## 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=4.36x10^{4}/R_{dd}, (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).

**Comments:** recovered from sciprint.org

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### Submission history

[v1] 14 Feb 2009

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