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The entries in the table of section 2 display changes applied to the 2005/JUL/93 draft of the Green Book which has been distributed at the Beijing Meeting 2005 (IUPAC GA).. Only those ch[r]

(1)

For Peer Review Only

Quantities, Units and Symbols in Physical Chemistry,3rd Edition

Journal: Pure and Applied Chemistry Manuscript ID: PAC-REC-05-11-10

Manuscript Type: Recommendation Date Submitted by the

Author: 10-Nov-2005

Complete List of Authors: Quack, Martin; Eidgenössische Technische Hochschule Zürich, Laboratorium für Physikalische Chemie

(2)

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+, p1 , V3+ < 6, p

1 V=! + - / / 11 μAr μ<=36,

+ - i + , 4,1611μi3

4 i 6, 61.!

'! - + ! ++ Δ

123 - - 12 < ,,=3

1 + Σ Π - , +1, /3 +!

<"! $ %*# .=3 <#!' ( #( .3 - , /=3 <;, - , =3

! - +01 -, , log </3 6=3

.+3 3 3-3 13 /13 ! +/1 1 +1/

6∇∇∇- /13∇∇∇× - 31∇∇∇·- +161-

! - !/! e - /3 ,1

+ + ;,P-, 1/,-

+1/ 6!

"# ΔH = H(ﬁnal)−H(initial)P <1pG1t= ,1 - - / - +,P

x ,1 - x! >, - 1+1

+,1 F -, - t / +1

;, F = F0exp(−δt) sin(ωt) δ X < ,D

+G= 1ω /, -;, < ,D 1G=! , -

- + - x3 x3 6, δ -

1 X +1, δt! +1, δt1 ωt

13 6,161/, +<+W = 1

<1W =3+!

(

(20)

(! -,1+4/11;,,65,

< ,/ 11 66= ,1 1/4

! -,1 + ,1 ,/ ,3 6,

/ 6! + Eh < "!*!#3 +!*%=!

43 U3 ,01 ,3 ,3 ,3

,3 /Q1 , - > 1/ /

6!

"# c0 - +1 -/ ,,3 me - 3h -

3 NA L - /1 e - /3 a0

- > 1,3!

U We· U W !&)# '& %"< $=× )

−19

B!

*! F7 ,1 /3 /3 ,3

,! ,1 <,+/=3 - +

;,! 1/ + - ,6, //? ?

161//11+,131/,+,,?61

,3 61 1, +1,!

- ?+,1 1/ ?

?3 !/! O?3 N?3 S?3 P?! H 11

111 1/! -J "K!

"# ?+

??$?++

6<η

4

?#?1++? 3"?1= ,

?<=?ω?+< 3$?+=

? ?/,+

% ?1?" ?

N?6Q1

O?

"H?+

+?#< H=?

*

(21)

(22)

-4/ 11 16- +

;, ,1 ! , ;, 6 -,1

1 J$K J%K!

,/ , - - ;, 1,3

+11 10 - / , 11 +

, - / -4 11 !

6 64 - , ,/ Q

+6! - 11 -6 16 +,

,3 ++ 11/ 1-/,6+ ,++3 ,

,++ ! @ ,65 +6 +-

- + 6/ ;,-/,6+ ,++34, 1,/ 6/,!

1+1 ,1 101! - 11

6,1 +, -, 101!

6/16,65! 0,6/-;,3

116<=36-1036- ,<4,,+

,6,++0.3 "!&3 +!* =31 -! @4

113 ,1 + ;, +63

1 +, +! ,1 +6 - / 12

;,! 10 / + - 10 +,+

+P ,1 /11 ,-, - 10!

;,1+310/ , 1,1

J $K! -, 10 - + ;, + / -,1 J %K

1 + J &K! ;, ,

, <"! )3+!*'=! , - 11131 64

63 +++! ,1 101 <

1- ++= 1!

(23)

(24)

11 / 11

J$K J%!63K!

, -* % ,

# /

+

1 ρPϑP/ 3

+ + PϑPϕ 3

1

/Q1 !3!i <=

+ W#xY yY/z

/

+6D

/

61

7 3δ

1

1,

1

+ /

/ -

3

2

, '3(v)

3

+/ α3β3 γ3ϑ3ϕ!!! α WsGr 13 #

1/ 3<ω= WAGr

2

3 #

3 1,

+1 W/, "

-;, ν3 ν W G Q3

−1

/, -;, ω ω W#ν

−1

3

−1

#3$

τ3 τ W|1G1 #|

3

/, ω ω W1ϕG1

−1

3

−1

#3%

3 3

.

W1G1

−1

+1 33 03 W||

−1

&

W1G1

−2

'

< = /11 +,1 n13 n ,

+!

,1 -,

Q/!

<#= , <1= 1 <=3 - + / 1 / +3

11! - <!! 1=3 ,11 +

- 11 , -+++3 1-1 / 6!

<"=N ,6- 1<+1= t!

<$= ,Q 6,1- /, -;,!

<%=/, 3ωωω!

<&= +1 -/ 1,1 ,!

<'= -6 ,1!

"

(25)

11 / 11

J$K J%!1K! 11 ;, 6,1, -,1 J$3%!K!

, -* % ,

7/

1,1 μ μ=m1m2/(m1+m2) 7/

131 ρ ρ=m/V 7/

−3

d d=ρ/ρ

◦ −

,- ρ

A3ρ

S ρA=m/A 7/

−2

+0 , v v=V /m= 1/ρ

3 7/

−1

, =m 7/

−1

/, , =× B #

- I, J I =

i

mir2

i 7/

2

"

- W1 G1t=m

3() =×

;,

/ E B

+ / E

3V3 E =−

·1 B $

7 / E

3T3K E

= (1/2)mv 2

B

47 W3A W =

·1 B

+4 P P =· W1WG1t @

/Q1 q <=

/Q1 , p <=

// -, L L(q,q˙) =T(q,q˙)−V(q) B

-, H H(q, p) =

i

piq˙i−L(q,q˙) B

S S =

L1t B %

+, p,(P) p=F/A

−2

,- γ, σ γ =1WG1A

−1

3B

−2

4/ G,(W, P) G=mg

/ G F =Gm1m2/r

2

2 7/

−2

< = , ρ ◦

−=ρ

<23 $ ◦

=!

<#= 6, , ++< #!&3 +!#%=!

<"= / % ;,D Iαα =

imi

βi2+γi23 I

αβ = −

imiαiβi - α = β3

4 α3β3γ +,-x3y3z! ,,16,,+1

6 /!

<$= +7/3 + / 12 + /03 , /

6+1 10 /3 -

Ep(r1, r2) =−

r2

r1

·1

+64 ,++

Ep(r) =−

∞

r

·1

<%= / // -,L34 ;,

p1q−

H1t

< J 'K=!

