Sources of the systematic errors in measurements of Po-214 decay half-life time variations at the Baksan deep underground experiments
E.N. Alexeyev, Yu.M. Gavrilyuk, A.M. Gangapshev, V.V. Kazalov, V.V. Kuzminov, S.I. Panasenko, S.S. Ratkevich
aa r X i v : . [ nu c l - e x ] A p r Sources of the systematic errors in measurements of
Po decayhalf-life time variations at the Baksan deep undergroundexperiments E.N. Alexeyev † , Yu.M. Gavrilyuk † , A.M. Gangapshev † , V.V. Kazalov † ,V.V. Kuzminov † , S.I. Panasenko † , ‡ , S.S. Ratkevich † , ‡† Baksan Neutrino Observatory INR RAS, Russiaa ‡ V.N.Karazin Kharkiv National University, Ukraine
Abstract
The design changes of the Baksan low-background TAU-1 and TAU-2set-ups allowed to improve a sensitivity of
Po half-life ( τ ) measurementsup to the 2 . · − are described. Different possible sources of systematicerrors influencing on the τ -value are studied. An annual variation of Pohalf-life time measurements with an amplitude of A = (6 . ± × − anda phase of ϕ = 93 ±
10 days was found in a sequence of the week-collected τ -values obtained from the TAU-2 data sample with total duration of 480days. 24 hours’ variation of the τ -value measurements with an amplitude of A = (10 . ± . × − and phase of ϕ = 1 ± . τ -value sequence formed from the same data sample. It wasfound that the Po half-life averaged at 480 days is equal to 163 . ± . µ s. At the last time in works intended to search for limits of the realizationof the decay constant conservation law, a level of sensitivity not less than2 × − was reached for several radioactive isotopes. In the work [1] theauthors showed an amplitude of a possible annual variation of the Au half-life ( T / = 2 . ± × − does not exceeds ± × − of the central value. Variationswith periods from several hours up to one year were excluded at the level of9 . × − (95% C.L.) during the measurements of the Cs half-life ( T / =10942 days) in the Ref. [2]. The annual variation was excluded at the levelof 8 . × − (95% C.L.). Variations of an activity with periods of 3-150 dayswere excluded at the level of 2 . × − (99.7% C.L.) during the measurement Talk at The International Workshop on Prospects of Particle Physics: ”Neu-trino Physics and Astrophysics” January 26 - Ferbuary 2, 2014, Valday, Russia
1f the K activity in the Ref. [3]. It was shown that an amplitude of theannual variation does not exceeds of 6 . × − (95% C.L.). Variations of anactivity with periods less then one year were excluded at the level of 4 × − during the measurement of the Th activity in the Ref. [3] too.A count rate of the detector recording the source radiation was a subjectof investigations in the all mentioned works. A high sensitivity of the mea-surements was reached by using of a relatively high count rate ( ∼ s − ),of a control and a stabilization of conditions of the measurements and by anuse of additional arrangements for a shield of the set-ups against of outerbackground.The reached limitations are multiply exceed amplitude values of ∼ . × − of the Si and
Ra count rates of annual variations discussed in thework [4]. The authors examined possibilities of an appearance of such vari-ations as a result of seasonal variations of the detector characteristics or ofthe one of an annual modulation of the isotope decay rates themselves underthe action of an unknown factor depending of the Earth-Sun distance. Itis obviously that any conclusions about a possible new physical effect couldbe made only after complete exclusions of variations caused by the influenceof the known terrestrial geophysical, climatic and meteorological factors onsource-detector couple count rates.Unfortunately, not all such factors could be detected and be taken intoaccount during the measurement and data processing. For example, an an-nual variation with the amplitude of (4 . ± . × − was found as a resultof a processing of collected during 500 days data sample of Earth’s surfacemeasurement with K source in the Ref. [3]. It was found that this variationcorresponded completely to the known annual variation of the cosmic raysintensity and could be explained by a cosmic rays background event contri-bution to the total detector count rate. A variation with the ∼
