• Purdue Nuclear and Many Body Theory Group (PNMBTG) Preprint PNMBTG-6-2011 (June 2011)

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Purdue Nuclear and Many Body Theory Group (PNMBTG) Preprint PNMBTG-6-2011 (June 2011)
Generalized Theory of Bose-Einstein Condensation Nuclear Fusion for
Hydrogen-Metal System
Yeong E. Kim
Department of Physics
Purdue University
West Lafayette, Indiana 47907, USA
June 18, 2011
Generalized theory of Bose-Einstein condensation nuclear fusion (BECNF) is used to carry out
theoretical analyses of recent experimental results of Rossi et al. for hydrogen-nickel system.
Based on incomplete experimental information currently available, preliminary theoretical
explanations of the experimental results are presented in terms of the generalized BECNF theory.
Additional accurate experimental data are needed for obtaining more complete theoretical
descriptions and predictions, which can be tested by further experiments.
I. Introduction
Over the last two decades, there have been many publications reporting experimental
observations of excess heat generation and anomalous nuclear reactions occurring in metals at
ultra-low energies, now known as „low-energy nuclear reactions‟ (LENR). Theoretical
explanations of the LENR phenomena have been described based on the theory of Bose-Einstein
condensation nuclear fusion (BECNF) in micro/nano-scale metal particles [1-3]. The BECNF
theory is based on a single basic assumption capable of explaining the observed LENR
phenomena; deuterons in metals undergo Bose-Einstein condensation. While the BECNF theory
is able to make general qualitative predictions concerning LENR phenomena it is also a
quantitative predictive physical theory. Some of the theoretical predictions have been confirmed
by experiments reported recently. The BECNF theory was generalized for the case of two
species of Bosons [4].
Recently, there were two positive demonstrations (January and March, 2011) of a heat
generating device called “Energy Catalyzer” [5]. The Energy Catalyzer is an apparatus built by
inventor Andrea Rossi, Italy. The patent application [5] states that the device transforms energy
stored in its fuel (hydrogen and nickel) into heat by means of nuclear reaction of the two fuel
components, with a consequent observed production of copper [5,6]. According to Rossi‟s patent
application [5], heating of the sample is accomplished by an electric resistance heater. Details of
March 2011 demonstration were reported by Essen and Kullander [7]. The report [7] also
contains references to January 2011 demonstration. In the following, we describe hydrogen-
nickel reactions in section II. Other possible reactions are discussed in section III. Conclusions
are given in section IV.
Purdue Nuclear and Many Body Theory Group (PNMBTG) Preprint PNMBTG-6-2011 (June 2011)
II. Hydrogen-Nickel Reactions
The generalized BECNF theory [4] can be applied to the case of hydrogen-nickel fusion
reactions observed in Rossi‟s device (the energy catalyzer) [5] under the following two
conditions: (1) additives used (not disclosed in the patent application) form Ni alloy and/or Ni
metal/alloy oxide in the surface regions of nickel nano-scale particles, so that Ni atoms/nuclei
become mobile with a sufficiently large diffusion coefficient and (2) local magnetic field is very
weak in the surface regions, providing a suitable environment in which two neighboring protons
can couple their spins anti-parallel to form spin-zero singlet state (S=0). Relatively low Curie
temperature (nickel has the Curie temperature of 631 oK (~358 oC)) is expected to help to
maintain the weak magnetic field in the surface regions. If Rossi‟s device is operated at
temperatures greater than the Curie temperature ~ 358 oC and with hydrogen pressures of up to ~
22 bars, the conditions (1) and (2) may have been achieved in Rossi‟s device.
The mobility of Ni atoms/nuclei (condition (1)) is enhanced by the use of an electric resistance
heater to maintain higher temperatures. This may provide a suitable environment in which more
of both Ni atoms/nuclei and protons become mobile, thus creating a favorable environment for
the case of two species of Bosons (Ni nuclei and composite Bosons of paired two protons). If the
velocities of mobile Ni atoms/nuclei under the condition (1) are sufficiently slow, their de-
Broglie wavelengths become sufficiently large and may overlap with neighboring two-proton
composite Bosons which are also mobile, thus creating Bose-Einstein condensation of two
species of Bosons. The generalized BECNF theory can now be applied to these two-species of
Bosons and provides a mechanism for the suppression/cancellation of the Coulomb barrier, as
shown in [4].
