Evidence against solar influence on nuclear decay constants

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Evidence against solar influence on nuclear decay constants

Pommé, S.; Stroh, H.; Paepen, J.; Van Ammel, R.; Marouli, M.; Altzitzoglou,

T.; Hult, M.; Kossert, K.; Nähle, O.; Schrader, H.; Juget, F.; Bailat, C.;

Nedjadi, Y.; Bochud, F.; Buchillier, T.; Michotte, C.; Courte, S.; Van Rooy, M.

W.; Van Staden, M. J.; Lubbe, J.; Simpson, B. R. S.; Fazio, A.; De Felice, P.;

Jackson, T. W.; Van Wyngaardt, W. M.; Reinhard, M. I.; Golya, J.; Bourke,

S.; Roy, T.; Galea, R.; Keightley, J. D.; Ferreira, K. M.; Collins, S. M.;

Ceccatelli, A.; Unterweger, M.; Fitzgerald, R.; Bergeron, D. E.; Pibida, L.;

Verheyen, L.; Bruggeman, M.; Vodenik, B.; Korun, M.; Chisté, V.; Amiot,

M.-N.

https://publications-cnrc.canada.ca/fra/droits

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Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Evidence

against

solar

influence

on

nuclear

decay

constants

S. Pommé

a

,

∗

,

1

_,

_{H. Stroh}

a

_,

_{J. Paepen}

a

_,

_{R. Van Ammel}

a

_,

_{M. Marouli}

a

_,

_{T. Altzitzoglou}

a

_,

M. Hult

a

,

K. Kossert

b

,

O. Nähle

b

,

H. Schrader

b

,

F. Juget

c

,

C. Bailat

c

,

Y. Nedjadi

c

,

F. Bochud

c

,

T. Buchillier

c

,

C. Michotte

d

,

S. Courte

d

,

M.W. van Rooy

e

,

M.J. van Staden

e

,

J. Lubbe

e

,

B.R.S. Simpson

e

,

A. Fazio

f

,

P. De Felice

f

,

T.W. Jackson

g

,

W.M. Van Wyngaardt

g

,

M.I. Reinhard

g

,

J. Golya

g

,

S. Bourke

g

,

T. Roy

h

,

R. Galea

h

,

J.D. Keightley

i

,

K.M. Ferreira

i

,

S.M. Collins

i

,

A. Ceccatelli

j

,

M. Unterweger

k

,

R. Fitzgerald

k

,

D.E. Bergeron

k

,

L. Pibida

k

,

L. Verheyen

l

,

M. Bruggeman

l

,

B. Vodenik

m

,

M. Korun

m

,

V. Chisté

n

,

M.-N. Amiot

n

a_European_Commission,_Joint_Research_Centre_(JRC),_Retieseweg_111,_{B-2440 Geel,}_Belgium b_{Physikalisch-Technische}_{Bundesanstalt}_(PTB),_Bundesallee_100,_{38116 Braunschweig,}_Germany c_Institut_de_{Radiophysique,}_Lausanne_(IRA),_Switzerland

d_Bureau_{International}_des_Poids_et_Mesures_(BIPM),_Pavillon_de_Breteuil,_{92310 Sèvres,}_France

e_{Radioactivity}_Standards_Laboratory_(NMISA),₁₅_Lower_Hope_Road,_{Rosebank 7700,}_Cape_Town,_South_Africa

f_National_Institute_of_Ionizing_Radiation_Metrology_(ENEA),_Casaccia_Research_Centre,_Via_{Anguillarese,}_301—S.M._Galeria_I-00060_Roma,_C.P._2400,_I-00100

Roma A.D.,Italy

g_Australian_Nuclear_Science_and_Technology_Organisation_(ANSTO),_Locked_Bag_2001,_Kirrawee,_{NSW 2232,}_Australia h_National_Research_Council_of_Canada_(NRC),₁₂₀₀_Montreal_Road,_Ottawa,_ON,_K1A0R6,_Canada

i_National_Physical_Laboratory_(NPL),_Hampton_Road,_Teddington,_{Middlesex TW11 OLW,}_UK

j_Terrestrial_Environment_Laboratory,_IAEA_Environment_{Laboratories,}_Department_of_Nuclear_Sciences_and_{Applications,}_{International}_Atomic_Energy_Agency

