections were determined using a farfield model for cylindrical samples (Parker, 1984). The linear attenuation coefficients were derived from the NIST XCOM database (Berger et al., 1998). The samples were set at large distances from the detector window, such that the solid angles were low (approximately 0.026 sr and 0.075 sr for BART and LORAX respectively, assuming the sample as a point source). Hence, no cascade summing coincidence corrections were applied. The measured FEP efficiencies for each calibration point are listed in Table 3. The FEP detection efficiency curve fitted to the calibration data set was of the form: ε(x, C) = ⎡ N ⎤ ⎢ ⎥ ⎢ ∑ c jbj(x, λ)⎥ ⎦ e⎣ j = 1 (2) where x = loge E 511 (3) with the FEP efficiency denoted ε and the basis functions bj (x) selected were quartic b-splines (Cox, 1972). The only adjustable parameter, for each value of j, was C. A series of six knots (where the piecewise polynomials are joined at λ = loge(Eλ/511)) were selected at intervals along the energy range; these knots were positioned based on a visual inspection of the shape of the FEP efficiency curve. The knot set was augmented by placing an additional four replicated knots both at the beginning and end of the sequence; the total number of knots was therefore fourteen and the number of fitted coefficients (N) was 9. The best fit was determined by a generalised least squares fit (Aitken, 1936) to the calibration points spanning the range of energies that were covered for each detector, 14 keV(57Co)–1836 keV (88Y) for BART and 46 keV (210Pb)–1836 keV (88Y) for LORAX. The respective fits and residuals of the fits can be seen in Fig. 5 and Fig. 6. 19 2.3.2. Measurements of 223Ra and detection of impurities The S1 samples were measured solely on BART over a period of approximately 20 d with a total of eight measurements; referred to as dataset S1B. Each source was measured at least twice with a typical measurement time of 50,000 s. A dead time of 0.50% was recorded at the start of the measurement campaign and 0.23% at the end of the measurement campaign. The S2 samples were measured over a period of 29 d and 18 d on both BART and LORAX respectively, with a total of nine measurements on each detector; the corresponding datasets are referred to as S2B and S2L. Each sample was measured three times on each detector, with a typical counting time of 86400 seconds. Dead times of 3.22% and 7.76% were recorded at the beginning of the measurement campaign and 0.58% and 2.43% at the end of the measurement campaign for BART and LORAX respectively. An example of a spectrum collected on BART can be seen in Fig. 7. All peak areas were corrected for dead time, integrated decay, pulse pile-up and background. Self-absorption corrections were made to convert the FEP efficiency from H2O to 1 M HCl, this correction was less than 0.2% at γ-ray emission energies greater than 100 keV. The count rates of those γ-ray emissions produced by the decay of 211Pb, 211Bi, 211Po and 207Tl have been corrected to take into account that these radionuclides exist in a transient equilibrium with that of 223Ra due to the half-life of 211Pb being approximately 36.1 min (Sargent, 1939). This correction was determined using the Bateman equation (Bateman, 1910): λp λ p − λd × BR (4) where λp and λd are the decay constants of the parent and daughter respectively and BR is the branching ratio of the parent to daughter. The correction of the γ ray emission probabilities for these decay progeny was approximately 0.22%. S1 and S2 were investigated for the presence of γ-ray emitting impurities and the precursors 227Ac and 227Th. The presence of 227 Ac – T1/2 ¼7952.1 d (Browne, 2001) – and 227Th – T1/2 ¼18.68 d (Browne, 2001) – in small quantities could affect the accuracy of the determination of the γ-ray emission probabilities as they will support the activity of the 223Ra, thus perturbing the expected radioactive decay rate. Neither solution showed any indication of impurities or the presence of 223Ra precursors, though additional consideration of the precursor 227Ac was required as this radionuclide exhibits relatively weak α- and subsequent γ-ray emissions that render α- and γ-spectrometry impractical. The activity of S1 was measured over a period of 72 d (3.6 times longer than the measurement period for the γ-ray emission measurements) using an ionisation chamber. There was no exhibited perturbation in the radioactive decay or trends within the residuals of least squares fit; Indicating that there was no significant presence of 227 Ac or 227Th within the solution. It has been assumed by comparison of the measurements of S2 over the measurement period and the agreement between the calculated γ-ray emissions of S1 and S2 that there was no significant presence of 227Ac in this solution either. 