The 55Fe half-life measured with a pressurised proportional counter

Applied Radiation and Isotopes 148 (2019) 27–34

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The

55

Fe half-life measured with a pressurised proportional counter ∗

T

S. Pommé , H. Stroh, R. Van Ammel European Commission, Joint Research Centre (JRC), Directorate for Nuclear Safety and Security, Retieseweg 111, B-2440, Geel, Belgium

H I GH L IG H T S

Fe half-life value of 1006.70 (15) days or 2.7563 (4) a. • Measured proportional counter at 0.1 MPa, 0.5 MPa, and 0.8 MPa gas pressure. • Used of reference value by order of magnitude. • Improvement • Literature data highly inconsistent and mostly discrepant with current value. 55

A R T I C LE I N FO

A B S T R A C T

Keywords: Half-life Decay constant Calibration Discrepancy Clearance Decommissioning

The half-life of 55Fe has been measured accurately by following the decay curve of three sources with a large pressurised proportional counter. An argon(90%)-methane(10%) mixture was used as counter gas, at atmospheric pressure (∼1 × 105 Pa) and at enhanced pressures of 5 × 105 Pa and 8 × 105 Pa (for 1 source), respectively. The first measurements were performed in 2001, but the experiment was executed more systematically between 2005 and 2018, covering a period of about 5 half-lives. The residuals from an exponential decay curve were of the order of 0.1% to 0.2% at 1 × 105 Pa, and 0.03% at 5 × 105 Pa and 8 × 105 Pa. The gain of stability with increased gas pressure was due to asymptotically reaching the maximum counting efficiency, resulting in lower sensitivity to pressure variations. The deduced half-life value of T1/2(55Fe) = 1006.70 (15) d or 2.7563 (4) a is more accurate than other data in literature, which are mutually discrepant. It is consistent with previous measurements at JRC with an X-ray defined solid angle counter.

1. Introduction Iron-55 (55Fe) is effectively produced by irradiation of stable iron with neutrons, through the reactions 54Fe(n,γ)55Fe and 56Fe(n,2n)55Fe. It is a major contributor to residual activity in steel and concrete hardware at high-energy accelerator facilities (Blaha et al., 2014) and in fallout from nuclear weapons (Palmer and Beasly, 1967; Simon et al., 2010). 55Fe predominantly decays via K electron capture to the ground state of 55Mn. The vacancy in the K shell is filled by an electron from a higher shell and the energy difference is released through emission of Auger electrons or X-rays, respectively in 60% and 28% of all decays (Bé and Chisté, 2006). The remaining fraction is accounted for by lower-energy transitions. The energies of the Kα1 and Kα2 X-rays are so similar that they are commonly perceived as mono-energetic 5.9 keV photons with an emission probability of 25%. An additional probability of 3.4% is associated with Kβ X-rays of 6.5 keV. The KX-rays from an iron-55 source are a convenient tool in laboratory techniques, such as e.g. X-ray diffraction and fluorescence.

∗

The half-life of 55Fe (2.756 a) is sufficiently long to produce X-rays continuously over many years, in a compact configuration which is easily portable and requires no electrical power. The monochromatic photons can be used in fluorescence methods for non-destructive analysis of elements in surface layers. At the JRC, an 55Fe excitation source was used to generate lower-energy photons of 1 keV to 5 keV in various fluorescer foils, thus constituting a set of calibration sources for efficiency calibration of low-energy photon detectors (Denecke et al., 1990a,b). Where 55Fe is used for calibrations or comparative methods involving long time scales, the value of its half-life should be known with sufficient accuracy. Unfortunately, 55Fe is one of the nuclides for which half-life measurements in the literature are discrepant (Woods and Collins, 2004; Van Ammel et al., 2006). It is a general problem in halflife measurements that uncertainties are being underestimated and that insufficient information is provided in the publications to re-evaluate all relevant sources of error (Pommé et al., 2008; Pommé, 2015a). Not only does this represent an unreliable basis for fundamental and applied

Corresponding author. E-mail address: [email protected] (S. Pommé).

https://doi.org/10.1016/j.apradiso.2019.01.008 Received 15 November 2018; Received in revised form 8 January 2019; Accepted 18 January 2019 Available online 29 January 2019 0969-8043/ © 2019 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/BY/4.0/).