(IAEA),ViennaInternationalCentre,POBox100,1400Vienna,Austria

k_Physical_Measurement_Laboratory,_National_Institute_of_Standards_and_Technology_(NIST),₁₀₀_Bureau_Dr.,_{Gaithersburg,}_{MD 20899-8462,}_USA l_Belgian_Nuclear_Research_Centre_(SCK

·CEN),Boeretang 200,B-2400 Mol,Belgium m_Jožef_Stefan_Institute_(JSI),_{Jamova 39,}_{1000 Ljubljana,}_Slovenia

n_CEA,_LIST,_Laboratoire_National_Henri_Becquerel_(LNHB),_Bât.₆₀₂_PC_111,_CEA-Saclay_{91191 Gif-sur-Yvette}_cedex,_France

a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Articlehistory:

Received1July2016

Receivedinrevisedform18August2016 Accepted19August2016

Availableonline24August2016 Editor:V.Metag Keywords: Half-life Decayconstant Uncertainty Radioactivity Sun Neutrino

ThehypothesisthatproximitytotheSuncausesvariationofdecayconstantsatpermillelevelhasbeen tested and disproved. Repeatedactivity measurements of mono-radionuclide sources wereperformed overperiodsfrom200daysuptofourdecadesat14laboratoriesacrosstheglobe.Residualsfromthe exponentialnucleardecaycurves wereinspectedforannualoscillations.Systematicdeviations froma purelyexponentialdecaycurvedifferfromonedatasettoanotherandare attributabletoinstabilities inthe instrumentationand measurementconditions.The moststableactivitymeasurements ofalpha, beta-minus, electroncapture,and beta-plusdecayingsourcesset anupper limitof0.0006% to0.008% to the amplitude of annual oscillations in the decay rate. Oscillations in phase with Earth’s orbital distance tothe Suncould not be observedwithin a10−6 _to ₁₀−5 _range _of_precision._There _are _also

noapparent modulations overperiods ofweeks ormonths. Consequently,there isno indicationofa naturalimpedimentagainstsub-permilleaccuracyinhalf-lifedeterminations,renormalisationofactivity toadistantreferencedate,applicationofnucleardatingforarchaeology,geo- andcosmochronology,nor inestablishingtheSIunitbecquerelandseekinginternationalequivalenceofactivitystandards.

2016TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3_.

*

Correspondingauthor.

E-mailaddress:[email protected](S. Pommé).

1 _Fax:₊₃₂₍₀₎₁₄₅₇₁_864.

1. Introduction

The exponential-decay law is one of the most famous laws of physics, already carvedin stone since the pioneering work of Ernest Rutherford [1], Maria Skłodowska-Curie [2] and others.It has withstood numerous tests [3–5] demonstrating that the

de-http://dx.doi.org/10.1016/j.physletb.2016.08.038

0370-2693/2016TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP3_.

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282 S. Pommé et al. / Physics Letters B 761 (2016) 281–286

cayofaradionuclidecanbecharacterisedsolelybyasingle decay constant – or equivalently by the half-life – which is invariable in spaceandtime. However, observations ofperiodic oscillations inmeasured decay ratesof radioactivesources [6–13] have been heavily debated in the last decade [6–25]. Controversy arose at two levels: (i) atthe observational level, withexperimental data setsshowingsigniﬁcantdifferencesinstabilityofdecayrateswith time,and(ii)attheinterpretationallevel,eitherascribingthe ob-servedmodulationstoinstabilitiesinthedetectionsystem,or ad-vocatingnewphysicstoexplainvariabilityinthedecayconstants. As much as the instability claims attract interest as inspira-tionfornewphysicaltheoriesandapplications[14,15],iftruethey wouldhavemajor implicationsontraceability andequivalencein thecommonmeasurementsystemofradioactivesubstances. Vari-ability of decay constants at permille level would limit the pre-cision by whicha half-life value could be assignedto a radionu-clide,aswellastheaccuracybywhichtheSI-unitbecquerelcould be established throughprimary standardisation [26] and interna-tionalequivalencedemonstratedthroughkeycomparisonsandthe Système International de Référence (SIR) [27]. The implications atmetrological levelwouldeventually affect sciencebuilt onthe decay laws, from renormalisation of activity to a reference date fornucleardosimetry toprecise nucleardating forgeo- and cos-mochronology.

