Evidence of Solar Influences on Nuclear Decay Rates · 2021. 7. 8. · Jere Jenkins Ephraim...
Transcript of Evidence of Solar Influences on Nuclear Decay Rates · 2021. 7. 8. · Jere Jenkins Ephraim...
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Fischbach, Jenkins, and Sturrock et al.;Rencontres de Moriond; La Thuile, Italy 2011
Evidence of Solar Influences on Nuclear Decay Rates
Jere JenkinsEphraim Fischbach
Peter SturrockEd MerrittJosh MattesTasneem MohsinallyDan MundyJohn NewportBen Revis
John BuncherTom GruenwaldJordan HeimDan JavorsekDennis KrauseAnthony LasenbyAndrew Longman
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Fischbach, Jenkins, and Sturrock et al.;Rencontres de Moriond; La Thuile, Italy 2011
Publications to date• Jenkins, J.H. and E. Fischbach, Perturbation of nuclear decay rates during the solar flare of 2006
December 13. Astroparticle Physics, 2009. 31(6): p. 407-411. [doi:10.1016/j.astropartphys.2009.04.005]
• Jenkins, J.H., et al., Evidence of Correlations Between Nuclear Decay Rates and Earth-Sun Distance. Astroparticle Physics, 2009. 32(1): p. 42-46. [doi:10.1016/j.astropartphys.2009.05.004]
• Fischbach, E., et al., Time-Dependent Nuclear Decay Parameters: New Evidence for New Forces? Space Science Reviews, 2009. 145(3): p. 285-335. [doi: 10.1007/s11214-009-9518-5]
• Jenkins, J.H., D.W. Mundy, and E. Fischbach, Analysis of environmental influences in nuclear half-life measurements exhibiting time-dependent decay rates. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 2010. 620(2-3): p. 332-342. [doi:10.1016/j.nima.2010.03.129]
• Sturrock, P.A., et al., Power spectrum analysis of BNL decay rate data. Astroparticle Physics, 2010. 34(2): p. 121-127. [doi:10.1016/j.astropartphys.2010.06.004]
• Lindstrom, R. M., et al., Study of the dependence of 198Au half-life on source geometry, Nucl. Instr. and Meth. A, 622 (2010) 93. [doi:10.1016/j.nima.2010.06.270]
• Javorsek II, D., et al., Power spectrum analyses of nuclear decay rates. Astroparticle Physics, 2010. 34(3): p. 173-178. [doi:10.1016/j.astropartphys.2010.06.011]
• Fischbach, E., et al., Evidence for Solar Influences on Nuclear Decay Rates. Proceedings of the Fifth Meeting on CPT and Lorentz Symmetry, editor V.A. Kostelecky, World Scientific, Singapore, In Press. 2010.
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Fischbach, Jenkins, and Sturrock et al.;Rencontres de Moriond; La Thuile, Italy 2011
Background
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Fischbach, Jenkins, and Sturrock et al.;Rencontres de Moriond; La Thuile, Italy 2011
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Fischbach, Jenkins, and Sturrock et al.;Rencontres de Moriond; La Thuile, Italy 2011
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Fischbach, Jenkins, and Sturrock et al.;Rencontres de Moriond; La Thuile, Italy 2011
116mIn Decay
y = -0.000203x + 6.044443R2 = 0.980358
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0 2000 4000 6000 8000 10000 12000 14000
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Fischbach, Jenkins, and Sturrock et al.;Rencontres de Moriond; La Thuile, Italy 2011
116mIn Decay
y = 421.762694e-0.000203x
R2 = 0.980358
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1 2 56 minT ≈
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Fischbach, Jenkins, and Sturrock et al.;Rencontres de Moriond; La Thuile, Italy 2011
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Fischbach, Jenkins, and Sturrock et al.;Rencontres de Moriond; La Thuile, Italy 2011
Motivation
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Fischbach, Jenkins, and Sturrock et al.;Rencontres de Moriond; La Thuile, Italy 2011
A New Test of Randomness
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Fischbach, Jenkins, and Sturrock et al.;Rencontres de Moriond; La Thuile, Italy 2011
Decay Rate Fluctuations
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Fischbach, Jenkins, and Sturrock et al.;Rencontres de Moriond; La Thuile, Italy 2011
Brookhaven National Laboratory
Measurement of 32Si Half-lifeDavid Alburger
Garman HarbottleEleanor Norton
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Fischbach, Jenkins, and Sturrock et al.;Rencontres de Moriond; La Thuile, Italy 2011
D.E. Alburger, G. Harbottle, E.F. Norton, Earth and Planetary Science Letters 78 (1986) 168.