300 daysperiod and of 4 × − amplitude was found in the data collected during 480days in the underground measurement with the Th source. It was foundthat this variation correlated with a variation of a daily averaged dead timeper event and could be explained by a modulation of the RC circuit providingthe shaping time of the amplifier.The weak point of the experiments intended to monitor a stability of acontrolled radiation count rate is their high sensitivity to the similar vari-ations of measurement conditions. It seems that this shortcoming becomesunimportant in the case of the decay constant determination based on andirect registration of a nuclear life time between its birth and its decay. Thesame method was realized by us Ref. [5] for the
Po which decays with264.3 µ s half-life [6] by emitting the 7.687 MeV α -particle. This isotope ap-pears mainly in the exited state ( ∼ Bi β -decay. Half-livesof the exited levels does not exceed 0.2 ps [7] and they discharge instantlyrelative to the scale of the Po half-life. Energies of the most intensive γ -lines are equal to 609.3 keV (46.1% per decay), 1120 keV (15.0%) and 1765keV (15.9%). So, the β -particle and γ -quantum emitted at the moment of abirth of Po nuclear form start-signal and the α -particle emitted at the de-cay moment forms stop-signal. Measurements of “start-stop” time intervalsallow one to construct decay curve at an observation time and to determinethe half-life time from it’s shape. The Ra source ( T / = 1600 years) wasused as a generator of Bi nuclei which arise in the decay sequence of themother isotope.The direct measurement of a nuclear life time allows one moreover tostudy the radioactive decay law itself. The theoretical models discussed inRef. [8, 9] predict that the decay curves could deviate from the exponentiallaw in the short- and very long-time regions of the time scale. The theo-retically predicted [10, 11, 12] so called quantum Zeno effect consisting ina slowing down of the decay rate in a case of constant observations at thedecaying object presents a special interest. Experimentally Zeno effect wasfound in repeatedly measured two-level system undergoing Rabi transitions[13], but not observed in spontaneous decays.At the first stage of our measurements, a limitation to the possible annualvariation amplitude was set at the level of 3 . × − . Factors limiting asensitivity were revealed and ways of its optimization were designed.In the present work the fulfilled improvements of the set-ups, of measure-ment methods and of data processing are described. An analysis of possiblesources of systematic errors is performed and obtained results are presented. The TAU-1 and TAU-2 set-ups used in the Ref. [5] consist of the two scin-tillation detectors D1 and D2 each. The D1 consisted of two glued discs of aplastic scintillator (PS) with the 18 mm diameter ( d ) and 0.8 mm thickness( h ). A thin transparent radium spot was deposited preliminary in the centerof inner surface of a one disc. The detector D1 records β -particles from the Bi decays and α -particles from the Po decays. The massive detector D2consisted of NaI(Tl) crystals destines for γ -quanta detections.In the TAU-1 set-up it was used a single NaI(Tl) crystal ( d =80 mm,3 =160 mm) as D2. The D1 is placed on the end of D2. The light collectionis fulfilled from a surface of the PS disc installed on a Teflon reflector.In the TAU-2 set-up it were used two NaI(Tl) crystals (D2a and D2b with d =150 mm and h =150 mm) placed by ends one to another with the gap of 10mm. The D1 is placed into a gap between D2a and D2b. The light collectionis fulfilled from a lateral side of the PS disc installed into deep narrow wellwith a reflecting wall.The measurements were carried out in the underground low backgroundconditions at the Baksan Neutrino Observatory of the Institute for Nu-clear Researches RAS (BNO INR RAS, North Caucasis). The TAU-1 set-up was located in the underground laboratory “KAPRIZ” at the depthof 1000 meters of water equivalent in a low background shield made fromPb(10cm)+Fe(15cm)+W(3cm). The time duration of the measurements wasequal to 1038 days. The value of a half-life time τ ( τ ≡ T / ) deducedfrom the analysis of the integrated decay curve was found to be equal to(162 . ± . µ s.The TAU-2 set-up was located in the low background room in the un-derground laboratory DULB-4900 [14] at the depth of 4900 meters of waterequivalent within the additional shield made from Pb(15 cm). The time du-ration of the measurements was equal to 562 days. The τ -value was foundto be (164 . ± . µ s.As one can see from shown results, both τ -values agree with the tableones within 1 σ table limit. However, they differ one from the other at thelevel of 13 σ due to our statistics. Such large difference indicates a presenceof a systematic error in the experimental results.The τ -value equal to [163 . ± .