$

(26)

, -* % ,

σ σ=F/A &

τ τ =F/A &

3 ε, e ε= Δl/l

/

1,, -3 E E=σ/ε &

,/M 1,,

γ γ = Δx/d &3'

1,,3 G G=τ /γ &

,6M1,,

, ϑ ϑ= ΔV /V0 &

6,7

6,7 1,,3 K K=−V0(1pG1V) &

+ 1,,

3 η,(μ) τxz =η(1vxG1z)

1

8,1 ϕ ϕ= 1/η 7/

−1

7 ν ν=η/ρ

2

−1

1 μ,(f) F =μF

,1/ 8, P, P

P =

1EG1t @

,-3

8 ρ ρ=P

/P0

(

6+ α

,(α) α = 1−ρ

*

τ τ =P

/P0

(

1+ δ δ=α

−τ

<&= / ;,!

<'=d 164 1+16Δx!

<(=P0 ,1/ 8,.3P

81 8,.1 P

1 8,.!

<*= 10 + , 12 - ,/ 13

6+- +1 , 1+-!

%

(27)

$

11 / 11

J$K J%!-K!

, -* % ,

, I, i

, , I =

·n

−2

#

/3 Q Q=

I 1t

;,-

/1 ρ ρ=Q/V

−3

,- 1-/ σ σ =Q/A

−2

+ V, φ V =1W/1Q U3B

−1

+ 123 U3ΔV,Δφ U =V2−V1 U

- E, E =

(/Q)·1 U

(Emf, EMK) "

01/ =/Q=−∇∇∇V U

−1

8, =

·eee

n #

1+ ∇∇∇ ·=ρ

−2

+ C C =Q/U U

−1

+ ε =ε

−1

$

ε0 ε0 =μ

−1

0 c− 2

0

−1

%

+- ,,

+ ε

ε=ε/ε0

&

1 +Q3 =−ε0

−2

+Q

< 1+

+,=

,+6 χ

χ=ε−1

+?,+6 χ

(2)

χ

(2) =ε

−1

0 ∂ 2

P/∂E2 B

−1

3U

−1

'

#1 +?,+6 χ

(3)

χ

(3) =ε

−1

0 ∂

3P/∂E3

2

2 B

−2

3 2

U

−2

'

< = , I 6;, A!

<#=eeen1A - < 3+! "=!

<"= -1 6-/113

+ 12 - < $3+!')=!

<$=ε 17 !

<%=c0 +1 - / ,,!

<&=;, 4-11 !

<'= +?,+6 X - ? .+ -

/,1P -1+Q+4-/,1E-01/D

P =ε0[χ(1) E+ (1/2)χ

(2) E

2+ (1/6)χ(3)

E

3+· · ·]

4 χ

(1)

,, ,+6χ

3;, ε −1

- / !

1, +χ

(1)

3χ (2)

1 χ

(3)

- 7#3"1 $3+!

+ 1,<,;,1= - 4, 3χ

(2)

Q6

! ;,Q11,4+Q6

α +?+Q6β Q ,! /, +

&

(28)

, -* % ,

1+ , μμμ =

i

Qi

i (

/ 8,.13 =Q× *

/ 1,

/ 8, =

·n @6 #

/ 01/3 ∇ ×=

−1

/Q/01 /

+6 μ Wμ

−2

3

−1

)

/ μ0 μ0= 4×10

−7

−1

+6 -,,

+6 μ

μ=μ/μ0

/Q =/μ0−

−1

</ 1+

+,=

/ ,+6 χ, κ,(χ

) χ=μ−1

/ ,+6 χ

χ=Vχ

3

−1

/ 1+ , μμμ E=−·

2 3B

−1

R R=U/I Ω #

1, G G= 1/R #

/ δ δ=ϕU −ϕI "

X X= (U/I) sinδ Ω

+13 Z Z WR YX Ω

<+ +1=

13 Y Y = GZ

<+ 1=

,+ B Y W GYB

ρ =ρ Ω $

1, κ, γ, σ =κκκ

−1

$3 %

-?1, L E=−L(1I/1t) 3U

−1

,, 1, M, L12 E1 =−L12(1I2/1t) 3U

−1

/ + =∇∇∇ × @6

−1

/ = × @

−2

&

<'=<,1=1,- ,V , Vm α=ε0χ

V

αm=ε0χ Vm

<

&3+!#$ #!'!#3+!$)=!

<(= @ 1+ +1 - + / Q −Q +1 r3

1 - 1+ 6- / + /! ++

,13 6, 1,/1! 1+ - 1+1

- /!

<*=;, ,1 61 L/ 01M!

< )=μ 17 + !

< = χ

,1 - / ,+63 6, ,1

/ ,+6!

< #= R= (U/I) δ31 G=R/(R

2+X2).

< "=ϕI 1ϕU + -, 1+ 12!

< $=;, + !

< %= /γ 1σ36, κ!

< &=;, /? !

'

(29)

- ;, ,1 ;,, 11

/ 11 J$K! - ;, ,1

01 - ;,, 6 - , +

01! - ,1 +,61 J (KP

+ *3+! %%!

, -* % ,

,+ =−i∇∇∇ B

−1

7 / + T T=−(

2/2m)∇∇∇2

B

+3 H H =T+V B

4-,3 , ψ, φ Hψ =Eψ <

−3/2

= #3"

-,

1/?7 ψ

nlm(r, θ, φ) ψnlm=Rnl(r)Ylm(θ, φ) <

−3/2

= " 4-,

+ Ylm(θ, φ) Ylm=N

l|m|Pl|m|(cosθ)e

imφ

$ -,

+661 P P =ψ

∗ψ

<

−3

= "3%

/1 ρ ρ=−eP <

−3

= "3%3 &

-

+66, =−(i/2m)× <

−2

−1

= "

13 (ψ

∗∇∇∇ψ−ψ∇∇∇ψ∗)

+668,

, =−e <

−2

= "3&

-

/ 1τ 1τ =1# 1/ <=

ij3||1 ij =

ψi∗Aψ j1τ <= '

- +A

.+ , A3A A=

ψ∗Aψ 1τ <= '

- +A

< = LM < ,8.=33 ,1 1/, + - /6 ;,!

10 ++ +3 ∇∇∇ + <

$!#3 +! )'=!

<#=+ 14 ψ-,1-?1+1-, (x, t)1 +?

,1-, ψ(x) +! , - (x, t) =ψ(x).+(−Et/)!

<"= Q1 4-, -/+ ?1 ++++

, / +! , ;,, 43 - +1

- , < "!*! +! *$ '!" <=3 +! $%P - J *K=!

13/3 /, / +11

r/a0,E/Eh3Q/e31 m/me +3 ;, 1!

<$=P

|m|

l 11/1-,-1/l11|m|! N

l|m|Q

!

