On decay constants and orbital distance to the Sun—part II: beta minus decay

Claims that proximity to the Sun causes variations of decay constants at the permille level have been investigated for beta-minus decaying nuclides. Repeated activity measurements of 3H, 14C, 60Co, 85Kr, 90Sr, 124Sb, 134Cs, 137Cs, and 154Eu sources were performed over periods of 259 d up to 5 decades at various nuclear metrology institutes. Residuals from the exponential decay curves were inspected for annual oscillations. Systematic deviations from a purely exponential decay curve differ in amplitude and phase from one data set to another and appear attributable to instabilities in the instrumentation and measurement conditions. Oscillations in phase with Earth’s orbital distance to the Sun could not be observed within 10−4–10−5 range precision. The most stable activity measurements of β− decaying sources set an upper limit of 0.003%–0.007% to the amplitude of annual oscillations in the decay rate. There are no apparent indications for systematic oscillations at a level of weeks or months.


Introduction
This is Part II of a trilogy investigating claims that radioactive decay deviates from the fundamental exponential-decay law due to solar influences (see introduction in [1]). In this work, a systematic search for annual modulations in the decay rates of beta-minus (β − ) emitters is performed. Decay rate measurements repeated over periods of 259 d up to 5 decades at various laboratories around the globe were collected for this purpose. The project encompasses different types of radioactive decay, including alpha decay presented in Part I [1] and beta plus/ electron capture decay discussed in Part III [2]. All data sets were checked for annual oscillations and the amplitude and phase of the best matching sinusoidal function to the residuals from exponential decay were tabulated and published in [3]. The common measurement system for radioactivity is solidly based on the famous exponential-decay law and doubt raised on the invariability of decay constants touches the foundations of nuclear physics, the establishment and international equivalence of the SI unit becquerel, quantitative predictions of activity and radiation dose, and accurate dating through nuclear chronometers. The issue at hand concerns the observation of permille-sized annual modulations in particular decay rate measurements repeated over several years [4][5][6][7] and the interpretation that they are caused by solar-induced variations in the decay constants [4,8] rather than instabilities in the detection system. Claims were made about a new interaction-the fifth force-by which solar neutrinos could affect decay constants, thus inducing changes in the decay rates in correlation with the variations of the solar neutrino flux due to the seasonal changes in Earth-Sun distance [8,9]. Other hypotheses link periodic changes in radioactivity to interactions with slow neutrinos which are part of dark matter, such as the relic neutrinos produced at the early stages of the existence of the Universe [7,10], to global anisotropy and a new force [11], to a gradient in Planck's parameter h across the Earth's orbit [12], or to the presence of an 'effective Lorentz noninvariance' [13]. Predictions from Cordus theory find against constancy of decay rates on theoretical grounds [14].
In 2001, Falkenberg [4] reported the result of a long-term experiment aimed at testing the hypothesis that radioactive β decay might be caused by the neutrino flux coming from the Sun and other sources. The author made a link with the speculation by Nicola Tesla that radioactivity might be caused by small particles which are omnipresent and capable of passing any (non-radioactive) matter almost without leaving any traces. Repeated decay rate measurements of tritium, incorporated inside a strip of phosphorescent material and placed in front of an array of photodiodes, showed sinusoidal deviations from a double exponential function with a peak amplitude of 0.37% over the measurement period 1980-1982. The author was confident that seasonal changes of the external conditions (incl. temperature) were ruled out and came to the conclusion that the measurements showed a periodic variation in the decay constant of tritium and suspected a positive correlation between β decay and the periodically changing solar neutrino flux. This conclusion was the result of a questionable analysis of unstable measurements, because (1) the tritium disappearance rate was much higher than expected from decay, with a 'half-life' of 2.26 a instead of T 1/2 ( 3 H) = 12.312 (25) a [15] and (2) the annual modulation was partly caused by the arbitrary fit function used to represent the 'degradation' of the experiment. The residuals of the data to a single exponential function do not follow a sinusoidal shape, as can be seen in figure 1 (based on Falkenberg's data published in the annex of [16]).
In 2009, Jenkins et al [5] re-opened the debate by observing 0.3% variations in decay rate measurement sets of 32 Si/ 32 P (β − emitter, measured relative to 36 Cl at Brookhaven National Laboratory) and 226 Ra sources (series of α and β − emitters measured at the Physikalisch-Technische Bundesanstalt). Since it was considered less likely that α decay was affected by (mildly varying) external conditions, it was argued by Jenkins et al [6] and Parkhomov [7] that the oscillations in the 226 Ra decay rates could be caused by solar influences on the β − emitters in the decay chain. This raises the variability claim on the β − decay constants even to percent level, considering that only 210 Pb (22.23 (12) a)-near the end of the decay chain, representing a small fraction of the activity measured in an ionisation chamber-has a sufficiently long half-life to depart significantly from equilibrium with the 226 Ra parent for more than a few weeks. Such high variability of the decay constant is contradicted by the consistency among the measured 210 Pb half-life values [15]. Moreover, in Part I of this work [1] experimental evidence was provided that the decay rate of a 226 Ra-series source is free of annual modulations within 0.000 25 (18) %.