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Table 1 Overview of measured 55Fe half-life values. The evaluated value of the DDEP is 1003.3 (30) d. Year

Authors

methoda

T1/2 (d)

1950 1956 1965 1980 1982 1982 1994 1998 2000 2006 2018

Brownell & Maletskos Schuman et al. Evans & Naumann Houtermans et al. Lagoutine & Legrand Hoppes et al. Morel et al. Karmalitsyn et al. Schötzig Van Ammel et al. This work

inside IC End window PC

1037 (11) 950 (7) 880 (44) 1000.4 (13) 977.9 (70) 1009.0 (17) 996.8 (60) 995 (3) 1003.5 (21) 1005.2 (14) 1006.70 (15)

2π PC DSA PC PC, Si(Li) HPGe 4π PPC Si(Li) DSA PC 4π PPC

a

IC = ionisation chamber, PC = proportional counter, PPC = pressurised proportional counter, HPGe = high-purity germanium γ-ray detector, Si (Li) = lithium-doped silicon detector for X-ray spectrometry.

Fig. 1. Simplified design of the large pressurised proportional counter (LPPC) used at the JRC.

research (Pommé, 2016a), it also leaves the door open for theories challenging the validity of the exponential-decay law (Pommé et al., 2016b; 2017a,b,c,d; 2018a,b;2019a,b). Pressurised re-entrant ionisation chambers (Amiot et al., 2015) are insensitive to low-energy radiation, so that their superior linearity (Pommé et al., 2018c) and stability (Pommé et al., 2017a,b,c) cannot easily be deployed to accurately measure the 55Fe half-life. Alternative options are Si detectors (Si-PIN, SDD), scintillation detectors (e.g. liquid scintillator, NaI(Tl) with a thin entry window) and gaseous detectors (proportional counters, wire chambers, micropattern gaseous detectors). Published results obtained by means of low-energy detectors (Brownell and Maletskos, 1950; Schuman et al., 1956; Evans and Naumann, 1965; Houtermans et al., 1980; Hoppes et al., 1982; Lagoutine and Legrand, 1982; Morel et al., 1994; Karmalitsyn et al., 1998; Schötzig, 2000) are inconsistent (see Table 1). The data scatter clearly exceeds the claimed uncertainties. Chechev and Egorov (2000), Bé (1999), and Woods and Collins (2004) published evaluated half-lives of 998 (5) d, 1001.1 (2.2) d and 1002.7 (2.3) d, respectively. The currently recommended value by the DDEP (Bé and Chisté, 2006) is 2.747 (8) a or 1003.3 (30) d. The JRC previously performed decay rate measurements of an 55Fe source with an X-ray counter at a small defined solid angle (Pommé, 2015b) and published a higher half-life value of 1005.2 (14) d (Van Ammel et al., 2006) with realistic uncertainty budget (Pommé, 2007a). This paper reports on an independent series of decay curve measurements with a large 4π pressurised proportional counter or LPPC (Pommé, 2007b). This work was undertaken to further reduce the uncertainty on the 55Fe half-life value.

