Lý thuyết về hạt khối lượng biến đổi và hiện tượng hạt nhân năng lượng thấp

Foundations of Physics - Tập 44 - Trang 144-174 - 2014
Mark Davidson1
1Spectel Research Corporation, Palo Alto, USA

Tóm tắt

Khối lượng hạt biến đổi đôi khi đã được viện dẫn để giải thích những bất thường quan sát được trong các phản ứng hạt nhân năng lượng thấp (LENR). Hành vi như vậy chưa bao giờ được quan sát trực tiếp và không được coi là khả thi trong vật lý hạt nhân lý thuyết. Tuy nhiên, tồn tại những lý thuyết biến phân covariant ngoài mặt phẳng về động học hạt relativistic, bắt nguồn từ các công trình của Fock, Stueckelberg, Feynman, Greenberger, Horwitz, và những người khác. Chúng tôi xem xét một số lý thuyết này và cũng xem xét các hạt ảo phát sinh trong các sơ đồ Feynman thông thường trong các lý thuyết trường tương đối. Các mô hình Lagrangian hiệu quả tích hợp lý thuyết hạt khối lượng biến có thể hữu ích trong việc mô tả các phản ứng hạt nhân bất thường bằng cách kết hợp sự dịch chuyển khối lượng cùng với hiện tượng đường hầm cộng hưởng và các hiệu ứng khác. Một mô hình chi tiết cho sự gộp fusion cộng hưởng trong phân tử deuterium với các deuteron và electron không nằm trên mặt phẳng được trình bày như một ví dụ. Các phương pháp thực nghiệm để quan sát hành vi không nằm trên mặt phẳng này một cách trực tiếp, nếu tồn tại, sẽ được đề xuất và mô tả. Các giải thích ngắn gọn cho việc chuyển hóa nguyên tố và sự hình thành các hố vi mô cũng sẽ được đưa ra, và một cơ chế thay thế cho sự dịch chuyển khối lượng trong lý thuyết Widom–Larsen được trình bày. Nếu các lý thuyết khối lượng biến đổi nhận được sự ủng hộ thực nghiệm từ LENR, thì chúng chắc chắn sẽ có những hệ quả quan trọng đối với nền tảng của cơ học lượng tử, và có thể phát sinh các ứng dụng thực tiễn.

Từ khóa

#hạt khối lượng biến đổi #phản ứng hạt nhân năng lượng thấp #lý thuyết Feynman #cơ học lượng tử #hạt ảo

Tài liệu tham khảo

Storms, E.: Science of Low Energy Nuclear Reaction: A Comprehensive Compilation of Evidence and Explanations about Cold Fusion. World Scientific Publishing Company (2007) Srinivasan, M., Miley, G., Storms, E.: Low-energy nuclear reactions: transmutations. In: Krivit, S.B., Lehr, J.H., Kingery, T.B. (eds.) Nuclear Energy Encyclopedia, pp. 503–539. Wiley (2011). URL http://onlinelibrary.wiley.com/doi/10.1002/9781118043493.ch43/summary Fock, V.: Die Eigenzeit in der klassischen und in der Quantenmechanik. Phys. Z. Sowjetunion 12, 404 (1937) Stueckelberg, E.: La signification du temps propre en mécanique ondulatoire. Helv. Phys. Acta 14, 322 (1941) Stueckelberg, E.: Remarque à propos de la création de paires de particules en théorie de la relativité. Helv. Phys. Acta 14, 588 (1941) Lacki, J., Ruegg, H., Wanders, G.: E.C.G. Stueckelberg, An Unconventional Figure of Twentieth Century Physics: Selected Scientific Papers with Commentaries. Springer (2008) Feynman, R.P.: Mathematical formulation of the quantum theory of electromagnetic interaction. Phys. Rev. 80(3), 440 (1950). doi:10.1103/PhysRev.80.440 Horwitz, L.P., Piron, C.: Relativistic dynamics. Helv. Phys. Acta 46(3), 316 (1973). URL