Parkhomov [7] and Jenkins et al [6] collected additional experimental evidence of time-dependent decay rates for β − emitters 3 H, 36 Cl, 56 Mn, 60 Co, 85 Kr, 90 Sr, 133 Ba, 137 Cs, and 239 Pu as well as for β + and electron capture decaying nuclides. In all of these data sets, a periodicity of 1 year was found by means of a time-frequency analysis and this was attributed to solar influences on the decay constants. Since no consistency was found concerning the amplitude of the annual modulations in the decay rates of different radionuclides, Jenkins et al concluded that 'different nuclides have different sensitivities to whatever external influences are responsible for the observed periodic variations'. Whereas the annual modulations first seemed a general phenomenon to all radioactive decays, the claims had to be narrowed down to certain types of decay, later also to specific nuclides. This created a demand for more data sets to investigate the presence of seasonal behaviour in the decays of different nuclides.
Beside the claims for annual modulations, there have been observations of non-exponential decay at other frequencies: for example Baurov et al observed periods of 1 d and 27 d in the decay of 60 Co and 137 Cs [11,17]. Various data sets have been subjected to frequency analysis (see e.g. [18][19][20]), yielding additional 'instabilities of interest'. Variations with periods of the order of months have been attributed to r-mode oscillations in solar activity and frequencies of the order of 10-12 a have been associated with internal solar rotation [21]. Again solar neutrinos were considered the root cause of non-exponential decay. However, also the conjecture that cosmic neutrinos stimulate decay has been further developed: Sturrock et al [20] found arguments to claim that there is a directional relationship between the incoming neutrino and the photons emitted from the neutrino-stimulated decay. In their reasoning, γ-ray measurements performed on top of the source would be sensitive to cosmic neutrinos at daytime and to solar neutrinos at night. Sturrock et al [22] found a similarity with the oscillations observed in the DAMA experiment, which is allegedly compatible with the influence of dark matter.
Metrologists have pointed out that the more likely explanation for non-exponential behaviour is instability of the measurement conditions leading to varying detection efficiency [23][24][25][26][27][28][29][30][31]. Precise measurements of 36 [29], and 137 Cs [30] decay rates performed in stable conditions show no annual modulations within 10 −4 level, thus contradicting the experimental evidence prone to instability and invalidating theories assuming a permille range variability of decay constants in phase with Earth-Sun distance. This counterevidence seems to be largely ignored by authors in search for new physics. The growing scientific literature devoted to this subject hardly considers experimental difficulties with repeatability of activity measurements as a plausible root cause for the observed deviations from perfect exponential decay. With good reason, Lindstrom [25] reminds the community that believable science is founded on believable uncertainty assessments: 'Although science is always open to new ideas, a lack of understanding of the real uncertainties in a measurement, in physics as well as statistics, has led to some conspicuously mistaken conclusions'.
In this work, the seasonal variability of decay rates for β − emitters has been investigated experimentally. Repeated activity measurements of 3 H, 14 C, 60 Co, 85 Kr, 90 Sr, 124 Sb, 134 Cs, and 137 Cs sources were performed over periods of 259 d up to 5 decades at various nuclear metrology institutes. Exponential decay curves were fitted to the data and the residuals were inspected for annual modulations, using the same methodology as in [1][2][3]. The residuals from the fitted decay curve were binned into 8 d periods of the year and averaged to obtain a reduced set of (maximum) 46 residuals evenly distributed over the calendar year. To the averaged residuals, a sinusoidal shape Asin(2π(t + a)/365) was fitted in which A is the amplitude, t is the elapsed number of days since New Year, and a is the phase shift expressed in days. The standard uncertainty on the fitted amplitude was determined as the value which increases the variable χ 2 /(χ 2 /υ) 0 by a value of one; the chi square χ 2 was divided by the reduced chi square (χ 2 /υ) 0 of the fit to protect against unrealistic uncertainty evaluations, e.g. due to correlations between measurements.
Throughout the paper, graphs are shown of residuals of integrated count rates or ionisation currents (for convenience all types of signals will be represented by the same symbol I) over the measured period as well as multi-annual averages (maximum 46 data, covering 8 d periods). The uncertainty bars are indicative only: for the individual data they often refer to a short-range repeatability, and for the annual averaged data they were derived from the spread of the input data and the inverse square root of the number of values in each data group. As a reference measure for the expected solar influence, a functional curve is included representing the annual variation of the inverse square of the Sun-Earth distance, 1/R 2 , renormalised to an amplitude of 0.15%, which is representative for the magnitude of the effect claimed by Jenkins et al [5]. The actual amplitude of the variation of 1/R 2 is smaller (0.033%).