<%=ψ ∗

+.5,/-ψ! ?Q1n4-,(r1,· · ·, r

n)3

+66 1-

2· · ·

n

∗

1τ2· · ·1τn34 /

1- 6, !

<&=−e /- !

<'= , - + ;, + +!

(

(30)

, -* % ,

5,/ A

†

A†

ij = (Aji)

∗

<= '

- +A

, [A,B]3[A,B]− [A,B] =AB−BA <= ( -A 1B

, [A,B]+ [A,B]+=AB+BA <= (

-A 1B

/, , ++3#!&! +!")

+

+4-, αPβ *

456%) /-)%5*)(' -'032() 27%-' 89:

6 χr

−3/2

" -,

, φi φi =

r

χrcri

−3/2

"3 )

,6 / H

rr3α

r Hrr =

χ∗rHχ r1τ B "3 )3

/ Hrs3 βrs Hrs=

χ∗rHχ s1τ B "3 )3 #

/ + x −x= (α−E)/β "

+ / S

rs3S S

rs =

χ∗rχs1τ )

/1 qr qr=

n i=1

bic2ri $3 %

611 p

rs prs=

n i=1

bicricsi %3 &

<(= , - +1,- + ;, 1$!

<*=+ 4-,- /3 α 1β3101 -

z + - + /, ,3sz3 α|sz|α = +(1/2),β|sz|β =

−(1/2),β|sz|α =α|sz|β = 0 , -. + 4-, -

4 11 F7 α3 β3 γ3 ! 1/ ,

ms3

/ -/14 4!

< )=H - / i j , 63 r

1 s6 6! C73Hrs ?Q - 611

+ - r 1s31 Srs ,1 Q- r=s!

< =L,6/M12 /<4

/ -6 χr 01- ,= -?71,1 64

<4 - 4? +, /=!

< #= + 16 61/ 64 r s!

?61/ 3+1// / 6/ ,-

/- 61/!

< "= + ++ -C7 -+ 5,/11?

63 α - β - 611 + -

P , C7 , -

+ x!

< $=−eqr /r! qr +06,-n

/ r34

qr =n!

< %=bi /,6-4,+/6/εiP-?1/

63bi ,)3 #!

< &=prs 611 64 r s!

*

(31)

$$ 3&323- ('2'%%;-56 +%),;5-&+3+2%&2 <%)= 27%-' 8(03&323-

, ;,, - +1 , < "!*! +! *$

'!"<=3+! $%=! /6-/3/3 3/

1 /, +11 +1/ ,3a03

Eh3me3e1 +! , ;, 13 , ,

-1!

, -* ,

, φ

i(μ) '

, +?6 φi(μ)α(μ)P '

φi(μ)β(μ)

4-, = (n!)

−1/2φ

i(μ) '3 (

- H

μ Hμ=−(1/2)∇2μ−

A

ZA/rμA '3 *

/

?/D

.+,- Hii Hii=

φ∗i(1)H1 φi(1)1τ1 '3 *

4? +,

/D

,6 / Jij Jij =

φ∗i(1)φ∗j(2) 1r

12φi(1)φj(2)1τ11τ2 '3 #)

./ / K

ij Kij =

φ∗i(1)φ∗j(2) 1r

12φj(1)φi(2)1τ11τ2 '3 #)

?6

/ εi εi =Hii+

j

(2Jij−Kij) '3 #

/ E E= 2

i

Hii+

i

j

(2Jij −Kij) '3 # 3##

=

i

(εi+Hii)

,6 + Ji Jiφj(2) = φi(1)

r112φi(1)

φj(2) '

./ + K

i Kiφj(2) = φi(1)r112

φj(1)

φi(2) '

7 + F F=H +

i

2Ji−Ki

'3 # 3#"

< '=1i1j ,631μ, 1#6

1!

< (= 1,66 ?Q1 +1,-,+1 , +?

6 φ

iα φ

iβ < 11 φ

i φ

i=P - 4,1

Q11! <nZ=

−1/2

Q1n,6-!

< *= ZA /,6 <,6= - ,, rμA 1- μ

-,, !H

ii / - φ

i 01- !

<#)=? +,/4 , 1D Jij =ij|ij

1 - - 1 -,

#! J

ij = (i∗i|j∗j)30 41 - 11

#! -, 1! / /

4 , 161D Kij =ij|ji

K

ij = (i∗j|j∗i)!

<# = ++ , ,+1

, 6!

<##=,j,14j=i3- J

ii=Kii, ,

+0 / 2Jii−Kii=Jii!

#)

(32)

$$ ('2'%%;-56; 27((& 27%-' *+3&> /-)%5*)(' -'032()+%?@(&=%= (+ )3&%(' 5-/03&(23-&+ -, (2-/35 -'032() 0(+3+ ,*&523-&+ ; 27%-'.9

, -* ,

6 χ

r #$

-,

, φi φi =

r

χrcri

+ Srs Srs=

χ∗rχsdτ,

r,s

c∗riSrscsj =ij

1 Prs Prs = 2

i

c∗ricsi #%

/

6-,D

? / H

rs Hrs =

χ∗r(1) ˆH1 χs(1)dτ1

4? / (rs|tu) (rs|tu) =

χ∗r(1)χs(1) 1r

12χ

∗

t(2)χu(2) dτ1dτ2 #&3#'

/ E E=

r

s

PrsHrs #%3#'

+(1/2) r

s

t

u

PrsPtu[(rs|tu)−(1/2) (ru|ts)]

7+ F

rs Frs =Hrs+

t

u

Ptu[(rs|tu)−(1/2) (ru|ts)] #%3#(

<,1=

<#"=?7;, 1(F−εj)φj = 0! 10-7+

- /-,φi ,/ ,6 1./ +3Ji 1Ki!

<#$= r s 6 -,! , +, -,

7?+6 <= /,+6<F=!

-,++1/-χ(r, θ, φ) =N r

n−1

.+(−ζ

nlr)Ylm(θ, φ)3

4 ζ

nl 1/ + +/ / ;,,

,6 n l! F -, ,, +1 13

-χ(x, y, z) =N xaybzcexp−αr2! - - , -,4/.+?

α ,13 , ! N Q !

<#%= +4 # +,+1 6! , / ,+1

, 6! Prs 611 64 r s!

<#&=1 - 4?/6-,3(rs|tu)361

,1 #)!

<#'= #? / +1 - / +

6 -,! H

ii J

ij3 K

ij +1

-/ +6 6-,1/ -4/ ;,D

Hii=

r

s

c∗ricsiHrs

Jij = (i∗i|j∗j) =

r

s

t

u

c∗ricsic∗tjcuj(r∗s|t∗u)

Kij = (i∗j|j∗i) =

r

s

t

u

c∗ricsic∗tjcuj(r∗u|t∗s)

<#(= ?7? ;,3 +1 - -

7 + Frs31 + Srs37 -D

s

(Frs−εiSrs)csi= 0

#

(33)

11 / 11

J$K J%!5K! 11 ;, ,1 , + +

-,1 J$3%!7K!