http://www.osti.gov/energycitations/product.biblio.jsp?osti_id=4355335 Reuse, F.: On classical and quantum relativistic dynamics. Found. Phys. 9(11–12), 865 (1979). doi:10.1007/BF00708697 Fanchi, J.R.: Parametrized Relativistic Quantum Theory. Springer GmbH (1993). Horwitz, L.P., Lavie, Y.: Scattering theory in relativistic quantum mechanics. Phys. Rev. D 26(4), 819 (1982). doi:10.1103/PhysRevD.26.819 Horwitz, L., Shnerb, N.: Second quantization of the stueckelberg relativistic quantum theory and associated gauge fields. Found. Phys. 28(10), 1509 (1998). doi:10.1023/A:1018841000237. URL http://www.springerlink.com/content/rw725423p4l33516/abstract/ Land, M.C., Horwitz, L.P.: The Lorentz force and energy-momentum for off-shell electromagnetism. Found. Phys. Lett. 4(1), 61 (1991). doi:10.1007/BF00666417 Land, M.C.: Pre-maxwell electrodynamics. Found. Phys. 28(9), 1479 (1998). doi:10.1023/A:1018813429428 Seidewitz, E.: Spacetime path formalism for massive particles of any spin. Ann. Phys. 324(2), 309 (2009). doi:10.1016/j.aop.2008.10.007. URL http://www.sciencedirect.com/science/article/pii/S0003491608001668 Aharonovich, I., Horwitz, L.P.: Radiation-reaction in classical off-shell electrodynamics. I. The above mass-shell case. J. Math. Phys. 53(3), 032902 (2012). doi:10.1063/1.3694276. URL http://jmp.aip.org/resource/1/jmapaq/v53/i3/p032902_s1?bypassSSO=1 Burakovsky, L., Horwitz, L.: Equilibrium relativistic mass distribution. Phys. A 201(4), 666 (1993). doi:10.1016/0378-4371(93)90135-Q. URL http://www.sciencedirect.com/science/article/pii/037843719390135Q Burakovsky, L., Horwitz, L.P.: Galilean limit of equilibrium relativistic mass distribution. J. Phys. A 27(8), 2623 (1994). doi:10.1088/0305-4470/27/8/003. URL http://iopscience.iop.org/0305-4470/27/8/003 Burakovsky, L., Horwitz, L.P.: Mass-Proper Time Uncertainty Relation in a Manifestly Covariant Relativistic Statistical Mechanics. ArXiv High Energy Physics-Theory e-prints, p. 4106 (1996). URL http://adsabs.harvard.edu/abs/1996hepth4106B Greenberger, D.M.: Theory of particles with variable Mass. I. Formalism. J. Math. Phys. 11(8), 2329 (1970). doi:10.1063/1.1665400. http://jmp.aip.org/resource/1/jmapaq/v11/i8/p2329_s1?isAuthorized=no Greenberger, D.M.: Theory of particles with variable mass. II. Some physical consequences. J. Math. Phys. 11(8), 2341 (1970). doi:10.1063/1.1665401. URL http://jmp.aip.org/resource/1/jmapaq/v11/i8/p2341_s1?isAuthorized=no Greenberger, D.M.: Some useful properties of a theory of variable mass particles. J. Math. Phys. 15(4), 395 (1974). doi:10.1063/1.1666658. URL http://link.aip.org/link/?JMP/15/395/1&Agg=doi Greenberger, D.M.: Wavepackets for particles of indefinite mass. J. Math. Phys. 15(4), 406 (1974). doi:10.1063/1.1666659. URL http://link.aip.org/link/?JMP/15/406/1&Agg=doi Corben, H.C.: Relativistic quantum theory of particles with variable mass I. Proc. Natl. Acad. Sci. USA 48(9), 1559 (1962) Corben, H.C.: Relativistic quantum theory of particles with variable mass, II. Proc. Natl. Acad. Sci. USA. 48(10), 1746 (1962). URL http://www.ncbi.nlm.nih.gov/pmc/articles/PMC221034/. PMID: 