3. Results The absolute γ-ray emission probabilities of 223Ra and its decay progeny were derived from the activity per unit mass determined by absolute standardisation techniques and measurement by the two HPGe γ-ray spectrometers. The absolute γ-ray emission intensities for each measurement were calculated using the equation: 20 S.M. Collins et al. / Applied Radiation and Isotopes 102 (2015) 15–28 Fig. 5. Full-energy peak efficiency curve and residuals of the B-spline fit for the HPGe γ spectrometer BART. Fig. 6. Full-energy peak efficiency curve and residuals of the B-spline fit for the HPGe γ spectrometer LORAX. Iγ = N × Ct × Cd × Cp × Cc t × m × A o × ε keV (5) The weighted mean of the measured absolute γ-ray emission probability from each measurement for a dataset was deduced using the uncertainties derived from the peak fitting software, dead time and radioactive decay to determine the weight of contribution from each measurement. The final value was deduced as the weighted mean of the three datasets with the FEP efficiency uncertainty combined with the standard uncertainty of the weighted mean of the γ-ray emission probability uncertainty from each dataset. The reduction in the standard uncertainty of the weighted mean was limited to the smallest of the standard uncertainty of the three datasets. The final uncertainties were determined by adding the additional systematic uncertainties in quadrature to the standard uncertainty calculated from the Fig. 7. An annotated spectrum of 223 Ra and decay progeny in equilibrium. weighted mean. The uncertainty budget is described in detail in Section 4. As the photopeaks below 100 keV are mainly the convoluted X-ray emissions of 223Ra and its decay progeny, only results for the observed γ-ray emissions from the decay of 223Ra and the resulting decay progeny that have energies greater than 100 keV are presented in Table 4. These are presented as the absolute γ-ray emission intensities per 100 disintegrations. Additionally the radionuclide source of the γ-ray emission is listed as deduced from the evaluations of the DDEP (Chechev, 2011a, 2011b, 2011c; Nichols, 2011; Kondev, 2013a, 2013b; Luca, 2010, 2011). The relative γ-ray emission probabilities of this work and those previously published for 223Ra (Blaton-Albicka et al., 1976; S.M. Collins et al. / Applied Radiation and Isotopes 102 (2015) 15–28 Table 4 Absolute γ-ray emission probabilities per 100 decays of 223 Ra and decay progeny in equilibrium. Energy (keV) Source Iγ (%) Energy (keV) Source Iγ (%) 103.9(5) 106.7(4) 223 0.0119(6) 0.0213(11) 323.9(6) 328.4(6) 223 110.8(5) 122.3(5) 130.6(5) 144.3(5) 154.2(5) 158.7(5) 175.6(5) 177.4(5) 179.7(5) 221.4(5) 224.0(5) 249.4(5) 251.9(5) 255.1(5) 269.5(6) 271.3(6) 288.2(6) 223 Ra Ra 219 Rn 223 Ra 223 Ra 223 Ra 223 Ra 223 Ra 223 Ra 223 Ra 219 Rn 223 Ra 223 Ra 223 Ra 223 Ra 219 Rn 223 Ra 0.0512(10) 1.312(6) 0.1478(10) 3.481(16) 6.02(3) 0.749(4) 0.01578(10) 0.0426(8) 0.1613(10) 0.0304(10) 0.0056(14) 0.0375(9) 0.0640(11) 0.0499(13) 13.37(7) 10.75(6) 0.1498(16) 333.9(6) 338.3(6) 342.9(6) 351.1(6) 355.5(6) 361.7(6) 363.0(6) 368.4(6) 371.7(6) 372.9(6) 376.2(6) 383.3(5) 386.3(5) 390.1(5) 401.8(6) 404.8(6) 427.1(6) Ra Ra, 211Po, 207 Tl 223 Ra 223 Ra 223 Ra, 211Pb 211 Bi 223 Ra 211 Pb 223 Ra 223 Ra 223 Ra 223 Ra 223 Ra 223 Ra 223 Ra, 219Rn 223 Ra 219 Rn 211 Pb, 215At 211 Pb 293.6(5) 313.7(6) 219 0.0688(7) 0.0276(5) 430.4(6) 432.4(6) 223 0.0206(19) 619.8(6) 0.0297(14) 623.4(5) 223 Ra Ra 223 Rn Pb 211 223 223 21 Ra, Ra 211 Pb Source Iγ (%) Energy (keV) Source Iγ (%) 3.655(18) 438.8(6) 0.2021(16) 445.0(6) 215 0.0533(7) 1.218(6) 675.4(6) 676.9(6) 211 0.0058(6) 0.0184(5) 0.0756(6) 2.605(13) 0.1958(21) 13.17(7) 0.0124(15) 0.0341(7) 0.0192(9) 0.0134(4) 0.435(3) 0.1133(13) 0.0056(4) 0.0023(6) 0.0052(7) 0.0053(7) 6.57(3) 4.011(19) 1.890(9) 219 0.0011(5) 0.0083(3) 0.0013(5) 0.0022(4) 0.0453(5) 0.0021(6) 0.0659(8) 0.0028(9) 0.0033(6) 0.0026(6) 0.0028(6) 0.0026(7) 0.0035(4) 0.0043(5) 0.0029(13) 0.0867(12) 0.0543(7) 704.6(7) 707.8(7) 711.4(7) 727.4(7) 766.4(7) 831.9(7) 835.6(7) 865.8(6) 891.3(7) 897.8(7) 1014.7(7) 1074.5(7) 1080.1(7) 1103.3(8) 1109.5(8) 1196.2(8) 1234.3(8) 211 0.0056(12) 1270.7(8) 0.0082(8) 211 Briançon et al., 1968; Davidson and Connor, 1970a; Hesselink, 1972; Krien et al., 1970; Sheline et al., 1998), 219Rn (Blaton-Albicka et al., 1976; Briançon and Leang, 1968; Dalmasso and Maria, 1967; Davidson and Connor, 1970b; Krien et al., 