29 (stat.) ± .
10 (syst.)] µ s, that is lyingbetween our values, was measured at the Gran Sasso in a recent work [15].A possible source of the supposed error could be a small difference ofsampling frequencies of the two digital oscilloscope (DO) used for the digitalrecord of pulses. A time duration of reference square-wave pulses from a highstability pulse generator was measured by both DO in order to determinea such possible difference. It was found that difference of measured timedurations is not exceeds ± × − .Later both set-ups were considerably modernized to improve the sensi-tivity.In the TAU-1 set-up the single-crystal detector D2 was substituted for thetwo-crystal detector, that is similar to one used at the TAU-2. The PS discs inthe D1 detector were replaced by two silicon surface-barrier semiconductor4etectors (SiD) with the diameter of a sensitive region of 25 mm. In thepreliminary measurements it was found that the SiD lost forever its workingcharacteristics at the ∼ . µ m and with the active spot deposited on the inner surfaceof the one disc. The source was installed hermetically between the two SiD.In the TAU-2 set-up just a similar source was installed between the freshPS discs in the detector D1 because of a scintillation characteristic degrada-tion of the PS under the active spot as it was also found at the first stageof measurements. The subsequent studies proved that the detection prop-erty degradations of the D1-detectors in the both set-ups were excluded. Anactivity of Ra was equal to 50 Bq in the each source.Registrations of the pulses in both set-ups are carried out by the two-channel digital oscilloscope LA-n20-12PCI which is inserted into a personalcomputer (PC). Pulses are digitized with 6.25 MHz frequency (160 ns/channel).The DO-pulse registration starts by a signal from the D2 which detected
Bidecay γ -quanta. A D2 signal opens a record of a pulse sequence within timewindow of 655.36 µ s in which the first time interval of 81.92 µ s representsan event “prehistory” and the last period of 573.44 µ s represents an event“history”. Duration of a “history” exceeds the three Po half-lives. Thedigitized pulses in the TAU-1 recorded into the PC memory on the whole.Total count rate was equal to ∼ − . A daily information volume was equalto ∼
10 Gb.In the TAU-2 set-up an each detected event is analyzed by the “on-line”program. A number of pulses and their time delays are defined for an eachevent. “Wrong” events are excluded. Only appearance times and amplitudevalues of pulses attributed to the “right” events were recorded in the PCmemory. A complete information for the each event allows to process datain the different pulse amplitude regions in the sequel. A count rate of the“right” events was equal to ∼
12 s − . A rate of the information accumulationwas equal to ∼
25 Mb × day − . Spectra of coincident pulses collected by the TAU-1 set-up during 270 hoursare shown in Fig.1. The spectrum represents the data from the detectorD1 and the spectrum is the data from the detector D2. An amplitude5
00 800 1200 16000400080001200016000800 1600 240004000800012000
Channel ( ) Channel ( ) C oun t s / ( c h a nn e l ) . Figure 1: Spectra of the coincided in 573.44 µ s D1 (spectrum ) and D2(spectrum ) pulses collected by the TAU-1 set-up at 270 hours.threshold value of triggering pulses in the D2 channel corresponds to 450keV. The main peak of the spectrum conforms to the 7.69 MeV α -particlefrom the Bi decays. The peaks from decays of the
Ra (4.79 MeV) and
Rn (5.49 MeV) are also presented at the spectrum. They were formedmainly as a result of random coincidences of the D2 background pulses withamplitude values above the threshold one and of the D1 α -pulses with thecorresponding energy that came into the frame of the window duration.The D2 background is created by a residual radioactivity of the shield andof the detector materials and also by γ -quanta from decays of the Pb ap-pearing in the