16591007 PMCID: PMC221034 Fanchi, J.R.: Review of invariant time formulations of relativistic quantum theories. Found. Phys. 23(3), 487 (1993). doi:10.1007/BF01883726 Adler, S.L.: Quantum theory as an emergent phenomenon: the statistical mechanics of matrix models as the precursor of quantum field theory. Quantum Theory as an Emergent Phenomenon: The Statistical Mechanics of Matrix Models as the Precursor of Quantum Field Theory. Cambridge University Press (2004) ’t Hooft, G.: The Free-Will Postulate in Quantum Mechanics. arxiv.org 0707.4568 (2007). doi:10.1063/1.2823751. URL http://arxiv.org/abs/0707.4568. AIPConf.Proc. 957:154-163 ’t Hooft, G.: Determinism beneath quantum mechanics. Quo Vadis quantum mechanics? In: Elitzur, A.C., Dolev, S., Kolenda, N. (eds.) The Frontiers Collection, pp. 99–111. Springer, Berlin (2005). URL http://www.springerlink.com/content/t545r734304254q3/ ’t Hooft, G.: Entangled quantum states in a local deterministic theory. arxiv.org 0908.3408 (2009). URL http://arxiv.org/abs/0908.3408 Weinberg, S.: Collapse of the State Vector. arXiv.org 1109.6462 (2011). URL http://arxiv.org/abs/1109.6462 Koonin, S.E., Nauenberg, M.: Calculated fusion rates in isotopic hydrogen molecules. Nature 339(6227), 690 (1989). doi:10.1038/339690a0. URL http://www.nature.com/nature/journal/v339/n6227/abs/339690a0.html Fleischmann, M., Pons, S., Hawkins, M.: Electrochemically induced nuclear fusion of deuterium. J. Electroanal. Chem. 261(2), 301–308 (1989). URL http://www.ftp.nic.funet.fi/pub/doc/Fusion/fp.ps Leggett, A.J., Baym, G.: Exact upper bound on barrier penetration probabilities in many-body systems: Application to “cold fusion”. Phys. Rev. Lett. 63(2), 191 (1989). doi:10.1103/PhysRevLett.63.191 Leggett, A.J., Baym, G.: Can solid-state effects enhance the cold-fusion rate?. Nature 340(6228), 45 (1989). doi:10.1038/340045a0. URL http://www.nature.com/nature/journal/v340/n6228/abs/340045a0.html Czerski, K., Huke, A., Biller, A., Heide, P., Hoeft, M., Ruprecht, G.: Enhancement of the electron screening effect for d + d fusion reactions in metallic environments. Europhys. Lett. (EPL) 54(4), 449 (2001). doi:10.1209/epl/i2001-00265-7. URL http://iopscience.iop.org/epl/i2001-00265-7 Czerski, K., Huke, A., Heide, P., Ruprecht, G.: The \({}^{2}\)H(d, p)\({}^{3}\)H reaction in metallic media at very low energies. Europhys. Lett. 68, 363 (2004). doi:10.1209/epl/i2004-10209-3. URL http://adsabs.harvard.edu/abs/2004EL68.363C Czerski, K., Huke, A., Heide, P., Ruprecht, G.: Experimental and theoretical screening energies for the \({}^{2}\)H(d, p)\({}^{3}\)H reaction in metallic environments. In: The 2nd International Conference on Nuclear Physics in Astrophysics, ed. by Z. Fülöp, G. Gyürky, E. Somorjai (Springer, Berlin Heidelberg, 2006), pp. 83–88. URL http://www.springerlink.com/content/k740562323673840/abstract/ Czerski, K., Huke, A., Martin, L., Targosz, N., Blauth, D., Górska, A., Heide, P., Winter, H.: Measurements of enhanced electron screening in d+d reactions under UHV conditions. Journal of Physics G: Nucl. Part. Phys. 35(1), 014012 (2008). doi:10.1088/0954-3899/35/1/014012. URL http://iopscience.iop.org/0954-3899/35/1/014012 Czerski, K.: Enhanced electron screening and nuclear mechanism of cold fusion. in ICCF-15, vol. 15, pp. 197–202. ENEA, Rome, Italy (2009). URL http://www.enea.it/it/produzione-scientifica/edizioni-enea/2012/proceedings-iccf-15-international-conference-on-condensed-matter-nuclear-science Tsyganov, E.N.: Cold nuclear fusion. Phys. At. Nucl. 75(2), 153 (2012). doi:10.1134/S1063778812010140 Atzeni, S., Meyer-ter Vehn, J.: The Physics of Inertial Fusion:BeamPlasma Interaction, Hydrodynamics, Hot Dense Matter: BeamPlasma Interaction, Hydrodynamics, Hot Dense Matter. J. Meyer-ter Vehn, The Physics of Inertial Fusion:BeamPlasma Interaction, Hydrodynamics, Hot Dense Matter: BeamPlasma Interaction, Hydrodynamics, Hot Dense Matter. Oxford University Press (2004). Nagel, D.J.: Scientific overview of ICCF15. Infinite Energy 88, 21 (2009). URL http://www.infinite-energy.com/images/pdfs/nageliccf15.pdf Widom, A., Larsen, L.: Ultra low momentum neutron catalyzed nuclear reactions on metallic hydride surfaces. Eur. Phys. J. C 46(1), 107 (2006). doi:10.1140/epjc/s2006-02479-8 Konopinski, E.J.: What the electromagnetic vector potential describes. Am. J. Phys. 46(5), 499 (1978). doi:10.1119/1.11298. URL http://link.aip.org/link/?AJP/46/499/1&Agg=doi Calkin, M.G.: Linear momentum of quasistatic electromagnetic fields. Am. J. Phys. 34(10), 921 (1966). doi:10.1119/1.1972282. URL http://link.aip.org/link/?AJP/34/921/1&Agg=doi Aguirregabiria, J.M., Hernández, A., Rivas, M.: Linear momentum density in quasistatic electromagnetic systems. Eur. J. Phys. 25(4), 555 (2004). doi:10.1088/0143-0807/25/4/010 Szalewicz, K., Morgan, J.D., Monkhorst, H.J.: Fusion rates for hydrogen isotopic molecules of relevance for “cold fusion”. Phys. Rev A 40(5), 2824 (1989). doi:10.1103/PhysRevA.40.2824 Rabinowitz, M.: High temperature superconductivity and cold fusion. Modern Phys. Lett. B 4, 233 (1990). doi:10.1142/S0217984990000301. URL http://adsabs.harvard.edu/abs/1990MPLB4.233R Jackson, J.: Catalysis of nuclear reactions between hydrogen isotopes by \(\mu \)-mesons. Phys. Rev. 106(2), 330 (1957). doi:10.1103/PhysRev.106.330. URL http://adsabs.harvard.edu/abs/1957PhRv.106.330J Evans, A.B.: 4-Space Dirac theory and LENR. J. Condens. Matter Nucl. Sci. 2, 7 (2009) Evans, A.B.: Four-space formulation of Dirac’s equation. Found. Phys. 20(3), 309 (1990). doi:10.1007/BF00731695 Fearing, H.W., Scherer, S.: Field transformations and simple models illustrating the impossibility of measuring off-shell effects. Phys. Rev. C 62(3), 034003 (2000). doi:10.1103/PhysRevC.62.034003 Tyutin, I.V.: Once again on the equivalence theorem. Phys. At. Nucl. 65(1), 194 (2002). doi:10.1134/1.1446571 Newton, T.D., Wigner, E.P.: Localized states for elementary systems. Rev. Mod. Phys. 21(3), 400 (1949). doi:10.1103/RevModPhys.21.400 Wightman, A.S.: On the localizability of quantum mechanical systems. Rev. Mod. Phys. 34(4), 845 (1962). doi:10.1103/RevModPhys.34.845 Alvarez, E.T.G., Gaioli, F.H.: Feynman’s proper time approach to QED. Found Phys. 28(10), 1529 (1998). doi:10.1023/A:1018882101146 Gorelik, V.S.: Effective mass of photons and the existence of heavy photons in photonic crystals. Phys. Scr. 2010(T140), 014046 (2010). doi:10.1088/0031-8949/2010/T140/014046 Gorelik, V.S.: Bound and dark photonic states in globular photonic crystals. Acta Physica Hungarica A 26(1–2), 37 (2006). doi:10.1556/APH.26.2006.1-2.6 Gorelik, V.S.: Optics of globular photonic crystals. Quantum Electron. 