1970; Liang et al., 1998), 215 Po (presented as absolute values for comparison) (Briançon and Leang, 1968; Davidson and Connor, 1970b) and 211Pb (Blaton-Albicka et al., 1976; Briançon and Leang, 1968; Cothern and Connor, 1965; da Silveira et al., 1971; Dalmasso and Maria, 1967; Davidson et al., 1967; Giannini et al., 1962a; Gorodetzky et al., 1968; Hamilton and Davies, 1968; Hindi et al., 1988; Mead and Draper, 1965; Vandenbosch et al., 1963) are presented in Tables 5–8. The 269.5 keV γ-ray emission of the 223Ra decay is convoluted with the 271.3 keV γ-ray emission of the 219Rn decay. Hence, the relative γray emission intensities of 223Ra were deduced as the γ-ray emission intensity normalised to the 154.2 keV γ-ray emission probabilities, as this transition has no known convolutions and should therefore be a reliable normalisation point. The 271.3 keV γ-ray emission has been used as the normalisation for the γ-ray emissions of 219Rn. Though it is convoluted with the 269.5 keV of 223 Ra, the only other significant emission of 219Rn, the 401.8 keV γray emission, is also convoluted by the 404.8 keV γ-ray emission of 211 Pb. The 211Pb values have been deduced relative to the 351.1 keV γ-ray emission. 4. Uncertainties 4.1. Uncertainty components of the γ-ray emission probabilities A summary of the uncertainty components for the absolute γray emission probability of the 269.5 keV γ-ray emission is presented in Table 9. The assigned uncertainty values of the components were combined in quadrature to determine the final uncertainty value. The dominating uncertainty components for the most significant γ-ray emissions of the 223Ra decay series (where the statistical uncertainties are less than 0.1%) are due to the standard uncertainty of the standardisation of the activity per unit mass, the FEP efficiency calibration and efficiency stability of the detector chain. The FEP efficiency uncertainties were calculated from the least Energy (keV) 462.8(6) 487.3(5) 500.2(6) 504.1(6) 517.6(6) 522.6(6) 527.6(6) 531.4(6) 537.5(6) 542.1(6) 545.9(6) 555.9(5) 564.4(5) 569.6(7) 573.7(7) 598.6(7) 609.3(7) Po Ra 223 Rn Ra 223 Ra 211 Pb 219 Rn 223 Ra 223 Ra 223 Ra 223 Ra 223 Ra 223 Ra 219 Rn 219 Rn 211 Po, 207Tl 223 Ra 223 Ra 223 Ra, 219Rn, 211 Pb 219 Rn 223 Ra 223 Pb Rn 219 Pb Rn 223 Ra 223 Ra 211 Pb 211 Pb 219 Rn 211 Pb 219 Rn 211 Po, 211 Pb 219 Rn 211 Pb 211 Pb 211 Pb 211 Pb 211 Pb 219 Pb 0.498(3) 0.0034(4) 0.0037(3) 0.0024(7) 0.685(4) 3.448(16) 0.00364(19) 0.00540(21) 0.00107(20) 207 Tl 0.2725(15) 0.0171(4) 0.00044(12) 0.01228(21) 0.00380(12) 0.1113(7) 0.01052(17) 0.00092(8) 0.00624(19) squares fit of the photopeak efficiency calibration including the input efficiency uncertainties (see Table 3) and taking into account the correlations and co-variances due to nuclear data, standardisation, etc. The calculated uncertainty of the FEP efficiency calibration can be seen in Figs. 5 and 6 as the dashed line in the residual plots. A systematic uncertainty of 5% was estimated for the dead-time and pile-up correction, which when propagated using the median recorded dead-time resulted in an overall uncertainty component of 0.05%. An additional uncertainty component was incorporated in the dead-time and pile-up uncertainty to take into account the perturbation on the photopeak shape that occurs at increasing count rates (Rajput, 2010). Within the range of dead times observed this was estimated to be insignificant. A radioactive decay uncertainty was determined using the evaluated uncertainty of the 223Ra half-life, in previous work by the authors (Collins et al., 2015), of 11.4354(17) d, using the median decay period of the measurements to the standardisation reference time to propagate the radioactive decay uncertainty. An estimated uncertainty of 0.10% was incorporated to account for the small but inevitable quantity of true coincidence summing events that may occur. As described previously in Section 3, due to the small solid angle subtended by the detector the number of events that would occur would be insignificant and therefore the assigned uncertainty value would be sufficient to account for these events. It cannot be assumed that the detector response will remain constant with small fluctuations that may occur in the detector itself or in the detector electronics chain; these effects can be small and hence obscured within the measurement series. This effect should be accounted for especially if the measurements are made over an extended period; the long term stability uncertainty has been estimated using a 152Eu source which had been measured over the measurement campaigns. The geometric reproducibility uncertainty for the positioning of the source in an identical geometry is 0.10% as the use of precision engineered source holders in tandem with the kinematic optical mounting system allows a very high level of positional reproducibility. 