Composite Model for LENR in linear defects of a lattice

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Grace Newman
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1 Composite Model for LENR in linear defects of a lattice A. Meulenberg a) and K. P. Sinha b) a) Science for Humanity Trust, Inc. Tucker, GA, USA mules333@gmail.com b) Department of Physics, Indian Institute of Science, Bangalore, , India

2 Important comments from early papers: J. Schwinger, Nuclear Energy in an Atomic Lattice, in The First Annual Conference on Cold Fusion This representation of the overall probability, per unit time, as the product of two independent factors, may be true enough under the circumstances of hot fusion. But in very low energy cold fusion one deals essentially with a single state, or wave function, all parts of which are coherent. It is not possible to totally isolate the effect of the electric forces from that of the nuclear forces. K. P. Sinha, A theoretical model for low-energy nuclear reactions in a solid matrix, Infinite Energy 29, 54 (1999) Sinha had located charge pairs on hydrogen atoms in "... the crevices, voids, or linear empty channels of the solid..." And: The chains of deuterons... will have their own spacing in the chain. (our emphasis).

3 Schwinger s model (1990) Problem: How to avoid creating neutrons in D-D fusion Proposed Solution: 1. Assume interaction Hamiltonian includes shortrange nuclear potential 2. Phonon action stimulates phonon emission 3. Use up some nuclear energy before fusion occurs Basis: 1. Potential well exists before fusion occurs. 2. D-wave functions overlap within Coulomb barrier 3. Phonon-induced motion: leads to non-linear and anharmonic regime phonon emission draws energy from protons 4. fusion occurs after d-d energy is lowered below neutron-fragmentation level.

4 Results: Schwinger s model (cont.) 1. nucleus is an additional attractive potential. 2. correlated phonon-induced motion of a D sub-lattice, Stimulated emission, (but no energy levels) Large D displacement => non-linearities Emission-enhanced displacement => more emission 3. If Ds move closer, on average, and/or radiate phonons, then the nuclear potential is doing work. 4. Work extracts energy from the nucleus, and 5. when/if fusion occurs, Q is lower than normal 6. QM says this is possible (Meulenberg does too!)

5 Questions: Schwinger s model (cont.) 1. Deuteron wave functions always overlap Why don t nuclear energies always dissipate? Same reason atomic ground-state orbitals don t radiate Same reason filled atomic orbitals don t radiate Reversible vs irreversible processes Work is done by electrons in bringing protons together. Work is done on electrons when protons move apart. Phonons dissipate energy => irreversible 2. If possible to get below neutron fragmentation level: Is it possible to get below proton fragmentation level? Schwinger did not live to answer that Phonons just a competitive pathway to tunnelling 3. How does phonon emission alter hydron motion? Increased number of phonons => more amplitude of motion High phonon emission gives local concentration above norm

6 Sinha s model (1999) Problem: How to overcome Coulomb barrier in D-D fusion Proposed Solutions: 1. Pair up bound electrons so that D+ and D- attract 2. Linear defect (1-dimensional sub-lattice) Sub-lattice spacing is not fixed by lattice Allows phonons to bring deuterons closer together Basis: 1. Electron pairing is well-known phenomenon 2. Pairing in s-orbit (at multi-ev level) is stable 3. Phonon-field-induced charge transfer (to D+ D-)

7 Result: Multi-variable Hamiltonian: Sinha s model (cont.) E(x,l,r) = ħ 2 /2m*r 2 - e 2 /ϵr - xw d (2M d E d ) 1/2 + ½x 2 w d2 M d (r p /l) 3 KE and PE of Electron KE and PE of Displaced Oscillator 1. electron kinetic and potential energies of the hydrogen atom (perhaps extended by bond sharing) are affected by the lattice. 2. kinetic energies are expressed in terms of the binding energies and the momentum related to the debroglie wavelength. 3. displaced oscillator energy, E d ties the hydrogen atom s kinetic and potential energy to the lattice. 4. radius of influence r p within sub-lattice vs its spacing, l, is critical.