Ra decay sequence. Random coincidences form a temporal-uniform background that is situated under the exponential decay curve whichis produced by the true delayed γ - α coincidences from decays of the Ponuclei. A small part of random coincidences is created by the Po α -pulsesthat have no accompanying γ -pulses in those cases when a Po nucleusappeared as a result of a Bi β -decay on the ground level ( ∼ Po decay was delayed for a time more then thetime window duration.A spectrum of the Bi β -particle energy-depositions in the SiD makes upa small part of the Po α -particle energy-depositions because of an absenceof a pulse amplitude dependence on particle types. The β -particle pulsesand α -particle pulses are overlapping at short delay times, and in the resultamplitude values of summarized pulses will fall into the right slope of the α -peak in the spectrum. Owing to this reason, the decay curve constructed6or the narrow energy region corresponding to this slope will be enriched inthe events with the short delay times in comparison with the lower energyevents. These decay curves will show different values of the τ . The τ -valuewill depend on the low delay times and of cut threshold value of a decaycurve at a process of its fitting by an approximation curve. It seems thatdifference of the found τ -values could be unessential at the appropriate valueof the threshold.In Fig.2 (left panel) it is shown a start-stop delay distribution obtained Time, m s N u m b e r o f e v e n t s p e r . m s Time, m shalf-life t = 163.85 – m sTAU-1 TAU-2half-life t = 163.45 – m s Figure 2: Left panel - a start-stop delays distribution obtained in 116 daysat the TAU-1. Right panel - a decay-curve of the
Po obtained in 480 daysat the TAU-2.as a result of a processing of the data collected in 116 days at the TAU-1 set-up. In addition at these measurements the TAU-1 was shielded withPb(15 cm)+Cu(8 cm) and was situated near the TAU-2 set-up in the DULB-4900. An algorithm of the ”off-line” program provided the determinations ofthe maximum positions t m and t m of pulses from D1 and from D2, used forthe determinations of the delay times. The following step put into operationa correction on the pulse front durations t f and t f in order to find startpoints of the pulses.A value of the delay time ∆ t was calculated as ∆ t = ( t m − t f ) − ( t m − t f ). The delay times distribution shown in Fig.2 is approximated by anexponential function in the form y = a × exp[ − ln(2) × t/τ ] + b (1)by means of variations of the parameter values a , b and of τ according to the7lgorithm of the minimum χ -square method. A value of the half-life time τ is found from this approximation. The approximations were repeated manytimes using different threshold cuts to reveal a possible influence of the β -particle pulse in the D1 channel on a determination accuracy of the γ - α delay time measurements. The dependences of the obtained τ -values on acut threshold ones (curve , left scale) and on the corresponding b -valuesof background contributions (curve , right scale) are shown in Fig.3 (leftpanel). They looks like strictly anti-phased at the used right vertical scales. t , m s Low threshold of the decay curve, m s t , m s Low threshold of the decay curve, m s b b Figure 3: Dependences of a half-life τ -value (curve , left scale) and a back-ground base amplitude b (curve , right scale) on a decay curve cut thresholdobtained with the TAU-1 in the DULB-4900 (left panel) and in the KAPRIZ(right panel).In the present experiment before data recording, an event selection real-ized strictly under the requirement in the presence of one and only oneevent within time window of ÷ µ s of ”history” . In accordancewith statistical laws [16], a distribution of random coincident events (underthis selection rule) will be uniform within chosen time interval. This meansthat an amplitude value of the background contribution does not depend onthe delays between the D2 and D1 pulses. So, the observed variations of b -values reflects only ratio changes of exponent-background for concrete partof decay curve due to using formal approximation rules. In the other words,a shape