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Fischbach, Jenkins, and Sturrock et al.;Rencontres de Moriond; La Thuile, Italy 2011
D.E. Alburger, G. Harbottle, E.F. Norton, Earth and Planetary Science Letters 78 (1986) 168.
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Fischbach, Jenkins, and Sturrock et al.;Rencontres de Moriond; La Thuile, Italy 2011
D.E. Alburger, G. Harbottle, E.F. Norton, Earth and Planetary Science Letters 78 (1986) 168.
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Fischbach, Jenkins, and Sturrock et al.;Rencontres de Moriond; La Thuile, Italy 2011
D.E. Alburger, G. Harbottle, E.F. Norton, Earth and Planetary Science Letters 78 (1986) 168.
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Fischbach, Jenkins, and Sturrock et al.;Rencontres de Moriond; La Thuile, Italy 2011
D.E. Alburger, G. Harbottle, E.F. Norton, Earth and Planetary Science Letters 78 (1986) 168.
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Fischbach, Jenkins, and Sturrock et al.;Rencontres de Moriond; La Thuile, Italy 2011
Physikalisch-TechnischeBundesanstalt (PTB)
Europium Half-lives and Long Term Detector Stability
Helmut SiegertHeinrich SchraderUlrich Schoetzig
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Fischbach, Jenkins, and Sturrock et al.;Rencontres de Moriond; La Thuile, Italy 2011
H. Siegert, H. Schrader, U. Schoetzig, Applied Radiation and Isotopes 49 (1998) 1397.
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Fischbach, Jenkins, and Sturrock et al.;Rencontres de Moriond; La Thuile, Italy 2011
H. Siegert, H. Schrader, U. Schoetzig, Applied Radiation and Isotopes 49 (1998) 1397.
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Fischbach, Jenkins, and Sturrock et al.;Rencontres de Moriond; La Thuile, Italy 2011
Purdue Experiments
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Fischbach, Jenkins, and Sturrock et al.;Rencontres de Moriond; La Thuile, Italy 2011
T1/2=1953d
T1/2=313.5d
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Fischbach, Jenkins, and Sturrock et al.;Rencontres de Moriond; La Thuile, Italy 2011
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Fischbach, Jenkins, and Sturrock et al.;Rencontres de Moriond; La Thuile, Italy 2011
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Fischbach, Jenkins, and Sturrock et al.;Rencontres de Moriond; La Thuile, Italy 2011
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Fischbach, Jenkins, and Sturrock et al.;Rencontres de Moriond; La Thuile, Italy 2011
(7.51 1.07) x 105
Events missing
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Fischbach, Jenkins, and Sturrock et al.;Rencontres de Moriond; La Thuile, Italy 2011
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Fischbach, Jenkins, and Sturrock et al.;Rencontres de Moriond; La Thuile, Italy 2011
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Fischbach, Jenkins, and Sturrock et al.;Rencontres de Moriond; La Thuile, Italy 2011
40 hours precursor
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Fischbach, Jenkins, and Sturrock et al.;Rencontres de Moriond; La Thuile, Italy 2011
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Fischbach, Jenkins, and Sturrock et al.;Rencontres de Moriond; La Thuile, Italy 2011
5 Dec 2006: X-9 class flare
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Fischbach, Jenkins, and Sturrock et al.;Rencontres de Moriond; La Thuile, Italy 2011
13 Dec 2006: X3/4B Flare
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Fischbach, Jenkins, and Sturrock et al.;Rencontres de Moriond; La Thuile, Italy 2011
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Fischbach, Jenkins, and Sturrock et al.;Rencontres de Moriond; La Thuile, Italy 2011
16.22
16.23
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11/28 12/2 12/6 12/10 12/14 12/18 12/22 12/26 12/30 1/3
ln(C
R)
Date (2008)
Logarithmic Decay of 54Mn for December 2008
ln(gross) Linear (ln(gross))
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Fischbach, Jenkins, and Sturrock et al.;Rencontres de Moriond; La Thuile, Italy 2011
16.245
16.25
16.255
16.26
16.265
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16.275
16.28
12/9 12/10 12/11 12/12 12/13 12/14 12/15 12/16 12/17 12/18 12/19 12/20 12/21 12/22 12/23
ln(C
R)
Date (2008)
Logarithmic Decay of 54Mn for December 2008
ln(gross) Linear (ln(gross))
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Fischbach, Jenkins, and Sturrock et al.;Rencontres de Moriond; La Thuile, Italy 2011
SOLAR ACTIVITY: Hours ago, something on the far side of the sun exploded and hurled a massive cloud of debris (a CME) over the eastern limb. Using a coronagraph to block the sun's glare, the Solar and Heliospheric Observatory (SOHO) photographed the cloud expanding into space:
NASA's Stereo-B spacecraft is stationed over the sun's eastern limb, but it was not taking pictures at the probable time of the eruption, so details of the blast are unknown. The CME could herald an active region (e.g., a sunspot or perhaps an unstable magnetic filament) turning to face Earth in the days ahead.
