Effects of a Periodic Decay Rate on the Statistics of Radioactive Decay: New Methods to Search for Violations of the Law of Radioactive Change
Author(s)
M. P. Silverman*
ABSTRACT
It is a long-held tenet of nuclear physics, from the early work of Rutherford and Soddy up to present times that the disintegration of each species of radioactive nuclide occurs randomly at a constant rate unaffected by interactions with the external environment. During the past 15 years or so, reports have been published of some 10 or more unstable nuclides with non-exponential, periodic decay rates claimed to be of geophysical, astrophysical, or cosmological origin. Deviations from standard exponential decay are weak, and the claims are controversial. This paper examines the effects of a periodic decay rate on the statistical distributions of 1) nuclear activity measurements and 2) nuclear lifetime measurements. It is demonstrated that the modifications to these distributions are approximately 100 times more sensitive to non-standard radioactive decay than measurements of the decay curve, power spectrum, or autocorrelation function for corresponding system parameters.
It is a long-held tenet of nuclear physics, from the early work of Rutherford and Soddy up to present times that the disintegration of each species of radioactive nuclide occurs randomly at a constant rate unaffected by interactions with the external environment. During the past 15 years or so, reports have been published of some 10 or more unstable nuclides with non-exponential, periodic decay rates claimed to be of geophysical, astrophysical, or cosmological origin. Deviations from standard exponential decay are weak, and the claims are controversial. This paper examines the effects of a periodic decay rate on the statistical distributions of 1) nuclear activity measurements and 2) nuclear lifetime measurements. It is demonstrated that the modifications to these distributions are approximately 100 times more sensitive to non-standard radioactive decay than measurements of the decay curve, power spectrum, or autocorrelation function for corresponding system parameters.
KEYWORDS
Radioactive Decay, Non-Exponential Decay, Time-Dependent Decay, Half-Life, Lifetime, Decay Curve
Radioactive Decay, Non-Exponential Decay, Time-Dependent Decay, Half-Life, Lifetime, Decay Curve
Cite this paper
Silverman, M. (2015) Effects of a Periodic Decay Rate on the Statistics of Radioactive Decay: New Methods to Search for Violations of the Law of Radioactive Change. Journal of Modern Physics, 6, 1533-1553. doi: 10.4236/jmp.2015.611157.
Silverman, M. (2015) Effects of a Periodic Decay Rate on the Statistics of Radioactive Decay: New Methods to Search for Violations of the Law of Radioactive Change. Journal of Modern Physics, 6, 1533-1553. doi: 10.4236/jmp.2015.611157.
References
[1] Magill, J. and Galy, J. (2005) Radioactivity, Radionuclides, Radiation. Springer, Heidelberg. [2] Rutherford, E. and Soddy, F. (1903) Radioactive Change. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 5, 576-591. [Reproduced in Romer, A., The Discovery of Radioactivity and Transmutation (Dover, 1964), 152-166]. (Quoted Lines Are from Page 157). [3] Lapp, R.E. and Andrews, H.L. (1973) Nuclear Radiation Physics. 4th Edition, Prentice-Hall, Englewood Cliffs, 177-178. [4] Bambynek, W., Behrens, H., Chen, M.H., Crasemann, B., Fitzpatrick, M.L., Ledingham, K.W.D., et al. (1977) Reviews of Modern Physics, 49, 77-221.
http://dx.doi.org/10.1103/RevModPhys.49.77 [5] Huh, C.-A. (1999) Earth and Planetary Science Letters, 171, 325-328.
http://dx.doi.org/10.1016/S0012-821X(99)00164-8 [6] Bosch, F., Faestermann, T., Friese, J., Heine, F., Kienle, P., Wefers, E., et al. (1996) Physical Review Letters, 77, 5190-5193.
http://dx.doi.org/10.1103/PhysRevLett.77.5190 [7] Heitler, W. (1954) The Quantum Theory of Radiation. 3rd Edition, Oxford University Press, London, 168-169. [8] Silverman, M.P. and Pipkin, F.M. (1972) Journal of Physics B: Atomic and Molecular Physics, 5, 2236-2256.