2.2. Pressurised proportional counter A simplified scheme of the LPPC is presented in Fig. 1. The detector consists of a cylindrical, aluminium gas chamber with an inner diameter of 80 mm and a central planar cathode dividing it into two Dshaped counters with an anode wire each. The anode wire is made of stainless steel and has a diameter of 21 μm and a length of 150 mm. It is positioned centrally in the D shape, at 20 mm distance from the cathode and inner wall. The radioactive source is placed in the 34-mm-diameter recess of the cathode and clamped with a copper or metal ring, thus being in electrical contact with the metal plate. The wall and source holder are kept at ground potential, whereas the anode wires are at positive potential. Typical values for the applied voltage at different counting gas pressure values are +1930 V at 0.1 MPa, +3750 V at 0.5 MPa, and +4750 V at 0.8 MPa, with the electronic amplification set at 300. For a comparable gas gain, the voltage is set roughly proportional with (pressure)0.45. The LPPC is operated with P10 counting gas, consisting of 90% argon and 10% methane. For a steady operation of the detector, the counter gas is continuously refreshed by a low gas-flow rate of less than 100 cm3 min−1. The input gas flow rate is adjusted and stabilised by mass-flow controllers, whereas the output flow (towards a vacuum pumped volume) is controlled by a two-stage back-pressure regulation system (Denecke et al., 1998). A manual back-pressure regulator releases the bulk of the overpressure, whereas a PID controls the gas flow through a small orifice by varying the expansion of a piezo translator. The outflow is regulated such that the gas pressure in the LPPC equals the pressure in a closed reference vessel, allowing for excellent gain stability throughout and among measurements. This high level of reproducibility is lost when the valve of the reference vessel is opened for applying a different working pressure. The pressure is read from a transducer which is not absolutely calibrated. The gas volumes can be pumped to evacuate (electronegative) oxygen, and to calibrate the gauge at zero pressure. The proportional counter has two distinct ionisation regions: an ion drift region in the bulk gas volume and an avalanche zone nearby the anode wires. The number of created ion pairs in the counter gas is proportional to the captured radiation energy. The electric field is strong enough to prevent re-combination of the ion pairs and to cause positive ions to drift towards the cathode and electrons towards the anode. Only in the immediate vicinity of the anode wires, the field strength is so strong that the collected charges produce a Townsend avalanche. The voltage is chosen high enough to profit from a controlled multiplication of the ionisation signal, without entering a nonproportionality zone in which the avalanches self-multiply. This improves the signal-to-noise ratio of the detector and reduces the

2. Measurement method 2.1. Preparation of

55

Fe sources

In 2002, the 55Fe source '55Fe0208′ was prepared at the JRC from a solution obtained from Isotope Products (Valencia, California, USA) with an initial activity concentration of about 18 MBq/mL. Its chemical form was FeCl3 in 1M HCl solution. The 55Fe solution was checked with a HPGe detector in the energy range of 10 keV to 1.5 MeV and no impurities were found. The source was prepared by electrodeposition in a slightly basic solution, on a 1-mm-thick copper disk of 10 mm diameter (Van Ammel, 2004). The iron-coated disk was glued in a punched hole in a copper disk of 34 mm diameter and 1 mm thickness, and then both were covered by a 17 μm Al-layer on either side. The Al foil stops the Auger electrons, but allows sufficient transmission of 5.9 keV KX-rays and produces some fluorescence X-rays. The two other sources used in this work, 'D97040′ and 'D9043′, were produced in a similar manner in 1997. 28

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subsequent electronic amplification required. The wires are occasionally replaced, because of their sensitivity to local depositions of polymers over the years. Polymer formation occurs in the avalanche plasma from the cloud of ions and free radicals of the gas filling, possibly accelerated by contaminant molecules (oil, finger grease, solvents) (Kadyk, 1991). The polymers have a high dipole moment and attach to the electrodes. Protruding deposits on the wire can be observed through a microscope. They modify the electric field around the anode wire. Indications at experimental level are degradation of the energy resolution, decrease of the gas gain, sparking and selfsustained discharges. The new wires are thoroughly cleaned with a dust free cloth charged with fine powders and/or propanol. 2.3. Signal processing The outputs from each half of the proportional counter can be mixed after the preamplifier. The output signal passes to a nuclear pulseshaping amplifier and is processed in two parallel branches: a singlechannel analyser (SCA) and a multi-channel analyser (MCA). The SCA branch is well suited for unbiased live time counting (Pommé et al., 2015) for accurate measurements of activity. The MCA branch is used for visual inspection of the energy spectrum. This is for example needed for identifying the cut-off energy corresponding to the SCA threshold. The SCA branch consists of an adjustable threshold discriminator succeeded by a dead-time generator which imposes a non-extending dead time on each counted event during which no new pulses are accepted by the system. The artificial dead time is chosen long enough (e.g. 10–20 μs) to override the characteristic dead times of the counter and the signal processing electronics. At an SI-traceable frequency of 100 kHz, the system is probed for its dead/live status. The live-time clock pulses are divided by 1000 and a logical signal is generated every 10 ms of live time. Real-time clock pulses are generated at a frequency of 100 Hz. Scalers keep track of the real-time and live-time duration of the measurement. The computer is continuously synchronised with a DCF-77 reference time receiver by means of the network time protocol (NTP). In the current configuration, the live-time system does not account for the cascade effect between pileup and dead time (Pommé et al., 2008). A pulse with finite width effectively prolongs the dead time of the system without the live-time clock accounting for it. A pulse at the very end of the imposed dead time will eliminate all pulses piling up with it from the counting process. The corresponding cascade correction factor on the dead-time corrected count rate ρˆ = RTR/ TL can be calculated with the following equation (Pommé et al., 2015): ˆ ˆ ) ρ / ρˆ ≈ (e ρτ − ρτ