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Fischbach, Jenkins, and Sturrock et al.;Rencontres de Moriond; La Thuile, Italy 2011
y = -0.0022514x + 105.8637406R² = 0.9977750
y = -0.0008937x + 51.8287553R² = 0.5886092
16.245
16.25
16.255
16.26
16.265
16.27
16.275
16.28
12/9 12/10 12/11 12/12 12/13 12/14 12/15 12/16 12/17 12/18 12/19 12/20 12/21 12/22 12/23
ln(C
R)
Date (2008)
Logarithmic Decay of 54Mn for December 2008
ln(gross) 12/14-12/16 Linear (ln(gross))
Linear (12/14-12/16) Linear (12/14-12/16)
Non Earth-directed large CMErecorded by SOHO at 0942 16 Dec 08 UT
T1/2=776d
T1/2=307d
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Fischbach, Jenkins, and Sturrock et al.;Rencontres de Moriond; La Thuile, Italy 2011
Data from Yoo, et al., Phys Rev D 68, 092002 (2003)
Solar Neutrinos?Super-K Data
0.8
0.85
0.9
0.95
1
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1.15
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10/28/95 3/11/97 7/24/98 12/6/99 4/19/01 9/1/02Date
Nor
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flux
0.96
0.97
0.98
0.99
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1/R
2 , a.u
.-2
7 Pt Avgd Normalized Phi-nu 1/R 2̂
Correlation = 0.38, 181 points, prob=3x10-7
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Fischbach, Jenkins, and Sturrock et al.;Rencontres de Moriond; La Thuile, Italy 2011
Eccentricity of Earth’s Orbit
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Fischbach, Jenkins, and Sturrock et al.;Rencontres de Moriond; La Thuile, Italy 2011
Back to BNL and PTB
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Fischbach, Jenkins, and Sturrock et al.;Rencontres de Moriond; La Thuile, Italy 2011
Pearson Correlation Coefficient r=0.52, N=239, Prob=4.17x10-18
Data from: Alburger, et al., Earth and Planet. Sci. Lett., 78, (1986) 168-176
Normalized BNL With Earth-Sun Distance
0.997
0.998
0.999
1.000
1.001
1.002
1.003
08/8
1
02/8
2
09/8
2
03/8
3
10/8
3
04/8
4
11/8
4
06/8
5
12/8
5
07/8
6
Date
BN
L U
(t)
0.96
0.97
0.98
0.99
1.00
1.01
1.02
1.03
1.04
1/R2 (a
.u.-2
)
Normalized Un-decayed BNL Uncertainty USNO 1/R^2
Representative 1σ Error for BNL Data
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Fischbach, Jenkins, and Sturrock et al.;Rencontres de Moriond; La Thuile, Italy 2011
Pearson Correlation Coefficient r=0.66, N=233, Prob=1.0x10-31
Data from: Alburger, et al., Earth and Planet. Sci. Lett., 78, (1986) 168-176
7 Pt Avg'd Normalized BNL With Earth-Sun Distance
0.9980
0.9990
1.0000
1.0010
1.0020
08/8
1
02/8
2
09/8
2
03/8
3
10/8
3
04/8
4
11/8
4
06/8
5
12/8
5
07/8
6
Date
Nor
mal
ized
BN
L
0.96
0.97
0.98
0.99
1.00
1.01
1.02