At the heart of this controversy are the metrological diﬃcul-ties inherent to the measurement of half-lives [28–30]. From a metrologicalpointofview,itisobviousthatinstruments, electron-ics,geometryandbackgroundmayvaryduetoexternalinfluences suchastemperature,pressure,humidityandnaturalorman-made sources of radioactivity. Claims of variability of half-lives on the basis ofdeviations from an exponential decaycurve can only be consideredwhentheinstrumentaleffectshavebeenfully compen-sated and/or accountedfor in the uncertainty budget. Jenkins et al. [9] claim to have done so before proposing their hypothesis thatpermillesizedseasonalvariationsofdecayratesof226_Ra_and 36_Cl_are_caused_by_solar_influences_on_their_decay_constants_[6–8]_.

Evidencehasbeencollectedtodemonstrateinstabilitiesinthe de-cayofotherradionuclides[10,11]andbymeansoftime-frequency analysisperiodicity at shorterand longer termthan 1 year have beenclaimed[11–13]. However, thisinterpretationis being chal-lengedbythepublicationofdatasetsconﬁrmingacloseadherence toexponentialdecaywithresidualsinthe10−5_range_{[16,18,20,21,}

23].

Authors of both convictions expressedthe need for collecting evidence for different radionuclides measured with different de-tectiontechniques[7,11,13,18,23].Atnationalmetrologyinstitutes (NMIs) taking responsibility for establishing the unit becquerel, mono-radionuclide sources are kept and regularly measured for standardisation purposes aswell as fordetermining half-lives.In addition, gamma-ray spectrometry laboratories keep records of quality control measurements on their spectrometerswhich pro-vide usefulinformation onlong-termtrends in activity measure-mentsofareferencesource.Inthiswork,thehypothesis that de-cayconstantsvarythroughsolarinfluenceinphasewithEarth–Sun orbital distancehasbeentestedthrough theanalysisofa unique collectionofactivity measurements repeatedover periodsof 200 daysup to fourdecades at14 laboratoriesdistributedacross the globe.

2. Measurements&analysis

Preciseactivity measurementseries were performedforalpha decay (209Po, 226Ra series, 228Th, 230U, 241Am), beta minus de-cay(3H,14C,60Co,85Kr,90Sr, 124Sb,134Cs,137Cs),electroncapture (54_Mn,55_Fe,57_Co,82,85_Sr,109_Cd,133_Ba),_a_mixture_of_electron

cap-tureandpositrondecay(22Na,65Zn,207Bi),andamixtureof elec-troncaptureandbetaminus/plusdecay(152Eu).Morethan60data sets were collected, some of which were performedover several decades.Some datasets excelinprecision, othersreveal vulnera-bilityofdifferentmeasurementtechniquesto externalconditions. CharacteristicsofthedatasetsaresummarisedinTable 1.

