Evidence against solar influence on nuclear decay constants

The hypothesis that proximity to the Sun causes variation of decay constants at permille level has been tested and disproved. Repeated activity measurements of mono-radionuclide sources were performed over periods from 200 days up to four decades at 14 laboratories across the globe. Residuals from the exponential nuclear decay curves were inspected for annual oscillations. Systematic deviations from a purely exponential decay curve differ from one data set to another and are attributable to instabilities in the instrumentation and measurement conditions. The most stable activity measurements of alpha, beta-minus, electron capture, and beta-plus decaying sources set an upper limit of 0.0006% to 0.008% to the amplitude of annual oscillations in the decay rate. Oscillations in phase with Earth’s orbital distance to the Sun could not be observed within a 10−6 to 10−5 range of precision. There are also no apparent modulations over periods of weeks or months. Consequently, there is no indication of a natural impediment against sub-permille accuracy in half-life determinations, renormalisation of activity to a distant reference date, application of nuclear dating for archaeology, geo- and cosmochronology, nor in establishing the SI unit becquerel and seeking international equivalence of activity standards.

As much as the instability claims attract interest as inspiration for new physical theories and applications [14,15], if true they would have major implications on traceability and equivalence in the common measurement system of radioactive substances. Variability of decay constants at permille level would limit the precision by which a half-life value could be assigned to a radionuclide, as well as the accuracy by which the SI-unit becquerel could be established through primary standardisation [26] and international equivalence demonstrated through key comparisons and the Système International de Référence (SIR) [27]. The implications at metrological level would eventually affect science built on the decay laws, from renormalisation of activity to a reference date for nuclear dosimetry to precise nuclear dating for geo-and cosmochronology.
At the heart of this controversy are the metrological difficulties inherent to the measurement of half-lives [28][29][30]. From a metrological point of view, it is obvious that instruments, electronics, geometry and background may vary due to external influences such as temperature, pressure, humidity and natural or man-made sources of radioactivity. Claims of variability of half-lives on the basis of deviations from an exponential decay curve can only be considered when the instrumental effects have been fully compensated and/or accounted for in the uncertainty budget. Jenkins et al. [9] claim to have done so before proposing their hypothesis that permille sized seasonal variations of decay rates of 226 Ra and 36 Cl are caused by solar influences on their decay constants [6][7][8]. Evidence has been collected to demonstrate instabilities in the decay of other radionuclides [10,11] and by means of timefrequency analysis periodicity at shorter and longer term than 1 year have been claimed [11][12][13]. However, this interpretation is being challenged by the publication of data sets confirming a close adherence to exponential decay with residuals in the 10 −5 range [16,18,20,21,23].
Authors of both convictions expressed the need for collecting evidence for different radionuclides measured with different detection techniques [7,11,13,18,23]. At national metrology institutes (NMIs) taking responsibility for establishing the unit becquerel, monoradionuclide sources are kept and regularly measured for standardisation purposes as well as for determining half-lives. In addition, gamma-ray spectrometry laboratories keep records of quality control measurements on their spectrometers which provide useful information on long-term trends in activity measurements of a reference source. In this work, the hypothesis that decay constants vary through solar influence in phase with Earth-Sun orbital distance has been tested through the analysis of a unique collection of activity measurements repeated over periods of 200 days up to four decades at 14 laboratories distributed across the globe.  65 Zn, 207 Bi), and a mixture of electron capture and beta minus/plus decay ( 152 Eu). More than 60 data sets were collected, some of which were performed over several decades. Some data sets excel in precision, others reveal vulnerability of different measurement techniques to external conditions. Characteristics of the data sets are summarised in Table 1.
Exponential decay curves were fitted to the data and the residuals were inspected for annual modulations. 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, e.g. due to gas loss from an ionisation chamber, uncompensated count loss through pulse pileup in a spectrometer, activity build-up from decay products in a source, etc. The residuals were binned into 8-day 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 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. The fitted amplitude values can be considered insignificant if they are of comparable magnitude as their estimated standard uncertainty (see Table 1).