1.03
1.04
1/R
^2 (a
.u.^
2)
Un-decayed 7pt avg USNO 1/R^2
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Fischbach, Jenkins, and Sturrock et al.;Rencontres de Moriond; La Thuile, Italy 2011
Pearson Correlation Coefficient r=0.62, N=1974, Prob=5.13x10-210
Data from Siegert, et al., Appl. Radiat. Isot. 49, 1397 (1998) Fig. 1
Raw Undecayed 226Ra PTB Data with Earth-Sun Distance
0.995
0.996
0.997
0.998
0.999
1
1.001
1.002
1.003
1.004
1.005
3/23
/83
3/22
/84
3/22
/85
3/22
/86
3/22
/87
3/21
/88
3/21
/89
3/21
/90
3/21
/91
3/20
/92
3/20
/93
3/20
/94
3/20
/95
3/19
/96
3/19
/97
3/19
/98
3/19
/99
3/18
/00
Date
Nor
mal
ized
226
Ra
Dat
a
0.92
0.94
0.96
0.98
1.00
1.02
1.04
1.06
1.08
1/R
2 (a.u
.-2)
Normalized Undecayed USNO 1/R^2
![Page 46: Evidence of Solar Influences on Nuclear Decay Rates · 2021. 7. 8. · Jere Jenkins Ephraim Fischbach. Peter Sturrock. Ed Merritt. Josh Mattes. Tasneem Mohsinally. Dan Mundy. John](https://reader036.fdocument.pub/reader036/viewer/2022071517/613ad874f8f21c0c8268ab2e/html5/thumbnails/46.jpg)
Fischbach, Jenkins, and Sturrock et al.;Rencontres de Moriond; La Thuile, Italy 2011
Pearson Correlation Coefficient r=0.65, N=1968, Prob=3.12x10-246
Data from Siegert, et al., Appl. Radiat. Isot. 49, 1397 (1998) Fig. 1
7 Pt Avg Undecayed 226Ra PTB Data with Earth-Sun Distance
0.997
0.998
0.999
1
1.001
1.002
1.003
3/23
/83
3/22
/84
3/22
/85
3/22
/86
3/22
/87
3/21
/88
3/21
/89
3/21
/90
3/21
/91
3/20
/92
3/20
/93
3/20
/94
3/20
/95
3/19
/96
3/19
/97
3/19
/98
3/19
/99
3/18
/00
Date
Nor
mal
ized
226
Ra
Dat
a
0.92
0.94
0.96
0.98
1.00
1.02
1.04
1.06
1.08
1/R2 (a
.u.-2
)
7 pt avg normalized undecayed USNO 1/R^2
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Fischbach, Jenkins, and Sturrock et al.;Rencontres de Moriond; La Thuile, Italy 2011
BNL/PTB Correlation
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Fischbach, Jenkins, and Sturrock et al.;Rencontres de Moriond; La Thuile, Italy 2011
Pearson Correlation Coefficient r=0.66, N=39, Prob=5.8x10-6
BNL 32Si and PTB 226Ra Data with Earth-Sun Distance
0.998
0.999
1
1.001
1.002
1983.50 1984.00 1984.50 1985.00 1985.50 1986.00 1986.50
Date
BN
L an
d P
TB U
(t)
0.960.970.980.9911.011.021.031.04
1/R
2 (a.
u.-2
)
Raw BNL Raw PTB USNO 1/R^2
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Fischbach, Jenkins, and Sturrock et al.;Rencontres de Moriond; La Thuile, Italy 2011
Pearson Correlation Coefficient r=0.87, N=35, Prob=3.78x10-12
BNL 32Si and PTB 226Ra Data with Earth-Sun Distance
0.998
0.999
1
1.001
1.002
1983.50 1984.00 1984.50 1985.00 1985.50 1986.00 1986.50
Date
BN
L an
d P
TB U
(t)
0.94
0.96
0.98
1
1.02
1.04
1.06
1/R
2 (a.