The measurement techniques employed are as follows: ioni-sation current measurements in a re-entrantionisation chamber (IC)orahospitalcalibrator(HIC)[31,32],netarea analysisof full-energy

γ

-ray peaks (and integral spectrum counting) by

γ

-ray spectrometry with a HPGe detector (HPGe) [33], particle count-ing in a planar silicon detector in quasi-2

π

configuration (PIPS) [34],X-raycountingatasmalldefinedsolidanglewithagas-filled proportionalcounter(PC)[35,36],live-timed

β

–

γ

anti-coincidence counting(LTAC)[37],triple-to-doublecoincidencecountingwitha liquid scintillationvial andthreephotodetectors (TDCR)[38], liq-uidscintillation counting(LSC)[38],particleandphotoncounting inasandwichCsI(Tl)spectrometer(CsI)[39],internalgascounting (IGC) [40],and

α

-particlecountingatasmalldeﬁnedsolid angle withalargeplanarsilicondetector(

α

DSA)[35,36].Anoverviewof standardisationtechniquesandtheirsourcesoferrorcanbefound inthespecialissues44(4)and52(3)ofMetrologia[41,42]and ref-erencesin[25,28].

Exponentialdecaycurveswereﬁttedtothedataandthe resid-uals were inspected forannual modulations. The data sets were ﬁrstcompensatedfor(1)thepresenceofoccasionaloutliervalues, (2)abruptsystematicchangesinthedetectorresponse,e.g.dueto replacementoftheelectronicsorrecalibrationsoftheinstrument, and (3) systematic drift extending over periods of more than 1 year,e.g. duetogas lossfroman ionisationchamber, uncompen-sated count loss through pulsepileup in a spectrometer, activity build-upfromdecayproducts inasource,etc.Theresiduals were binned into 8-day periods of the year andaveraged to obtain a reduced set of (maximum) 46 residuals evenly distributed over the calendar year. To the averaged residuals, a sinusoidal shape Asin

(

2

π

(

t

+

a

)/

365

)

hasbeenfittedinwhich A istheamplitude, t istheelapsednumberofdayssinceNewYear,anda isthephase shift expressed in days.The fittedamplitude values can be con-sideredinsignificantiftheyare ofcomparablemagnitudeastheir estimatedstandarduncertainty(seeTable 1).

3. 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_between₁₉₈₃_and_1998.

The averagedresiduals,showninFig. 1A,havea sinusoidalshape withamplitude A

=

0

.

083 (2)% andphasea

=

59 days.An expla-nation through solar influence on the alpha or beta decay con-stants ofnuclidesin the226_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

/

R2 _{(renormalised} _to

0.15%amplitudeintheFigs. 1–2ofthiswork).Therealcauseisof instrumental nature, since the modulations were signiﬁcantly re-duced afterchanging theelectrometer ofthe IC [22,25].There is a remarkable correlation withaverage seasonalchanges of radon concentrationinair( A

=

16 (2)%,a

=

57 days)measuredinsidethe laboratoryfrom2010to2016,butcausalityhasnotbeenproven.

At other institutes, annual modulations of smaller amplitude anddifferentphase havebeen observed,whichdemonstrates the localcharacterofthenon-exponentialbehaviour.Thedatasetsfor

226_Ra _show _a _different _level _of _instrumental _instability, _but _the

most stable 226_Ra _measurements _prove _{invariability} _of _its _decay

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Table 1

Characteristicsofthedecayratemeasurementsetsanalysed.Themethodacronymsareexplainedinthetext.Theperiodindicatestheﬁrstandlastyearinwhichdatawere collected.Thestandarddeviationisanindicationoftheuncertaintyontheannualaverageddata(maximum46data,covering8-dayperiods),derivedfromthespreadof theinputdataandtheinversesquarerootofthenumberofvaluesineachdatagroup.Theamplitudeandphasearetheresultoftheﬁtofasinusoidalfunctiontothe averageddata.Inboldaretheamplitudesat10−6_–10−5_level._The_estimated_standard_uncertainty_on_the_amplitude_is_indicated_between_parentheses,_its_order_of_magnitude

correspondingtothatofthelastdigitofthevalueofA.

