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Au197 +N14 →Au198 +N13

σI = 2

N

RN

RN≈~√N

2mec=c√N

2ωe

=re√N

2,

re=c

ωe=λe

2π

ωe=mec2

/~

ρ(ω) :

ρ(ω) = ~ω3

2π2c3dω.

N= 1011 D

D= 2RN≈0.12 µm

dE

dE≈r4πR2

N

N=√πre≈1.78re≈0.68 ·10−12 m.

N

re=λe

/2π≈0.38 ·10−12 m.

FCA

FC(d)

A=π2~c

240d4.

d c

A=π(λe

/4π)2

FC(d)

Fe(d) :

FC(d) = π~cλ2

e

3840d4,

Fe(d) = 1

4πε0

e2

d2.

db≈2λe

/2π≈0.77 ·10−12m

re

A=π(λe

/2π)2=πr2

e

db≈4λe

/2π≈

1.54 ·10−12m

ΦM=h

/e

h e

e c

FL

FL(d) = ecB (d) = µo

4π·e2c2

d2=1

4π0·e2

d2,

B(d) = µoec

4πd2

c~

d

d

d=nλe

±~

/2~

~

FL

LD

LD=

N

X

a=1 hma

2v2

a−ea

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 =|ra−rb|

ruab =ra−rb

|ra−rb|

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 h−ea

2φa(ra) + ea

2cva·Aat (ra)i

Aazp

Aaz

Aaz.

e

~=c= 1,

Lz=

N

X

a=1

[eaca·Aa(ra)−eaφa(ra)]

L=T−U

T=

N

X

a=1

eaca·Aa(ra)

U=

N

X

a=1

eaφa(ra)

dϕaM =eaAa(ra)·dl

dl=cadt

dϕaM =eaAa(ra)·cadt

dϕaE =eaφa(ra)dt

dt

ea, a

ωzbw =dϕaM

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 =ra−rb

rab =|ra−rb|

ruab =rab

rab

ca·cb= cos (ϑab1)

ca·ruab = cos (ϑab2)

cb·ruab = cos (ϑab3)

ϑab1=ϑab2−ϑab3

Lz=

N

X

a=1 X

b6=a

α[cos (ϑab2−ϑab3) + cos (ϑab2) cos (ϑab3)−1]

rab

Lzab =α[cos (ϑab2−ϑab3) + cos (ϑab2) cos (ϑab3)−1]

rab

raeaca

(c2

a= 1) α=e2

a(α−1≈137.036) rea

rab tab

ruab rab

(mea =r−1

ea )αrea

δ(S)=0

S=ˆ4T

Lzdt.

S=

N

X

a=1 X

b6=aˆ4T

α[cos (ϑab2−ϑab3) + 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 (ϑab2−ϑab3) + cos (ϑab2) cos (ϑab3)−1]

r2

ab

∂Lz

∂ϑab2

=α[−sin (ϑab2−ϑab3)−sin (ϑab2) cos (ϑab3)]

rab

∂Lz

∂ϑab3

=α[sin (ϑab2−ϑab3)−cos (ϑab2) sin (ϑab3)]

rab

r2

ab −c2t2

ab = 0

(ϑab1= 2πn)∩ϑab2=π

2+πm=⇒δ(S) = 0 (n, m ∈Z).

(tz'8.1·10−21s)

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 =ρdφ

dt

eS =edφ

dt

δωzbw

ωzbw fS

eφ =dϕ

dt

δωzbw =dϕ

dt

eS=deφ

dt

eS=d2ϕ

dt2

eS=dωzbw

dt

φ=ˆSdt

fS=−e∇φ

eS.

S.

(λe≈2.43 ·10−12m)

I= 0.25A

dne

dt =I

e= 1.56 ·1018ne

/s

Ee=1

4πε0

e2

λe

wout =Ee

dne

dt '150w

(10−12 m) (10−10 m)

(10−15 m)

rq=~

/2mec≈0.192

re

(rq=re

/2)

~

re= 0.38 pm Bzbw

Bzbw = 32.21 ·106T.

gH

gH= 267.52 ·106rad ·s−1·T−1

νNMR =gHBz bw

2π= 1.3714 ·1015 Hz

νp

νp=νNMR

/2= 6.8571 ·1014 Hz.

λp=c

νp

= 4.372 ·10−7m

(gD= 41.066 ·106rad ·s−1·T−1)

220 V

(200 kV )

b

λmax

Tk=b

λmax

Tk=2.898 ·10−3

0.3575 ·10−6= 8106 K.

Wout =σεT 4

kA≈22 kW

Eout = 22 k W h

σ= 5.67 ·10−8W m−2K−4ε= 0.9

A≈10−4m2l≈1cm

d≈0.3cm

m3

/h'kg

/h

Kcal

/hkWh

/h

m3

/h

CO2

Einp

Einp = 380 W h

COP =Eout

Einp ≈54

R.P.Y∞X

σI=2