Decay characteristics
Tritium or 3 H (12.312 (25) a) is the lightest radioactive nuclide. It decays 100% by β − emission directly to the ground state of 3 He. In radionuclide metrology, it plays a role as a reference source for quantifying quenching effects in liquid scintillator cocktails. No gamma rays are emitted in its decay and the average beta energy is only 5.68 keV (with a maximum of 18.56 keV) [15], which makes detection difficult and dependent on the energy threshold of the detection system.
The measurements by Falkenberg [4] between 1980 and 1982 show significant deviations from the expected exponential decay, as discussed in the introduction and shown in figure 1. Falkenberg claimed the presence of annual sinusoidal oscillations in the decay rate with 0.37% peak amplitude. Residuals from a single exponential decay curve (with a hypothetical half-life value of 2.26a) fitted to the 3 H decay rate measurements of Falkenberg [4]. The line represents the best fitting sinusoidal function to the data. Veprev and Muromtsev [32] observed 27 d and daily variations of counting rate in the high-energy region of the tritium beta spectrum and suggested that the 27 d variations with 11%-22% amplitude could be caused by the interaction of tritium nuclei with low-energy solar neutrinos. Bikit et al [33] reinvestigated the liquid scintillation measurements (LSC) of the 3 H decay rate and concluded that the measurement of the high-energy tail of the beta spectrum may be significantly influenced by instrumental instability. They observed 22 d oscillatory behaviour of only 0.5% amplitude when selecting the high-energy tail of the beta spectrum and no significant variations when selecting the total spectrum.

3 H @JRC
At the radionuclide metrology laboratory of the JRC in Geel (Belgium), a series of 706 activity measurements of a tritium source was performed from 2002 to 2014 by means of liquid scintillation counting with a Packard Tri-Carb 3100 TR/AB LSC. The decay-corrected activity values of the 3 H source show a standard deviation of 0.4%, which is one or two orders of magnitude lower than the residuals claimed by others [4,32]. The residuals from exponential decay shown in figure 2 do not reveal a systematic pattern at annual level, which is confirmed by a plot of the averaged residuals grouped over 8 d periods of the year in figure 3. The best fitting sinusoidal function has an amplitude of A = 0.048 (24)% and a phase of a = 197 d. A search for periodicity in the neighbourhood of 1 month did not yield a significant result (A = 0.023 (22)% at a period of 28 d). This refutes the claims that the decay of tritium is modulated at the percent level and puts to question the quality of the metrological processes which led to this conclusion.