of the decay curve does not described by a single exponent withinthe time region of 10-30 µ s at a level of an accuracy of ∼ . τ could be found in a case when the amplitudeb of the background contribution would be known. Such possibility was foundat the present phase of the experiment during the data analysis.The method is consists on the measurement of the delays between theD2 start pulses and the preceded D1 pulses within settled time interval,that is from the “prehistory”. A distribution of the delay times for suchrandom events will be the same as for the random event in the “history”.Unfortunately, in the before collected data a determinations the precededdelays were impossible because of the “on-line” PC treatment program of apreliminary event selections excluded such events before the recording. Atpresent time this forbidden is eliminated and all TAU-1 events are collected.In principle, a difference of the τ -value measurements obtained at theTAU-1 and TAU-2 set-ups could be explained by the other way. The differentgravitation potentials at the KAPRIZ and DULB-4900 laboratories could bea reason of such a difference, if there is any dependence of the τ -value onvalues of the gravitation potentials at places on the Earth where the set-upsare situated. A gravity force in the DULB-4900 is less at 1 × − than theone in the KAPRIZ laboratory due to the gravitation of the rock mass abovethe deep laboratory as it was measured in the Ref. [17]. This difference ismuch more than the periodic variations of the Earth’s surface gravitationpotential caused by the Sun or by the Moon orbital moving.In order to check this assumption, the TAU-1 set-up was replaced fromthe DULB-4900 laboratory into the KAPRIZ one. The conditions of themeasurements and data processing were kept in the same way by chance.Time of the data accumulation was equal to 88 days. The results, thatare similar to data shown in Fig.3 (left panel), are presented in Fig.3 (rightpanel). One can find from a comparison of the data in regions of minimumsof the τ -values at 24 µ s that the τ -value is equal to 163 . ± . µ s in theDULB-4900 place and is equal to 164 . ± . µ s in the KAPRIZ place. Theresults are in agreement within the 1.5 σ interval. A scintillation detector D1 in the TAU-2 has a relative α/β light output equalto ∼ . α -particles and β -ones havethe comparable amplitudes. This circumstance was used to a preliminaryselection of the “useful” events by the “on-line” program prepared the data9or a PC recording. The record program selects only the events with the twopulses in the D1 channel. The first of them ( β ) is in a prompt coincidenceand the second one ( α ) is in a delayed coincidence with the start pulse ( γ ) inthe D2 channel. The corresponding spectra of the β -pulses (spectrum ) and α -pulses (spectrum ) from the D1 detector and of the γ -pulses (spectrum ) of the D2 detector collected at 435 hours are shown in Fig.4. The peak at ) C oun t s / ( c h a nn e l *453 h ) ) ) Channel
Figure 4: Spectra of the delay coincident D1 (spectrum ) and D2 (spectrum ) pulses and the spectrum of the first D1 pulses collected by the TAU-2set-up at 435 hours.the channel ∼ is formed by the 7.69 MeV α -particles.The total time of the data collection is equal to 480 days in the period ofOctober 2012 – January 2014.A decay curve constructed for the total data set is shown in Fig.2 (rightpanel). The dependences of the τ -value measurements (curve , left scale)and of the defined b -parameter values (curve , right scale) on the cut thresh-old values are presented in Fig.5 (left panel). A value of the τ is equal to10
40 80 120 160163,3163,4163,5163,6163,7 0 10 20 30 40 50 60 70161162163164165 t , m s Low threshold of the decay curve of TAU-2 m s t , m s time, weak b Figure 5: Left panel - dependences of a half-life τ -value (curve , left scale)and a background base amplitude b (curve , right scale) on a decay curvecut threshold obtained with the TAU-2. Right panel - dependence in time ofthe τ -value obtained at the TAU-2 with the week step.163 . ± .
