On decay constants and orbital distance to the Sun—part I: alpha decay

Claims that proximity to the Sun causes variation of decay constants at permille level have been investigated for alpha decaying nuclides. Repeated decay rate measurements of 209Po, 226Ra, 228Th, 230U, and 241Am sources were performed over periods of 200 d up to two decades at various nuclear metrology institutes around the globe. 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. The most stable activity measurements of α decaying sources set an upper limit between 0.0006% and 0.006% 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. Oscillations in phase with Earth’s orbital distance to the sun could not be observed within 10−5–10−6 range precision.

Keywords: half-life, decay constant, non-exponential decay, radioactivity, Sun, neutrino (Some figures may appear in colour only in the online journal)

Introduction
The exponential decay of radionuclides as a function of time is a cornerstone of nuclear physics and radionuclide metrology [1,2]. Decay constants for spontaneous radioactive decay are considered invariable in time and space [3,4]. This convenient trait allows projecting activity values to a point of time in the past as well as into the future. The statistical laws ruling the temporal behaviour of a decay series [5,6] are even applied for accurate dating in archaeology [7], geo-and cosmochronology [8], nuclear forensics [9], monitoring of nuclear events [10,11], or age dating of radiopharmaceuticals [11]. Significant violations of the invariability of decay constants would compromise the accuracy by which one can compare activity measurements or even define a reference for the SI-unit becquerel. There would be a natural limit to the precision by which a halflife value can be assigned to a radionuclide, unless conditions could be specified for which an attained value applies.
The premise of invariability of the decay constants of radionuclides decaying by α, β − and β + emission has withstood many experimental tests, showing independence to physical and chemical conditions such as temperature, pressure, and material surroundings [3,4]. Internal conversion and electron capture (EC) decays are considered to be in a separate category, since the direct involvement of atomic electrons could in principle be affected by the ionisation state and chemical environment, particularly for low-Z nuclides like 7 Be, but the magnitude of these effects are still debated [12][13][14]. Halflife measurements of radionuclides performed over a century in different laboratories show occasional discrepancies [15] which are generally ascribed to incomplete uncertainty assessment [2]. In the last decades, more attention is paid to precision, uncertainty evaluation, and documentation, which is resulting in a growing convergence of published half-life values at a sub-permille level [16].
In 2009, controversy arose due to claims by Jenkins et al that seasonal effects at a level of 10 −3 in repeated decay rate measurements of 32 Si/ 36 Cl and 226 Ra were due to an annual modulation of the decay constants rather than instabilities in the detection system [17,18]. Fischbach et al postulated a causal correlation with the orbital Earth-Sun distance, possibly through interactions with solar neutrinos or a scalar field affecting the terrestrial fine structure constant [19]. They found support for the neutrino theory by a perturbation of measured 54 Mn decay rates coinciding with a solar flare [20] and solar storms [21]. Jenkins et al collected experimental evidence of time-dependent decay rates for 3 H, 22 Na/ 44 Ti, 36 Cl, 54 Mn, 56 Mn, 60 Co, 85 Kr, 90 Sr/ 90 Y, 108m Ag, 133 Ba, 137 Cs, 152 Eu, 154 Eu, 222 Rn, 226 Ra and 239 Pu, in which the most often cited periodicity was 1 a, but also cycles of 1 d, 2 a, 11.7 a to 13.5 a were found by means of a time-frequency analysis [22]. Parkhomov [23] found 7 data sets of beta-decaying radionuclides exhibiting periodic variations with a period of 1 year. Influence by the chemical environment was put back on the table when reports claimed changes at a 10 −2 level in α, β − and β + and EC decay constants depending on temperature and conductivity of the hosting material (see references in [24,25]). Theoretical considerations predict an influence of the electron environment on α decay, leading to significantly shorter half-lives at high matter densities (up to 10% at 10 4 g cm −3 in a high-Z matrix) [25] which has implications for cosmochronology.
As much as these claims attract interest as inspiration for new physical theories or hope for revolutionising cosmic neutrino detection and radioactive waste management [26][27][28], if true they would have major implications on traceability and equivalence in the common measurement system of radioactive substances. Primary standardisation of activity concentration of a radionuclide in solution [29,30] is performed down to an accuracy of typically 0.1% [31], and international equivalence is established through key comparisons organised under the auspices of the BIPM [32]. Through the International Reference System (SIR) [33] standardisations performed over half a century worldwide can be compared. Whereas the key comparison data sets may show signs of slight inconsistency [34,35], there are reasons to assume that these are mainly caused by imperfections in the uncertainty assessments [31,36,37] rather than variability in the decay constants. Oscillations of the order of 10 −3 in primary standardisations would not easily go unnoticed at this level of acc uracy, and are therefore unlikely to have occurred.