3 H @NIST
Due to the low energy of the emitted beta particle and the absence of subsequent gamma-ray emission in the decay of 3 H, not many techniques are suitable for absolute activity measurements of this nuclide. Internal gas proportional counting [34] is a method applied at the NIST for the standardisation of 3 H in gas. The radioactive gas is mixed with counter gas and measured in a set of proportional counters of different length. Measurements on the same 3 H standard performed between 1961 and 1999 were collected and the residuals from exponential decay are shown in figure 4. Whereas the data should be free of bias, there is an appreciable standard deviation of 0.8% (after elimination of two extreme data) which demonstrates the difficulty of measurement reproducibility in this case. Nevertheless, the averaged data set in figure 5 shows no annual modulations at the percent level (A = 0.18 (20)%, a = 149 d).

Decay characteristics
Carbon-14 (5700 (30) a) disintegrates 100% by β − decay to the ground state of the stable nuclide 14 N. The average emission energy of the beta particle is 49. 16 Figure 3. Annual average residuals from exponential decay for 3 H decay rate measurements by LSC at JRC. One (red) line represents relative changes in the inverse square of the Earth-Sun distance, normalised to 0.15% amplitude, and the other (blue) line a sinusoidal function fitted to the data. . It is used as a nuclear chronometer for determining the age of organic material [35]; 'radiocarbon dating' has become a standard tool for archaeologists. In recent work, Mueterthies et al [13] referred to prepublication results from Scott Mathews on measured seasonal variations in the decay rate of 14 C with an amplitude in the order of 2-4 permille. This is similar to the permille level oscillations claimed for other beta decaying radionuclides, including 3 H, 22

14 C @JRC
In parallel with the tritium measurements discussed in section 2.2, the JRC has performed a series of 706 activity measurements of a 14 C standard over a period of 12 years, from 2002 to 2014, by means of liquid scintillation counting with a Packard Tri-Carb 3100 TR/AB LSC. The decay-corrected 14 C activity values have a comparably smaller standard deviation of 0.28%, probably because the beta energy is 10 times higher than in the decay of 3 H. The residuals from exponential decay presented in figure 6 show no discernible systematic pattern and the annual average residuals in figure 7 disprove the occurrence of significant oscillations at the permille level: they show perfect exponential behaviour down to the 10 −4 level (A = 0.013 (16)%, a = 92 d).
Just as for tritium, the observation of non-exponential behaviour in beta decay of 14 C seems to be more of a metrological issue than a physical one. As for nuclear dating purposes, there is no indication that significant variations in the decay constant are present which could affect the accuracy of the method. There is also no sign of a common effect on the decay rate of 3 H and 14 C-be it driven by solar neutrinos, relic neutrinos or instrument bias-since the measurements performed on the same day show no correlation in the respective residuals plotted in figure 8.     Figure 8. Residuals from exponential decay for 14 C as a function of residuals for 3 H for 706 measurements performed at the same day with the same LSC instrument at JRC.

14 C @NMISA
The activity of pure beta emitters like 14 C can also be measured in an absolute way with triple-to-double coincidence ratio counting (TDCR), a method in which the source material is mixed into a liquid scintillation cocktail and light flashes are collected from three photomultiplier tubes [36]. The NMISA (South-Africa) performed 33 TDCR measurements of 14 C activity (of which one data point was omitted as outlier). The residuals from an exponential decay curve are shown in figure 9 and the annual averaged data in figure 10.
The data show no modulations of permille level (A = 0.067 (80)%, a = 59 d) in the decay of 14 C. The invariability of the 14 C decay constant is therefore confirmed in the southern as well as the northern hemisphere (section 3.2).

Decay characteristics
Cobalt-60 disintegrates by β − emission to excited levels of 60 Ni, followed by emissions in cascade of the characteristic 60 Ni gamma rays of 1173.2 keV and 1332.5 keV [15]. The radionuclide 60 Co has applications in reference sources for gamma detector calibrations, radiation sources for medical radiotherapy, sterilisation of medical equipment, food and blood and as a tracer for cobalt in chemical reactions. On the basis of measurements with a Geiger-Müller counter, Parkhomov [7] claimed that the decay rate of a 60 Co source shows systematic annual variations with a magnitude of 0.2% and related this effect to seasonal changes in cosmic neutrino flux affecting beta decay.