22 S.M. Collins et al. / Applied Radiation and Isotopes 102 (2015) 15–28 Table 5 Normalised γ-ray emission probabilities of 223Ra observed in this work and published values. All values normalised to the 154.2 keV γ-ray emission. Energies marked with an n have interferences with γ-ray emissions from decay progeny in equilibrium. Energy/keV This work Briançon et al. (1968) Krien et al. (1970) Davidson and Connor (1970a) Hesselink (1972) Blaton-Albicka et al. (1976) Sheline et al. (1998) Kossert et al. (2015) χ 2 /(n − 1) 103.9(5) 106.7(4) 110.8(5) 122.3(5) 144.3(5) 154.2(5) 158.7(5) 175.6(5) 177.4(5) 179.7(5) 221.4(5) 249.4(5) 251.9(5) 255.1(5) 269.5(6) 288.2(6) 323.9(6) 328.4(6)n 333.9(6) 338.3(6) 342.9(6)n 355.5(6) 363.0(6) 368.4(6) 371.7(6) 372.9(6) 376.2(6) 383.3(5)n 386.3(5) 390.1(5) 430.4(6)n 432.4(6) 445.0(6) 487.3(5) 500.2(6) 522.6(6) 527.6(6) 531.4(6) 537.5(7) 542.1(7) 545.9(7) 573.7(7) 598.6(6) 609.3(7)n 623.4(5) 711.4(7) 727.4(7) – 0.43(8) 1.04(17) 21(4) 57(7) 100(–) 13.0(16) – 0.54(19) 2.8(8) 0.65(19) 0.67(19) 1.3(3) 1.1(3) 260(40) 3.0(5) 69(9) 3.7(5) 1.6(3) 50(6) 3.7(5) – – – 10.1(13) – – – – – – 0.622(91) 22.5(20) 0.184(39) – – 1.30(16) – – – – – 1.48(19) 0.93(13) 0.15(8) 0.065(19) – – 0.34(7) 0.81(7) 21.3(6) 57.9(17) 100(–) 12.2(4) 0.24(7) 0.83(8) 2.6(7) 0.54(10) – 0.66(17) – 243(7) 2.82(13) 71.5(20) 3.70(18) 1.85(15) 51(12) 4.14(23) – – – 8.66(24) – – – – – – 0.63(10) 26.8(20) 0.24(7) – – 1.31(12) – – – – – 1.85(17) 1.31(17) – – – – 0.42(11) 1.08(15) 26(4) 61(9) 100(–) 14.7(22) – – 2.9(5) – – 1.1(4) 1.0(4) 260(40) 2.8(5) 70(10) 3.1(7) 2.4(6) 50(8) 3.9(11) – – – 10.5(19) – 0.23(8) 0.29(11) – – – – 25(4) – – – 1.3(3) – – – – – 1.8(4) 1.21(22) – – – – 0.43(14) 0.47(20) 19.6(15) 62(6) 100(–) 11.9(11) 0.34(9) 0.79(14) 2.6(4) 0.56(10) 0.7(3) 1.1(4) 0.54(16) 225(16) 2.1(4) 60(5) 2.7(5) 1.6(3) 43(3) 1.6(4) – – – 9.5(11) – – 0.07(5) 0.23(9) 0.05(4) 0.32(9) 0.54(14) 20.7(20) 0.18(9) – – 1.1(3) – – – – – 1.5(3) 0.68(25) – – – 0.35(6) 0.41(6) 1.05(15) 20(3) 57(8) 100(–) 12.1(17) – – 2.7(4) – – 1.24(23) 0.87(21) 260(30) 2.8(4) 71(8) 3.7(5) 1.42(24) 49(6) 3.9(5) – – – 8.3(10) 1.9(3) – – – – – 0.49(9) 22(3) – – – 1.08(13) – – – – – 1.65(19) 0.98(12) – – – 0.34(5) 0.42(3) 1.02(8) 21.2(6) 57.3(19) 100(–) 12.2(4) 0.34(7) 0.83(8) 2.68(5) 0.63(10) 0.68(17) 0.73(24) 0.93(12) 244(8) 2.80(10) 70.0(21) 3.7(12) 1.78(11) 49.8(16) 3.9(3) 0.073(24) 0.49(12) 0.15(7) 8.5(4) 0.878(21) 0.22(7) – 0.27(10) 0.12(5) 0.34(10) 0.61(5) 22.7(9) 0.195(25) 0.024(10) 0.024(10) 1.24(8) 0.024(10) 0.037(12) 0.024(10) 0.020(10) 0.020(10) 1.66(8) 1.00(6) 0.15(7) 0.063(17) 0.0049(24) – – 0.93(5) 21.63(12) 57.53(24) 100(–) 12.22(8) 0.284(16) 0.632(18) 2.54(5) 0.463(18) 0.60(5) 1.05(3) 0.73(3) 218.2(13) 2.42(3) 60.71(25) 3.28(3) 1.244(22) 43.35(17) 2.90(3) – 0.292(10) 0.252(19) 8.3(3) 0.85(3) 0.093(5) – – – 0.393(4) 0.496(21) 20.27(8) 0.100(11) – – 1.056(18) – – – – – 1.425(14) 0.507(12) – – – 7.8 0.8 2.3 0.9 0.2 – 0.3 0.9 4 1.2 1.3 0.1 1.2 2.1 4.2 3.6 7.3 1.6 6.6 2.8 15 15 2.3 1.7 10 440 2.0 2.7 2.8 0.9 1.2 1.3 3.0 3.7 0.1 0.6 1.9 1.5 1.4 1.9 4.0 1.6 2.3 102 0.3 0.1 8.2 0.198(10) 0.354(18) 0.850(17) 21.79(11) 57.8(3) 100(–) 12.27(6) 0.2620(17) 0.708(13) 2.678(18) 0.504(16) 0.622(14) 1.062(19) 0.829(21) 221.9(11) 2.488(27) 60.7(3) 3.36(3) 1.255(9) 43.25(21) 3.25(4) 0.206(25) 0.318(15) 0.223(5) 7.22(5) 1.882(22) 0.092(5) 0.038(9) 0.086(11) 0.088(11) 0.34(4) 0.493(23) 20.22(10) 0.137(5) 0.021(8) 0.034(9) 1.094(13) 0.047(16) 0.055(10) 0.043(9) 0.047(10) 0.049(21) 1.441(19) 0.902(10) 0.135(14) 0.061(5) 0.040(12) Table 6 Normalised γ-ray emission probabilities of 219 Rn observed in this work and published values. All values normalised to the 271.3 keV γ-ray emission. Energy/keV This work Dalmasso and Maria (1967) Briançon et al. (1968) Davidson and Connor (1970b) Krien et al. (1970) Blaton-Albicka et al. (1976) Liang et al. (1998) Kossert et al. (2015) χ 2 /(n − 1) 130.6(5) 224.0(6) 271.3(6) 293.6(5) 401.8(6) 462.8(6) 517.6(6) 555.9(5) 564.4(5) 619.8(6) 676.9(6) 707.8(7) 835.6(7) 891.3(7) 1074.5(5) 1.40(14) – 100(–) 0.64(6) 58(6) – 0.44(10) – – – 0.21(3) 1.18(23) – 100(–) 0.70(14) 61(4) – 0.44(4) – – – 0.21(2) – – – – 1.05(25) – 100(–) 0.59(15) 65.2(65) – 0.22(5) – – – 0.06(3) – – – – 1.21(10) – 100(–) 0.51(27) 69(3) – – – – – – – – – – 1.10(11) – 100(–) 0.72(5) 58.4(27) – 0.41(3) – – – 0.15(1) – – – – 1.7(2) 0.013(2) 100(–) 