In the last decade, new experimental evidence has been presented refuting the variability claims of the decay constants. Stability within a level of <10 −4 at annual time scale was observed in the decay of 22 [45,46], 222 Rn [47], and daughter nuclides of 225 Ac [48,49] showed consistency over different periods in the year. No significant deviation of 40 K, 137 Cs, 232 Th decay rates could be observed during the occurrence of the strongest solar flares in 2011 and 2012 [50]. The 198 Au half-life is identical in a gold wire and sphere, showing independence of the internally generated neutrino flux of ~10 11 s −1 through the surface of the sphere and ~10 10 s −1 of the wire [51]. No evidence could be found for an antineutrino flux of 5 × 10 10 cm 2 s −1 from a reactor influencing the decay of 22 Na (EC, β + ) and 54 Mn (EC) [52]. Even in the presence of a 3 × 10 12 cm 2 s −1 reactor antineutrino flux, the measured differences in decay rates of 22 Na, 54 Mn and 60 Co (β − ) sources are only in the 10 −5 range [53]. Geo-and cosmochronology does not provide any support for heliocentrically variable decay rates in meteorites for 36 Cl, 40 Ar, 87 Rb, 147 Sm and 235,238 U [54], and neither does the power of a 238 Pu source in the Cassini spacecraft show dependence on neutrino flux through proximity to the Sun [55,56]. The half-lives of 198 Au in gold and 97 Ru in ruthenium proved to be the same within 0.04% and <0.1%, respectively, between room temperature and 19 K [24]. A 210 Po source imbedded in silver showed the expected decay rate within 0.6% after having been cooled down to 4.2 K for 28 d [57], which is incompatible with a claim that the decay constant would reduce by 6.3% in these conditions.
In summary, the anomalies in the 36 Cl and 226 Ra decays have been disproved with new, more stable measurements and additional evidence demonstrates the invariability of various decay constants under different physical and chemical constraints. Nevertheless, arguments were raised that the variability may differ from one nuclide to another and that experimental proof for a variety of nuclides and a variety of detectors is needed [17,22]. In this work, 14 radionuclide metrology laboratories from across the globe present repeated activity measurements of various mono-radionuclide sources performed over a period of years or decades. Different decay modes were investigated, including α, β − , β + and EC decay. Residuals from the exponential nuclear decay curves were inspected for annual oscillations. The data sets were first compensated for (1) the presence of occasional outlier values, (2) abrupt systematic changes in the detector response, e.g. due to replacement of the electronics or recalibrations of the instrument, and (3) systematic drift extending over periods of more than 1 year. This paper is part I of a trilogy, presenting experimental evidence for α decay. Part II [58] groups the evidence for beta minus decay and in part III [59] β + and EC decay are investigated. 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 taken over fixed 8 d periods of the year. The uncertainty bars are indicative only: for the individual data they often refer to a short-range repeatability, and for the annual averaged data (maximum 46 data, covering 8 d periods) 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 , renormalized to an amplitude of 0.15% (which is the magnitude of the effect claimed by Jenkins et al). To the averaged residuals plotted as a function of time, a sinusoidal shape A sin (2π (t + a)/365) has been 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. This function is occasionally included in the residual plots. A summary table of the sinus parameter fit values for each data set has been published in [60].

Decay characteristics
Radium-226 is typically used as a reference source for gammaray spectrometers and for ionisation chambers (IC) [61] acting as secondary standardisation devices for activity. The 226 Ra has a half-life of 1600 (7) a and decays by α-emission to 222 Rn (3.8232 (8) d), followed by a series of mostly short-lived alpha and beta emitters (T 1/2 < 5 d), except for 210 Pb (22.23 (12) a) and 210 Po (138.3763 (17) d) [16]. To measure the activity of 226 Ra and its progeny in equilibrium, more than a century old material needs to be used in a closed configuration that is radon tight. After a sudden loss of 222 Rn, the activity of the first 2/3rd of the decay series would re-establish itself in a few weeks, whereas the last 1/3rd of the chain would remain in equilibrium with the activity of 210 Pb for decades. Only the half-lives of the α emitters 226 Ra and 210 Po and the β − emitter 210 Pb are long enough to be relevant for explaining annual variations in the decay rates as a result of seasonal changes in the decay constants through solar influence.