http://dx.doi.org/10.1088/0022-3700/5/12/018 [9] Silverman, M.P. (2000) Probing the Atom: Interactions of Coupled States, Fast Beams, and Loose Electrons. Princeton University Press, Princeton, 123-126. [10] Wilkinson, S.R., Bharucha, C.F., Fischer, M.C., Madison, K.W., Morrow, P.R., Niu, Q., Sundaram, B. and Raizen, M.G. (1997) Nature, 387, 575-577.
http://dx.doi.org/10.1038/42418 [11] Rothe, C., Hintschich, S. and Monkman, A. (2006) Physical Review Letters, 96, Article ID: 163601.
http://dx.doi.org/10.1103/PhysRevLett.96.163601 [12] Peshkin, M., Volva, A. and Zelevinsky, V. (2014) EPL, 107, Article ID: 40001.
http://dx.doi.org/10.1209/0295-5075/107/40001 [13] Aston, P.J. (2012) EPL, 97, Article ID: 52001.
http://dx.doi.org/10.1209/0295-5075/97/52001 [14] Zelevinsky, V. and Volya, A. (2011) Bulletin of the American Physical Society, 56, Abs. JD006Z. [15] Scholl, S.E., Kolombet, V.A., Pozharskii, E.V., Zenchenko, T.A., Zvereva, I.M. and Konradov, A.A. (1998) Uskekhi, 41, 1025-1035. [16] Jenkins, J.H., Fischbach, E., Buncher, J.B., Gruenwald, J.T., Krause, D.E. and Mattes, J.J. (2009) Astroparticle Physics, 32, 42-46.
http://dx.doi.org/10.1016/j.astropartphys.2009.05.004 [17] Baurov, Y., Sobolev, Y. and Ryabov, Y. (2014) American Journal of Astronomy and Astrophysics, 2, 8-19. [18] Silverman, M.P. and Strange, W. (2009) EPL, 87, Article ID: 32001.
http://dx.doi.org/10.1209/0295-5075/87/32001 [19] Norman, E.B., Browne, E., Shugart, H.A., Joshi, T.H. and Firestone, R.B. (2009) Astroparticle Physics, 31, 135-137.
http://dx.doi.org/10.1016/j.astropartphys.2008.12.004 [20] Cooper, P.S. (2009) Astroparticle Physics, 31, 267-269.
http://dx.doi.org/10.1016/j.astropartphys.2009.02.005 [21] Silverman, M.P. (2015) EPL, 110, Article ID: 52001. [22] Pommé, S. (2007) Problems with the Uncertainty Budget of Half-Life Measurements. Proceedings of the 230th American Chemical Society National Meeting, Workshop on Applied Modeling and Computation in Nuclear Science, Washington DC, 28 August-2 September 2005, American Chemical Society, 282-292. [23] Silverman, M.P. (2014) EPL, 105, Article ID: 22001.
http://dx.doi.org/10.1209/0295-5075/105/22001 [24] Martin, R., Burns, K. and Taylor, J. (1997) Nuclear Instruments and Methods in Physics Research Section A, 390, 267-273.
http://dx.doi.org/10.1016/S0168-9002(97)00354-9 [25] Mood, A., Graybill, F. and Boes, D. (1974) Introduction to the Theory of Statistics. 3rd Edition, McGraw-Hill, New York, 122-123. [26] Seshadri, V. (1999) The Inverse Gaussian Distribution: Statistical Theory and Applications. Springer, New York, 43.
http://dx.doi.org/10.1007/978-1-4612-1456-4 [27] Silverman, M.P. (2014) A Certain Uncertainty: Nature’s Random Ways. Cambridge University Press, Cambridge, 287-304.
http://dx.doi.org/10.1017/cbo9781139507370 [28] Silverman, M.P., Strange, W. and Lipscombe, T.C. (2004) EPL, 67, 572-578.
