Condensed Matter

0902 Submissions

[3] viXra:0902.0005 [pdf] submitted on 14 Feb 2009

Basics of Deuteron-Cluster Dynamics by Langevin Equation

Authors: Akito Takahashi
Comments: recovered from sciprint.org

This paper gives the follow-up study on the basics for our previous papers, Study on 4D/Tetrahedral Symmetric Condensate Condensation Motion by Non-Linear Langevin Equation, Symposium 998-Low Energy Nuclear Reactions Source Book, ACS, published on August 2008 from Oxford University Press. Pertaining to the quantum mechanics, the basics of new approach using the stochastic differential equation (Langevin equation) is written for quantifying dynamic motion of known molecules as D2+, D2 and D3+ as well as D-atom state. The role of the Platonic symmetry in these known molecules are discussed for deducing simple one-dimensional (Rdd dependent; here Rdd is distance between nearest d-d pair) Langevin equation and making quantum-mechanical ensemble averaging to obtain equation for expectation value. The methodology is applied for more complicated D-clusters as 4D/TSC and 6D/OSC which would keep the Platonic symmetry, by introducing the force fluctuation deviating from the ideal Platonic symmetry. Time-dependent TSC and OSC trapping potentials which take balance to getting back to the Platonic symmetry from the distorted states were defined and used for numerical solution of Langevin equation. Finally, time-dependent fusion rate formula for simultaneous 4D interaction was obtained based on the Fermi's golden rule and one-pion exchange potential of strong interaction. The 4D fusion is regarded to cause radiation-less excess heat and 4He ash in metal-deuterium systems under dynamic conditions
Category: Condensed Matter

[2] viXra:0902.0004 [pdf] submitted on 14 Feb 2009

Study on 4D/TSC Condensation Motion by Non-Linear Langevin Equation

Authors: Akito Takahashi, Norio Yabuuchi
Comments: recovered from sciprint.org

Tetrahedral symmetric condensate (TSC) with 4 deuterons and 4 electrons has been proposed as a seed of clean 4D fusion with 4He product in condensed matter. To solve molecular dynamics motion of 4D/TSC condensation, a nonlinear Langevin equation was formulated with a Coulombic main condensation force term under Platonic symmetry, 6 balancing forces by quantum mechanical electron clouds of dde*(2,2) EQPET molecules on 6 faces of TSC cube and a random quantum mechanical fluctuation term f(t) for d-d distance. Gaussian wave functions for d-d pairs and their ground state energies were first obtained by variational method, for D2 and EQPET molecules. Then same sigma-value was used for time-dependent Gaussian wave functions of d-d pairs of TSC system to calculate the ensemble-averaged <f(t)> for changes of Coulomb energy and force of distorted TSC system deviated from the ideal double Platonic symmetry. Molecular dynamics calculation with TSC Langevin equation by the Verlet time-step method was then done. We obtained mean relative final-stage d-d kinetic energy 13.68 keV with -130.4 keV deep trapping TSC potential at Rdd-minimum = 25 fm and time-to-TSC-minimum =1.4007 fs. Mean kinetic energy of electron of a "d-e-d-e" EQPET molecule of TSC system was estimated as 57.6 keV at Rdd =25 fm. These time-dependent trapping potential for d-d pair of TSC can be approximated by HMEQPET potentials with the empirical relation of m=4.36x104/Rdd, (Rdd in fm unit), continuously as a change of condensation time or Rdd(t). Barrier factors for fusion reactions as a function of Rdd(t) and 4D fusion rate per TSC generation were calculated using these HMEQPET potentials and Fermi's golden rule. We found that 4D/TSC got to the TSC-minimum state with 10 fm-20 fm radius in 1.4007 fs and 4D fusion rate was 100 % per 4D/TSC generation-condensation. Thus we concluded that 4He production rate by 4D/TSC was equal to two times of 4D/TSC generation rate in condensed matter (e.g., PdDx).
Category: Condensed Matter

[1] viXra:0902.0003 [pdf] submitted on 14 Feb 2009

Dynamic Mechanism of TSC Condensation Motion

Authors: Akito Takahashi
Comments: recovered from sciprint.org

This paper gives further discussions and explanations on the timedependent quantum-mechanical behaviors of electron-clouds in 4D/TSC condensation motion by Langevin equation, in comparison with steady ground state electron orbits and their de Broglie wave lengths for D-atom and D2 molecule.
Category: Condensed Matter