Once the Coulomb barrier is overcome in the entrance reaction channel, many possible allowed
exit reaction channels may become open such as reactions (i) ANi(2p(S=0), p)A+1Cu, with even
A=58, 60, 62 and 64. These reactions will produce radioactive isotopes 59Cu and 61Cu with A =
58 and 60, respectively. 59Cu has a half-life of 81.5 seconds and decays by the electron capture to
the 59Ni ground state (58.1%) which has a half-life of 7.6 x 104 years and to the 59Ni excited
states (41.9%) which in turn decay to the 59Ni ground state by emitting gamma-rays with
energies ranging from 310.9 keV to 2682.0 keV [8]. 61Cu has a half-life of 3.333 hours and
decays by the electron capture to the stable 61Ni ground state (67%) and to the 61Ni excited states
(33%) which in turn decay to the 61Ni ground state by emitting gamma-rays with energies
ranging from 67.412 keV to 2123.93 keV [8]. Gamma-rays (and neutrons) have not been
observed outside the reactor chamber during the experiment [6]. These gamma-rays may have
been present inside the reaction chamber. If no radiations are observed, reactions (i) are ruled out.
Focardi and Rossi [6] reported that the experimental results of Rossi et al. indicate the
production of stable isotopes 63Cu and 65Cu with an isotopic ratio of 63Cu /65Cu ~ 1.6 (natural
abundance is 63Cu/ 65Cu = 2.24). This production of Cu may be due to reactions (i). The
production of 63Cu and 65Cu with isotopic ratio of 63Cu /65Cu different from the natural isotopic
ratio is expected and can be explained by estimating the reaction rates for 62Ni(2p(S=0), p)63Cu
and 64Ni(2p(S=0), p)65Cu. Reaction rates estimates based on transmission probability calculated
from a barrier tunneling model similar to the alpha-decay theory indicate that the reaction rates
for stable Cu productions, 62Ni(2p(S=0), p)63Cu and 64Ni(2p(S=0), p)65Cu, are expected to be
Purdue Nuclear and Many Body Theory Group (PNMBTG) Preprint PNMBTG-6-2011 (June 2011)
much larger than the reaction rates for production of radioactive Cu, 58Ni(2p(S=0), p)59Cu and
Ni(2p(S=0), p)61Cu. This leads to the prediction that intensities of the gamma-rays from the
decays of 59Cu and 61Cu are expected to be weak and do not commensurate with the observed
heat production, which is mostly from stable Cu production reactions 62Ni(2p(S=0), p)63Cu and
Ni(2p(S=0), p)65Cu.
There are other exit reaction channels which are (nearly) radiation-less, such as reactions (ii)
Ni(2p(S=0), α)A-2Ni, (even A=58, 60, 62, and 64) [9]. For this case, we expect that the natural
isotopic ratio of Ni isotopes will be changed in a particular way, which can be checked from the
sample after each experiment. Even though reactions (ii) produce radioactive isotope 56Ni, it can
be shown using the alpha-decay theory that its reaction rate is much slower (by many order of
magnitudes) than those of other reactions.
Other exit reaction channels, ANi(2p(S=0), d)ACu, ANi(2p(S=0), 3He)A-1Ni, and ANi(2p(S=0),
t) Cu (all with even A=58, 60, 62, and 64) are ruled out since these reactions all have negative
Q-values. There are possibilities of neutron-emission exit reaction channels, such as reactions
(iii) ANi(2p(S=0), n)A+1Zn, (even A= 62, and 64; Q is negative for A = 58 and 60). However,
reaction rates for reactions (iii) are expected be substantially smaller than those for reaction (i).
Reactions (iii) involve emission of a tightly bound neutron (62Ni → 61Ni + n, Q = -10.597MeV
or 64Ni → 63Ni + n, Q = -9.657MeV) while reactions (i) involve emission of a loosely bound
proton from an excited compound nuclear state consisting of ANi (even A) and 2p(S=0).
Therefore, the transmission probability of a neutron tunneling through the centrifugal barrier in
reactions (iii) is expected to be substantially smaller than that of a proton tunneling through the
centrifugal barrier in reactions (i).