Discussion
The controversy started with the interpretation [7,8] of A ≈ 0.15% modulations in the decay rate measurements of a sealed 226 Ra reference source in an IC at the PTB between 1983 and 1998. The averaged residuals, shown in Fig. 1A, have a sinusoidal shape with amplitude A = 0.083 (2)% and phase a = 59 days. An explanation through solar influence on the alpha or beta decay constants of nuclides in the 226 Ra decay series seems unlikely, since the residuals are out of phase with the annual variation of the inverse square of the Sun-Earth distance, 1/R 2 (renormalised to 0.15% amplitude in the Figs. 1-2 of this work). The real cause is of instrumental nature, since the modulations were significantly reduced after changing the electrometer of the IC [22,25]. There is a remarkable correlation with average seasonal changes of radon concentration in air (A = 16 (2)%, a = 57 days) measured inside the laboratory from 2010 to 2016, but causality has not been proven.
At other institutes, annual modulations of smaller amplitude and different phase have been observed, which demonstrates the local character of the non-exponential behaviour. The data sets for 226 Ra show a different level of instrumental instability, but the most stable 226 Ra measurements prove invariability of its decay constant against annual modulations within 0.0025% to 0.005%. An example is shown in Fig. 1B, comprising 4000 226 Ra ionisation current measurements over a period of 22 years at the NPL.
Stability is best achieved where the detector efficiency is least influenced by geometrical and environmental variations and where the signal of the radiation is easily separated from interfering signals and electronic noise. For example, measuring 241 Am decay through alpha-particle detection with close to 100% detection efficiency would typically be more stable than through fractional detection of its low-energy photon emissions in a gas-filled pro-portional counter. For the alpha emitters, 209 Po, 226 Ra, 230 U, and 241 Am, the invariability of the decay constants was confirmed within the 10 −5 level.
Comparably lower stability could be anticipated for beta-minus decay. Parkhomov [10] found 7 data sets of beta-decaying radionuclides exhibiting periodic variations of 0.1% to 0.3% amplitude with a period of 1 year. Fischbach et al. [8,14,15] suggested new theories in which the variable flux of anti-neutrinos from the Sun would significantly modulate the probability for β − emission. From metrological point of view, instability in the detection efficiency for a pure beta emitter can be expected due to the continuous energy distribution of the beta particle which makes the count rate subject to threshold variations at the low-energy side and possibly incomplete detection probability at the high-energy side. However, measurements based on γ-ray emission subsequent to the β − emission -possibly through the decay of a short-lived daughter nuclide -can be made more robust.
High-quality measurement data were collected for β − emitters in Table 1, mostly obtained by IC but also with primary activity measurement techniques such as the triple-to-double coincidence ratio (TDCR) method and live-timed 4π β-γ anti-coincidence counting (LTAC). It was demonstrated for 36 Cl [20], 60 Co (Table 1) and 90 Sr/ 90 Y [23] that primary standardisation techniques like TDCR and LTAC are more stable than routine counting techniques, because each measurement provides information about the detection efficiency and automatically corrects for its fluctuations. Some IC measurements show remarkable stability, too, and refute the conclusions made about variability of the decay constants as well as the hypothesis of a significant solar influence on the decay rate. In Fig. 2A, averaged residuals for 134 Cs in an IC demonstrate stability within the 10 −5 range. Evidence of stability down to the 10 −5 level was found for the beta minus emitters 60 Co, 90 Sr, 124 Sb, 134 Cs and 137 Cs, and down to the 10 −4 level for 3 H, 14 C, and 85 Kr. These results are in direct contradiction with the permille level oscillations for 3 H, 60 Co, 90 Sr, and 137 Cs reported by Parkhomov [10] and Jenkins et al. [11].
Radionuclides disintegrating by electron capture (EC) and β + decay - 22 Na, 54 Mn, 55 Fe, 57 Co, 65 Zn, 82 Sr/ 82 Rb+ 85 Sr, 109 Cd, 133 Ba, 152 Eu, and 207 Bi -were investigated by the same techniques as α and β − emission and, also here, stability within the 10 −5 to 10 −4 range was observed in most cases. An example is shown in Fig. 2B for 22 Na measured in the same period with the same IC as 134 Cs in Fig. 2A. The tiny modulations in the residuals for both nuclides are highly correlated, which is most likely a seasonal effect of instrumental origin. Clear evidence of annual modulations being of instrumental origin has been found in thousands of γ-ray spectrometry measurements with 8 HPGe detectors at the SCK, as shown in Fig. 3: the modulations in measured decay rates for the alpha decay of 241 Am and mixed EC, β − , and β + decay of 152 Eu are highly correlated but the amplitude differs from one detector to another. In other words, the modulations are linked to the instrument, not to the type of decay.

Conclusions
The experimental data in this work are typically 50 times more stable than the measurements on which recent claims for solar influence on the decay constants were based. The observed seasonal modulations can be ascribed to instrumental instability, since they vary from one instrument to another and show no communality in amplitude or phase among -or even within -the laboratories. The exponential decay law is immune to changes in Earth-Sun distance within 0.008% for most of the investigated α, β − , β + and EC decaying nuclides alike.
Owing to the invariability of decay constants, there is no impediment to the establishment of the becquerel through primary standardisation at 0.1% range accuracy nor to the demonstration of equivalence of activity at international level over a time span of decades. It is normal for repeated activity measurements to show varying degrees of instability of instrumental and environ-mental origin and such auto-correlated variability should be taken into account next to statistical variations when setting alarm levels in quality control charts. Taking into account such instabilities and adhering to proper uncertainty propagation, no fundamental objections need to be made against half-life measurement with sub-permille uncertainties, nor against applying exponential decay formulas to calculate activity at a future or past reference time or to perform accurate nuclear dating. A. Annual average residuals from exponential decay for 226 Ra activity measurements with an IC at PTB from 1983 to 1998. The line represents relative changes in the inverse square 1/R 2 of the Earth-Sun distance, normalised to an amplitude of 0.15%. B. Same for 226 Ra activity measurements with the Vinten IC of NPL from 1993 to 2016, after renormalisation per calendar year.