60 Co @NIST (#1)
Between 1968 and 2007, 250 current measurements of the 60 Co source #4203 were performed in an ionisation chamber (IC 'A') at the NIST (USA). Whereas the chamber suffered from geometrical changes in the suspension of the source holder over these 4 decades (see section 9.5), the effect on the 60 Co measurements was relatively small owing to the high energy of the emitted gamma rays. Linear corrections were applied to the data, even though this had little effect on the residuals to an exponential fit (besides a difference in slope of the fitted exponential). The residuals in figure 11 show residuals in the permille range and the averaged values in figure 12 are free of annual oscillations at the 10 −4 level or even lower (A = 0.007 (7)%, a = 0 d). An additional set of 46 measurements of source #274 was analysed as well, yielding incomplete coverage over the year and less conclusive evidence of stability (A = 0.036 (15)%, a = 80 d). The stability of these results proves that annual oscillations at the permille level are neither a common feature of beta decay in general, nor of 60 Co decay in particular.

60 Co @NIST (#2)
Between 2007 and 2015, the NIST has performed 26 primary standardisation measurements of two 60 Co sources by means of live-timed anticoincidence counting (LTAC). This method is accurate in the sense that it gives a precise absolute value of the source activity which is largely insensitive to small changes in the efficiencies of the LTAC detectors [37]. In the same period, a few measurements of a higher-activity 60 Co source were performed with comparable precision in the 'AutoIC' ionisation chamber and these data were added to the analysis. The residuals for the LTAC and IC data are all within 0.1% of an exponential slope (figure 13), and the annual averages ( figure 14) show no statistically significant seasonal effects (A = 0.007 (9)%, a = 18 d). This is evidence of purely exponential decay down to the 10 −5 level.

60 Co @JSI
In the frame of quality control of gamma-ray spectrometry, the JSI (Slovenia) has performed 2183-3250 60 Co point source measurements on 6 HPGe detectors between 1998 and 2016. The activity values were recorded relative to the   Figure 11. Residuals from exponential decay for 60 Co activity measurements with ionisation chamber 'A' at NIST, after applying linear corrections for the gradual efficiency changes due to slippage of the source holder.  certified value of the source. In figures 15-17, the data sets are presented for three detectors. They show explicit jumps due to recalibrations of the detectors. Two subjective actions were performed to produce the annual averages in figure 18: (1) groupings were identified by eye and renormalised, and (2) an 8% fraction of extreme data was eliminated. Assuming that these interventions were mainly compensating for temporary instrumental instabilities and recalibrations, one can conclude that the spectrometry data were barely affected by annual changes through physical processes (A = 0.041 (14)%, a = 161 d).
Considering that the residuals in the 6 data sets show nonrandom, auto-correlated deviations from the exponential law, some authors may be tempted to perform a frequency analysis to extract 'relevant frequencies' and look for correlations with cosmic phenomena which could have influenced the decay rate. However, the fact that the structure of the residuals for the same source in one laboratory over the same time period differs from one detector to another should be a hint that the instabilities are of a local nature rather than of cosmic origin.    taking a ratio with the ionisation current of the 226 Ra check source or another long-lived radionuclide measured in parallel [38,39].

85 Kr @NIST
A series of 98 decay rate measurements were performed of a 85 Kr source in the NIST IC 'A' from 1980 until 2007. As can be seen from the residuals to the fitted exponential curve ( figure 19) and the annual averaged data (figure 20), the measurements are not evenly distributed in time and do not cover every period in the year. The amplitude of the fitted sinusoidal remains nevertheless well below the permille level (A = 0.036 (15)%, a = 153 d).