226 Ra series @PTB (<1999)
On several occasions, series of activity measurements obtained with an ionisation chamber (type IG12, 20th Century Electronics, UK) at the PTB [62][63][64][65] have been used by others [17,22,[66][67][68] to make claims about a solar influence on decay constants. Metrologists of the PTB have always emphasized that variations in the ionisation current are caused by instrumental and environmental parameters in the laboratory [40,42,[62][63][64][65]. Recent tests in the Khalifa university (Abu Dhabi, UAE) [69] have confirmed that activity measurements with several detector types are sensitive to environmental conditions, such as temperature, humidity and pressure. Nevertheless, Jenkins et al claimed that 'sensitivities to seasonal variations in the respective detectors are likely too small to produce the observed fluctuations' [18].
The most cited case is 226 Ra, used as reference source for IC stability checks. As shown in figure 1, the residuals from an exponential decay curve to old data obtained from 1983 to 1998 show annual periodicity of about 0.15% magnitude. These oscillation effects-also present in residuals for 85 Kr, 90 Sr, 108m Ag, 133 Ba, and 152,154 Eu [58,59]-have been significantly reduced when the Townsend balance current measurement method was replaced by a commercial Keithley electrometer [42,65] (see next section). Consequently, the effect is of instrumental nature and should not be interpreted as an indication of changing decay constants. Figure 2 shows the averaged residuals grouped in bins of 8 d in the year, which take a sinusoidal shape as a function of time in which the amplitude is A = 0.083 (2) % and the phase shift a = 59 d. The phase does not coincide with the variations of orbital distance Earth-Sun (a = 89.5 d), nor with average humidity and temperature in the Braunschweig region [70]. Semkow et al [71] proposed an explanation through ambient conditions in the laboratory, however some of their arguments were criticised by Schrader [65]. The discharge of the capacitor through radon decays in the air, as suggested by Siegert et al [62], is a possible explanation, considering that the seasonal variations for atmospheric radon concentration follow a sinusoidal model [72]. There is indeed a remarkable correlation with average seasonal changes of radon concentration in air (A = 16 (2)%, a = 57 d) measured inside the laboratory from 2010 to 2016 (see figure 3), but causality has not been proved.

226 Ra series @PTB (>1999)
The 226 Ra data collected with the same IC from 1999 to 2016 are presented in figure 4. Since the replacement of the Townsend balance with commercial electrometers Keithley 6517A and B [42,65], the annual modulations have reduced drastically and their phase has changed as well. The annually averaged residuals in figure 5 now show a modulation with an amplitude of A = 0.016 (1)% and a phase shift of a = 194 d. This measurement series shows mild correlation with the room temperature (figure 6, ρ = 0.23) and humidity (figure 7, ρ = 0.25), but not with the radon concentration in the laboratory (figure 3, ρ = 0.0). Nähle and Kossert [42] already pointed out that temperature and humidity can have an effect on the electrical    properties of the signal cables and the electrometer. The manufacturer of the Keithley electrometers used at PTB claims a temperature coefficient of 0.1%/°C of the reading in the relevant current range (see [42] and references therein).