0.680(42) 59.0(23) 0.0015(3) 0.40(22) 0.0005(3) 0.014(3) 0.003(1) 0.160(20) 0.003(1) 0.015(3) 0.007(2) 0.003(1) – – 100(–) – 60.9(5) – – – – 0.0469(78) – – – – – 2.3 8.8 – 0.7 1.4 3.3 3.5 14 19 25 4.7 60 30 1.0 0.6 1.375(9) 0.052(13) 100(–) 0.640(7) 61.1(3) 0.010(5) 0.421(4) 0.024(6) 0.033(3) 0.052(11) 0.171(4) 0.031(4) 0.0339(17) 0.0100(19) 0.0041(10) 0.015(7) da Silveira et al. (1971) – – 0.198(15) 30.6(4) 14.44(10) – – 3.776(28) 5.166(38) 25.91(17) – – – – – – – – 29.3(9) 13.9(4) 0.045(6) – 3.6(1) 4.94(16) 26.7(8) 0.042(6) 0.129(8) 0.095(6) 0.033(4) 0.90(3) 0.072(5) – 0.043(4) 0.20(3) 0.326(24) 30.2(14) 14.2(7) – 0.130(8) 3.6(3) 5.1(4) 25.4(20) 0.033(4) 0.122(8) 0.090(7) 0.049(5) 0.82(6) 0.081(6) – 0.057(5) – – 26(5) 12.5(25) – – 3.8(11) – 24.8(25) – – – – 1.07(16) – – – Bi. 211 Briançon et al. (1968) Gorodetzky et al. (1968) Hamilton and Davies (1968) Dalmasso and Maria (1967) – – 34(4) 22(3) – – 5.5(4) 6.1(4) 34.2(13) – 0.38(19) – – 1.46(19) – – – A total of 83 absolute γ-ray emission probabilities have been determined in this work. The determined probabilities show significant improvement in their precision compared to some previously published values. For example the uncertainty of the 269.5 keV γ-ray emission probability is a factor of 4 lower than previously quoted by Sheline et al. (1998) and a factor of 2 more precise than quoted by Kossert et al. (2015). Previously no detailed uncertainty budgets have been published therefore it is difficult to specify the exact reasons for the improvement. One possible reason is the use of higher activity samples of 223Ra that has allowed 313.7(6) 361.7(6) 404.8(6) 427.1(6) 504.1(6) 675.4(6) 704.6(7) 766.4(7) 831.9(7) 865.8(6) 1014.7(7) 1080.1(7) 1103.3(8) 1109.5(8) 1196.2(8) 1234.3(8) 1270.7(8) 5.1. Results 0.24(3) – 30.0(9) 13.5(6) 0.12(2) – 3.77(19) 5.55(28) 29.8(7) 0.050(8) 0.14(1) 0.120(12) 0.040(6) 1.15(8) 0.10(1) 0.010(2) 0.070(7) Hindi et al. (1988) 5. Discussion Davidson et al. (1967) Following the determination of the fitted parameters C, from Eq. (2), and uncertainty matrix UC the covariance of the fitted parameters was determined by the linear propagation of uncertainties for multivariate models as described in supplement 2 of the GUM (BIPM, 2011). The correlations between pairs of the most intense measured γ-ray emissions (41%) associated with the decay of the radionuclides 223 Ra, 219Rn and 211Pb in the series are given in Tables 10–12. Mead and Draper (1965) (7) Vandenbosch et al. (1963) Cov(xi , xj ) Var(xi )Var(xj ) Giannini et al. (1962a) r (x i , x j ) = Energy/keV This work where Pb observed in this work and published values. All values are normalised to the 351.1 keV γ-ray emission of (6) 211 ⎡ r (P , P ) … r (P , P ) ⎤ 1 N ⎢ 1 1 ⎥ R=⎢ ⋮ ⋱ ⋮ ⎥ ⎢⎣r (PN , P1) ⋯ r (PN , PN)⎥⎦ Table 8 Normalised γ-ray emission probabilities of The majority of the uncertainty components are significantly correlated between the solutions S1 and S2 (as the standardisation methodology is identical) as well as between the two detectors. This is due to the process of determining the efficiency curve where the standard solutions used to calibrate the detectors were of similar provenance i.e. ionisation chamber, and identical nuclear data used. Failure to account for these correlations will often undermine the quality of the measurements and calculations relying on such data. These effects are not routinely dealt with in publications of γ-ray emission probabilities. In this work the calibration standards were all of NPL provenance and therefore the off-diagonal terms of the matrix used to weight the generalised least-squares fit were estimated from the ionisation chamber calibration factor uncertainties for the radionuclides concerned. Correlations due to sample preparation decay and dead time corrections were not included as these were relatively small contributors to the final uncertainty. Correlations in published γ-ray emission values may be more significant; however data were not available to allow the covariance to be estimated. The correlation matrix R as defined in GUM supplement 2 (BIPM, 2011) contains the correlation coefficients associated with pairs of measured γ-ray emission probabilities such that: Blaton-Albicka et al. (1976) 4.2. Uncertainty correlations of γ-ray emission probabilities 0.19(4) 0.30(8) 30.8(15) 14.3(8) – 0.173(15) 3.68(23) 5.04(30) 25.6(23) 0.053(15) 0.128(15) 0.083(10) 0.023(5) 0.79(8) 0.079(15) 0.005(2) 0.048(8) 9.1 0.10(5) – 29.6(20) 13.7(10) – 0.25(5) 3.7(3) 4.9(3) 24.1(17) 0.07(2) 0.15(1) 0.08(1) – 0.81(6) 0.08(1) – 0.08(1) 0.054 (4) 0.048(5) – – 28.6(11) 11.6(7) – – 2.9(1) 