37(5), 409 (2007). doi:10.1070/QE2007v037n05ABEH013478. URL http://www.turpion.org/php/paper.phtml?journal_id=qe&paper_id=13478 John, S., Wang, J.: Quantum electrodynamics near a photonic band gap: photon bound states and dressed atoms. Phys. Rev. Lett. 64(20), 2418 (1990). doi:10.1103/PhysRevLett.64.2418 André, P.J.J.-M.: Effective mass of photons in a one-dimensional photonic crystal. Phys. Scr. 84(3), 035708 (2011). doi:10.1088/0031-8949/84/03/035708 Weinberg, S.: Nuclear forces from chiral lagrangians. Phys. Lett. B 251(2), 288 (1990). doi:10.1016/0370-2693(90)90938-3. URL http://65.54.113.26/Publication/18408213/nuclear-forces-from-chiral-lagrangians Weinberg, S.: Phenomenological lagrangians. Phys. A 96(1–2), 327 (1979). doi:10.1016/0378-4371(79)90223-1. URL http://www.sciencedirect.com/science/article/pii/0378437179902231 Epelbaum, E.: Nuclear forces from chiral effective field theory: a primer. arXiv:1001.3229 (2010). URL http://arxiv.org/abs/1001.3229 Land, M.C., Horwitz, L.P.: Off-Shell Quantum Electrodyn (1996). URL http://arxiv.org/abs/hepth/9601021 arXiv:hepth/9601021 Coleman, S.: Fate of the false vacuum: semiclassical theory. Phys. Rev. D 15(10), 2929 (1977). doi:10.1103/PhysRevD.15.2929 Tomsovic, S., Ullmo, D.: Chaos-assisted tunneling. Phys. Rev. E 50(1), 145 (1994). doi:10.1103/PhysRevE.50.145 Hagelstein, P.L.: Resonant tunneling and resonant excitation transfer. In: Proceedings, ICCF-12, pp. 871–886. Cambridge, MA, USA (2005). doi:10.1142/9789812701510_0079. URL http://adsabs.harvard.edu/abs/2005cmns.conf.871H Li, X.Z.: Overcoming of the gamow tunneling insufficiencies by maximizing the damp-matching resonant tunneling. Czechoslovak J. Phys. 49(6), 985 (1999). doi:10.1023/A:1021485221050 Grifoni, M., Hänggi, P.: Driven quantum tunneling. Phys. Rep. 304(5–6), 229 (1998). doi:10.1016/S0370-1573(98)00022-2. URL http://www.sciencedirect.com/science/article/pii/S0370157398000222 Saad, D., Horwitz, L.P., Arshansky, R.I.: Off-shell electromagnetism in manifestly covariant relativistic quantum mechanics. Found. Phys. 19(10), 1125–1149 (1989). doi:10.1007/BF00731876 Horwitz, L.P., Arshansky, R.I., Elitzur, A.C.: On the two aspects of time: The distinction and its implications. Found. Phys. 18(12), 1159 (1988). doi:10.1007/BF01889430 Land, M.C., Horwitz, L.P.: Green’s functions for off-shell electromagnetism and spacelike correlations. Found. Phys. 21(3), 299 (1991). doi:10.1007/BF01883636 Land, M.C.: Particles and events in classical off-shell electrodynamics. Found. Phys. 27(1), 19 (1997). doi:10.1007/BF02550153 Land, M.: Abraham-Lorentz-Dirac equation in 5D Stuekelberg electrodynamics. J. Phys. Conf. Ser. 