, -* % ,

, ,63 A

,6

+,63 Z

,6

,,6 N N =A−Z

m

7/ 3#

-3 m

, m

7/

m

m=m(

12

)/12 7/ 3"

=m

−Am

7/

/3 e #

+ /

7 h B

7 111 6# =h/2 B #

>1, a0 a0 = 4ε0

2/m e

2

#

/ E

Eh=

2/m a

2

0 B #

16/ R∞ R∞=E

/2hc

−1

0?,, α α=e

2/4 ε0c

Q / E

, I

B $

X E

, A

B $

/ χ χ= (1/2) (E

+E)

B %

< = /,6 ,1- +4 ,6+D + - +3 - ,3

- -,,3!

<#=;,,1,<"!*! 3+!*$1'!"<=3+! $%=!

<"= m

;, ,01 ,3 ,3 !! m

= 1

, < "!'3

+! *#=! 13 ,1 - ,01

,J#)K!

<$= Q / -;, Q + <I

=! X

/ 11 - / !

<%= + - / 1,1 ! ,/ +4 -

, -! - 10/ ;, J# K!

/ + / - / 1, ! ! ,7!

-;, ,1 31, ,/3 61 61 1/ Ed U

, 11 / 12

101! >

χ−χ =

E(

>) U

− 1

2 [E(

) +E (

>>)] U

4 χ

1 ,/ /!

/ - 1/ χ

= 2.1

! 1X, / / -

;,3 /- χ

−χ

! ,/ ,!

##

(34)

, -* % ,

1/ E

, D

B

- /,1 D0 B &

- + , D

B &

++ ;,,,6 n E =hcZ

2R

∞/n2 '

<1/ =

/, , ++3 #!&

;,, ,6

/ 1+ , μμμ Ep =−· B

−1

(

- ,

/Q6 ζ =ζ B

−2

- ,

>/ μ μ =e/2m

B

−1

, / μ

μ= (m/m)μ

B

−1

// γ γ =μ/L

−1

*

<// =

?- g g= 2μ/μ

, ?- g

g=μ/Iμ

/, -;, ω

ω= (e/2m)B

−1

)

-;, ν

ν =ω/2

Q

.3

/,1 T1

T2

1+ , μμμ E

=− ·

#

- ,

;,1,+ ; E

= (1/2) :

= (1/3)

:

2

"

- ,

<&=6D0 1D

,1-1/-11+,!

<'= ,6 01- ,,- ,6 Z!

<(= / - +0 + 11 ,6+3 !/! μ

μ

-

3+31,! 6,1,,,-.,.+,

- / +! U, - 6, / &!"3+! # !

<*=μ / /, ,!

< )=;, , -;,!

< = ;, ,1 - , ++3 +,

+? ++< #!&3 +!#'?#(=!

< #= #!&3(3 +!#&!

< "= ;,1,+ - , +16É

É

É3101

// 1ρD

Qαβ =

rαrβρ 1V

4 α β x3y z3 - Q101

αβ = (1/2) 3rαrβ−αβ r 2ρ

1V W(1/2) [3Qαβ−αβ(Qxx+Qyy+Qzz)]

11 - +D

Vαβ =−qαβ =∂2V /∂α∂β

6, + / /

Ep= (1/2):

= (1/2)

α

β

QαβVαβ

#"

(35)

, -* % ,

;,1,+ eQ eQ= 2

zz

2

$

- ,,

01/1 q

αβ =−∂2V /∂α∂β U

−2

;,1,+ χχχ χαβ =eQqαβ B %

/

+Q6 ααα α

ab =∂pa/∂Eb

2

2 B

−1

&

- ,

+?+Q6 βββ β

abc=∂2pa/∂Eb∂Ec 3

3

B

−2

&

#1 +?+Q6 γγγ γabcd =∂

3

pa/∂Eb∂Ec∂Ed

4

4 B

−3

&

<- 1? A A=−1N /1t >; '

,6=

1<= λ, k A=λN

−1

'

1/ <=

t1

/2, T1/2 N (t1/2) =N (0)/2 '3 (

-3 - τ τ = Gλ (

41 =/τ B

1/ / Q B

σ

2

47 /- QW QW≈Z(1−4 sin

2θ

W)−N *

,,

< $= , ;,1,+ 101 12 - ,

;,1,+! 1- /!

, + , - // ! , - -

, 1&!"3 +! # !

< %= , ;,1,+ / χχχ ,, ;,1 Q3+1/

,- eQq/h3 ,/ ,,1!

< &=+Q6ααα1+?+Q6βββ, γγγ,· · · X.+

- 1+ +4 - 01 1/ ;,D

= (0)+ααα + (1/2)βββ 2+ (1/6)γγγ 3+· · ·

4ααα3βββ31γγγ -7#3"1 $3+! +-

1/,16,6+1· · ·31110301

1/+- 31,6;,+-01! +Q6

1 +?+Q6 ++! , ααα ,,

1 + - βββ Q - , - ! U, -

+Q6-;,1,αG$ε034,! ,-.+1

, - [

3

<4 1+1= , - a

3

0 < ,3 "!*! +! *$=!

++ +?+Q6 β/(4ε0)

2

, - a

5

0e−13 γ/(4ε0) 3

, -a

7

0e−23!

< '=N ,6 - 1/ >!

< (= - - / <=3 '!#3 $3 +! "'!

t1/2=τ # -.+ 1!

< *= 47 / - ,, ++ / , ,6 N

+ ,6 Z 47 / / θW < + %3 +! )*=! +

, - 1, ++ ,1/47, J##K!

#$

(36)

#

616.11+14/,J !?K14

+1/ 1,J$K! 611-

B-++J#"3#$K1,+0144+1

676Q6/J#%\#'K! ,,,1++

+,61, 67 , J#(\"*K!

, -* % ,

T T =Etot/hc

−1

3#

4,6 ν ν=T

−T

−1

-;, ν ν= (E

−E)/h

Q

Te Te=Ee/hc

−1

3#

6 G G=Evib/hc

−1

3#

F F =Erot/hc

−1

3#

+?6,+/ A Tso =A <·>

−1

++ I

A;IB;IC IAIB IC 7/

2

-

4,6 A;B;C A=h/8

2cI

A

−1

3#

-;, A;B;C A=h/8

2I

A Q

1- =IC−IA−IB 7/

2

+ κ κ=

2B−A−C

A−C "

-,/1

1, DJ;DJK;DK;d1;d2

−1

$

1,

J;

JK;

K;δJ;δK

−1

$

6 ωe;ωr

−1

% 4,6

6 ωexe;x

rs;gtt

−1

%

< = ++ ,

−1

,1 - ;, 4,63

, 4,6 - + 4/ - ;,

,,! c 10 E/hc - +1 - / ,,! >,

94,6: ,6 ,//,-++44,6J%3&K!