Fig. 2. Typical energy spectrum of X-rays generated by the decay of the Alcovered 55Fe source, measured in the LPPC filled with argon-methane gas.

work in the period 2001–2005. Since 2011, more precise measurements have been performed systematically with the aim of improving the halflife value of 55Fe. A typical 55Fe X-ray energy spectrum obtained with the LPPC is presented in Fig. 2. It shows the KX-ray peak from 55Mn at a mean energy of 5.958 keV and a fluorescence peak from Al at a mean energy of 1.487 keV. When using P10 counting gas, an additional peak near 2.979 keV results from the combination of the 2.974 keV (mean energy) argon fluorescence peak together with the 2.984 keV (MneAr) escape peak. The energy peak width (FWHM = 2.355σ) is about 16% at 5.9 keV, 24% at 3 keV, and 29% at 1.5 keV. The energy resolution is limited because both the initial ionisation events and the subsequent 'multiplication' events are subject to statistical fluctuations. The observed resolution (FWHM) is comparable to the Poisson uncertainty on the number of primary electron-ion pairs created: 2.355(E(eV)/ 26.5)−0.5 = 16%, 22%, and 31% respectively. The lower-level discriminator of the SCA was set at channel 100, which was made to correspond to about 1 keV by adapting the anode voltage and electronic amplification. Some variation of the cut-off energy may have occurred from one measurement to another, but in general it is placed left of the smallest X-ray peak, just above the noise. 3.2. Counting efficiency

(1) The absolute counting efficiency of the LPPC for 55Fe decays has not been determined, but experiments have been performed to compare count rates at different pressure values of the counting gas. The pressure was varied in steps of 0.1 MPa between 0.1 MPa and 0.9 MPa, with an additional test at 0.15 MPa. The relative counting efficiency is shown in Fig. 3. The maximum count rate, here normalised to 100%, is stable between 0.6 MPa and 0.9 MPa. At pressure values below 0.5 MPa there is an exponential negative slope towards 83.4% at atmospheric pressure. The following function has been fitted to the data:

This correction factor was applied using τ = 1 μs, whereas a larger value of τ = 2.5 μs was applied for an estimation of the standard uncertainty on the dead-time compensation. The cascade effect can be avoided electronically, e.g. by triggering a dead time at the start and end of each pulse. The JRC has recently developed a single channel discriminator (Schmitt trigger) which passes on the pulse width to the dead time module in order to reduce the live time accordingly. 3. Decay rate measurements

ε (P ) = 1 − exp(−(P − P0)/ a)

3.1. Typical spectrum

(2)

It yielded fit parameters P0 = −0.094 MPa for the pressure at zero efficiency and a = 0.608 MPa for the slope of the exponential. By taking a first derivative

The LPPC at the JRC is used for primary standardisation (Pommé, 2007b) of activity for alpha and beta emitters, e.g. 39Ar (Goeminne, 2002) and 238Pu (Johansson et al., 2003). Prior to such standardisation measurements, an energy calibration in the low-energy region was performed using the X-rays from a solid 55Fe/Al source, mostly to define the threshold energy of the low-level pulse discriminator. In addition, it supplied information on the energy resolution and counting efficiency. This is the basis of the first measurements performed in this

∂ε (P ) 1 = exp(−(P − P0)/ a) ∂P a

(3)

one obtains the sensitivity factor of the count rate for small changes in gas pressure. At 0.1 MPa one gets 27.2% and at 0.5 MPa it is a much smaller value of 0.038%. Variations in gas pressure by 0.003 MPa near 29

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Fig. 4. Decay curves for three 55Fe sources measured at 0.5 MPa gas pressure in the LPPC.