4.5(1) 27.4(4) – – 0.0025(1) – 0.011(1) – – 0.0006(1) 0.064(2) 0.0533(7) 0.26(5) – 28.0(28) 14.0(14) – – 3.0(3) 4.0(4) 23.0(23) 0.03(1) 0.13(2) 0.08(2) – 0.70(15) 0.08(2) – 0.05(1) 438.8(6) 0.21(7) – 29.9(35) 13.9(17) – – 3.3(4) 5.1(6) 26.4(35) 0.0347(14) 0.125(21) 0.104(14) – 0.87(10) 0.076(14) – 0.042(7) χ 2 /(n − 1) – – 27.4(12) 14.5(14) – – 3.7(2) 5.2(2) 27.4(12) 0.04(2) 0.14(2) 0.13(12) – 1.03(10) 0.11(3) – 0.06(2) Kossert et al. (2015) 0.209(3) 0.259(4) 30.45(14) 14.34(7) 0.017(3) 0.044(3) 3.782(21) 5.20(3) 26.17(13) 0.0410(16) 0.130(3) 0.0932(16) 0.0289(9) 0.845(5) 0.0799(11) 0.0070(6) 0.0474(14) Davidson and Connor (1970b) Kossert et al. (2015) Energy/keV This work Briançon et al. (1968) χ 2 /(n − 1) Table 7 Absolute γ-ray emission probabilities per 100 decays of 215Po observed in this work and published values. 23 1.2 8.0 1.1 2.3 21 59 8.7 5.9 6.8 2.2 0.9 431 5.3 2600 1.0 1.8 180 S.M. Collins et al. / Applied Radiation and Isotopes 102 (2015) 15–28 24 S.M. Collins et al. / Applied Radiation and Isotopes 102 (2015) 15–28 Table 9 Uncertainty budget for the 269.5 keV γ-ray emission of 223 Ra. Uncertainty component Relative uncertainty (k ¼ 1) Standard uncertainty of the weighted mean (includes the full-energy peak efficiency) Activity per unit mass Dead time and pile-up correction Radioactive decay correction Geometric reproducibility Gravimetric Detector stability Peak fitting True coincidence summing Total uncertainty 0.24% 0.33% 0.050% 0.010% 0.10% 0.10% 0.20% 0.10% 0.10% 0.50% Table 10 Correlation coefficient matrix of the most intense γ-ray emissions (4 1%) of 223 Ra. Energy/keV Energy/keV 122.3 144.3 154.2 269.5 323.9 338.3 445.0 122.3 144.3 154.2 269.5 323.9 338.3 445.0 100% 85% 75% 67% 72% 73% 77% – 100% 96% 75% 74% 75% 77% – – 100% 75% 72% 72% 74% – – – 100% 96% 95% 85% – – – – 100% 97% 89% – – – – – 100% 90% – – – – – – 100% Table 11 Correlation coefficient matrix of the intense γ-ray emissions ( 41%) of 219 Rn. Energy /keV Energy/keV 271.3 401.8 271.3 401.8 100% 85% – 100% Table 12 Correlation coefficient matrix of the intense γ-ray emissions ( 41%) of Fig. 8. Results of the (a) 269.5 keV and (b) 271.3 keV absolute γ-ray emissions for the three datasets. The solid line indicates the final weighted mean result reported and the dashed lines indicate the final uncertainty of the absolute gamma emission probability. The error bars are composed of the statistical and efficiency uncertainties only. 211 Pb. Energy/keV Energy/keV 404.8 427.1 831.9 404.8 427.1 831.9 100% 95% 83% – 100% 83% – – 100% the collection of greater than 106 counts in the photopeaks, therefore a low statistical uncertainty, of the most intense γ-ray emissions. This has also allowed many of the relatively small γ-ray emission probabilities to be quantified, which have only previously been seen in γ–γ coincidence measurements (Sheline et al., 1998). The 269.5 keV absolute γ-ray emission values determined for the three datasets of S1B, S2B and S2L are in good agreement, shown in Fig. 8(a), with only the statistical and FEP efficiency uncertainty included in individual dataset uncertainty. The agreement between S1B and the results of S2B and S2L indicate a consistency in the standardisations of the solutions S1 and S2. The agreement between S2B and S2L indicates that there is no significant difference between the FEP efficiency calibrations of the two detectors. These two observations Fig. 9. The peak fits of the convoluted photopeaks of the 269.5 keV and 271.3 keV γ-ray emissions. S.M. Collins et al. / Applied Radiation and Isotopes 102 (2015) 15–28 25 Fig. 10. The reduced χ2 of the published literature for the most intense γ-rays normalised to the 154.2 keV (hollow squares) and the 269.5 keV (hollow triangles) γ-ray emissions. Fig. 12. Difference and z-score of the γ-ray emission probabilities (normalised to the 154.2 keV γ-ray) of Krien et al. (1970) and this work before (hollow squares) and after (hollow triangles) adjustment for the 75Se nuclear data. It is the authors' hope that the provision of the correlation data will help to inform any future decay data evaluation of 223Ra. While the magnitude of the correlation will to some extent be dependent on both the choice of radionuclides for the efficiency calibration and on the selection of the fitting function, it is suggested that by assuming the same level of correlation is present across other measurements of the emission probability, a more realistic evaluation, than the usually applied assumption of no correlation between the emission probabilities, could be achieved. 