, -41 94,6: + -,

−1

,611!

<#= , 101 4,6 ,

<!/! T =E/hc=31 -;,, <!/! T =E/h=! @6

3 1/, 4,6 ;, 1<!/! ν,T , A, B, C

;, 101 4,6 ,=3,/ , +!

<"= @/ + ,1D - ++

bp= (C−B)/(2A−B−C)31 - 6+ bo = (A−B)/(2C−A−B)!

<$= 1 - 1, -

+P J$)K - , +6 + - -,/

1!

<%= ,D G(v) = ωe

v+ 12−ωexe

v+122+· · ·! + ,

3N −6 61<3N −5 -= 61 1r, s, t,· · ·3 i, j, k,· · ·!

1.r ,,/1 6/ 411/4,63 +6

#%

(37)

, -* % ,

6 ;,, v

r;lt %

,6

6 -,1 νr,νr,ν

0

r νr=T(vr = 1)−T(vr= 0)

−1

% 4,6

Q ζ

α

rs &

/, , #!&! +!")

;,, ,6

1/3 g, d, β '

4/

1+ , μμμ E

p =− · (

- ,

1+ , W

ψ∗ ψ 1τ (3*

- ,

<%= <,1= +/ +! t 7+

- 1/1! -,

G(v) =

r

ωr(vr+dr/2) +

rs

xrs(vr+dr/2) (vs+ds/2) +

tt

gttltlt +· · ·

-, 101 4+ /,1

T(v) =

i

viνi+

rs

xrsvrvs+

tt

gttltlt+· · ·

6/- ,11/ - !

<&= ;, ,+/ ξ

vv

α , -

−1

,1 ?

<α=x, y, z=! -,1 44,6 ωr ωs

1 4ζ

α

rs 6;,<vr= 1 vs= 1=

ξαvv =Bαζrsα ωs/ωr+ωr/ωs

4 Bα α ! ;, ++ Bα - ξ

vv

α 101

;,4-;, ,!

<'=d ,,,1- 1/31β - , + 1/!

<(=, 1+- +1 ? ,1634

≈ "!""% &$× )

−30

! , - +/ , 1+

34 ,,1 ,-1+116 ()!

, ,3 ea0! - +/ 1+ ;,

1+/3lp =p/e3/, ,;,1,+;,1<

#!%3 " $3 +! #"?#$ &!"3 +! # =! / 64

/ - ;, 1+ +, ,

1! #!"3 '3+! '!

+ +/

"# !,!

p/ p/ p/ea0 lp/+

"!&)× )

−30 1.08 0.425 22.5

2 &!#"× )

−30 1.87 0.736 38.9

"!))× )

−29 9.0 3.52 187

<*= ;, 16/ 61 #!'3+! "$!

#&

(38)

, -* % ,

13 )3

;,6, re

Q?+ / rz

/,1 r0

,6, ,, rs

6 13 )

R

i, ri, θj,! <=

Sj <=

15,1 Qr 7/

1/2

1 q

r

6 -3

1 f,(k) f =∂

2

V /∂r2 B

−2

3

−1

)3 # +3

fij fij =∂

2

V /∂ri∂rj <=

1 F

ij Fij =∂2V /∂Si∂Sj <=

1 φrst···, krst···,

−1

"

1 Crst···

%)%52'-& +@3& '%+-&(&5% 89 %)%52'-& @('(/(>&%235 '%+-&(&5% 89:

// γ γ =μ/s

−1

g?- g hν =gμBB $

+0,+/

3

;,1 a, A Hhfs/h=a· Q $

1 Ì

Ì

Ì Hhfs/h=·Ì Ì

Ì· Q $

< )= <,= 1 1+ - +1

? ,]/T3 [W )

−10

W)! W ))+! ,-[ 41+1!

< = , / 12 - +/ 13 1/,1

,6+3 12 // 6,P 1,1 J$ K3

/ ,, - - , 1! ;,6, re

+ /1 ++.! + r0

- - /,16 1+1 +

/0 - +,!

< #= - +1 [

−1 =

B [

−2

- / 13

1 [W B -61/13 1 WB [

−1

- ?61 ! J$#K

- -, 10 - -!

< "= - 1 ,, 101 4,6

, ;,V /hc=

φrst···qrqsqt· · ·34 ,

1r, s, t,· · · ,1!

< $=

ˆ

Hhfs +0,+/!++4;,,,?

6S < #!&! 3+!")=! ,+/ a ,,;,1 Q36,

;,1/1,,<F=61611/6

gμB/h3 , QGP geμB/h ≈ 28.025 FQ

−1

=#!()#%Q F

−1

3 ge g?- - - ! - ;,1 +0 ,?

+/ +3 ,+/ a! ,+/ +3

,+/ "×" ÌÌÌ! ++ g?- /,

#'

(39)

, -* % ,

&*5)%(' /(>&%235 '%+-&(&5% 89:

/ 01- 0 %

+

1-;, / 1,2 %

01

+? Q &3 '

+? ,+/ CA Q &

-,,

1+ Q &3 '

1+ ,+/ DAB DAB=

μ0

8 2

γAγB

r3

AB

Q &

64 , 3>

-;, - F1, F2Pf1, f2 Q

4?1 +,

, ++ A,A (

- ,,

;,, ,6 IA

1 4A

1 +,+/ Q '

, +?+,+/

nJ

Q *

,/ n61

1,1, +?+ KAB KAB=

JAB

h

2

γA

2

γB

2

B

−1

3

−2

−3

*

,+/

/, -A

z mA #)

;,6,+ 0 B

−1

−3

#

/Q +,

, ;,1,+ eQ

2

##

< $= <,1= +! - g?- ++13

/ - g + 1+ + /, , /3

4 +! , 4,1;, g? 1+

/, / J$"K!

< %= 6/ <1=1 1/ <2= 1-;, 01 4-;,

ν1 ν2 , /, -;, <,1 1 23 += 1,2!

101 ,/ 1=−γ1 2=−γ2! #!"3 (3+! '!

< &=, - /Q! -

/,161/,-;,,<1

−1

36,-11

−1

=!

#$!

< '= ;,!

< (=A,A +IAx,IAy,IAz SAx,SAy,SAz3+!

< *= ,1 + - , ,+13 !/! J(

13C,1H)

113 ,+/ +3 !/! J<=! @ 6/,

63 / ,6+3 !/! JCH! ,, - / ,1 /

0! ++ 1,1 ,+/ !

<#)= M m -;, 113 6, + , m

1-, 4/Q!

<# = - + +- / 010!

<##= #!%3 " $3 +!#" #$!