85 Kr @PTB
As with the IC measurements of 226 Ra at the PTB before 1999 [1], ionisation current measurements of 85 Kr from 1990 to 1995 showed a clear annual modulation of permille-level amplitude which can be attributed to instability of the Townsend balance current measurement system. The residuals have been published and discussed by Schrader [38]. In the current work, analysis is performed on 2163 85 Kr measurements collected from 1996 to 2016 in the same IC, but with a more stable electrometer [39]. The data were taken relative to the 226 Ra reference source (A = 0.016 (1)%, a = 194 d) [1,3] to compensate-at least partly-for instrumental instability. The decay-corrected IC output in figure 22 shows a permille-level long-term drift which was also observed with other nuclides measured over the same period (e.g. 133 Ba [2]). This was compensated for in this work by linear adjustments over 4 time regions and exclusion of 46 extreme data (in value or uncertainty). The resulting residuals in figure 23 have a standard deviation of 0.06% and show some local   On a time scale of weeks or months, the activity of the short-lived daughter 90 Y may be assumed to be in equilibrium with its long-lived parent nuclide 90 Sr, irrespective whether the 90 Y half-life is constant or modulated as a function of time.
According to Parkhomov [7], count rate measurements with a Geiger-Müller counter of beta particles emitted by a 90 Sr-90 Y source show a distinct annual modulation with 0.13% amplitude. Sturrock et al [40] claim the presence of an 11 a modulation in at least one of the 90 Sr-90 Y decay rate measurements performed at the PTB (see section 6.3), and called it 'suggestive of an influence of internal solar rotation'.

90 Sr-90 Y @PTB (#1)
From the end of 1989 until 2016, in total 2207 measurements were performed of a 90 Sr solid source in the IG12/A20 IC at the PTB. Since the data set showed trending behaviour over different multi-annual periods of time, the data were subdivided in five time regions and realigned through a linear transformation in each region. By doing so, possible annual modulations would remain visible in the residuals to an exponential fit, whereas the effects of long-term instabilities would be suppressed. The residuals in figure 25 are in the permille level and show some autocorrelation. The annually averaged residuals in figure 26 show a distinct but small sinusoidal seasonal   ) and other nuclides with the same IC [2]. Since the measurement results were analysed relative to the signals of the 226 Ra check source, one has to take into account that the modulations in the 226 Ra data (A = 0.016 (1)%, a = 194 d) [1,3] have been transferred inversely through the normalisation procedure.

90 Sr-90 Y @PTB (#2)
In 2015, Kossert and Nähle [28] published a long-term measurement series performed between 24 April 2013 and 26 May 2014 of three 90 Sr-90 Y sources. They used a custom-built liquid scintillator set-up with three photomultiplier tubes and a sample changer and applied TDCR. With this primary standardisation technique, the detection efficiency is derived from the measurement itself, thus leading to a more reliable activity measurement [36] than e.g. the unstable Geiger-Müller measurements of 90 Y by Parkhomov [7]. The PTB collected 4493 data ( figure 27) with a standard deviation of 0.05%, and the averages in figure 28, show remarkable stability (A = 0.004 (2)%, a = 362 d). This refutes the conjecture that beta decay of 90 Sr-90 Y would be modulated at the permille level [7]. The data exclude systematic modulations at any frequency between a day and a year. On the basis of these data, Sturrock et al [40] admitted that earlier reports of annual oscillations in 90 Sr-90 Y decay could have been caused by environmental factors instead of solar proximity, but then tried to make a new case for solar rotation effects occurring at a frequency of 11 a. They claim that a power analysis of the data set (covering only 1 year of measurement!) shows significant proof for the presence of an 11 a modulation, at least for source S2 (mostly measured at night) but not for source S4 (mostly measured during the day). They give an unsubstantiated explanation in which it is assumed that neutrino-induced beta decay not only confines beta particle emission to a cone in the direction of the incoming neutrino, but apparently also the scintillation photons produced in the cocktail, thus giving rise to an angular dependency of triple coincidences in the TDCR. In this work, an 11 a sinusoidal function was fitted to the residuals of the S2 and S4 data and no significant amplitude was found (A < 4 × 10 −6 ) in comparison to the standard deviation of the data (5 × 10 −4 ).

Decay characteristics
The relatively short-lived radionuclide 124 Sb (60.208 (11)           . This nuclide is often used as mono-energetic γ ray calibration source. It is of major concern in environmental measurements after nuclear accidents, due to its high production yield in the fission process.