Decay mode(s)

Nuclide Laboratory Method Period (year) #Data Rel.std devin% AmplitudeA in% Phaseshifta indays α 209_Po _JRC _PIPS _2013–2016 ₁₅₃₉ _0.024 0.006 (5) 6 α+β− 226_Ra _PTB _IC _1983–1998 ₁₉₇₃ _0.011 _{0.083 (2)} ₅₉ α+β− 226_Ra _PTB _IC _1999–2016 ₂₁₈₄ _0.005 _{0.016 (1)} ₁₉₄ α+β− 226_Ra _ENEA _IC _1992–2015 ₁₆₁ _0.025 _{0.043 (5)} ₃₂₄ α+β− 226_Ra _NIST _{IC #1} _2008–2016 ₉₉ _0.016 _{0.015 (3)} ₂₅₅ α+β− 226_Ra _NIST _{IC #2} _2012–2016 ₂₇₂ _0.036 _{0.002 (8)} ₈ α+β− 226_Ra _BIPM _IC _2001–2015 ₁₃₆ _0.015 0.004 (3) 4 α+β− 226_Ra _JRC _IC _2005–2015 ₁₇₃₇ _0.005 0.003 (2) 363 α+β− 226_Ra _NPL _{IC #1} _1993–2016 ₄₀₅₅ _0.014 _{0.0025 (18)} ₆₀ α+β− 226_Ra _NPL _{IC #2} _1993–2016 ₃₉₉₆ _0.005 _{0.005 (1)} ₇₃ α+β− 226_Ra _NMISA _IC _1992–2015 ₂₇₆ _0.343 _{0.106 (60)} ₆₇ α+β− 226_Ra _ANSTO _IC _2012–2015 ₇₀₀ _0.015 _{0.005 (3)} ₂₅₆ α+β− 226_Ra _ANSTO _HIC _2008–2014 ₁₇₄₉ _0.077 _{0.009 (18)} ₈₂ α+β− 226_Ra _LNHB _{IC #1} _1998–2016 ₄₅₅ _0.026 _{0.026 (6)} ₃₂₈ α+β− 226_Ra _LNHB _{IC #2} _1998–2016 ₄₉₈ _0.028 _{0.042 (7)} ₂₉₄ α 228_Th _NIST _IC _1968–1978 ₇₀ _0.107 _{0.031 (22)} ₃₂₇