http://dx.doi.org/10.1209/epl/i2004-10097-5 [29] Forbes, C., Evans, M., Hastings, N. and Peacock, B. (2011) Statistical Distributions. 4th Edition, Wiley, Hoboken, 66-68. [30] Hogg, R.V. and Craig, A.T. (1978) Introduction to Mathematical Statistics. 4th Edition, Macmillan, New York, 192-199. [31] Shannon, C.E. (1949) Communication in the Presence of Noise. Proceedings of the IRE, 37, 10-21.
http://dx.doi.org/10.1109/jrproc.1949.232969 [32] Kendall, M., Stuart, A. and Ord, J.K. (1983) The Advanced Theory of Statistics. Vol. 3, 4th Edition, Macmillan, New York, 443-445. [33] Bendat, J.S. (1958) Principles and Applications of Random Noise Theory. Wiley, Hoboken, 65-70. [34] Lee, T.D. and Yang, C.N. (1956) Physical Review, 104, 254-258.
http://dx.doi.org/10.1103/PhysRev.104.254 [35] Wu, C.S., Ambler, E., Hayward, R., Hoppes, D. and Hudson, R. (1957) Physical Review, 105, 1413-1415.
http://dx.doi.org/10.1103/PhysRev.105.1413
[1] Magill, J. and Galy, J. (2005) Radioactivity, Radionuclides, Radiation. Springer, Heidelberg. [2] Rutherford, E. and Soddy, F. (1903) Radioactive Change. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 5, 576-591. [Reproduced in Romer, A., The Discovery of Radioactivity and Transmutation (Dover, 1964), 152-166]. (Quoted Lines Are from Page 157). [3] Lapp, R.E. and Andrews, H.L. (1973) Nuclear Radiation Physics. 4th Edition, Prentice-Hall, Englewood Cliffs, 177-178. [4] Bambynek, W., Behrens, H., Chen, M.H., Crasemann, B., Fitzpatrick, M.L., Ledingham, K.W.D., et al. (1977) Reviews of Modern Physics, 49, 77-221.
http://dx.doi.org/10.1103/RevModPhys.49.77 [5] Huh, C.-A. (1999) Earth and Planetary Science Letters, 171, 325-328.
http://dx.doi.org/10.1016/S0012-821X(99)00164-8 [6] Bosch, F., Faestermann, T., Friese, J., Heine, F., Kienle, P., Wefers, E., et al. (1996) Physical Review Letters, 77, 5190-5193.
http://dx.doi.org/10.1103/PhysRevLett.77.5190 [7] Heitler, W. (1954) The Quantum Theory of Radiation. 3rd Edition, Oxford University Press, London, 168-169. [8] Silverman, M.P. and Pipkin, F.M. (1972) Journal of Physics B: Atomic and Molecular Physics, 5, 2236-2256.
http://dx.doi.org/10.1088/0022-3700/5/12/018 [9] Silverman, M.P. (2000) Probing the Atom: Interactions of Coupled States, Fast Beams, and Loose Electrons. Princeton University Press, Princeton, 123-126. [10] Wilkinson, S.R., Bharucha, C.F., Fischer, M.C., Madison, K.W., Morrow, P.R., Niu, Q., Sundaram, B. and Raizen, M.G. (1997) Nature, 387, 575-577.
http://dx.doi.org/10.1038/42418 [11] Rothe, C., Hintschich, S. and Monkman, A. (2006) Physical Review Letters, 96, Article ID: 163601.
http://dx.doi.org/10.1103/PhysRevLett.96.163601 [12] Peshkin, M., Volva, A. and Zelevinsky, V. (2014) EPL, 107, Article ID: 40001.
http://dx.doi.org/10.1209/0295-5075/107/40001 [13] Aston, P.J. (2012) EPL, 97, Article ID: 52001.