226 Ra series @ENEA
At ENEA (Italy) between 1992 and 2016, 213 ionisation current measurements were performed on a 226 Ra source, using a Centronic IG11 ionisation chamber with a Keithley 617 electrometer. The decay-corrected current measurements cover a period of 24 years and have a standard deviation of 0.05%. The residuals from exponential decay are presented in figure 8, together with a polynomial trend line fitted to the data. By compensating for this sub-permille trend line, the standard deviation of the residuals could be reduced to 0.04%. Whereas annual sinusoidal oscillations are not immediately apparent from the individual residuals, they do appear in the annual average (detrended) residuals in figure 9 with an ampl itude of A = 0.037 (4)% and a phase of a = 319 d. Without the detrending correction, the modulation of the data is less smooth and the fitted amplitude is lower (A = 0.026 (6)%, a = 305 d). The modulations are not in phase with Earth-Sun distance, nor with the PTB data, therefore are unlikely to be generated by the same global phenomenon.
Between 24 March and 12 May 2016, thousands of systematic measurements have been performed to investigate correlations between the IC readouts for a 226 Ra source and room temperature, ambient pressure, relative humidity and radon concentration in air in the same laboratory room. The graphs in figure 10 illustrate the significant correlation (ρ = 0.84) between temperature and (averaged) IC currents, whereas the other environmental conditions have a lower impact (−0.2 < ρ < 0.2). This suggests that the seasonal variations in the IC signals at ENEA may find their origin in temperature variations in the laboratory.
Since multiple measurements were performed during day and night, the readouts could be investigated for diurnal modulations as well. For each hour of the day an average value was calculated. The average temperature over this 49 d period    shows a daily cycle with minimum values (23.08 °C) in the morning and maximum values (23.50 °C) in the afternoon. The average IC current shows nominally less variation (0.005%), but follows a similar pattern. The close correlation between the IC current and temperature variations are immediately apparent when plotting them as a z-score (z = (x − µ)/σ) as a function of time, as shown in figure 11. Since the diurnal modulations in the IC are proportional to and synchronous with the temperature changes, causality may be inferred. The specifications of the electrometer mention a temperature coefficient of 0.15%/ °C in the 200 pA range. The correlation plots reveal a slope of 0.1%/°C for an average current of 0.71 nA. This study is a good illustration of the point raised that one should rule out instrumental uncertainties before reverting to new physics [2,36,37].

226 Ra series @BIPM
The BIPM (located in France) houses the SIR [33], a system of two Centronics IG11 ICs used as long-term reference instruments by which mono-radionuclide solutions with standardised activities can be compared for equivalence. The stability of the SIR is monitored with 226 Ra check sources and the residuals from exponential decay between 2001 and 2015 for source #4 in IC #389 are presented in figure 12. The residuals are small, mostly within 0.05%, and in the annual averages of figure 13 the residual sinusoidal effect-if any-appears to be in the order of A = 0.004 (3)% and phase a = 4 d. This is an order of    magnitude smaller than the natural dispersion of the data, out of phase with Earth-Sun distance, and firm evidence of the invariability of the 226 Ra decay constant to solar proximity.

226 Ra series @JRC
The Joint Research Centre (JRC) of the European Commission contributes to the establishment of a common measurement system of activity through its radionuclide metrology laboratory in Geel (Belgium). Two 226 Ra sources (#1 and #2) are frequently measured in the IG12 welltype IC (20 th Century Electronics, UK) filled with argon to 2 MPa. The ionisation current is measured by sampling a voltage over an external feedback air-spaced capacitor [73]. In off-line data analysis, it is corrected for average background signal and decay. Figures 14 and 15 show the residuals from a smooth decay curve obtained between 2005 and 2015 with sources #1 and #2, respectively. The current readouts (66 pA) from source #1 reveal a bimodal pattern, tentatively ascribed to occasional leakage of radon and progeny from the metal container. Source #2 is more active and its residuals are much smoother, however its decay-corrected current (139 pA) had to be compensated for a quasi-parabolic increase of 0.092% in 10 years. The latter is likely due to ingrowth of 210 Pb, assuming that the 226 Ra was not in perfect equilibrium with its daughter nuclides when the source was produced. A weighted mean of the weekly averages of the residuals is presented in figure 16: there is no indication of an annual effect (A = 0.003 (2)%, a = 363 d).

226 Ra series @NPL
At the NPL (UK) ICs are intensively used for secondary standardisation of activity. A long history of 226 Ra check source measurements were provided for two well-type re-entrant ICs: a PA782 (2 MPa argon gas, steel inner well) and a Vinten (1 MPa nitrogen gas, 3 mm Al inner well). Figure 17 shows 4306 raw decay-corrected current readouts in the PA782 from 1993 to 2016. The apparent small systematic shifts are caused by application of changing calibration factors. The data were analysed in a pragmatic manner by applying a renormalisation for every    The 4017 current readouts obtained with the Vinten (figure 20) show even less dispersion, but make noticeable jumps on long-term due to recalibrations. Applying renormalisation per calendar year and removal of 0.6% of extreme data, the residual plot in figure 21 was obtained and the averages in figure 22. In spite of the crude renormalisation procedure, there is only a small residual trend in the annual averages (A = 0.005 (1)%, a = 73 d).