#(

(40)

, -* % ,

01/1 qαβ =−∂

2V /∂α∂β

U

−2

'3#"

, ;,1,+ χ χ=eqzzQ/h Q &

,+/

1- t1, t2

4?1

+? T

A

1 #$3#%

</,1= - ,,

+?+ T

A

2 #$

<= - ,,

+4-, α;β #&

// γ γ =μ/

I(I+ 1)

−1

##3#'

- - δA δA= (νA−νref)/νref #(

,,

, , η #*

, / μN μN= (me/mp)μB B

−1

")

-;, ν Q %

- - , νref

- 61 - 01 ν1

- 1/- 01 ν2

11Q1 -;, A Q "

- ,,

1/ σσσ '3"#

1/ σA BA= (1−σA)B0 "#

τc #$

<#"= 11 - 01 /1 ,

U

−2

< #!%3 +! #$=! @ 101 43 ;,1,+ ,+/

χ=eqzzQ/h! 01/1 e1 ;,1,+

,+/ χ=e

2q

zzQ/h! ++ +qXX, qY Y, qZZ!

<#$= / , - !

+7/3 -

−1

!

<#%= +? - ,, - - - / 1

11T

A 1ρ!

<#&= #!$3+! *!

<#'=μ /,1- , /!

<#(= - <- = - ,, - <+ +

/-;, =! , - /1/3 -3

,, - /6,++ ,6+ +!

<#*= , , 23 1 +η3 101 - / - I

, +3 61 ,1 - , - S , +3 ;,6,

/ - I , +!

<")= me mp + +! μB > /!

#!%3 +!## 1+ %3+! )*!

<" = -;,- ,, - / 01,+

<= )) Q!

<"#=6σA<11-1/ +=,1-

1/ 6, <- 47=! 1/ -3

,σA−σref ,16,1! BA+1/2/8,.1<

#!"3 (3+! '=!

#*

(41)

$$ /0-)+,-' (&>*)(' /-/%&2*/ -@%'(2-'+ (&= 1*(&2*/ &*/0%'+

-4/63-+611

1116! ,/ ,+-;,,,63 ,,

+6134+4,1 ,D B!

, 1/L3+#4 +?0.1 +3 1/5/+#4

,?0.1 + /.< + ,=3

.- ;,Q!

1

3+# /+# ,

6 L M

L #

l ml λ #

+ S MS

s m

s σ

6 +,+ + = + #

, 6<= R K

R, kR

, + I MI

+ + l(lζ) K

l "

, l(lζ) #3"

,- R+L(+j) N K, k #

,- N+S J MJ K, k #3$

,- J+I F MF

< = + + ;,, ,6

/, ;,/, D

2

ψ=J(J+ 1)ψ, JZψ=MJψ, J

z ψ=Kψ,

4 + ;,, ,6 MJ K / -?11 , /

−J MJ +J,−J K +J. < - + +

3 111 3 /, ;, ,1

2

ψ =J(J+ 1)2ψ,JZψ =MJψ31Jzψ =Kψ.) l -;, Q, ;,?

,,6 1m

l /;,,,6!

<#=,3 6Q6/J#%\#'K3 + ;,, ,6 ,, l K

7/ + Q , ?Q , - ;,, ,6

4 4-, ++ /- +++ /, , +! @

13 k -/11 /1 ;,,,63 K K =|k|!

43 1, + ;,, ,6 ,,1 /13

7/6 + 1/ ,!

<"= ,- -1/ /,,P j, π, p

1 G ,1! + , + - j

11 ;,, ,6 l3 l , /

−v l +v + - #! +1/ + - /, , , lζ3

l34 ζ < &3+!#&=!

<$=+ 616 , -J <N -S= 0=34,6+

Ka, Kc,4 4K =|k|;,,,66,a1c

+1 + +!

"# JK

a,Kc = 52,3 - +, !

")

(42)

$$ /0-)+ ,-' +.//%2' -@%'(2-'+ (&= )(0%)+ ,-' +.//%2' +@%53%+

839 //%2' -@%'(2-'+ 3& +@(5%;<?%= '=3&(2%+J"'3$$K

1 E

+, P3p

+?0.1 E

∗ 3<P=

+,? P

∗(=P E∗)

3p ∗

+, +P +, - 1,!

"# 3 ,3- 1/ , 61 3# 1"3P = (123)

4,1 6Q+, +1 6#3# 6"31 " !

+E

∗

/-+1+?0.1/3

,?0.1 +1! 1+

+ -;, 11 P3 ,/ + P

+,34,161164p! 01?-+16

-+3 ,/-,- - + +Y<,/1=

-/+−</ /=,1E

∗.

66,11/,4

1/+ -16 ?1,6/ <1/ = l?1,6/<

1/6=,36K?1,6/<?1,6/=/

+! ,3 ? l?1,61 + 1/,1

6-J$%KP-/+1+++−-J

-J11<6,J$%K=! ,1/ ?1,61

661Π (A

)

Π (A

) (

Δ (A

)

3Δ (A

)

!)J$&K! 6A

16 - 4-, /J 4+

+ - <6, J$&K - -, 1=!

6 +, ,-,

- - - ,1 +1!

+, +,++ + − ,1

1/ +3 ,1 1/ + +,

/,+! , - - /,+ <+?

, /,+= Sn J$'K3 +, /,+ 6/11 S

∗

n -

1-,+, /,+! +/6+ P(Sn)J$(3$*K!

.+/ +- S

∗

434 + / ;, 67 JK!

4+ <J#!6K1 J"%\ "'3$'\ %)K=!

"#

+

1 +4+ +,3 + +3J$K

+

−

1 +4+ +,3 / +3J$K

−

+

1,6 1/+4+ +,3+ +3 J#

2 K

+

−

1,6 1/+4+ +,3/ +3 J#

2 K

−

+

1 +1/ +4+ +,3 + +3J#3

2 K

+

−

1 +1/ +4+ +,3 / +3J#3

2 K

−

?,/ - + ,1 - / #!(!

<=3 +!$$!

8339 //%2' -@%'(2-'+ 3&/-)%5*)%;<?%= '=3&(2%+ 857A&B3%+ +./0-)+9 J#%\ #'K

1 E

62/n Cn

8 σ, σv, σd, σh

i

?8 Sn(=Cnσh)

"

(43)

- Cn + - 4-, ,/1 / / ,1

+ Cn / + > +3 4-,

,+1 6.+(±2s/n) / +6

s! @-, ,/1

/ / ,1 i 61 / </1= , <,/1= +! @-,

,/1 / / ,1 σh + +

1,6 +

+! 11 , J#$\ #'K!

$$ 27%' +./0-)+ (&= 5-&C%&23-&+ 3& -@235() +@%52'-+5-@

839 %'/ +./0-)+ ,-' (2-/35 +2(2%+

-616,-;,,,6 L-!

