Results of a search for daily and annual variations of the 214Po half-life at the two year observation period.

(1)Institute for Nuclear Research of the RAS, Russia(2)V.N.Karazin Kharkiv National University, Ukraine

E.N. Alexeev1, Yu.M. Gavrilyuk1, A.M. Gangapshev1, V.V. Kazalov1, V.V. Kuzminov1, S.I. Panasenko1,2, S.S. Ratkevich1,2.

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1. Search for decay constant time variations.No theoretical predictions about decay constant time variations

exist nowadays. We have only experimental results.

2. Test of an exponetiality of the fundamental decay law.Deviation from an exponentiality at a region of small values of a decay curve

argument has been predicted by some theoretical models. In particular, it

could appear due to the theoretically proved Zeno quantum effect.

Estimations of rare processes (proton decay, double beta-decay, cosmic chronology and others )

Tasks of the experiment

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Experiments

Investigated isotopes: 3H – 239Pu

Observed periods of variation: 1 day – 13.5 years

Amplitudes: n∙(10-2 – 10-4) (n- a few units)

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Decay rates data1. 32Si/36Cl (half-life of 32Si →(172y)/(3∙105y))D.E. Alburger, G. Harbottle, E.F. Norton, Earth Planet Sci. Lett. 78 (1986) 168. (Brookhaven National Laboratory (BNL)) 2. 226Ra (long-lived comparison standard)H. Siegert, H. Schrader, U. Schötzig, Appl. Radiat. Isot. 49 (1998) 1397.Physikalisch-Technische Bundesanstalt (PTB) in Germany

J.H. Jenkins et al. / Astroparticle Physics 32 (2010) 42–46Evidence of correlations between nuclear decay rates and Earth–Sun distance

Correlation between the raw decay rates of 32Si/36Cl at BNL and 226Ra at PTB.

A365d ≈ 8∙10-4

“We have presented evidence for an annual variation of nuclear decay rates seen in overlapping data sets from BNL and PTB whose origin is at present unknown. Since the observed BNL and PTB correlations of each data set with 1/R2, as well as with each other, could arise from a variety of conventional and unconventional sources, further experiments on a number of different nuclides will be required to determine the origin of these correlations.”

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Temperature

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Limitations

198Au: 1 year period - A < 0.02% (99% C.L.) (J.C.Hardy, J.R. Goodwin and V.E. Jacob arXiv:1108.5326)

137Cs: (a few hours – 1 year) period - A < 0.0096% (95% C.L.) (E. Bellotti et al, arXiv:1108.5326) 40K: ~ 1 year period - A < 0.0061% (95% C.L.) (E. Bellotti et al, arXiv: 1311.7043)

108Ag, 133Ba, 154Eu, 85Kr, 226Ra, 90Sr: 1 year variations, A = (0.068 – 0.088)% Ā = (0.081±0.007)% (11σ) P. A. Sturrock, E. Fischbach and I. Jenkins arXiv:1408.3090

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1. Count rate instability (background; electric and

Decay rate variations = F{ magnetic fields; temperature; pressure; humidity; } aging; source-detector characteristics …)

2. Half-life variations

Decay rate measurements → Life time measurements

214Po (Т1/2= 163.42±0.06 μs) E.N.Alexeev, Yu.M. Gavrilyuk, A.M. Gangapshev et al. “Sources of the systematic errors of 214Po half-life measurements.” arXiv: 1404.5769v1 [nucle-ex] 23 Apr 2014.

