Applied Radiation and Isotopes 102 (2015) 15–28
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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. Collins et al. / Applied Radiation and Isotopes 102 (2015) 15–28
Laboratory, nor does it imply that the products or services identiﬁed are necessarily the best available for the purpose.
Acknowledgements
The authors would like to thank Andrew Fenwick, Kelley Ferreira and Lynsey Keightley for the preparation of the samples,
Dr. Stefaan Pommé for providing the ﬁgure of the decay scheme,
Mily Brewer for translation of texts and Algeta ASA (Norway) for
provision of the 223Ra solutions. This work was supported by the
National Measurement System Programmes Unit of the UK's Department for Business, Innovation, and Skills and the European
Metrology Research Programme (EMRP). The EMRP is jointly
funded by the EMRP participating countries within EURAMET and
the European Union.
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