u.-2
)
5 Pt Avg BNL 5 Pt Avg PTB USNO 1/R^2
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Fischbach, Jenkins, and Sturrock et al.;Rencontres de Moriond; La Thuile, Italy 2011
Data from other institutions
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Fischbach, Jenkins, and Sturrock et al.;Rencontres de Moriond; La Thuile, Italy 2011
ELLIS: CNRCData from other institutions
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Fischbach, Jenkins, and Sturrock et al.;Rencontres de Moriond; La Thuile, Italy 2011
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Fischbach, Jenkins, and Sturrock et al.;Rencontres de Moriond; La Thuile, Italy 2011
0.96
0.97
0.98
0.99
1.00
1.01
1.02
1.03
1.04
0.992
0.994
0.996
0.998
1
1.002
1.004
1.006
1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988
1/R
2(a
.u.-2
)
Nor
mal
ized
Dec
ay D
ata
Date
CNRC 238Pu/56Mn Data with 1/R2
Data from K. Ellis, Phys. Med. Biol., 35, 1079-1088 (1990)
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Fischbach, Jenkins, and Sturrock et al.;Rencontres de Moriond; La Thuile, Italy 2011
OSURRData from other institutions
![Page 55: Evidence of Solar Influences on Nuclear Decay Rates · 2021. 7. 8. · Jere Jenkins Ephraim Fischbach. Peter Sturrock. Ed Merritt. Josh Mattes. Tasneem Mohsinally. Dan Mundy. John](https://reader036.fdocument.pub/reader036/viewer/2022071517/613ad874f8f21c0c8268ab2e/html5/thumbnails/55.jpg)
Fischbach, Jenkins, and Sturrock et al.;Rencontres de Moriond; La Thuile, Italy 2011
0.92
0.94
0.96
0.98
1.00
1.02
1.04
1.06
1.08
0.98
0.985
0.99
0.995
1
1.005
1.01
1.015
1.02
12/31/2003 6/30/2004 12/30/2004 6/30/2005 12/30/2005 7/1/2006 12/30/2006 7/1/2007 12/31/2007 6/30/2008 12/30/2008 6/30/2009 12/30/2009
Hel
iola
titu
de a
nd 1
/R2
Nor
mal
ized
Cl-3
6 Co
unts
Date
Ohio State (Preliminary 36Cl)
Normalized Cl-36 Counts Fxn F (Heliolatitude and 1/R2)
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Fischbach, Jenkins, and Sturrock et al.;Rencontres de Moriond; La Thuile, Italy 2011
OSU Power Spectrum
![Page 57: Evidence of Solar Influences on Nuclear Decay Rates · 2021. 7. 8. · Jere Jenkins Ephraim Fischbach. Peter Sturrock. Ed Merritt. Josh Mattes. Tasneem Mohsinally. Dan Mundy. John](https://reader036.fdocument.pub/reader036/viewer/2022071517/613ad874f8f21c0c8268ab2e/html5/thumbnails/57.jpg)
Fischbach, Jenkins, and Sturrock et al.;Rencontres de Moriond; La Thuile, Italy 2011
PARKHOMOVData from other institutions
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Fischbach, Jenkins, and Sturrock et al.;Rencontres de Moriond; La Thuile, Italy 2011
Parkhomov, A.G., Researches of alpha and beta radioactivity at long-term observations, arXiv:1004.1761v1 [physics.gen-ph], (2010)
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Fischbach, Jenkins, and Sturrock et al.;Rencontres de Moriond; La Thuile, Italy 2011
SIEGERT, PTB (EUROPIUM)Data from other institutions
![Page 60: Evidence of Solar Influences on Nuclear Decay Rates · 2021. 7. 8. · Jere Jenkins Ephraim Fischbach. Peter Sturrock. Ed Merritt. Josh Mattes. Tasneem Mohsinally. Dan Mundy. John](https://reader036.fdocument.pub/reader036/viewer/2022071517/613ad874f8f21c0c8268ab2e/html5/thumbnails/60.jpg)
Fischbach, Jenkins, and Sturrock et al.;Rencontres de Moriond; La Thuile, Italy 2011
H. Siegert, et al., Appl. Rad. & Isot., 49 (1998) 1397-1401
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Fischbach, Jenkins, and Sturrock et al.;Rencontres de Moriond; La Thuile, Italy 2011
Data Summary
Experiment Detector TypeDecayType
MeasuredRadiation
TypeObservedVariations
PTB (226Ra) Ion Chamber Gas α, β, γ γ Annual
PTB (152Eu) GeLi Solid State ε, γ γ Annual
BNL (32Si/36Cl) Prop. Counter Gas β- β- Annual
Purdue (54Mn) NaI(Tl) Scintillator ε, γ γ Flare
CNRC (56Mn) NaI(Tl) Scintillator β-, γ γ Annual
OSU (36Cl) G-M Gas β- β- Annual
Parkhomov (90Sr/90Y-I) G-M Gas β- β- Annual
Parkhomov (90Sr/90Y-II) G-M Gas β- β- Annual
Parkhomov (60Co) G-M Gas β-, γ β-, γ Weak Annual
Parkhomov (239Pu) Si Solid State α α None
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Fischbach, Jenkins, and Sturrock et al.;Rencontres de Moriond; La Thuile, Italy 2011
Possible Mechanisms
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Fischbach, Jenkins, and Sturrock et al.;Rencontres de Moriond; La Thuile, Italy 2011
Possible Mechanisms and New Long Range Forces
• The Sun can influence nuclear decays either through new long-range fields or through particles such as neutrinos, axions, or other non-standard objects
• If the effect arises from a new long-range field, then any such field must have a range of ~1 a.u. Such spin-independent fields are highly constrained.
