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Abstract

Abstract Some theoretical frameworks that explore the possible formation of dense exotic electron clusters in the E-Cat SK are presented. Some considerations on the probable role of Casimir, Aharonov-Bohm, and collective effects in the formation of such structures are proposed. A relativistic interaction Lagrangian, based on a pure electromagnetic electron model, that suggests the possible existence of very low entropy charge aggregates and that highlights the primary role of the electromagnetic potentials in these clusters is presented. The formation of these cluster may be associated to a localized Vacuum polarization generated by a rapid radial charge displacement. The formation of these dense electron clusters are introduced as a probable precursor for the formation of proton-electron aggregates at pico-metric scale, stressing the importance of evaluating the plausibility of special electron-nucleon interactions, as already suggested in [#GullstromRossi]. An observed isotopic dependence of a particular spectral line in the visible range of E-Cat plasma spectrum seems to confirm the presence of a specific proton-electron interaction at electron Compton wavelength scale.
Au197 +N14 Au198 +N13
σI = 2
N
RN
RN~N
2mec=cN
2ωe
=reN
2,
re=c
ωe=λe
2π
ωe=mec2
/~
ρ(ω) :
ρ(ω) = ~ω3
2π2c3dω.
N= 1011 D
D= 2RN0.12 µm
dE
dEr4πR2
N
N=πre1.78re0.68 ·1012 m.
N
re=λe
/2π0.38 ·1012 m.
FCA
FC(d)
A=π2~c
240d4.
d c
A=π(λe
/4π)2
FC(d)
Fe(d) :
FC(d) = π~2
e
3840d4,
Fe(d) = 1
4πε0
e2
d2.
db2λe
/2π0.77 ·1012m
re
A=π(λe
/2π)2=πr2
e
db4λe
/2π
1.54 ·1012m
ΦM=h
/e
h e
e c
FL
FL(d) = ecB (d) = µo
4π·e2c2
d2=1
4π0·e2
d2,
B(d) = µoec
4πd2
c~
d
d
d=e
±~
/2~
~
FL
LD
LD=
N
X
a=1 hma
2v2
aea
2φa(ra) + ea
2cva·Aa(ra)i
Aa(ra) =
N
X
b6=a
eb[vb+ (vb·ruab)ruab ]
2crab
φa(ra) =
N
X
b6=a
eb
rab
rab =|rarb|
ruab =rarb
|rarb|
a b
raeavamaAa(ra)
φ(ra)raN
pa
pa=mava=ea
cAazp
Aazp Aaz
va
ma
2v2
a=p2
a
2ma
p2
a
2ma
=e2
aA2
azp
2c2ma
ma=eaAaz
c2
p2
a
2ma
=eaA2
azp
2Aaz
Aazp
Aaz 'va
c
vaAazp
ma
2v2
a=eavaAazp
2c=ea
2cva·Aazp
Aat (ra) = Aazp +Aa(ra)
LD=
N
X
a=1 hea
2φa(ra) + ea
2cva·Aat (ra)i
Aazp
Aaz
Aaz.
