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On Condensation Force of TSC Akito Takahashi and Norio Yabuuchi High Scientific Research Laboratory Tsu-city Japan

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Motivation EQPET/TSC model has been developed and elaborated in ICCF10,11, 12 and Asti- series Workshops. Models could explain well major experimental claims. However, open questions are remained. This work treats driving force strength for TSC squeezing motion and condensation.

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Outline To estimate condensing force of TSC Coulomb energy of D-atom Coulomb energy of D 2 molecule Wave functions and Pauling-Wilson-type potentials Coulomb energy and condensing force of TSC

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Feature of QM Electron Cloud b) D 2 molecule (stable): Ψ 2D =(2+2Δ) -1/2 [Ψ 100 (r A1 ) Ψ 100 (r B2 )+ Ψ 100 (r A2 ) Ψ 100 (r B1 )]Χ s ( S1,S2 ) Bohr orbit of D (H) Electron center; =(e↑ + e↓)/2 Deuteron a) D atom (stable) c) 4D/TSC (life time about 60 fs) R B = 53 pm Bosonized electron Center torus for (e↑ + e↓) 73 pm Orbit of Bosonized Electron coupling For (e↑ + e↓) │rΨ 100 │ 2 A B

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I: D(H)-atom 1S-wave function System Coulomb Energy With r = Bohr radius (52.9 pm), we get

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D(H)-atom-II Total system energy is given by Hamiltonian integral: Kinetic energyCoulomb energy

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Adiabatic Potential for Molecule dde* r0 b0 dde* ground state -V 0 0r Bare Coulomb Potential Screen Energy V s (r) Strong F. (~5fm) e*: bosonized-electrons or heavy-fermion V smin R dd (gs)

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Comparison of dde* potentials Arrow: b 0 value

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Parameters of dde* potentials e*(m, Z)V SMIN (eV) b 0 (pm)R dd (gs) (pm) (1, 1); Normal electron - 15.4 40 101 (1, 1)x2; D 2 - 37.8 20 73 (2, 2); Cooper pair - 259.0 4 33.8 (4, 4); Quadruplet e - 2,460 0.36 15.1 Trapping Depth Ground State

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Classical Model of D 2 Molecule Attractive Potential: (-e 2 /R de ) x 4 with a B = 52.9 pm Repulsive Potential: (e 2 /R dd ) + (e 2 /R ee ) Electrons rotate around d-d axis d-d axis +d R dd =73 pm -e Electron torus R de =a B

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D 2 molecule-I System wave function: System Energy at ground state System Coulomb Energy Electron Kinetic E 16.25 eV per e

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Wave Function for 4D/TSC (t=0) Ψ 4D ~a1 [Ψ 100 (r A1 ) Ψ 100 (r B2 ) + Ψ 100 (r A2 ) Ψ 100 (r B1 )]X s ( S1,S2 ) +a2 [Ψ 100 (r A1 ) Ψ 100 (r D4 ) + Ψ 100 (r A4 ) Ψ 100 (r D1 )]X s ( S1,S4 ) +a3 [Ψ 100 (r A2 ) Ψ 100 (r C4 ) + Ψ 100 (r A4 ) Ψ 100 (r C2 )]X s ( S2,S4 ) +a4 [Ψ 100 (r B1 ) Ψ 100 (r D3 ) + Ψ 100 (r B3 ) Ψ 100 (r D1 )]X s ( S1,S3 ) +a5 [Ψ 100 (r B2 ) Ψ 100 (r C3 ) + Ψ 100 (r B3 ) Ψ 100 (r C2 )]X s ( S2,S3 ) +a6 [Ψ 100 (r C3 ) Ψ 100 (r D4 ) + Ψ 100 (r C4 ) Ψ 100 (r D3 )]X s ( S3,S4 ) 6-Bonds of “Bosonozed” electron-pairs (e↑+ e↓), which forms Regular Tetrahedron 4-Electron-Centers at Vertexes of Regular Tetrahedron u 1s1 (r) = Ψ 100 (r) = (1/π) 1/2 (1/a B ) 3/2 exp(-r/a B )

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Feature of QM Electron Cloud b) D 2 molecule (stable): Ψ 2D =(2+2Δ) -1/2 [Ψ 100 (r A1 ) Ψ 100 (r B2 )+ Ψ 100 (r A2 ) Ψ 100 (r B1 )]Χ s ( S1,S2 ) Bohr orbit of D (H) Electron center; =(e↑ + e↓)/2 Deuteron a) D atom (stable) c) 4D/TSC (life time about 60 fs) R B = 53 pm Bosonized electron Center torus for (e↑ + e↓) 73 pm Orbit of Bosonized Electron coupling For (e↑ + e↓) │rΨ 100 │ 2 A B

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Classical View of Tetrahedral Sym. Condensation Transient Combination of Two D2 Molecules (upper and lower) Squeezing only from O-Sites to T-site 3-dimension Frozen State for 4d+s and 4e-s Quadruplet e* (4,4) Formation of Electrons around T-site d+d+ d+d+ d+d+ d+d+ e- Orthogonal Coupling of Two D 2 Molecule makes Miracle !

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+ a) TSC b) Electron tetrahedron c) Deuteron tetrahedron 12 Attractive Coulomb forces Between d-e pairs on 6 surfaces And 4 Attractive Forces between 4 diagonal d-e pairs 6 repulsive Coulomb Forces Between electrons 6 repulsive Coulomb Forces Between deuterons

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Coulomb Energy of TSC System Coulomb Energy In keV unit with R in pm unit

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Condensing Force of TSC Condensing force In keV/pm unit with R in pm unit

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Condensation Force of TSC The smaller the d-e (or d-d) distance, the larger the system Negative Coulomb Energy (Binding Energy) The smaller the d-e (or d-d) distance, the Larger the TSC Condensation Force TSC shrinks into Small Charge-Neutral Entity until when charge neutrality is broken in getting into strong force range

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Coulomb Energy of TSC At R de = 11 pm, Ec = - 0.9 keV At R dd = 15 pm (Rde = 11 pm), V smin = - 2.46 keV for dde*(4,4) Bosonization of paired electrons makes Trapping deeper (larger condensing force)

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Electron 15 fm Deuteron 4 He 4r e = 4x2.8 fm p or d Electron d+d+ d+d+ d+d+ d+d+ e- 3) 8 Be* formation 4) Break up 2) Minimum TSC 1) TSC forms

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Conclusions Coulomb energy and condensing force was estimated By Platonic symmetry in TSC formation, system Coulomb energy becomes very large as decrease of d-e distance, by the help of charge-neutrality and un-balance of attractive and repulsive forces makes condensing force very large

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