, - L 11 ,+/ + D 3 3 F3 31 I3 · · ·3 ,1

L W )3 #3 "3 $3 %3 &3 '3 · · ·3 +! +1/ ,1

/, , - / ! ? +

,+(2S+ 1)611-?1,++ 1,-

/, , J /?1 ,6+! - L S Q , - J

+63 ,6+ ,, ,++1! 0/, -

11 6// ,+ - ? 6.+64!

"# >D (1) 2

(2) 2

<#+= 1

3 2

◦

1/2 D (1)

2

(2) 2

(#+) 2, 3

0 D ( )

2( #)

2 <#+)

3, 4

◦

/ ,++

o

,1 11 +</ +−=! - ,?

++ e

6+1+<+++=! 16/,

,-, 1/ + + − / ,++ <!!

4

−

3/2 -

3

+

0 - =!

8339 %'/ +./0-)+ ,-' /-)%5*)(' +2(2%+

-,616 +6-4-,

, + /,+! ,1 F7 ,+/ + ! -

+,+(2S+ 1)6116-,++! ,,

- (= + ) 6111 / ,6+ </, J - =! - ,-

+013 - + / ,6+

111 + /, </ )

</1 4= +!

- , / + / -4!

/,161^3.1-,+613>33· · ·3

1/1- /31.1- 12 ,+6144

63 · · ·! + , <6, ,= , 11

<!/! X= + + +6 -, +

6!

? 61 +1/

0/,11 /, -!

"# /,1 - (1)

2(2 )

2(3 )

2(1 )

1 3X

2Π

r, 2Π

1/2

+ 64

2Π

3/2 +3116,6+

- /,!

"#

(44)

"# <,1=

/,1 - (1)

2(2 )

2(3 )

2(1 )

3 3^

2Π

i3 2Π

3/2

+ 64

2Π

1/2 +3116,6+

- 1!

4 -2 · · ·(21)

2

(162) 2

(31) 2

,_

1 1, · · ·(21)

2(1 62)

2(3 1)

1(1 61)

1, ^

3 >1.

/,1 -66 <6Q= · · ·(2u)

2

(1g) 4, X 1

1g.

- , ,, 11 // ;,,

,6 - 1!

"# ,

(0,0,0) /,13

(1,0,0) 1 3!! v1 = 1,1

(1,2,0) 1+ 22 3!! v1 = 1, v2 = 23!

83339 -2(23-& ,-' +@%52'-+5-@35 2'(&+323-&+

,++14-++116+

11,6+

+!

"# hν =E

−E

/ 11 // 63 -41 /,1

63 +16 1- <

/3 6+ -=!

"# >− 64 / / >

1 / ;

>→ - > ;

>← 6+- >;

→> / -

>7< #! #3 +!&#=P

(0,2,1)←(0,0,1) 2ν2+ν3−ν3 61 ,!

+ J% K ,1 6 < 6=

+ , 13 r / ,+?

+v

r ,6+ v

r 1/ ,++1 ,

6 ;,,,6! @ v

r =vr= 0 +1/1 ,++1!

"# 1 1

0 (1,0,0)−(0,0,0) ;

220 311 (0,2,1)−(0,0,1).

11 ,

4!

"# #20 #2←0 /,1

-v2 = 0 v2= 2!

, - ΔJ = J

−J

11 6/

6 - 61D ΔJ = −2,−1,0,1, 2 61 ?63 ?63

A?63 ?63 ?6 +! / ;,, ,6 <,

K - +3 Ka1 Kc - += 11 11/

-,++ 1/ ,!

"# p

A6 L+?+A?6M + ,3 !! ΔK =−1,ΔJ = 0!

,-K411/,6+3!/!

p A

K

p

A2<%=1/

- K

= 2

K

= 1

3,-J

6/111 +!

""

(45)

% $

;, / 6 -

J$K3 J%!/K3 J%#\ %%K34 67/, +01

- +! ,1 + J%&K 11 43 6, 10

!

, -* % ,

4/ λ

+1 -/

,, c

c = 299 792 458

−1

1, c c=c

/n

−1

4,6 ,, ν ν =ν/c

= 1/nλ

−1

#

4,6 σ σ= 1/λ

−1

< 1,=

-;, ν ν =c/λ Q

/, -;,3 ω ω= 2ν

−1

31

−1

+,

- n n=c0/c

7 h B

7 111 6# =h/2 B

1 / Q, W B "

1 /1 ρ, w ρ=1Q/1V B

−3

"

+1 / "

- -;, ρν, wν ρν =1ρ/1ν B

−3

Q

−1

- 4,6 ρe

ν, wνe ρνe=1ρ/1ν B

−2

- 4/ ρ

λ, wλ ρλ =1ρ/1λ B

−4

1 +4<1 / P, P =1Q/1t @ "

+= "

1 Ie Ie=1P/1 @

−1

"3$

1 M M =1P/1A @

−2

"3$

< =@ -6/, ,6+1/ ,, -1!

<#= ,

−1

41,1- ;, 4,6,,!

<"= - ;, , ,1- ?

+1/;, /6 13 !! ,, ;, +;,!

,6+-/3-631+-+61114-,64

;,/4,! ,,1- ,,;,11-

6, 1(1)3 "!"3 +!('!

"# I

, I=

1P/1 ,D @

−1

,, I

,

,D

+ I

,

,D

−1

I

,1 1/,1 - + I

< %=! 11 ,6+ 1/, 661 <6=3 <= 81

<8= ;, 61113 -!

<$= 1 +4 + / - +

4 , 6/ 61! 1 +4 +

Asource - ,3 - 4/! 1 +

- ,P /64 1

- - ,!

"$

(46)

, -* % ,

1 L I

=

Lcos1A @

−1

−2

"3$

3 I, E I =1P/1A @

−2

"3%

+3 Ie

ν, Eνe Ieν =1I/1ν @

−1

&

+1

8, F,(H) F =

I1t=

<1PG1A)1t B

−2

'

X3 (3*

+, A

ij 1N

j/1t=−

i

AijNj

−1

,1 1,1

B

ij 1N

j/1t=−

i

ρeν(νij)BijNj 7/

−1

6+ Bji 1Ni/1t=−

j

ρeν(νij)BjiNi 7/

−1

ε ε=M/Mbb )

-?>Q σ Mbb=σT

4

@

−2

I

−4

)

O1,<,/+,3 E,(e) E=A=P/L

2

/ //+4=

<%=11+4+1,-!

6 I3 ,, ,1 1, / - /3 ++

6?> 4-+! -/1

101 1,, - / < #!"3 +! ' '!$3 +! $&=!

+ ,1- 1 ,

6,11 13- 6E +-1J%&K!

<&=+;, 6101 4+ -;,ν,4/ λ 4,6 νP

- +1 / 6!