→214Bi→(β, Т1/2= 19.9 m)→214Po*→γ→ 214Po (α,Т1/2= 164.3±2.0 μs)→

214Po (Т1/2= 163.58±0.29(stat.)±0.10(syst.)) µsG. Bellini, J.Benziger, D.Bick et al. “Lifetime measurements of 214Po and 212Po with the CTF liquid scintillator detector at LNGS”. Eur. Phys. J. A (2013) 49:92

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2

2222

14

1/ 2

2101/

2181/ 2

261/ 2 1/ 2

2

4.78 5.49

6.00

( 1600 ) ( 3.8

( 26.8 )

( 2

( 3.05 )

25

2

)

.3 )

E MeV E MeV

E MeV Pb T m

Pb

Ra T y

Po T

T

y

n

T

R

m

d

-214

1

214

2-4

1/ /2β α

E=7.69MeVPo(T = 1.6Bi(T = 1 109.9 s)m)210

1/ 2

202101/

6

2 5.31

( 5.01

( 138

)

).) (E MeVP

Bi T d

Pb stablT eo d

Scheme of Scheme of 222266RRaa decaydecay

214Bi→214Po (19.9% - ground level; 80.1% - exited levels)

Eγ ≥ 609 keV – 1.187 γ/decay

γ-β-(delayed α) – coincidence

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Plastic PETP 2.5 μm film “Goodfellow”

Glue

226Ra

d=3 mm

d=14 mm

0.05 mm

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226Ra-source + PS-detector

PS-disc

9

TAU-2 4900 m w.e. NaI(Tl)×2 - 150×150 mm25 cm PE+1mm Cd+(15 cm+15 cm Pb) A ≈ 50 Bk

Schematic view of TAU-2 installation

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Example of coinciding event at TAU-2: delayed α-pulse in the “history” follows the prompt coinciding γ- and β-pulses.

NaI(Tl)-γ-pulse α-det., β-pulsePrompt coinc.

α-detector, α-pulsedelayed coinc.

1. NaI(Tl)-signal triggers the data record.

Time interval duration - 655.36 µs (4096×160ns),

81.92 µs –“prehistory”, 573.44 µs –“history” >3τ

2. TAU-2 ~12 s-1 “On line” program selection of

useful events, data-compression – writing amplitudes

and time of pulse appearing: 25 Mb∙d-1.

3. NaI(Tl)-background (E>400 keV): ~2.3×2 ≈ 4.6 s-1

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DULB-4900TAU-2, (L=3670 m, T=(26.5±0.2)oC)

Schematic view of BNO underground laboratories

B – Gallium Germanium SN-Telescope

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Fig2. α-spectrum from the PS-detector. (STOP)

Fig1. γ-quantum spectrum from the NaI-detector. (START)

γ-quantum energies – 609.3 keV (46.1%/decay), 1120 keV (15%/decay),1765 keV (15.9%/decay)

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Time of measurement - 590 days

Fig.3. Distribution of delay time between γ(β)-pulse (start) and α-pulse (stop) [μs].

μs

[γ(β)+α] delay time, μs

Nu

mb

er o

f ev

ents

/ 0.1

6 μ

s

1/²{Y-f(t)}² →min; f(t) =A∙exp(-t/)+ B

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Fig.4 Distribution in time of half-life of 214Po for a week data sets of TAU-2 for the ORIGIN fitting

Time, [weeks]

21

4 Po

hal

f-li

fe [

μs]

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Search for a variation with the 1 year periodicity

Moving-average method (moving summation)1. Choose an interval equal to ≈ 0.5 of the expected one. Determine a value of the half-life for it.2. Shift the interval for one step and repeat the procedure, and so on. The interval and step were chosen equal to be 0.5 year and 1 week

Fig.4. Distribution in time of half-life of 214Po for a week data sets of TAU-2 for the ORIGIN fitting

Fig.5. Distribution in time of the 214Po half-life values obtained by the “moving-average method”

Time, [weeks] Time, [weeks]

214 P

o h

alf-

life

[μ

s]

214 P

o h

alf-

life

[μ

s]

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1σ ≈ 0.25 μs 1σ ≈ 0.05 μs

16

Time, [weeks]

214 P

o h

alf-

life

[μ

s]

Fig.6. (▼)Distribution in time of the 214Po half-life values obtained by the “moving-average method” .(1) – approximation by τ(t)=τ0∙[1+A∙sin(ω∙(t+φ))],ω = 2π/365 d-1; A = 5.4∙10-4 ; φ = 83 d (since the 1st of January). (2) - τ(t) = τ0 ∙[1+8.9∙10-4∙sin(ω∙(t+174))]