04 at the threshold of 24 µ s. It is compatible with the τ -valuewithin 1 σ interval, that was found in the DULB-4900 experiment with theTAU-l.The constant linear contributions of 500, 1000 and 1400 were subtractedfrom the decay curve data to test a dependence of the procedure for the a -, b - and τ -values definitions on the background contributions. The a -, b - and τ -values were determined with the standard procedure for each new decaycurve. The a - and τ -values were found to be the same for all three back-ground contributions, and the b-values was reduced exactly by the subtractedconstants.This means that: 1) a shape of a background contribution is really flatsince in the opposite case the parameters of the exponent should be changedto compensate an increased contribution of the background nonlinear part;2) an accuracy of the separation of the experimental decay curve form bythe exponential part and by the flat one does not depend on the backgroundvalues in the treated limits.The time-continuous data set was divided to the equal duration time in-tervals to search for possible time variations. The decay curves have been con-structed for each data portions and the corresponding τ -values have been de-fined. So, the continuous time-interval sequence of the τ -value measurementswithin the specified time step has been found. The dependence of the found τ -values on time with a week time step of the distribution is shown in Fig.5(rigth panel). The τ -values were defined by means of a χ -approximation of11he decay- curves, each collected during 7 days, by an exponential function(1). The used time window of delays was 3 . ÷ µ s.There is the statistically more powerful maximum likelihood method forestimation of exponent parameters in experimental data treatments, but inorder to use it a value of the background contribution b should be determinedby means of an independent direct measurements or of any additional dataanalysis.To search for a possible annual variation of the found τ -data, they werenormalized to the averaged values and were compared with a periodical func-tion f ( t, ϕ ) = 1 + A × sin { ω ( t + ϕ ) } , (2)where ω = 2 π/
365 days − , t – day of year, A – an amplitude of the variation, ϕ – a phase shift relative to the 1 January. Here A and ϕ are used as trialparameters for to find best fit. The ϕ -parameter was varied from 1 to 365with the step of 1 day. A correlation coefficient k ( ϕ ) between τ -value se-quence and f ( t, ϕ ) was calculated for the each ϕ -value. The maximum value k = 0 .
23 has been reached at ϕ = 90 ±
10 days. So, the ϕ -phase value of theperiodical function was found. Then a choice of A-value corresponding to the χ minimum was done and was found to be A = (6 . ± . × − . A max-imum of the f ( t, ϕ ) has achieved on the 22 September. The correspondingdependences are shown in Fig.6 (left panel).The other natural periodic variations exist which are connected with therotation of the Earth around its axis. In particular, oscillations with periodsof 24 hours in the Sun’s time. Siderial time are related to such phenomena.A τ -values sequence obtained for the one hour step decay curves putting inthe 24 hours Sun’s day averaged from the TAU-2 data collected during 16month is shown in Fig.6. The normalized sequence was approximated bythe expression (2), where ω = 2 π/
24 h − . A maximum correlation value of k = 0 . ϕ = 1 . ± . A = (10 . ± . × − at the χ = 1 .