α 230_U _JRC _α_{DSA, PIPS, CsI, LSC, HPGe} _2010–2011 ₅₄₅₁ _0.083 _{0.007 (7)} ₁₇₃

α 241_Am _JRC _PC _2004–2008 ₂₄₅ _0.022 _{0.101 (16)} ₁₀₄ α 241_Am _SCK _{HPGe #8} _2008–2016 ₄₃₀ _0.13 _{0.024 (28)} ₅₅ α 241_Am _SCK _{HPGe #26} _2013–2016 ₁₆₆ _0.12 _{0.002 (23)} ₃₀₄ α 241_Am _SCK _{HPGe #11} _2008–2016 ₄₀₂ _0.12 _{0.055 (22)} ₂₄₂ α 241_Am _SCK _{HPGe #16} _2008–2016 ₃₈₂ _0.13 _{0.079 (26)} ₂₉₀ α 241_Am _SCK _{HPGe #25} _2011–2016 ₂₄₅ _0.12 _{0.079 (22)} ₂₃₆ α 241_Am _SCK _{HPGe #10} _2008–2016 ₄₆₆ _0.14 _{0.115 (27)} ₂₅₉ α 241_Am _SCK _{HPGe #27} _2011–2015 ₂₃₈ _0.45 _{0.095 (91)} ₂₈₀ α 241_Am _SCK _{HPGe #13} _2008–2016 ₄₃₄ _0.12 _{0.167 (26)} ₂₃₅ α 241_Am _PTB _LSC _2014–2016 ₅₇₄ _0.004 0.0006 (7) 260 β− 3_H _JRC _LSC _2002–2014 ₇₀₆ _0.112 _{0.048 (24)} ₁₉₇ β− 3_H _NIST _IGC _1961–1999 ₂₁ _0.75 _{0.18 (20)} ₁₄₉ β− 14_C _JRC _LSC _2002–2014 ₇₀₆ _0.075 _{0.013 (16)} ₉₂ β− 14_C _NMISA _TDCR _1994–2014 ₃₂ _0.250 _{0.067 (80)} ₅₉ β− 60_Co _NIST _IC _1968–2007 ₂₅₀ _0.050 _{0.007 (7)} ₀ β− 60_Co _NIST _LTAC₊_IC _2006–2014 ₂₆₊₇ _0.036 _{0.007 (9)} ₁₈ β− 60_Co _JSI _{HPGe #1–6} _1998–2016 ₁₅₂₅₄ _0.079 _{0.041 (14)} ₁₆₁ β− 85_Kr _NIST _IC _1980–2007 ₉₈ _0.035 _{0.036 (15)} ₁₅₃ β− 90_Sr _PTB _TDCR _2013–2014 ₄₄₉₃ _0.009 _{0.004 (2)} ₃₆₂ β− 90_Sr _PTB _IC _1989–2016 ₂₂₀₇ _0.009 _{0.018 (2)} ₂₆ β− 124_Sb _JRC _IC ₂₀₀₇ ₅₉ _0.005 _{0.003 (2)} ₂₄₁ β− 134_Cs _JRC _IC _2010–2015 ₁₀₆₅ _0.002 _{0.0051 (5)} ₄₈ β− 137_Cs _IRA _IC _1984–2012 ₂₇₆ _0.043 _{0.018 (9)} ₃₄₂ β− 137_Cs _NRC _{IC #1–3} _1995–2009 ₆₂ _0.074 0.006 (22) 147 β− 137_Cs _PTB _IC _1997–2016 ₂₁₄₉ _0.005 _{0.014 (1)} ₂₉ β− 137_Cs _NIST _IC _1968–2011 ₂₅₄ _0.034 _{0.004 (6)} ₃₃ β+ , EC 22_Na _JRC _IC _2010–2016 ₄₄₃ _0.003 _{0.0047 (6)} ₅₃ EC 54_Mn _JRC _IC _2006–2009 ₁₅₆ _0.007 _{0.005 (1)} ₂₈ EC 54_Mn _PTB _IC _2010–2016 ₇₁₆ _0.011 _{0.014 (2)} ₇₈ EC 55_Fe _JRC _IC _2004–2005 ₅₉₅ _0.007 _{0.004 (3)} ₁₈₇ EC 57_Co _NIST _IC _1962–1966 ₉₇ _0.089 _{0.055 (22)} ₃₂₄ EC,β+ 65_Zn _JRC _IC _2002–2003 ₁₄₀ _0.026 _{0.008 (4)} ₁₆₃ EC(, β+ ) 82_Sr/82_Rb₊85_Sr _NIST _IC _2007–2008 ₁₅₈ _0.011 _{0.0006 (27)} ₂₄₀ EC(, β+ ) 82_Sr/82_Rb _NIST _HPGe _2007–2008 ₂₃ _0.46 _{0.073 (75)} ₂₅₅ EC 109_Cd _JRC _IC _2006–2010 ₁₂₅ _0.017 _{0.015 (4)} ₁₈ EC 109_Cd _JSI _{HPGe #3, 4} _1998–2016 ₅₄₁₄ _0.139 _{0.035 (24)} ₃₄₆ EC 109_Cd _NIST _IC _1976–1981 ₁₆₇ _0.058 _{0.013 (15)} ₂₂₀ EC 133_Ba _NIST _IC _1979–2012 ₁₃₁ _0.042 _{0.028 (8)} ₇₄ EC,β− ,β+ 152_Eu _IAEA _{HPGe #1, 2} _2010–2016 ₁₄₃ _0.113 _{0.020 (24)} ₁₆₂ EC,β− ,β+ 152_Eu _SCK _{HPGe #8} _2008–2016 ₁₂₂₈ _0.10 _{0.006 (19)} ₂₄₂ EC,β− ,β+ 152_Eu _SCK _{HPGe #26} _2013–2016 ₄₉₉ _0.10 _{0.027 (23)} ₁₇₈ EC,β− ,β+ 152_Eu _SCK _{HPGe #11} _2008–2016 ₁₁₆₈ _0.10 _{0.048 (21)} ₂₈₀ EC,β− ,β+ 152_Eu _SCK _{HPGe #16} _2008–2016 ₁₂₆₀ _0.08 _{0.062 (18)} ₂₈₅ EC,β−_,_β+ 152_Eu _SCK _{HPGe #25} _2011–2016 ₇₂₃ _0.10 _{0.080 (23)} ₂₁₃ EC,β−_,_β+ 152_Eu _SCK _{HPGe #10} _2008–2016 ₁₃₇₄ _0.08 _{0.094 (16)} ₂₀₆ EC,β− ,β+ 152_Eu _SCK _{HPGe #27} _2011–2015 ₆₉₈ _0.16 _{0.155 (34)} ₂₂₈ EC,β− ,β+ 152_Eu _SCK _{HPGe #13} _2008–2016 ₁₂₄₉ _0.11 _{0.161 (24)} ₂₁₄ EC,β− ,β+ 152_Eu _NIST _IC _1976–2011 ₉₆ _0.040 _{0.021 (9)} ₂₁₄ EC,β− ,β+ 152_Eu _PTB _IC _1989–2016 ₂₁₉₉ _0.007 _{0.018 (1)} ₁₁ EC(, β+ ) 207_Bi _NIST _IC _1971–2011 ₁₅₂ _0.05 _{0.004 (11)} ₂₃