<Y> = sin(x)= (1/π)∙∫Ydx → Y = (π/2)∙cos(x) = (π/2)∙sin(x+ π/2) x+π

x

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Fig.7. (▼)Distribution in time of the 214Po half-life values for one week data sets.(∙) - τ(t) = τ0 ∙[1+8.9∙10-4∙sin(ω∙(t+174))]

А=(8.9±2.3)∙10-4

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Time, [weeks]

214 P

o h

alf-

life

[μ

s]

18

Search for diurnal variations

1. Solar-daily variation (24 hours)

Moving-average methodThe interval and step were chosen to be 12 hours and 1 hour.The data in the time region of 0-12 h were summed in all 590 days statistic and the half-life obtained. Then the 1-13 h interval was taken and the procedure repeated, and so on.

214 P

o h

alf-

life

[μ

s]

214 P

o h

alf-

life

[μ

s]

Day time, [hours] Interval step, [hours]

Fig.8a. Solar-daily variation of half-life of 214Po obtained by means of epoch superposition method

Fig.8b. Solar-daily variation of half-life of 214Po obtained by means of moving-average method

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1σ ≈ 0.15 μs 1σ ≈ 0.04 μs

19

Fig.9a.(▼) Solar-daily variation of half-life of 214Po obtained by means of moving-average method. (1) Approximation by τ(t)=τ0∙[1+A∙sin(ω∙(t+φ))],ω = 2π/24 h-1; A = 4.8∙10-4 ; φ =-6 h. (2) τ(t) = τ0 ∙[1+7.5∙10-4∙sin((2π/24) ∙t)] {φ=-6+24/4=0}

Fig.9b. (▼) Solar-daily variation of half-life of 214Po obtained by means of epoch superposition method .(∙) τ(t) = τ0∙[1+7.5∙10-4∙sin((2π/24) ∙t)].

Day time, [hours]

214 P

o h

alf-

life

[μ

s]

214 P

o h

alf-

life

[μ

s]

Interval step, [hours]

Amplitude of the solar-daily variation is A = (7.5±1.2)∙10-4

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2. Sidereal-daily variation (SD duration = 23 h 56 min 4.09 s ≡ 24 hsd). Δt = 3 min 55.91 s

Interval step, [hsd] Interval step, [hsd]

214 P

o h

alf-

life

[μ

s]

214 P

o h

alf-

life

[μ

s]

Fig.10.(▼) Sidereal-daily variation of half-life of 214Po obtained by means of moving-average method. (1) Approximation by τ(t)=τ0∙[1+A∙sin(ω∙(t+φ))], ω = 2π/24 hsd

-1; A = 4.6∙10-4 ; φ =-6 hsd. (2) Sought SD variation τ(t) = τ0∙[1+7.2∙10-4∙sin((2π/24) ∙t)].

Amplitude of the sidereal-daily variation is A = (7.2±1.2)∙10-4

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If the starting point shifts for 182 days (in solar time) than phase of sidereal-daily wave shifts for (3 min 55.91 s)∙182 ≈ 12 h

182 days

Sidereal-daily variation.

Fig.11a.(▼) Sidereal-daily variation of half-life of 214Po obtained by means of moving-average method. Starting point shifted for 182 days.

Fig.11b.(▼) Anti-Sidereal-daily variation of half-life of 214Po obtained by means of moving-average method. dasd = d+Δt = 24 h 3 min 55.9 s

Interval step, [hsd] Interval step, [hasd]

214 P

o h

alf-

life

[μ

s]

214 P

o h

alf-

life

[μ

s]

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3. Lunar-daily variation (lunar day mean duration = 24 h 50 min 28.2 s ≡24 hld)

Fig.12.(▼) Lunar-daily variation of half-life of 214Po obtained by means of moving-average method. (1) Approximation by τ(t)=τ0∙[1+A∙sin(ω∙(t+φ))], ω = 2π/24 hld

-1; A = 4.4∙10-4 ; φ =6 hld. (2) Sought SD variation τ(t) = τ0 ∙[1+6.9∙10-4∙sin((2π/24) ∙(t+12))].