330, 012015 (2011). doi:10.1088/1742-6596/330/1/012015. URL http://iopscience.iop.org/1742-6596/330/1/012015 Horwitz, L.: Spin, angular momentum and spin-statistics for a relativistic quantum many-body system. J. Phys. A 46(3), 035305 (2013). URL http://stacks.iop.org/1751-8121/46/i=3/a=035305 Horwitz, L.P., Arshansky, R.: On relativistic quantum theory for particles with spin 1/2. J. Phys. A 15(12), L659 (1982). doi:10.1088/0305-4470/15/12/002. URL http://iopscience.iop.org/0305-4470/15/12/002 Fanchi, J.: Resolution of the Klein paradox for spin-1/2 particles. Found. Phys. 11(5), 493 (1981). doi:10.1007/BF00727077. URL http://www.springerlink.com/content/v3211wt465115256/abstract/ Piron, C., Reuse, F.: Relativistic dynamics for the spin 1/2 particle. Helv. Phys. Acta 51, 146–176 (1978) Horwitz L.P., Piron, C., Reuse, F.: Relativistic dynamics for the Spin 1/2 particle. Helv. Phys. Acta 48(4), 546–548; 48(4) (1975). URL http://www.osti.gov/energycitations/product.biblio.jsp?osti_id=4018859 Proca, A.: J. Phys. Rad. 7, 347–353 (1936) Lee, T.D., Yang, C.N.: Theory of charged vector memons interacting with the electromagnetic field. Phys. Rev. 128(2), 885 (1962). doi:10.1103/PhysRev.128.885 Ruck, H.M., Greiner, W.: A study of the electromagnetic interaction given by relativistic spin-1 wave equations in elastic scattering of polarized spin-1 nuclei or mesons. J. Phys. G 3(5), 657 (1977). doi:10.1088/0305-4616/3/5/013. URL http://iopscience.iop.org/0305-4616/3/5/013 Kaplan, D.B., Savage, M.J., Wise, M.B.: Perturbative calculation of the electromagnetic form factors of the deuteron. Phys. Rev. C 59(2), 617 (1999). doi:10.1103/PhysRevC.59.617 Horwitz, L.P., Katz, N., Oron, O.: Could the classical relativistic electron be a strange attractor? Discret. Dyn. Nat. Soc. 2004(1), 179 (2004). doi:10.1155/S1026022604401034. URL http://www.hindawi.com/journals/ddns/2004/205916/abs/ Roitgrund, A., Horwitz, L.: Simulation of the radiation reaction orbits of a classical relativistic charged particle with generalized off-shell Lorentz force. Discret. Dyn. Nat. Soc. 2010 1(2010). doi:10.1155/2010/602784. URL https://eudml.org/doc/230976 Burakovsky, L., Horwitz, L.P., Schieve, W.C.: New relativistic high-temperature Bose-Einstein condensation. Phys. Rev. D 54(6), 4029 (1996). doi:10.1103/PhysRevD.54.4029 Land, M.: Higher-Order Kinetic Term for Controlling Photon Mass in Off-Shell Electrodynamics (2006) 2003, doi:10.1023/A:1025670806787. URL http://arxiv.org/abs/hepth/0603074. Found. Phys. 33:1157-1175 arXiv:hepth/0603074 Horwitz, L., Schieve, W., Piron, C.: Gibbs ensembles in relativistic classical and quantum mechanics. Ann. Phys. 137(2), 306 (1981). doi:10.1016/0003-4916(81)90199-8. URL http://www.sciencedirect.com/science/article/pii/0003491681901998 Berestetskii, V.B., Pitaevskii, L.P., Lifshitz, E.M.: Quantum Electrodynamics, Second Edition: Volume 4, 2nd edn. Butterworth-Heinemann (1982). Hagelstein, P.L., Chaudhary, I.U.: Electron mass shift in nonthermal systems. J. Phys. B 41(12), 125001 (2008). doi:10.1088/0953-4075/41/12/125001. URL http://iopscience.iop.org/0953-4075/41/12/125001 