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Fig. 1A. Annualaverageresidualsfromexponentialdecayfor226_Ra_activity

measure-mentswithanICatPTBfrom1983to1998.Thelinerepresentsrelativechangesin theinversesquare1/R2_of_the_Earth–Sun_distance,_normalised_to_an_amplitude_of

0.15%.

Fig. 1B. Samefor226_Ra_activity_measurements_with_the_Vinten_IC_of_NPL_from₁₉₉₃

to2016,afterrenormalisationpercalendaryear.

exampleisshowninFig. 1B,comprising4000226_Ra_ionisation

cur-rentmeasurementsoveraperiodof22yearsattheNPL.

Stabilityisbest achievedwherethedetectoreﬃciencyisleast influencedbygeometricalandenvironmentalvariationsandwhere thesignaloftheradiationiseasilyseparatedfrominterfering sig-nals and electronic noise. For example, measuring 241_Am _decay

throughalpha-particle detectionwithclose to100% detection ef-ficiency would typically be more stable than through fractional detectionof its low-energy photon emissionsin a gas-filled pro-portionalcounter. Forthe alpha emitters, 209_Po, 226_Ra, 230_U, _and 241_Am, _the _{invariability} _of _the _decay _constants _was _confirmed

withinthe10−5 _level.

Comparablylowerstability couldbeanticipatedforbeta-minus decay.Parkhomov[10]found7datasetsofbeta-decaying radionu-clidesexhibitingperiodicvariationsof0.1%to0.3%amplitudewith a period of1 year.Fischbach etal. [8,14,15] suggestednew the-ories in which the variable flux of anti-neutrinos from the Sun wouldsigniﬁcantlymodulatetheprobabilityfor

β

−_emission._From

metrologicalpointofview,instabilityinthedetectioneﬃciencyfor apurebetaemittercanbeexpectedduetothecontinuousenergy distributionofthebetaparticlewhich makesthecount rate sub-ject to threshold variations at the low-energy side and possibly

Fig. 2A. Annualaverageresidualsfromexponentialdecayfor134_Cs_activity

measure-mentswiththeIG12ICattheJRCfrom2010to2016.

Fig. 2B. Same for22Na.

incomplete detection probability at the high-energy side. How-ever, measurements based on

γ

-ray emission subsequent to the

β

−_emission_–_possibly_through_the_decay_of_a_short-lived

daugh-ternuclide–canbemademorerobust.