Fig. 3. Relative count rate for an 55Fe source measured at different counting gas pressures in the LPPC. The arrows indicate the gas pressures used in this work.

4. Analysis and results

0.1 MPa induce 0.8% variation in count rate, which is large compared to 0.0011% at 0.5 MPa. At 0.8 MPa, the predicted effect is negligible (< 0.00001%). Therefore, the experiment gains stability at gas pressures above 0.4 MPa. Apart from the counting efficiency for the 55Fe X-rays emitted by the source, variations may also occur in the count rates induced by external radiation. The 'background' count rate not only varies with the counting gas pressure (typically 3.8/4.4/4.8 s−1 at 0.1/0.5/0.8 MPa), but also may be sensitive to environmental conditions (temperature and air pressure inside and outside the laboratory). Since measurements of the source and background are performed over long periods of time on different days, they are generally recorded in different weather conditions. This may result in non-negligible systematic errors in the background subtraction applied to obtain net 55Fe count rates.

4.1. Decay curves & half-lives The measured net 55Fe decay rates follow an exponential dependency with time, as expected. In Fig. 4, the decay curve of each source measured at 0.5 MPa gas pressure is shown. Similar curves were obtained at other gas pressure settings. Least squares fits of exponential functions were performed on all data sets, with the amplitude and halflife as free parameters, only for the purpose of deriving the half-life value, not for determining its uncertainty. The data were weighted according to their variance, however after including a common uncertainty component such that the reduced χ2 was close to 1. Information on the measurements and derived half-life values has been collected in Table 2. The fitted half-life values at 0.5 MPa agree closely among the three sources, 1006.7 d, 1006.6 d and 1006.9 d, respectively. The residuals from the individually fitted decay curves are presented in Fig. 5. The plotted standard uncertainty bars include uncertainty components for counting statistics in 55Fe decay and background rates (Poisson statistics), as well as the cascade effect of pulse pileup on the imposed dead time (Eq. (1)). They do not include the variability in amplification and discriminator settings, nor the more important uncertainty components

3.3. Decay rate measurements The 55Fe source activity was measured in sufficiently long runs to obtain in excess of 108 events. The decay rates were calculated from the number of counts divided by the system live time and corrected for the 'pileup-dead time cascade effect' (Eq. (1)). A background measurement was performed in identical conditions with a dummy source, typically with more than 3 × 105 events, and the corresponding count rate of 4–5 s−1 was subtracted from the 55Fe total count rate. The net 55Fe count rate was corrected for decay during the measurement (Pommé et al., 2015a). The initial net count rates for the three sources were 14010 s−1 (D97040, 16 March 2001, 0.5 MPa), 947 s−1 (D97043, 3 June 2001, 0.1 MPa), and 9960 s−1 (55Fe0208, 7 Oct 2003, 0.8 MPa). At the highest count rate, the standard uncertainty due to cascade effects of pulse pileup on the imposed non-extending dead time was estimated to be in the order of 0.25% (Eq. (1)). From 2005 on, the uncertainty on the cascade effect is less than 0.04%. The longest measurements took nearly 10 days, necessitating a decay correction of 0.34% to assign the decay rate to the start of the measurement. The uncertainty on the net count rates for the first measurements in 2001 is comparably high, because the background measurements may not have matched exactly the conditions of the 55Fe measurements. Therefore, the first data carry less weight in the half-life analysis and the emphasis is on the best data taken from 2005 onwards.

