## 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

**Download:** **PDF**

### Submission history

[v1] 14 Feb 2009

**Unique-IP document downloads:** 187 times

**Add your own feedback and questions here:**

*You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.*

*
*