• If the sun influences nuclear decays through emission of particles, then these can influence nuclear decays through relatively short-range fields which tend to be less highly constrained.
• Spin-dependent long-range forces are relatively poorly constrained, and may provide an appropriate mechanism to explain time-varying decay rates.
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Fischbach, Jenkins, and Sturrock et al.;Rencontres de Moriond; La Thuile, Italy 2011
Possible Mechanisms-I
• Spatial Variation of the Fine Structure Constant α– This is an example of a mechanism whose
existence depends on a field whose range is ~1 a.u.
– Such a field is strongly constrained by both 5th force type experiments, and atomic physics experiments.
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Fischbach, Jenkins, and Sturrock et al.;Rencontres de Moriond; La Thuile, Italy 2011
Spatial Variation of the Fine Structure Constant alpha
For alpha decay (e.g., 226Ra arrow 222Rn + 4He)31 6.3 10
4v
Z cδα δ δα π α
−Γ Γ ≈ → × Γ Γ From our 226Ra data,
3 53 10 2 10δ δαα
− −Γ≈ × ⇒ ≈ ×
Γ
This may be incompatible with existing WEP and 5th force constraints.
References: D. J. Shaw, gr-qc/0702090; J.D. Barrow and D. J. Shaw,
arXiv:0806:4317; J.-P. Uzan, Rev. Mod. Phys. 75, 403 (2003)
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Fischbach, Jenkins, and Sturrock et al.;Rencontres de Moriond; La Thuile, Italy 2011
Possible Mechanisms-II
• Spin-dependent long range force coupling to neutrinos– This is an example of where a spin-
dependent force of relatively short range could provide an explanation of the decay data.
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Fischbach, Jenkins, and Sturrock et al.;Rencontres de Moriond; La Thuile, Italy 2011
Spin-dependent long range force coupling to neutrinos
Δ
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Fischbach, Jenkins, and Sturrock et al.;Rencontres de Moriond; La Thuile, Italy 2011
1. For beta-decay, where Gamma is extremely sensitive to small shifts in E0
2. Assume E0 arrow E0+Delat, where Delta arises from solar neutrinos, then
3. Next, assumewhere
4. For an un-polarized sample,
Variation in Solar Neutrino Flux2 2 2
0( )ed E E m E EdEΓ∝ − −
2 2 20 0 0( ) ( ) 2 ( )E E E E E E− → − + ∆ − + ∆
1 2 1 23ˆ ˆ[3( )( )A r r
rσ σ σ σ∆ = ⋅ ⋅ − ⋅
1 = νe , 2 = p,e,n,νe
(E0 − E)2 → (E0 − E)2 + ∆2
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Fischbach, Jenkins, and Sturrock et al.;Rencontres de Moriond; La Thuile, Italy 2011
Variation in Solar Neutrino Flux (cont’d)5. Compare this to the change induced by
2 2 2 2 20
1 ( ) , 2v vFor E E m m− ∆ ⇒ ∆ ≈ −
(E0 − E)2 → (E0 − E) (E0 − E)2 − mv2
mν2 ≠ 0
2 2 2
2 2 2
= 100 eV to 10 eV .
50 eV to 5 eVvm − −
⇒ ∆ =This may be compatible with current limits on neutrino magnetic dipole moments.
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Fischbach, Jenkins, and Sturrock et al.;Rencontres de Moriond; La Thuile, Italy 2011