49 for N = 23. The corresponding dependences are shown in Fig.6(right panel). There are no variations in the similar data sequences treated inthe sidereal time which exceed statistical dispersions with the values higherthan A ≤ × − (90% C.L.). The fulfilled modernization of the TAU-1 and TAU-2 set-ups allowed us toimprove considerably a stability of the results and a sensitivity of long du-12
10 20 30 40 50 60 700,9920,9961,0001,0041,008 0 5 10 15 20 250,9920,9961,0001,0041,008 time, weeks t no r m a li ze d t o t no r m a li ze d t o time, hours Figure 6: Left panel - dependence in time of the normalized on average τ -value obtained at the TAU-2 with the week step (black points) and anapproximation function (2) f ( t ) = 1 + 6 . × − × sin { π/ × ( t + 93) } (colour curve). Right panel - dependence with 1 hour step of the τ -value onsolar day time, colour curve - f ( t ) = 1 + 1 × sin { π/ × ( t + 1) } .ration measurements of a half-life value of the Po decay as it follows fromthe description given above. An assumption that obtained in Ref. [5] ∼ . τ -values measured at the old-version of TAU-1 and of TAU-2set-up versions could be connected with the difference of the calibrations ofthe used digitizers was examined by means of measurements of the stablerectangle pulse durations. It was found that an accuracy of the DO calibra-tions was not worse than 3 × − . A hypothesis about possible correlationof τ -values measured by the old TAU-1 and TAU-2 and of values of grav-ity in the corresponding underground laboratories was tested. The values ofa gravitational acceleration in used two laboratories are differ at 1 × − .Firstly, a measurement was done with the TAU-1 set-up in one laboratoryand than it was repeated in the other one. A weak dependence of the mea-sured τ -values on decay curve cut thresholds in the low delays region wasobtained in the both series. The changes of the τ -values do not exceeded 3 σ or 3 . × − for the 3 . ÷ µ s threshold changes at the achieved statisticallevel. A difference of the τ -values at the threshold of 30 µ s does not exceedsa value of 3 . × − and this difference is much lower than the one measuredin Ref. [5]. A statistic of measurements in the each laboratory should beincreased to a further improvement of the estimation accuracy.A dependence of a τ -value on a decay curve cut threshold could beexplained by small distortions of the exponent form at low delay times13ue to mistakes of the “off-line” program in processes of determinations ofreal delays in cases of front overlapping of β -pulses and of α -pulses. The τ -value variations at the time delay above ∼ µ s could be connectedwith statistical deviations of the exponent form since the statistical weightsof the such deviations changed at the threshold growth. The approxima-tion program redistributes the exponent part and background line contribu-tions in accordance with these weights. Variations of the τ -value and thebackground contribution b are in anti-phase in accordance with expression∆ τ /τ ≈ − . × ∆ b / b as it seen in Figs. 3 and 5 (left panel).It is evidently that contribution b is really constant under any part of theexponent. A steadiness on the b -values of the χ -algorithm of ORIGIN usedfor a decay-curve division between the the exponent part and backgroundline part was tested by comparing of the results extracted by the program inthe processing of the decay curves obtained as results of constant line sub-tractions from the primary decay curves. The identical exponent parameterswere found in all tested cases. The background values b were found to beequal to the difference of the primary b -value and subtracted constant val-ues. This observation gives a certainty in the interpretation of the data timesequences with different time steps.The uncertainties of interpretations could arise on account of possible in-dependent changes of the exponent and of the background parameters duringa chosen time step under influences of the external reasons. The values of theparameters could be found by different ways, in principle. First, the τ -valuefor a long time interval could be calculated as average of the τ -values forshort component time intervals. Second, the parameters could be obtainedfrom the decay curve collected during whole analyzed time-interval by usingof a standard approximation procedure. Third, the background contributionb could be excluded from a number of variable parameters before the ap-proximation procedure by using of a constant value obtained by means of anormalization of the total data set b -value to the number of events in theanalyzed time interval. A value of a standard deviation will decreased in ac-cordance with the ratio of the time step duration to the total measurementtime duration. An adequacy of these approaches was