226 Ra series @NMISA
Additional evidence was collected from the southern hemisphere, at NMISA (South Africa) and ANSTO (Australia) (see next section). The 226 Ra readouts between 1994 and 2015 (figure 23) in the Isocal IV well-type IC at NMISA showed large variability and regular adjustments were done to keep them within specifications. The averages in figure 24 do not have the required precision to make statements about     sub-permille variations, but this case exemplifies the notion that instrumental instabilities can be significant and should be considered prior to postulating new physics.

226 Ra series @ANSTO
ANSTO (Australia) provided 9 data sets of IC measurements of 226 Ra sources#1, #3, #4, #5, #6, #7 in standard as well as special configurations (source #4 in vial, #5 in ampoule, and #7 in Al Au). The IC is a TPA Mk-II filled with 2 MPa of argon and operated at a bias of 520 V. Ionisation current is measured with a Keithley 6517A electrometer. A selection of 4 sets of residuals from an exponential curve are presented in figures 25-28. All data were renormalised after mid February 2015, when a new electrometer was brought in use. The latter had a noticeable effect on the background current and readout for low-activity sources. In figure 29 a mean is shown from 7 data sets for sources #4-7. There is some residual time dependence, but annual effects are negligibly low (A = 0.005 (3)%, a = 256 d) also in the southern hemisphere.
ANSTO kept additional records of the response of a medical calibrator (TPA ionisation chamber with Keithley electrometer) to a 226 Ra reference source. The statistical precision of these data is in the 1% range (see figure 30), but averages of the 1749

209 Po @JRC
Pommé and Benedik [76] published an improved half-life value for 209 Po based on the continuous measurement of emitted alpha particles from two drop-deposited sources in close geometry with a planar silicon detector (PIPS © ). The decay curve of source #1 is presented in figure 40 (and of source #2 in [76]). The residuals are purely of statistical nature, and therefore the annual oscillations in figure 41 (A = 0.006 (5)%, a = 6 d) are insignificant. This type of measurement is quasi-free of interference because the alpha particles have a high energy of 5 MeV and can be easily separated from electronic noise in the detection chain. The background signal is close to zero and the geometry was stable because the 209 Po source was resting in a source mount placed directly on the detector housing in a vacuum chamber and the whole set-up remained untouched for two years.

Decay characteristics
Americium-241 (432.6 (2) a) decays 100% by α emission to 237 Np, mostly populating the excited level at 59.54 keV. There is a small spontaneous fission branch of 3.6 (9) × 10 −10 %. Two (partly converted) characteristic γ transitions useful for spectrometer calibration at low energy are 26.34 keV and 59.54 keV. The main alpha emission energy is at 5.5 MeV. This radionuclide is frequently used in calibration sources for gamma and alpha spectrometry.

241 Am @JRC
Whereas the 209 Po experiment in section 2.8 is an example of how an alpha emitter can be measured free of interference and with stable counting efficiency, the opposite can be realised by applying unfavourable measurement conditions. At the JRC, an 241 Am source was used for checking the stability of an x-ray counter with defined solid angle [77] in the frame of an 55 Fe half-life experiment [78] (see part II [58] of this trilogy), but eventually turned out to be unsuited for the task. The alpha particles were stopped by a Be window and the photons were measured in a proportional counter (PC) at a counter gas pressure of 1.14 × 10 5 Pa (compared to a reference pressure vessel). The count rate (figure 42) appeared to increase as a function of time, tentatively ascribed to the ingrowth of 237 Np and/or rising of the room temperature from 19 °C to 22 °C and later 24 °C ( figure 43). Possibly, small changes in the detector volume and threshold settings may have affected the counting efficiency for the wide range of photons (and conversion electrons) emitted in 241 Am and 237 Np decay (figure 44), whereas for the 0.6-6 keV x-rays from 55 Fe it remained fairly stable (close to 100% efficiency). The instabilities in the measurement conditions seemingly support the idea of variability of decay constants (figure 45) with an amplitude of A = 0.101 (16)% (a = 104 d) or half that size in the period from mid 2004 to mid 2005 (with laboratory temperatures within 18.6 °C-22.9 °C). In this context, publication of a failure report is instructive.