5.2. Published literature of Fig. 11. The relative FEP efficiency curves for BART determined using the relative γray emission probabilities of 75Se; using the nuclear data of Krien et al. (1970) (hollow triangles) and Negret and Singh (2013) (hollow squares). provide supporting evidence in the confidence of the reliability in the presented absolute γ-ray emission probabilities. A potential source of error could be from the de-convolution of the 269.5 keV and 271.3 keV γ-ray emissions by the peak fitting software. Although the use of high resolution γ-ray spectrometry allowed the individual peaks to be relatively well resolved (see Fig. 9) any inaccuracy in the peak shape fitting calibration could lead to inaccuracies in the determined peak areas. Fig. 8(b) shows the results for the 271.3 keV absolute γ-ray emission from the 219 Rn decay, showing a consistency in the results between the datasets. It can therefore be inferred that no significant errors occurred from the de-convolution of these two photopeaks by the software. The effect of the diffusion of 219Rn from the aqueous phase to gas phase in the air space at the top of the ampoules was considered and then discounted, as this effect has been previously investigated by Cessna and Zimmerman (2010) and Bayer (2012). 223 Ra γ-ray emission probabilities A comparison of the values reported for the 223Ra γ-ray emissions in this work to those in the currently published literature, which had been normalised to the 154.2 keV γ-ray emission, are shown in Table 5. A review of the reduced χ2 for each of the main γ-ray emissions (41%) shows that for γ-ray emissions of the 122.3 keV, 144.3 keV and 158.7 keV all the reported values are in good agreement; with reduced χ2 values less than one. Alternatively, the reduced χ2 values for the γ-ray emissions of the 269.5 keV, 323.9 keV, 338.3 keV and 445.0 keV indicate significant differences within the datasets. The reported values of this work and Kossert et al. (2015) are in good agreement for these γ-ray emissions. In the majority of cases the reported values of the remaining published literature show a significantly positive bias; 10% and 15% for the 269.5 keV and 323.9 keV γ-ray emissions respectively. Normalisation of the γ-ray emission to the 269.5 keV γ-ray indicates that the discrepancies in the datasets reverse; whereby the datasets of the 122.3 keV, 144.3 keV and 158.7 keV γ-rays become discrepant and vice-versa. This is shown in Fig. 10. The switch in the discrepancies would suggest that the relative ratio of the efficiency in the region of the 269.5 keV to the region of 154.2 keV differs between that of the FEP efficiency calibration used in this work and Kossert et al. (2015) to the earlier publications. In the majority of the previous literature it is impossible to test the veracity of this supposition as only Krien et al. (1970) has reported any details about the methodology of the FEP efficiency calibration. The details provided by Krien et al. (1970) have 26 S.M. Collins et al. / Applied Radiation and Isotopes 102 (2015) 15–28 Table 13 Comparison of published experimental probabilities of the α transition to those deduced from the P(γ þ ce) balance determined from the evaluations of the DDEP (Chechev, 2011a) and the measured γ-ray emission probabilities determined in this work. α-particle energy/MeV 5.747 5.716 5.607 5.540 5.502 5.434 Feeding level/keV 126.77 158.64 269.48 338.27 376.26 445.03 þ 446.82 This work Chechev (2011c) Pilger (1957) Walen et al. (1962) Davidson and Connor (1972) Iα Giannini et al. (1962b) Iα Iα Iα Iα Iα 10.94(24) 52.0(8) 24.3(3) 9.70(11) 0.67(2) 2.19(6) 10.0(3) 49.6(9) 25.8(6) 10.60(17) 0.74(3) 2.10(9) 10.5(–) 50.4(–) 23.6(–) 10.3(–) 0.86(–) 2.4(–) 10.2(–) 48.0(–) 25.7(–) 10.2(–) 1.3(–) 2.5(–) 8.85(18) 52.2(11) 25.3(5) 8.85(18) 0.78(–) 2.24(–) 9.50(58) 52.8(8) 24.2(4) 9.16(30) 1.00(15) 2.27(20) allowed investigation of the difference in the FEP efficiency calibrations to be made. 5.3. Krien et al. (1970) Krien et al. (1970) describe that the FEP efficiency calibration was performed using a 75Se source to determine a relative efficiency over the photon energy range 66–400 keV. While 75Se is commonly used for performing efficiency calibrations of HPGe γray spectrometers, there are significant problems with the use of 75 Se in this case, where true coincidence summing corrections can play an important role; this can be a source of significant error. The relative γ-ray emission probabilities of 75Se used by Krien et al. (Krien et al., 1970) differ significantly from the evaluated relative γ-ray emission probabilities determined by Negret and Singh (2013). The differences in