137 Cs @IRA
At the IRA (Switzerland), a 137 Cs source was measured 281 times in an ionisation chamber between 1980 and 2012 [42] (see figure 35). The IC is a sealed well type 4πγ Centronic IG11, filled with argon at a pressure of 2 MPa. The chamber is surrounded by a 5 cm-thick lead shielding and is located in a temperature-controlled room. The chamber operates at a positive DC voltage of 1000 V and an automated electronic system-based on the principle of the Townsend balance with stepwise compensation-measures the current. A typical measurement cycle corresponds to the time needed to collect the charge produced by the ionisation in the chamber and to load a given capacitor up to 0.1 V. The obtained current is corrected for saturation, background and decay during the measurement. From the average residuals in figure 36, it appears that there are no annual oscillations at permille level (A = 0.018 (9)%, a = 342 d).

137 Cs @PTB
The decay of a 137 Cs source was followed from 1997 to 2016 with the PTB IG12/A20 IC, the same instrument as for the 226 Ra measurements from 1984 to 1998 in [1], but under more stable conditions due to a commercial electrometer replacing a Townsend balance method since October 1998 [39]. An exponential curve was fitted to the ratio of the 137 Cs current with the corresponding current from the 226 Ra reference source and the residuals are shown in figure 39. Whereas some auto-correlated effects are still present, they are smaller and less cyclic than in the past [1]. Averaged on a yearly basis (figure 40), the amplitude of the oscillations is down by an order of magnitude (A = 0.014 (1)%, a = 29 d). Just as for 90 Sr in section 6.2 (and 54 Mn and 152 Eu in Part III [2]), it seems no coincidence that the oscillation is of similar magnitude as for the 226 Ra reference source measured in the time period 1999-2016 (A = 0.016 (1)%, a = 194 d) [1,3] and that the phase shift differs by about half a year.

137 Cs @NIST
The NIST (USA) has a tradition of long-term activity measurements with the IC 'A' and is a major decay data provider [43,44]     sample holder of the NIST IC, causing slow variation of the detection efficiency [45]. Applying energy-dependent correction factors, the discrepancies for the mentioned nuclides were resolved [44,46].
In figure 42, the residuals of the linearly corrected data to an exponential fit are presented. The corrections have adequately compensated for the slope changes, but in the residuals some signs of autocorrelation have remained. For example, one can see that a significant efficiency increase must have occurred between 1977 and 1982. This systematic trend results in increased scatter in the annual averages in figure 43, but even then the data disprove the conjecture of seasonal effects at sub-permille level (A = 0.004 (6)%, a = 33 d). The same conclusion could be drawn from an independent fit to the uncorrected values, which show similar residuals for a different slope.

Decay characteristics
Europium-154 (8.601 (4) a) disintegrates by 99.982% by β − decay to excited levels of 154 Ga and by 0.018% electron capture via excited levels of 154 Sm [15]. Transitions to the ground states of 154 Ga and 154 Sm have not been observed.

154 Eu @PTB
Europium-154 is one of the radionuclides measured in the IG12/A20 IC at the PTB covering periods before and after October 1998, i.e. the date at which the Townsend balance method for the current readout was replaced by a commercial electrometer [31,38,39]. Schrader [38] has published raw-i.e. not relative to a reference source-residuals from exponential decay, showing the characteristic 0.

Conclusion
A unique collection of long-term decay rate measurements of β − emitting nuclides was obtained from radionuclide metrology laboratories. Excellent measurement stability was achieved with ICs for β − decay accompanied by γ-ray emission of sufficiently high energy. Maintaining a constant gain, stable working conditions and a clear separation of the measurand from interfering signals contributed to the accuracy of the measurements. Primary standardisation methods (LTAC, TDCR) have shown their remarkable repeatability capabilities without need for corrections or rescaling over a long measurement campaign.
Just as for α decay [1,3] and EC/β + decay [2,3], no evidence was found of annual oscillations in β − decay in phase with Earth-Sun distance. For the most stable decay rate measurements, the amplitudes of annual sinusoidal modulations are below 0.007% for 60 Co, 90 Sr, 134,137 Cs, 124 Sb and 154 Eu and below 0.05% for 3 H, 14 C, and 85 Kr. This appears to be an instrumental limitation rather than a physical one. Even though non-random periodical deviations from exponential behaviour do occur in some data sets, they show no mutual coherence in amplitude or phase. Since the deviations differ from one instrument to another, even within the same  laboratory, it appears more likely that they originate from local conditions rather than from cosmic influences on the decay rates of radionuclides.