Table 2 Half-life value and uncertainty derived from the decay rate measurements of three 55Fe sources with the LPPC at three different gas pressures. The number of measurements N performed, the time period ΔT spanned, and the standard deviation of the residuals u(A)/A (see Figs. 5–7) to an exponential decay curve (see Fig. 4) give a first indication of the quality of the data sets. The powermoderated mean (PMM) was taken as final value and a correlated uncertainty was added for a possible hidden bias. Nr

Source

T1/2

N

ΔT

u(A)/A

10 Pa

days

#data

years

%

8 5 5 5 1 1 1

1006.78 (23) 1006.69 (19) 1006.61 (16) 1006.91 (60) 1009.8 (46) 1008.6 (20) 1008.4 (20) 1006.70 (11) 0.10 1006.70 (15)

7 12a 18a 11 10a 16a 14a

15.0 13.5 17.3 13.5 7.3 17.4 17.2

0.044 0.019a 0.026a 0.12 0.10a 0.18a 0.16a

Pressure 5

30

1 2 3 4 5 6 7

55Fe0208 55Fe0208 D97040 D97043 55Fe0208 D97040 D97043 PMM (1–4) Uncertainty bias Final result

a

Excluding an 'outlier'.

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Fig. 5. Residuals from an exponential fit to the decay curves of three 55Fe sources measured at 0.5 MPa gas pressure in the LPPC. The uncertainty bars account for counting statistics and pileup effects only. (Not shown: residuals for D97040 at 15 d and 27 d with about 0.14% uncertainty and 0.14% and 0.24% deviations from the fit.)

Fig. 7. Residuals from an exponential fit to the decay curves of three 55Fe sources measured at 0.1 MPa gas pressure in the LPPC. The uncertainty bars account for counting statistics and pileup effects only. The data scatter is comparably large due to sensitivity of the counting efficiency to variations in gas pressure.

associated with the efficiency variations due to changes in gas counter pressure and environmental conditions. The observed data scatter is of the order of 0.02%–0.1%, which is significantly larger than the plotted uncertainty bars. Obviously, the uncertainty evaluation (in section 4.2) has to go far beyond counting statistics. Very few measurements were taken at other enhanced pressures, except for a small data set of the '55Fe0208′ source decay rates at 0.8 MPa. The corresponding residuals in Fig. 6 representing 7 measurements over a period of 15 years are quite small, of the order of 0.02%, and the resulting half-life value of 1006.8 d is consistent with the results at 0.5 MPa. The uncertainty on the oldest measurement is comparably high, by lack of a precise background measurement in the same configuration as the 55Fe source. A typical background rate value was adopted on the basis of the other background measurements at 0.8 MPa, and an inflated uncertainty of 6.5% was assigned to it. More extensive data sets were taken at 0.1 MPa. Independent fits result in consistently higher half-life values of 1010 d, 1009 d and 1008 d. The residuals, shown in Fig. 7, scatter by about 0.2%, which is an order of magnitude higher than the high-pressure measurements. Since the counting efficiency in this working region is sensitive to variations in gas pressure (see Fig. 2), it is conceivable that the bias towards longer half-life values resulted from slightly lower reference pressures in the early phases of the experiment. The residuals, not being randomly distributed, propagate to a large uncertainty on the derived

half-life values (Pommé et al., 2008; Pommé, 2015a). Moreover, the biases in the half-live values of the three sources at 0.1 MPa are positively correlated and should be propagated accordingly when calculating a weighted mean. As the reference value for the 55Fe half-life, a power-moderated mean (Pommé and Keithley, 2015) was taken of the 4 results obtained at enhanced pressure (Fig. 8), resulting in T1/2(55Fe) = 1006.70 (11) d.

4.2. Uncertainties The Poisson uncertainty on the 55Fe count rate (14000–23 s−1) is typically 0.01% and on the background rate (4–5 s−1) it is about 0.10%, which is significant only at the end of the decay curve. Another random source of error is variability in amplification, which implies a slight difference in cut-off energy. Also the reference pressure is not identical

Fig. 6. Residuals from an exponential fit to the decay curve of an 55Fe source measured at 0.8 MPa gas pressure in the LPPC. The uncertainty bars account for counting statistics and pileup effects only.