http://dx.doi.org/10.1209/0295-5075/97/52001 [14] Zelevinsky, V. and Volya, A. (2011) Bulletin of the American Physical Society, 56, Abs. JD006Z. [15] Scholl, S.E., Kolombet, V.A., Pozharskii, E.V., Zenchenko, T.A., Zvereva, I.M. and Konradov, A.A. (1998) Uskekhi, 41, 1025-1035. [16] Jenkins, J.H., Fischbach, E., Buncher, J.B., Gruenwald, J.T., Krause, D.E. and Mattes, J.J. (2009) Astroparticle Physics, 32, 42-46.
http://dx.doi.org/10.1016/j.astropartphys.2009.05.004 [17] Baurov, Y., Sobolev, Y. and Ryabov, Y. (2014) American Journal of Astronomy and Astrophysics, 2, 8-19. [18] Silverman, M.P. and Strange, W. (2009) EPL, 87, Article ID: 32001.
http://dx.doi.org/10.1209/0295-5075/87/32001 [19] Norman, E.B., Browne, E., Shugart, H.A., Joshi, T.H. and Firestone, R.B. (2009) Astroparticle Physics, 31, 135-137.
http://dx.doi.org/10.1016/j.astropartphys.2008.12.004 [20] Cooper, P.S. (2009) Astroparticle Physics, 31, 267-269.
http://dx.doi.org/10.1016/j.astropartphys.2009.02.005 [21] Silverman, M.P. (2015) EPL, 110, Article ID: 52001. [22] Pommé, S. (2007) Problems with the Uncertainty Budget of Half-Life Measurements. Proceedings of the 230th American Chemical Society National Meeting, Workshop on Applied Modeling and Computation in Nuclear Science, Washington DC, 28 August-2 September 2005, American Chemical Society, 282-292. [23] Silverman, M.P. (2014) EPL, 105, Article ID: 22001.
http://dx.doi.org/10.1209/0295-5075/105/22001 [24] Martin, R., Burns, K. and Taylor, J. (1997) Nuclear Instruments and Methods in Physics Research Section A, 390, 267-273.
http://dx.doi.org/10.1016/S0168-9002(97)00354-9 [25] Mood, A., Graybill, F. and Boes, D. (1974) Introduction to the Theory of Statistics. 3rd Edition, McGraw-Hill, New York, 122-123. [26] Seshadri, V. (1999) The Inverse Gaussian Distribution: Statistical Theory and Applications. Springer, New York, 43.
http://dx.doi.org/10.1007/978-1-4612-1456-4 [27] Silverman, M.P. (2014) A Certain Uncertainty: Nature’s Random Ways. Cambridge University Press, Cambridge, 287-304.
http://dx.doi.org/10.1017/cbo9781139507370 [28] Silverman, M.P., Strange, W. and Lipscombe, T.C. (2004) EPL, 67, 572-578.
http://dx.doi.org/10.1209/epl/i2004-10097-5 [29] Forbes, C., Evans, M., Hastings, N. and Peacock, B. (2011) Statistical Distributions. 4th Edition, Wiley, Hoboken, 66-68. [30] Hogg, R.V. and Craig, A.T. (1978) Introduction to Mathematical Statistics. 4th Edition, Macmillan, New York, 192-199. [31] Shannon, C.E. (1949) Communication in the Presence of Noise. Proceedings of the IRE, 37, 10-21.
http://dx.doi.org/10.1109/jrproc.1949.232969 [32] Kendall, M., Stuart, A. and Ord, J.K. (1983) The Advanced Theory of Statistics. Vol. 3, 4th Edition, Macmillan, New York, 443-445. [33] Bendat, J.S. (1958) Principles and Applications of Random Noise Theory. Wiley, Hoboken, 65-70. [34] Lee, T.D. and Yang, C.N. (1956) Physical Review, 104, 254-258.
http://dx.doi.org/10.1103/PhysRev.104.254 [35] Wu, C.S., Ambler, E., Hayward, R., Hoppes, D. and Hudson, R. (1957) Physical Review, 105, 1413-1415.
http://dx.doi.org/10.1103/PhysRev.105.1413