the relative γ-ray emission probabilities for the most intense γ-rays range from 0.4% to 14%. To estimate the effect of this difference in the nuclear data, a 75 Se source was measured on BART. The relative FEP efficiencies were determined using both sets of emission probabilities (assuming that the 125.99 keV γ-ray reported by Krien et al. (1970) was a typographical error and should represent the 136.0 keV γray). The relative FEP efficiency calibration points were fitted with a 3rd order and 4th order polynomial for the Krien et al. (1970) and Negret and Singh (2013) data respectively. The respective fits of the data points are shown in Fig. 11. It was observed that the FEP efficiency calibration, relative to the 269.5 keV, using the Krien et al. (1970) 75Se nuclear data was significantly different to that using the nuclear data evaluated by Negret and Singh (2013). Using the two FEP efficiency curves, an estimate of the effect on the γ-ray emission probabilities reported by Krien et al. (1970) was made, and the results are shown in Fig.12. While the estimated corrections do not completely resolve the differences in the reported values, the z-scores (Devore, 2011) show an improvement in the agreement between the γ-ray emission probabilities of Krien et al. (1970) and this work. The analysis shows that the inaccuracy of the nuclear data used and hence the accuracy of the FEP efficiency calibration can lead to a significant error on the accuracy of the final values. No additional information is available at this time to investigate further the differences in the values e.g. true-coincidence summing effects. Hence, these corrections should only be considered as qualitative and not as a ‘true’ correction. 5.4. provisional rebalancing of the decay scheme was attempted to see if the observed differences in absolute γ-ray emission probabilities could explain this disagreement. The energy, positioning and multipolarity of the γ-ray transitions were taken from the Evaluated Nuclear Structure Data File (ENSDF) adopted levels and γ-rays (Browne, 2001). The total conversion coefficients were recalculated using the BrIcc code v2.3S (Kibédi et al., 2008) based on the adopted energies and multipolarities. For γ-rays not observed in this work, relative intensities were also adopted from ENSDF. The compiled data were assembled into an ENSDF file and processed with the GABS code (Browne and Baglin, 2004). The results are presented in Table 13. The differences between the α-emission probabilities thus calculated and the experimental data are generally lower than previously reported (Chechev, 2011c). It should be noted these values are purely indicative and a full decay-scheme evaluation incorporating data from this work as well as that from PTB (Kossert et al., 2015) is merited to determine to what extent the discrepancies have been truly resolved. 6. Conclusion A total of 83 absolute γ-ray emission probability values have been determined experimentally for the 223Ra decay series, derived from absolute standardisations of two 223Ra solutions. The use of two high accuracy calibrated HPGe γ-spectrometers has allowed the precise measurement of the γ-ray emission probabilities presented, with reduced quoted uncertainties of the most significant γ-ray emissions of the decay series. In this work significant discrepancies have been shown in the current absolute γray emission values of 223Ra decay series. Correlation coefficient matrices have been presented for the first time showing the correlations within the uncertainties between pairs of the most intense γ-ray emission probabilities of 223 Ra and decay progeny, to enable improved decay data evaluations in the future. The differences in the experimental α-transition probabilities and those deduced by the P(γ þ ce) balance using the γ-ray emission probabilities are reported here and show some improvement in the agreement to the published experimental values of Davidson and Connor (1970a). There remains a paucity of precise measurements of the α-transition probabilities and further investigation of the 223Ra nuclear data is recommended to finalise the 223Ra decay scheme. α-transitions As previously reported by Kellett and Nichols (2013) there is disagreement between the P(γ þ ce) deduced α transition probabilities and those determined experimentally (Davidson and Connor, 1970a; Giannini et al., 1962b; Pilger, 1957; Walen et al., 1962). A Disclaimer Identification of commercial services or products does not imply recommendation or endorsement by the National Physical S.M. 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