High-quality measurement data were collected for

β

−

emit-ters 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 4

π

β

–

γ

anti-coincidence counting (LTAC). It was demonstrated for 36Cl [20],

60_Co₍_{Table 1}₎_and90_Sr/90_Y_[23]_that_primary_{standardisation}

tech-niques likeTDCRandLTAC aremorestablethanroutinecounting techniques,becauseeachmeasurementprovidesinformationabout the detectioneﬃciencyandautomaticallycorrectsforits fluctua-tions. Some ICmeasurements show remarkablestability,too,and refute the conclusions made about variability of the decay con-stantsaswell asthehypothesisofasigniﬁcantsolarinfluenceon the decay rate. In Fig. 2A, averaged residuals for 134Cs in an IC demonstrate stability within the 10−5 _range. _Evidence _of

stabil-itydowntothe10−5 _level_was_found_for_the_beta_minus_emitters 60_Co,90_Sr,124_Sb,134_Cs_and137_Cs, _and_down_to_the ₁₀−4 _level_for 3_H,14_C,_and85_Kr._These_results_are_in_direct_{contradiction}_with_the

permilleleveloscillationsfor3H,60Co,90Sr,and137Csreportedby Parkhomov[10]andJenkinsetal.[11].

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Fig. 3. Amplitudeofaverageannualoscillationsinthedecayratesof241_Am_and 152_Eu_measured_by_γ_-ray_spectrometry_with₈_HPGe_detectors_at_SCK_between₂₀₀₈

and2016.Theindexreferstothedetector number.Amixed241_Am–152_Eu_point

sourcewasmeasured166–466timesinaﬁxedgeometryatabout11cmfromthe endcapusingthe59 keVlineof241_Am_and_the_{122 keV,}_{779 keV}_and_{1408 keV}

linesof152_Eu.

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. 2Bfor22NameasuredinthesameperiodwiththesameICas

134_Cs_in_{Fig. 2A}_._The_tiny_modulations_in_the_residuals_for_both

nu-clidesarehighly correlated,whichismostlikelyaseasonaleffect ofinstrumental origin. Clear evidence ofannual modulations be-ing ofinstrumental originhasbeen found inthousands of

γ

-ray spectrometrymeasurementswith8HPGedetectorsattheSCK,as showninFig. 3:themodulationsinmeasureddecayratesforthe alphadecayof 241Am andmixedEC,

β

−_, _and

_β

+ _decay_of 152_Eu

arehighly correlatedbutthe amplitudediffers fromonedetector toanother. Inother words,themodulations are linkedto the in-strument,nottothetypeofdecay.

4. Conclusions

Theexperimentaldatainthisworkaretypically50timesmore stablethanthemeasurementsonwhichrecentclaimsforsolar in-fluenceonthedecayconstantswerebased.Theobservedseasonal modulationscanbeascribedtoinstrumentalinstability,sincethey varyfrom one instrument toanother and show no communality inamplitude orphaseamong–orevenwithin–thelaboratories. TheexponentialdecaylawisimmunetochangesinEarth–Sun dis-tancewithin0.008%formostoftheinvestigated

α

,

β

−_,

β

+_and_EC

decayingnuclidesalike.

Owingto the invariability of decayconstants, there is no im-pediment tothe establishmentof thebecquerel through primary standardisation at 0.1% range accuracy nor to the demonstration ofequivalence of activity atinternational level over a time span of decades. It is normal for repeated activity measurements to show varying degrees ofinstability ofinstrumental and environ-mentaloriginandsuchauto-correlatedvariabilityshouldbetaken intoaccountnext tostatisticalvariations whensettingalarm lev-elsinqualitycontrolcharts.Takingintoaccount suchinstabilities andadhering to proper uncertaintypropagation, no fundamental objections need to be made against half-life measurement with sub-permilleuncertainties,noragainstapplyingexponentialdecay

formulastocalculateactivityatafutureorpastreferencetimeor toperformaccuratenucleardating.

Acknowledgements

The authors thank all past and present colleagues who con-tributeddirectlyorindirectlyto thevastdata collectionover dif-ferentperiodsspanningsixdecades.

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