Fig. 8. Half-life values derived from measurements of three the LPPC at different counting gas pressures. 31

55

Fe sources with

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At the higher pressure settings, it is the combined effect of all random variation components in the residuals that dominates for the more active sources. The long-term effects from pileup and pressure variations are relatively small. The measurements at atmospheric pressure (see Fig. 8) are a reminder of the danger of hidden biases which make uncertainty assessment of half-life measurements particularly delicate. In anticipation of a residual bias, an additional correlated uncertainty of 0.1 d has been taken into account in the final result (see Table 2).

from one experiment to the other, since the transducer is not absolutely calibrated and the reference pressure changes with temperature. If these uncertainty factors are insufficient to explain the variance of the residuals, also medium term instabilities have to be taken into account. The following formula is used for the propagation of random deviations in the decay rate data (Parker; 1990; Pommé, 2015a)

σ (T1 / 2 ) 2 ≈ T1 / 2 λT

3(n − 1) σ (A) n (n + 1) A

(4)

in which n represents a number of equidistant activity measurements in the case of short-term uncertainty components, or the number of covered periods of medium-term fluctuations, T is the duration of the measurement campaign, and σ(A)/A is a typical relative uncertainty on the decay rate associated with the error component under scrutiny. An average value of σ(A)/A is taken when it differs at the start and stop of the campaign. It would be highly insufficient to restrict the uncertainty assessment on the decay rates to random variations only and to derive the half-life uncertainty from the least-squares fitting algorithm (Pommé, 2007a). Medium and long-term instabilities have a much higher impact on the derived half-life value than random variations associated with each measurement, because they have a larger uncertainty propagation factor (Pommé et al., 2008; Pommé, 2015a). For systematic errors or long-term instability, a convenient propagation formula is

σ (T1 / 2 ) 2 σ (A) ≈ T1 / 2 λT A

4.3. Periodogram A small group of authors have claimed observations of violations of the exponential-decay law, mostly on the basis of cyclic patterns in unstable decay rate measurements. Extensive research has refuted the presence of claimed cyclic patterns at annual and monthly level associated with solar and cosmic neutrinos (Pommé et al., 2016b; 2017a,b,c,d; 2018a,b; 2019a,b). In this work, possible claims that the 55 Fe activity may show correlation with the 11 a/22 a solar cycle are anticipated. The residuals of the measurements at 0.5 MPa and 0.8 MPa to an exponential decay curve were collected in one data set and analysed for the hypothetical presence of cyclic deviations from the exponentialdecay law. From a weighted Lomb-Scargle periodogram, using equations published in (Pommé et al., 2018a), an unnormalised power of p (ω) < 0.014 was calculated for cycles at 11.1 a and 22.2 a periods, which means that the variance of the residuals hardly reduces by fitting a sinusoidal function to them. The amplitude of the fitted sinusoidal function at 11.1 a period is 0.021 (15) %, which is indistinguishable from zero. There are also no annual oscillations, since the corresponding amplitude of 0.008 (13) % is smaller than its uncertainty.

(5)

which is equivalent with n = 2 in Eq. (4). The standard uncertainty σ(A) represents a mean value applicable to the initial and final conditions (Pommé, 2015a). The most consideration should go to long-term effects which are not clearly apparent from the residuals, but which cause the fitted half-life to be biased. One such component is under- or overcompensation of count loss through dead time and pulse pileup. Physical degradation of the sources and detector are in principle additional potential risks. Importantly, possible differences between source and background (with a dummy) measurements have to be treated as a systematic error, not only as a purely statistical uncertainty on the count rates. Last but not least, a trend in the reference pressure settings (apart from a random variation) over the measurement campaign affects the counting efficiency in a systematic way, as seems to be the case with the biased 0.1 MPa data set. The uncertainty on the dead time compensation was estimated from Eq. (1) for the cascade effect, applying a hypothetical half pulse width uncertainty of 2.5 μs. In 2001, this corresponded to σ(A)/A≈0.06% on the highest decay rates, whereas in the more relevant period after 2005 it was already below 0.01% and practically zero at the end of the campaign. In order to avoid underestimation of the half-life uncertainty, the early measurements of 2001 have practically been excluded from analysis (by applying a low statistical weight) and a shorter time period T is applied in the uncertainty propagation factor (∼2/λT). In fact, this safety margin has been applied on all uncertainty components, which explains why the propagation factors in the uncertainty Table 3 pertain to fewer data points (n < N) and shorter time periods than in Table 1 showing the full information of the experiment. One could say that the uncertainty calculation has mainly been restricted to the period 2005–2018 – i.e. leading to more conservative uncertainty values – and the early measurements are somewhat treated as additional confirmation only. The largest uncertainty component in Table 3 is related to a hypothetical trend in the reference pressure along the measurement campaign, i.e. in the case of the 0.1 MPa data set. A somewhat arbitrary 0.5% uncertainty was assigned to a hypothetical systematic error on the background rate, which is significant at the later stages of the experiment when the source has lost most of its activity (cf. source D97043).