8 Sinha s model (cont.) Minimized wrt x => E(x,l,r) = ħ 2 /2m*r 2 - e 2 /ϵr - E d (l/r p ) 3 1. Energy terms depend on: proton-electron and proton-proton interactions electron-electron interactions electron- and proton-lattice interactions 2. Two standard variables: x = displacement of nuclei from their equilibrium location r = distance between the nuclei and the nearest electron), 3. Five parameters that are constant in some ranges: M d = displaced oscillator mass, that produces E d = displaced oscillator energy, with W d = oscillator frequency (from polarization of the lattice), r p = the radius of influence of a charge within lattice Є = the dielectric constant of the local lattice 4. seven parameters are variable within different dimensional regimes with non-linear interdependence as well. 5. l = lattice spacing also is variable - unique for 1-D structures

9 Sinha s model (cont.) Results: 1. Lattice-dominated regime Charge polarization of lattice => Increased effective mass Dielectric constant Lateral confinement/constraint of linear sub-lattice Sub-lattice spacing changes allowed Charge polarization into D+ & D- Coulomb barrier changed to attraction 2. Sub-lattice regime Dipole-, rather than monopole-, charge effects Reduces lattice polarization and other effects Sub-lattice spacing and charges => independent of lattice Proton-proton potential - more linear with proximity 3. Coalescence Regime Closer alignment of electrons means Ds move closer Closer alignment of electrons as Ds move closer Lattice spacing shrinks to fusionable dimensions.

10 Composite model Linear defect => low-barrier sub-lattice & lateral confinement Fixed Lattice vs variable-lattice spacing l Sub-lattice spacing can oscillate as well as atoms High loading allows forcing H into sub-lattice during periods when the sub-lattice motion opens gaps Variable spacing enhances fusion Phonons allow nuclear potential energy to be sent to lattice Energy loss allows irreversible shrinkage of orbits & sub-lattice Energy extracted from nuclear potential allows fusion beneath the fragmentation levels

Relative Probability Composite model Linear defect => low-barrier sub-lattice & lateral confinement Extended, linear, Hn molecule Deuteron separation = 1500 Fermi Electron probability distributions

11 Relative Probability Composite model Linear defect => low-barrier sub-lattice & lateral confinement Extended, linear, Hn molecule Deuteron separation = 1500 Fermi Electron probability distributions Deuteron separation = 1500 Fermi 1500 F Deuteron Deuteron separation Deuteron separation Deuteron = 1500 separation = Fermi 1500 separation = Fermi 1500 = Fermi 1500 Fermi 1500 F 1500 F 1500 F 1500 F Note different scale dimensions 400 F 400 F 400 F 400 F 400 F 400 F 4000 F 4000 F 4000 F 4000 F4000 F4000 F

12 Composite model (cont.) Variable sub-lattice spacing Linear array Linear array Time ==> Time ==> l variable lattice spacing a Fixed lattice spacing Sub-lattice atoms can get much closer together in the variable array

13 Present View: 1. Cold fusion is enhanced in a linear defect (Sinha s model): permits multiple hydrogen atoms coming together simultaneously (allows lowering of sub-lattice spacing). quasi-free linear array gives enhanced freedom But, in host-bound sub-lattice, H or D approach only as pairs. 2. electron effective mass (from E&M coupling to lattice, Sinha): Increases attractive Coulomb potential at normal spacing At close inter-nuclear distances, r p is greatly reduced Distance-dependent effects alter shape of the potential well 3. Total potential well of 1-dimensional sub-lattice can include: Coulomb contributions of the electrons and protons Interactions with the lattice electrons and phonons Phonon-induced charge separation within the sub-lattice Spin coupling of electron pairs Nuclear wells

14 Present view (cont.): 4. Schwinger's model for dropping below neutron fragmentation level: Phonon coupling of nuclear energy can be extrapolated to the 4He ground state. (Sinha, 1957, => stimulated phonon generation) does not eliminate fragmentation, it alters the probabilities 5. D-D fusion is dependent on: time spent at tunnelling distances, proximity of the bound electron(s) to the nuclei, and the actual tunnelling distances. 6. Early in the process, the hydrons are further apart: longer process => more energy dissipated to the lattice longer process => tunnelling will take place lower into the 4 He nuclear potential well. In good CF process, early tunnelling to the higher nuclear states is highly retarded relative to later tunnelling to deeper level. 7. Different models for CF are converging to a coherent picture; fitting the data without violating any physics and chemistry principles.

DEEP-ORBIT-ELECTRON RADIATION EMISSION IN DECAY

Energy Barrier (ev) DEEP-ORBIT-ELECTRON RADIATION EMISSION IN DECAY FROM 4 H* # TO 4 HE A. Meulenberg 1 and K. P. Sinha 1 National Advanced IPv6 Centre, Universiti Sains Malaysia, 11800 Penang, Malaysia,