Amplitude of the lunar-daily variation is A = (6.9±2.0)∙10-4

Interval step, [hld] Interval step, [hld]

214 P

o h

alf-

life

[μ

s]

214 P

o h

alf-

life

[μ

s]

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Lunar-daily variation (lunar day mean duration = 24 h 50 min 28.2 s ≡24 hld)

If the starting point shifts for 15 days (in solar time) than phase of lunar-daily wave shifts for (50 min 28.2 s)∙15 ≈ 12 h

Fig.13.(▼) Lunar-daily variation of half-life of 214Po obtained by means of moving-average method. Starting point shifted for 15 days (15 Oct. 2012).

Interval step, [hld]

214 P

o h

alf-

life

[μ

s]

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Analysis of the Data

1. Annual variation

Time, [weeks] Time, [weeks]

Nor

mal

ized

214 P

o h

alf-

life

Nor

mal

ized

214 P

o h

alf-

life

Ear

th-S

un

dis

tan

ce (

a.u

.)

E

arth

to

Su

n v

eloc

ity

(km

/s)

Fig.14. (▼)Distribution in time of the 214Po half-life values for a week data sets.1. τ(t)/τ0 = [1+8.9∙10-4∙sin((2π/365 )∙(t+174))].2. Time dependence of E.-S. distance. (1) – (2) phase shift ~ 15 weeks3. Time dependence of E. to S. velocity. (1) – (3) phase shift ~ 0 (±1 week)

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EarthDirection to the Sun

V

Starting point

2. Solar-daily variation (24 hours)

Fig.15.(▼) Solar-daily variation of half-life of 214Po obtained by means of moving-average method. (1) Approximation by τ(t)=τ0∙[1+A∙sin(ω∙(t+φ))], ω = 2π/24 h-1; A = 4.8∙10-4 ; φ =-6 h. (2) τ(t) = τ0 ∙[1+7.5∙10-4∙sin((2π/24) ∙t)] {φ=-6+24/4=0}.(3) Earth surface point velocity relative to the Sun due to the Earth rotation.

Interval step, [hours] Interval step, [hours]

214 P

o h

alf-

life

[μ

s]

214 P

o h

alf-

life

[μ

s]

ES

poi

nt

to

Su

n v

eloc

ity

(km

/s)

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3. Lunar-daily variation

Direction to the Moonv

Lunar zenith at 30.09.2012 - 23 h 40 min

Earth

214 P

o h

alf-

life

[μ

s]

214 P

o h

alf-

life

[μ

s]

Interval step, [hld] Interval step, [hld]

ES

poi

nt

to

Moo

n v

eloc

ity

(km

/s)

Fig.15.(▼) Lunar-daily variation of half-life of 214Po obtained by means of moving-average method. (1) Approximation by τ(t)=τ0∙[1+A∙sin(ω∙(t+φ))], ω = 2π/24 h-1; A = 4.8∙10-4 ; φ = 6 h. (2) τ(t) = τ0 ∙[1+7.5∙10-4∙sin((2π/24) ∙(t+12)] {φ=6+24/4=12}.(3) Earth surface point velocity relative to the Moon due to the Earth rotation.

Starting point

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Thus, annular, solar-daily and lunar-daily variations of the 214Po half-life valueare correlated with velocities of the Earth movement relative to the Sun and Moon.

Conclusions1. Averaged value of the 214Po half-life measured by TAU-2 for 590 days is equal to 163.46±0.04 μs.

2. Annular, solar-daily, sidereal-daily and lunar-daily variations of the 214Po half-life searched out in the TAU-2 data. Amplitudes are equal to: (8.9±2.3)∙10-4; (7.5±1.2)∙10-4; (7.2±1.2)∙10-4 and (6.9±2.0)∙10-4.

3. Strong correlations of annular, solar-daily and lunar-daily variations of the 214Po half-life value with velocities of the Earth movement relative to the Sun and Moon have been found.

Plans:1. To continue data taking at the TAU-2.2. To test the effect with the 213Po source having T1/2= 4.2 μs.

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