examined for the weekstep data decomposition. It was found that all methods gave similar resultsbut different in details.An independent measurement of the background contribution value shouldbe done to obtain the result unambiguity. It was aware of possibility ofrealization of such measurements by using of delays between random coin-cide D1-pulses from “prehistory” and starting D2-pulses. Another possibility14ould be realized by admixing of seldom specially prepared stable generatorpulses to the flow of the real pulses. An admixture could be done by directinput of the pulses into the electronic chain or by the pulse lighting of thePMTs.The amplitude and phase in the annual variation of the τ -value sequencewith the week data step was found to be A = (6 . ± . × − and ϕ =93 ±
10 days.In order to check a possible occurrence of cyclical variations with twenty-four hour period, the total data set collected at the 16 months was trans-formed to the 24 hour data set by summing of the information within thesame numbered hour in the repeated 24 hours fragmentation. The transfor-mation was repeated for solar, lunar and stellar times. The twenty-four hourvariation with the amplitude A = (10 . ± . × − and phase ϕ = 1 ± . A ≤ × − at 90% C.L.) in the sidereal time.It is possible to suppose that the annual variation and the twenty-fourhour one can have a common origin. In principle, the found effect of thedecay constant variation could be created by variations of the DO samplingfrequency; by variations of the delay times of the D1 and D2 pulses due topossible variations of the PMT’s time characteristics under the action of theEarth magnetic field variations; by an unknown physical effect synchronizedwith the day Earth circulation and with the annual one.An instability of the DO characteristics could be created by a noticeablechanging of an environmental temperature. However, due to the continuousmonitoring it was shown that a temperature in the TAU-2 compartment isconstant within the limits of 26 . ± . ◦ . This means that the temper-ature variations should be excluded from a list of possible reasons of the τ -variations.Variations of the supply powers were not considered as an instabilitysource because of all electronic systems feed by stabilized voltages. So, bythe discussed reasons it seems not likely that DO characteristics instabilitycould be a reason of the observed τ -variations.Possible influences of the Earth’s magnetic field variations to the PMT’scharacteristics is supposed to be investigated in the nearest future.In the result of the treatment of the whole data sample recorded by theTAU-2 set-up during 16 months, the new value of Po half-life time averagedover the total observational period was found to be τ = 163 . ± . µ s.The value is compatible with the values from other measurements. Using15his new value of decay constant τ , it is necessary to take into account themechanisms shown above. The results of analysis of the data obtained with the upgraded TAU-1 andTAU-2 set-ups at the new step of measurements are shown in the presentedwork. The set-ups are intended to carry out a long-term control of the
Pohalf-life constant value. It is shown that the constant feels the twenty-fourhour variation and the annual one of an unknown nature. The measurementsare in progress.
References [1]
Hardy J.C., Goodwin J.R. and Iacob V.E. // Appl.Radiat.Isot. 2012.V.70. P.1931; arXiv:1108.5326 [nucl-ex].[2]
Bellotti E. et al. // Phys. Lett. B. 2012. V.710. P.114; arXiv:1202.3662[nucl-ex].[3]
Bellotti E. et al. // ”Search for time modulations in the decay rate of Kand
Th and influence of a scalar field from the Sun.” arXiv:1311.7043[astro-ph.SR][4]
Jenkins J.H. et al. // Astropart. Phys. 2009. V32. P.42; arXiv:0808.3283[astro-ph].[5]
Alexeyev E.N. et al. // Astropart. Phys. 2013. V46. P.23;arXiv:1112.4362 [nucl-ex].[6]
S.-C. Wu // Nucl. Data Sheets 2009. V110. P.681.[7] Table of Isotopes, Seventh Edition, Edited by Firestone R.B. et al., 8thed. Willey, New York 1996.[8]
Gavriljuk Ju.M. et al. // Nucl. Instr. Meth. A 2013. V729. P.576;arXiv:1204.6424 [physics.ins-det].[9]
Gopych P.M. and Zaljubovsky L.I. // Fiz. Elem. Chast. Atom. Yadra.1988. V.19. P.785. 1610]
Fonda L. et al. // Rep. Prog. Phys. 1978. V41. P.587.[11]
Khalfin L.A. // Physics-Uspekhi 1990. V160(10). P.185.[12]
Misra B. and Sudarshan E.C.G. // J. Math. Phys. 1977. V18. P.756.[13]
Facchi P. and Pascasio S. // J. Phys. A: Math. Theor. 2008. V41.P.493001.[14]
Itano W. et al. // Phys. Rev. A. 1990. V.41. P.2295.[15]
Bellini G. et al. (BOREXINO Collaboration) // Eur. Phys. J. A 2013.V.491. P.92; arXiv:1212.1332v1 [nucl-ex].[16] Stochastic processes. Doob J. L. Wiley, New York 1953.[17]
Medvedev M.N. // ”
Report from gravity works in the Baksan Valley in2013 ”. Report SAI, Moscow, November 2013.[18]