241 Am @SCK
The γ-ray spectrometry service of the SCK•CEN (Belgium) provided 8 data sets of quality control measurements of a mixed 241 Am-152 Eu source on HPGe spectrometers #8, 10, 11, 13, 16, 25, 26, 27 between 2008 and 2016. The background-and decay-corrected area of the 59 keV peak for each detector (see e.g. figure 46 for detector #10) shows a quasilinearly increasing trend with time and a jump in 2011 due to a change in data acquisition system [79]. The trend probably results from uncompensated count loss by pulse pileup     [80]. The data groups have been linearised and connected by means of the fit of two slopes and a scaling factor. The residuals have varying statistical accuracy, mainly depending on the detection efficiency at 59 keV, and also the stability for annual oscillations is largely different from one detector to another. Three groups of results were averaged: two detectors showing no annual effects in figure 47  The amplitudes (and phases) of the oscillation effects in each detector are almost identical for the 152 Eu data (see part III [59]), as can be verified in figure 50. They are mostly likely caused by seasonal effects on the detection efficiency, possibly through temperature effects on the geometry and electronics. One can exclude an explanation through changes in the decay constants in correlation with Earth-Sun distance, because the most stable data sets confirm the invariability of the 241 Am decay constant down to sub-permille level.

241 Am @PTB
At the PTB, 704 decay rate measurements were performed between 2014 and 2016 by means of a commercial TriCarb 2810 TR liquid scintillation counter. Two 241 Am and one background sample were prepared with Ultima Gold AB and water in glass vials. The duration of individual measurements was 12 h in all cases. The net counting rate was about 1200 s −1 and the relative statistical uncertainty was about 0.014%. One outlier (December 2014) was removed from the data sets. The background-and decay-corrected count rates show a slightly negative slope with time (figure 51). A possible explanation for this trend could be sample instability due to slight colour quenching [81]. Rate-related nonlinearity of the counter is less plausible considering that the counting rates did not vary much due to the long half-life of 241 Am. After having applied a linear correction, the average

230 U @JRC
At the JRC, the decay of 230 U has been followed between November 2010 and mid 2011 with 5 detectors [82] (PIPS © alpha particle counter at defined solid angle, liquid scintillation counter, CsI sandwich spectrometer, HPGe γ-spectrometer, and PIPS © in 2π geometry [29]). The residuals to the exponential fits for parent and daughter nuclides have been published [82]. The averaged residuals over a period of nearly 200 d in figure 53 (excluding data affected by the ingrowth of the daughter products) show stability at a sub-permille level (A = 0.007 (7)%, a = 173 d). Since not a full year was covered, one could argue that oscillation effects may have been partly obscured by fitting the best matching exponential function, but the presence of annual oscillations at a permille level can be excluded.

Decay characteristics
Thorium-228 (T 1/2 = 1.9126 (9) a) decays 100% by alpha emission to 224 Ra (3.631 (2) d). The main alpha emission energy is at 5.4 MeV. The 228 Th decay can also be measured through characteristic γ rays of 224 Ra at 84 keV, 216 keV and some less intense peaks at higher energies.

228 Th @NIST
At the NIST, the decay of a 228 Th source has been measured in IC 'A' 70 times between 1968 and 1978 [85]. Smoothly varying correction factors (<0.03%) were applied to compensate for geometrical instability of the source holder [86], which explains some remaining auto-correlation effects in the residuals of figure 54. In spite of the slight trending, the average of the residuals (figure 55) show absence of annual oscillations at permille level (A = 0.031 (22)%, a = 327 d).

Conclusions
The 226 Ra decay curves from different laboratories show differences in stability which are uncorrelated in amplitude or time, but are strongly dependent on source activity and changes in the measurement set-up. The observed oscillations in the decay rates are not in phase with Earth-Sun distance, nor mutually coherent. Instability in the instrument and its local environment are the most plausible root cause of the variation of the detector signals. On an annual time scale, the decay curves show no obvious synchronous perturbations that could hint to influence from cosmic events. The most stable measurements confirm that the alpha decay of 226 Ra is purely exponential: if annual modulations of the 226 Ra decay constants exist, their amplitude must be less than A = 0.0025 (18)%. The 209 Po, 241 Am and 230 U decay constants are stable within A < 0.01% and 228 Th within 0.03%.