e
~=c= 1,
Lz=
N
X
a=1
[eaca·Aa(ra)eaφa(ra)]
L=TU
T=
N
X
a=1
eaca·Aa(ra)
U=
N
X
a=1
eaφa(ra)
aM =eaAa(ra)·dl
dl=cadt
aM =eaAa(ra)·cadt
aE =eaφa(ra)dt
dt
ea, a
ωzbw =aM
dt =ma
T=
N
X
a=1
ma
Aa(ra)eaca
αrea
Aa(ra) = eaca
αrea
+X
b6=a
eb[cb+ (cb·ruab)ruab ]
rab
φa(ra) = ea
αrea
+X
b6=a
eb
rab
Lz=
N
X
a=1 (1
rea
+X
b6=a
αca·cb+α(cb·ruab) (ca·ruab )
rab "1
rea
+X
b6=a
α
rab #)
Lz=
N
X
a=1 X
b6=a
α[ca·cb+ (cb·ruab) (ca·ruab )1]
rab
rab =rarb
rab =|rarb|
ruab =rab
rab
ca·cb= cos (ϑab1)
ca·ruab = cos (ϑab2)
cb·ruab = cos (ϑab3)
ϑab1=ϑab2ϑab3
Lz=
N
X
a=1 X
b6=a
α[cos (ϑab2ϑab3) + cos (ϑab2) cos (ϑab3)1]
rab
Lzab =α[cos (ϑab2ϑab3) + cos (ϑab2) cos (ϑab3)1]
rab
raeaca
(c2
a= 1) α=e2
a(α1137.036) rea
rab tab
ruab rab
(mea =r1
ea )αrea
δ(S)=0
S=ˆ4T
Lzdt.
S=
N
X
a=1 X
b6=aˆ4T
α[cos (ϑab2ϑab3) + cos (ϑab2) cos (ϑab3)1]
rab
dt
S=
N
X
a=1 X
b6=aˆ4T
Lzabdt
δ(Lzab) = 0 =δ(S) = 0
δ(Lzab (rab, ϑab2, ϑab3)) = ∂Lz
∂rab
δrab +Lz
∂ϑab2
δϑab2+Lz
∂ϑab3
δϑab3= 0
∂Lz
∂rab
=α[cos (ϑab2ϑab3) + cos (ϑab2) cos (ϑab3)1]
r2
ab
∂Lz
∂ϑab2
=α[sin (ϑab2ϑab3)sin (ϑab2) cos (ϑab3)]
rab
∂Lz
∂ϑab3
=α[sin (ϑab2ϑab3)cos (ϑab2) sin (ϑab3)]
rab
r2
ab c2t2
ab = 0
(ϑab1= 2πn)ϑab2=π
2+πm=δ(S) = 0 (n, m Z).
(tz'8.1·1021s)
ωzbw
m
ωzbw =m
m m0Ek
m=m0+Ek
γt
S
A
A=A+γtφ
·A=S
γt,
U
P
1
8πAγtg
A=Uγt+P
P=1
4π(E×B− SE)
P
S
E.
(·A= 0) SE
SE
/4π
P
ρ
SρS
4πρ =∇ · E
ρS=1
4π∇ · ES
dU
dt =ρS
φ
dU
dt =ρ
dt
eS =e
dt
δωzbw
ωzbw fS
=
dt
δωzbw =
dt
eS=deφ
dt
eS=d2ϕ
dt2
eS=zbw
dt
φ=ˆSdt
fS=eφ
eS.
S.
(λe2.43 ·1012m)
I= 0.25A
dne
dt =I
e= 1.56 ·1018ne
/s
Ee=1
4πε0
e2
λe
wout =Ee
dne
dt '150w
(1012 m) (1010 m)
(1015 m)
rq=~
/2mec0.192
re
(rq=re
/2)
~
re= 0.38 pm Bzbw
Bzbw = 32.21 ·106T.
gH
gH= 267.52 ·106rad ·s1·T1
νNMR =gHBz bw
2π= 1.3714 ·1015 Hz
νp
νp=νNMR
/2= 6.8571 ·1014 Hz.
λp=c
νp
= 4.372 ·107m
(gD= 41.066 ·106rad ·s1·T1)
220 V
(200 kV )
b
λmax
Tk=b
λmax
Tk=2.898 ·103
0.3575 ·106= 8106 K.
Wout =σεT 4
kA22 kW
Eout = 22 k W h
σ= 5.67 ·108W m2K4ε= 0.9
A104m2l1cm
d0.3cm
m3
/h'kg
/h
Kcal
/hkWh
/h
m3
/h
CO2
Einp
Einp = 380 W h
COP =Eout
Einp 54
R.P.YX
σI=2
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