Condensed Matter

   

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

Authors: Akito Takahashi, Norio Yabuuchi

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).

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[v1] 14 Feb 2009

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