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Posted on 12/02/2013 4:31:18 PM PST by Kevmo
J. Condensed Matter Nucl. Sci. 12 (2013) 105–142 Research Article
Phonon–nuclear Coupling for Anomalies in Condensed Matter Nuclear Science
Peter L. Hagelstein ∗ Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA Irfan U. Chaudhary Department of Computer Science and Engineering, University of Engineering and Technology. Lahore, Pakistan
Abstract
Excess heat in the Fleischmann–Pons experiment is thought to have a nuclear origin, yet there are no energetic particles observed in amounts commensurate with the energy produced. This in our view is the most fundamental issue in connection with theory. In earlier work we developed a mathematical model (the lossy spin–boson model) which shows coherent energy exchange between two-level systems and an oscillator under conditions of fractionation. Recently, we have found an interesting physical model that is closely connected, and which is capable of coherent energy exchange with fractionation; this model is based on a relativistic description of composite nuclei in a lattice. In this work we present a much stronger development of the model directly from field theory than given previously. In the lossy spin–boson model, the ability of the model to fractionate a large quantum depends on the presence of suitable loss mechanisms; the same is true in the case of the new physical model. The new model predicts anomalies such as excess heat without energetic nuclear radiation, 4 He production, low-level gamma emission, and collimated X-ray emission in the Karabut experiment; however, as yet we have not demonstrated agreement between theory and experiment.
Last summer we concluded (erroneously) that coupling with strong static transitions might impact the fractionation power of the model on dynamic transitions, and the resulting model appeared to be in agreement with our interpretation of the experiment. Here we review this kind of model more carefully, and find that no such enhancement is present. Our conclusion in the end is that the theory, model, and interpretation are “close” to the experimental results in the case of the Karabut experiment, but some problem remains.
© 2013 ISCMNS. All rights reserved. ISSN 2227-3123
Keywords:
Phonon theory, fractionation, Fleischmann-Pons experiment, Karabut experiment, fundamental Hamilton
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Summary and Conclusions
Accounting for excess heat in the Fleischmann–Pons experiment has proven to be a tough theoretical problem over the years. By now a very large number of theoretical proposals have been put forward, but even more than 24 years after the effect was first announced there is no consensus within the community as to how it might work. From our perspective the biggest theoretical issue has to do with where the energy goes, since energetic nuclear particles are not present in amounts commensurate with the energy produced. For example, if coherent energy exchange could proceed efficiently under conditions where the large (MeV) nuclear quantum is fractionated into small (eV) quanta of the condensed matter system, then there would be no difficulty in accounting for the anomalies.
In earlier work we showed that the lossy spin–boson model as a toy mathematical model describes exactly such an effect. The difficulty has been in the identification of a relevant physical model which makes use of this mechanism. From a comparison of different models with experiment in the case of Karabut’s collimated X-ray emission, we have evolved to focus now on a model for phonon–nuclear coupling mediated by relativistic coupling (under conditions where the Foldy–Wouthuysen transformation is unhelpful).
From the discussion of Sections 2–4 in this work, we have argued that the new model is on a solid theoretical foundation. We know that it implements coherent energy exchange under conditions of fractionation based on the same mechanism demonstrated previously in the lossy spin–boson model; and in addition it has the strongest phonon–nuclear coupling possible (stronger by orders of magnitude than indirect coupling mechanisms).
The new model is in addition elegant, in that it describes a straightforward relativistic generalization of the con- densed matter system to include coupling with internal nuclear degrees of freedom in a very fundamental and obvious formulation. In a Born–Oppenheimer picture, we can describe physical systems now using a Hamiltonian of the form ˆ H = j M c 2 + a · c ˆ P j + jThere is no difficulty in working with a more fundamental version of the problem where the electrons are included explicitly, as in ˆ H = j M c 2 + a · c ˆ P j + k | ˆ p k | 2 2 m + jIn the case of a highly excited phonon mode, we would expect this model to describe coherent energy exchange under conditions of fractionation. This is interesting for many reasons. These new models under discussion constitute a clear improvement over text book models, since they greatly extend the realm of physics under discussion, while retaining (including) a basic description of known results in both condensed matter physics and in nuclear physics. In addition we are able to work with the new models, and carry out calculations without undo heroics. These models describe coupling of vibrational energy to the nuclear system, qualitatively consistent with collimated X-ray emission in the Karabut experiment; excess heat in PdD with 4 He production; and low-level gamma emission effects. In all cases the effects predicted are qualitatively very much like experiment.
Unfortunately, in our use of the models we have as yet not obtained quantitative agreement between theory and experiment. For example, if we make use of a result from the lossy spin–boson model [31], we obtain an approxi- mate constraint for coherent energy exchange which should give us a threshold for nuclear excitation in the Karabut experiment; this constraint can be written as g n 2 → 1 n 2 acP √ S 2 − m 2 E > 5 × 10 − 4 , (81) where g is the dimensionless coupling constant, n is the number of phonons exchanged, a is the coupling matrix element for the E = 1565 eV transition, P is the Hg atom momentum matrix element, and where √ S 2 − m 2 is the Dicke number. We have so far been unable to find model parameters for the Karabut experiment consistent with our interpretation of the experiment which allow this constraint to be satisfied.
Our conclusion then is that we are in a sense “close,” in that we have new models which have a good physical basis, which describe the phenomena observed in experiment, and which can fractionate a large quantum. But because we do not obtain consistency so far with the experimental parameters of our interpretation of the Karabut experiment, we know that something important is missing. There is a problem either in the theory, in the particular model, or in the interpretation.
We have understood within the past year that in metals that electron-phonon coupling can lead to phonon fluctuations, and that these phonon fluctuations have the potential for increasing the fractionation power in the phonon–nuclear problem. This effect would be included in the model of Eq. (80) ([ut not in models of the form of Eq. (79)). Our efforts over the past several months have been focused on the analysis of this problem; we will describe our efforts in a forthcoming paper.
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T4BTT
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T4BTT
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Your words:
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T4BTT
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T4BTT
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Oh well, T4BTT.
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T4BTT
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T4BTT
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T4BTT
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