The branching ratios of reactions (i) and (ii) need to be determined by measurements of
gamma-ray energies and changes in isotopic ratios from future Ross-type experiments.
Theoretically, the branching ratios can be estimated by calculating transmission probability of an
emitted charged particle tunneling through both Coulomb and centrifugal barriers in the exit
reaction channel, as done in the alpha-decay theory.
III. Other Possible Reactions
In addition to the above reactions described in II, there are possibilities of reactions involving
additives used (not disclosed so far). For an example, if lithium is added as an additive, reaction
(iv) 6Li(2p(S=0), p 3He)4He may be possible. As in cases of reactions (i) and (ii), Ni nano-
particles would be still playing an important role of providing two-proton singlet composite
Bosons for reaction (iv). Reaction (iv) would not change the isotopic ratios of Ni.
IV. Conclusions
In order to explore validity and to test predictions of the generalized BECNF theory for the
hydrogen-metal system, it is very important to carry out Rossi-type experiments independently in
order to establish what are exact inputs and outputs of each experiment. If the entrance and exit
reaction channels are established experimentally, we can investigate selection rules as well as
estimates of the reaction rates for different exit reaction channels, based on the generalized
Purdue Nuclear and Many Body Theory Group (PNMBTG) Preprint PNMBTG-6-2011 (June 2011)
BECNF theory [1-4]. Once these experimental results are established, further application of the
generalized BECNF theory can be made for the purpose of confirming the theoretical mechanism
and making theoretical predictions, which can then be tested experimentally.
Basic description of the above theoretical concepts for BECNF in the hydrogen-metal system
will be included in an invited talk at a forthcoming nuclear physics conference [10], and will be
published in the conference proceedings [10].
1. Y. E. Kim, “Theory of Bose-Einstein Condensation Mechanism for Deuteron-Induced Nuclear
Reactions in Micro/Nano-Scale Metal Grains and Particles”, Naturwissenschaften 96, 803 (2009)
and references therein.
2. Y. E. Kim, “Bose-Einstein Condensate Theory of Deuteron Fusion in Metal”, J. Condensed
Matter Nucl. Sci. 4, 188 (2010), Proceedings of Symposium on New Energy Technologies, the
239th National Meeting of American Chemical Society, San Francisco, March 21-26, 2010.
3. Y. E. Kim, “Theoretical interpretation of anomalous tritium and neutron productions during Pd/D
co-deposition experiments”, Eur. Phys. J. Appl. Phys. 52, 31101 (2010).
4. Y. E. Kim and A. L. Zubarev, “Mixtures of Charged Bosons Confined in Harmonic Traps and
Bose-Einstein Condensation Mechanism for Low Energy Nuclear Reactions and Transmutation
Processes in Condensed Matter”, Condensed Matter Nuclear Science, Proceedings of the 11th
International conference on Cold Fusion, Marseilles, France, 31 October – 5 November, 2006,
World Scientific Publishing Co., pp. 711-717.
HYDROGEN EXOTHERMAL REACTION”, United States Patent Application Publication (Pub.
No.: US 2011/0005506 A1, Pub. Date: Jan. 13, 2011);
http://www.wipo.it/pctdb/en/wo.jsp? WO+2009125444
6. S. Focardi and A. Rossi, “A new energy source from nuclear fusion”, March 22, 2010.
http://www.journal-of-nuclearphysics.com/?p=66, February 2010
7. H. Essen and S. Kullander, “Experimental test of a mini-Rossi device at the Leonardocorp,
Bologna, 29 March 2011”, a travel report, April 3, 2011;
8. Table of Isotopes, 8th Edition, Volume I: A = 1-150, edited by R. B. Firestone et al., published by
John Wiley and Sons, Inc. (1999), pages 270 and 284.
9. Reactions (ii) were suggested by T. E. Ward, private communication, May 11, 2011.
10. Y. E. Kim, “Deuteron Fusion in Micro/Nano-Scale Metal Particles”, an invited talk to be
presented at the Fifth Asia Pacific Conference on Few-Body Problems in Physics
2011(APFB2011), August 22-26, 2011, Seoul, Korea.
PDF-files of [1-3] are available at:

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