4.4. Comparison with literature Table 1 provides an overview of measured 55Fe half-life values published in the literature. The data from before 1980, being highly uncertain and discrepant, were excluded from evaluation by the DDEP. However, there is also a big discrepancy among the more recent data, shown in Fig. 9. None of the previous measurements have an uncertainty below 1.3 days, which means that the current work claims an accuracy which is an order of magnitude higher. Surprisingly, only one measurement agrees within about one standard uncertainty with 1006.70 (15) days. It is the measurement performed by Van Ammel et al. (2006) at the JRC with an X-ray DSA counter. Three other results agree within a zeta score of 1.3–1.7 (Hoppes et al., 1982; Schötzig, 2000; Morel et al., 1994). Other data can be discarded as having a zeta score between −4 and −5. The result obtained in this work can be adopted directly as a recommended value. The default PMM of the set of 5 best data, 1005.6 (15) d, provides too conservative accuracy due to the perceived inconsistency.

5. Conclusions The half-life of 55Fe was measured at the JRC over a period of 17 years with the 'LPPC′, a 4π large pressurised proportional counter. The resulting half-life value, 1006.70 (15) d, is at least one order of magnitude more accurate than other data in literature. A full uncertainty budget is provided, accounting for systematic uncertainties and longterm instabilities. Most of the published 55Fe half-life data appear to have an incomplete uncertainty estimate. The JRC measurement result from a previous experiment with X-ray DSA counter agrees within about one standard uncertainty. Three more data in the literature comply with a zeta score of 1.3–1.7. All other data can be regarded as discrepant. 32

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Table 3 Uncertainty budget for T1/2(55Fe) derived from the 7 measurements, in which 'non-equidistant' data (including the oldest data from 2001) were excluded, thus increasing the uncertainty propagation factors (from decay rate to half-life). The columns represent the measurement number (see Table 2), the number of 'equidistant' data (n ≤ N), the (reduced) time period (ΔT'≤ΔT), the uncertainty propagation factor for statistical/short-term PF(n) and long-term PF(2) uncertainty components, a typical standard uncertainty u(A)/A on the residuals (including random effects of Poisson statistics, threshold setting, counting efficiency), relative uncertainty on pileup correction (secondary effect on dead-time compensation, mean value for first and last considered data point), systematic uncertainty due to long-term instability (mainly efficiency variations due to changes in gas pressure, systematic error in background subtraction, hypothetical source degradation), the propagated uncertainties on the half-life and their quadratic sum. Nr

1 2 3 4 5 6 7

uncertainty propagation

u(A)/A

u(T1/2)/T1/2

n (−)

ΔT' (a)

PF(n) (−)

PF(2) (−)

Random %

Pileup %

Stability %

Random %

Pileup %

Stability %

Total %

4 10 13 6 10 12 9

15.0 13.5 13.4 13.5 7.3 13.7 13.6

0.36 0.29 0.26 0.35 0.54 0.27 0.30

0.53 0.59 0.46 0.59 1.1 0.46 0.46

0.06 0.06 0.06 0.12 0.20 0.17 0.20

0.016 0.008 0.004 0 0 0.003 0

0.005 0.005 0.006 0.071 0.41 0.41 0.41

0.021 0.018 0.016 0.042 0.11 0.045 0.06

0.0083 0.0047 0.0020 0 0.0003 0.0014 0

0.003 0.003 0.003 0.042 0.45 0.19 0.19

0.023 0.018 0.016 0.060 0.46 0.19 0.20

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Fig. 9. Published values (since 1980) of the 55Fe half-life compared to the result in this work (arrow). Three previous measurement values agree within 1.5 standard uncertainty u (blue), 1 agrees within 2 u (orange) and three others are outside 3 u (red). (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

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