Huke, A., Czerski, K., Heide, P., Ruprecht, G., Targosz, N., Żebrowski, W.: Enhancement of deuteron-fusion reactions in metals and experimental implications. Phys. Rev. C 78(1), 015803 (2008). doi:10.1103/PhysRevC.78.015803 Huke, A., Czerski, K., Heidea, P.: Experimental techniques for the investigation of the electron screening effect for d+d fusion reactions in metallic environments. Nucl. Phys. A 719(0), C279 (2003). doi:10.1016/S0375-9474(03)00932-1. URL http://www.sciencedirect.com/science/article/pii/S0375947403009321 Huke, A., Czerski, K., Heide, P.: Measurement of the enhanced screening effect of the d + d reactions in metals. Nucl. Instrum. Methods Phys. Res. B 256(2), 599 (2007). doi:10.1016/j.nimb.2007.01.082. URL http://www.sciencedirect.com/science/article/pii/S0168583X07001784 Arensburg, A., Horwitz, L.P.: A first-order equation for spin in a manifestly relativistically covariant quantum theory. Found. Phys. 22(8), 1025 (1992). doi:10.1007/BF00733394 Rolfs, C.: Enhanced electron screening in metals: a plasma of the poor man. Nucl. Phys. News 16(2), 9 (2006) Firestone, R.B., Baglin, C.M., Chu, S.Y.F.: Table of isotopes. Wiley (1999). Ziegler, J.F., Biersack, J.P., Ziegler, M.D.: SRIM–The Stopping and Range of Ions in Matter. SRIM Co. (2008). Kołos, W., Wolniewicz, L.: Accurate adiabatic treatment of the ground state of the hydrogen molecule. J. Chem. Phys. 41(12), 3663 (1964). doi:10.1063/1.1725796. URL http://jcp.aip.org/resource/1/jcpsa6/v41/i12/p3663_s1?isAuthorized=no Hagelstein, P.L., Senturia, S.D., Orlando, T.P.: Introductory Applied Quantum and Statistical Mechanics. Wiley (2004). Iwamura, Y., Itoh, T., Tsuruga, S.: Increase of reaction products in deuterium permeation induced transmutation. In: ICCF-17, p. 6. South Korea, Daejeon (2012). Nagel, D.: Characteristics and energetics of craters in LENR experimental materials. J Condens. Matter Nucl. Sci. 10, 1 (2013) Szpak, S., Mosier-Boss, P.A., Young, C., Gordon, F.E.: Evidence of nuclear reactions in the Pd lattice. Naturwissenschaften 92(8), 394 (2005). doi:10.1007/s00114-005-0008-7 Toriyabe, Y., Mizuno, T., Ohmori, T., Aoki, Y.: Elemental analysis of palladium electrodes after Pd/Pd light water critical analysis. In: Proceedings, ICCF-12. World Scientific Publishing Co., Pte. Ltd., Yokohama, Japan (2006), pp. 253–263. doi:10.1142/9789812772985_0025. URL http://adsabs.harvard.edu/abs/2006cmns12.253T Zhang, W.S., Dash, J.: Excess heat reproducibility and evidence of anomalous elements after electrolysis in Pd/D2 + H\(_{2}\)SO\(_{4}\) electrolytic cells. In: Proceedings, ICCF-13, p. 202. Russia, Sochi (2007). Iwamura, Y.: Detection of anomalous elements, X-Ray, and excess heat in D2-Pd system. Fusion Sci. Technol 33(4), 476 (1998) Iwamura, Y., Itoh, T., Sakano, M., Yamazaki, N., Kuribayashi, S., Terada, Y., Ishikawa, T., Kasagi, J.: Observation of nuclear transmutation reactions induced by D2 gas permeation through pd complexes. In: ICCF-11, vol. 11, pp. 339–350. Marseilles, France (2006) doi:10.1142/9789812774354_0027. URL http://adsabs.harvard.edu/abs/2006cmns11.339I