<'= , ,1 + +- / + 11 /

<- +,=P 8, / - 8, !

1,6164118,J%&KP8,1,1

- / - / ++1, ,-! /

- 11 +,!

<(= i j - 11, P E

j > Ei, Ej −Ei = hcνij, B

ji = Bij

10/ ;,! X B 101 ,/ / ρe

ν

4,6P 101 ,/ / - -;, ρν3

4 B , 7/

−1

3 B

ν = c0Bνe B

ν 101 ,/ -;, Be

ν

,/ 4,6!

<*= 64 XA Be

ν A= 8hc0ν 3B

e

ν. ?

,1 6+ X B 64

i1 jP- 1+

Beν,ij = 8

3

3h2c

0(4ε0)

ρ |

i|μρ|j|2

4 ,ρ /+?0.1 31μρ+?0.1 +?

- 1+ +! /3 ;, 61 4,6 10

- X B <!! Be

ν B

ν=!

< )= - + - +

1 166761 +,PMbb;,!

+%3+! )* - ,- -?>Q !

< = `1, - + ,! , - / //

+43 !! +4 1+1 -,! A -, /

"%

(47)

, -* % ,

, ν

−1

#3 #3 "

/+4 R R =ν/ν "

-+/ Δν Δν= 1/2l

−1

#3 $

0 f f = Δν/ν $

;, - Q Q= 2ν

W

−1W/1t

$3 %

01 c1 c1 = 2hc

2

0 @

2

1 c2 c2 =hc0/k I &

3 τ, T τ =P

/P0

'3 (

-6+3 6+ α α =P

/P0

'3 (

-83 ρ, R ρ=P

/P0

'3 (

-<11= 66 A10,A A10=−lg(1−α

)

'−#)

+66 A

, B A=−ln(1−α)

'−#)

6+X3

<= 11 a, K a=A10/l

−1

(3 #

<= + α α =A

/l

−1

(3 #

<11= ε ε=a/c=A10/cl

2

−1

(3 # 3##

+ κ κ=α/c=A

/cl

2

−1

(3 # 3##

< = <,1= +P / +1 - + - , +,

+!

< #= + 10 - , 1+1 +3 6, ,, ,

-, 41 -., <@= 4,63 ν3 -;,3ν3

! ;, , -/+43- 3+-6!

< "=;,Q+ +31/4+

< 6= ! 101 ,/ -;, ν3 4/

λ!

< $= ;, Q 6? ! l +/3

1 2l ,1?+ + /! - +/ 4,6 64

,/,1 1!

< %= W / −dW/dt -1 - /! Q

41- /1D Q=ν/ν =ν/ν! , /Q /

4 41!

< &=k >Q < #!*3 +!$%1 +%3+! )*=!

< '= -/1,6/13τ+α+ρ= 1! +++

++ <11 ,6+ = 101 ,1 ,- 21 - ,

, 3τ

+α= 1

3 -/ , /1!

1 , 6?> 43 P

/P0 =I/I0 =τ= 1−α= exp (−κcl).

Ae=−ln(τi)3A10=−lg(τi)!

< (= ++ - ;, ,, 6101 - +

3Ie

ν(ν)3 /11-,-4,6 ν <-;,ν=

+,! ,3 - +3 6+ X α(ν) -, - 4,6 ν

10 6++, -+P T(ν) 10 +,!

++,I(ν) 1-Ie

ν(ν)!

< *=10 / 66 A10 Ae 6+α

;

'! 4,6+6+α-1! +1,?

,1 - 83 / ,3 - 66

"&

(48)

, -* % ,

6+ σ

σ =κ/NA

2

#"

6+X

/1 ν A,

¯

A A= κ(ν) 1ν

−1

#"3 #$

S S =A/NA #"3 #$

¯

S S¯= (1/pl) ln (I0/I) 1ν

−1

−2

#"−#%

/1 lnν =

κ(ν)ν−1 1ν

2

−1

#"3 #$

/16+

G

G =

σ(ν)ν

−1

1ν

2

#"3 #$

6+1.3

/ - k k=α/4ν #&

+ - nˆ nˆ =n+ ik

-3

- R R =

n2−1

n2+ 2

Vm

3

−1

/- + α 31 #'

+0 + +4 [α]

θ

λ [α]θλ =α/γl

2 7/

−1

#'

+ +4 αm αm=α/cl

2

−1

#'

< *= <,1= 6, /! + 66 ,1

/ - - / ,/ - <4 =

1 ,/ +!

<#)= -J%"K 6A,1-11 6631B -+66!

<# =l 66/ + /31c , <-,6= !

<##= 11 6+ X ε -;, L XM

+,61,! -,, ,- L XM-;,1

4,+-/,P6-,,,,

−1

1 3

−1.

J%'K! 41L.M,1++61-,-2-6+3

/3 1,!

<#"=;,/6+Xκ36+

σ

31 , -A, S,S,¯ ,1G

3, -21,

6+1 1,1 ! 1, #!'! 3+!"(!

<#$= 10 /10/ ;, +01 - /

+3 !/! G(ν1,ν2)! / / ,11 67 6+

6+61! A,

¯

S,1,-/-61-,

P G

=

/N

1 S =A/NA +1/ , ;,! /

+ - ;, +66 1,1

64#!'! !

¯

A6 ,1-/16+ XA

+6- -,4 +, X Aij!

/1 - - +1 -

/ 9f ,:34 13 - +66Aij

64 13 ,

−1.

@ Aij + , +1

/ < +! "%=3 12/ , - f! + /

;,

fij = [(4ε0)mec0/8

2e2]λ2A

ij or fij ≈

1.4992×10−14(A

ij/

−1) (λ/

) 2

4 λ 4/3 i j - 11, ! / 41

f - ,!

<#%= ;, S¯ ,1 - /P 101 A3 +

"'

(49)

$$ *(&2323%+ (&= +./0-)+ 5-&5%'&%= D327 27% /%(+*'%/%&2 -, (0+-'@23-& 3&2%&+32

.+1/1,-+6+3,/

6+1,2-6+-4/m,++/

n3 , 1,1 - n m! ++, 1+1 +,3

,1 6+! ++ ;, 101

6 ,6+ ,/ - hc0ν kT +,

1+1 - ν > 1000

−1

+, 1,1

6/1!

-,1 ++ 10 σji(ν) - 1,1

- ij <6+=! 16+

.+ 4 i ++,1 /1 6+ -

j←i /6

Gji=

σji(ν)ν−11ν =

σji(ν)ν−11ν

-,++1 4/ 1/ 61 / / 6,/

64 i / m j ,++

/ n3 ,+/ - ++, p

i +++

! // 1,1 /

G(n←m) =

i,j

piGji

<,1=

<#%=<,1=++,p-/+c.4+,p

i ≈

ciRT3S¯1A16;,S¯≈A/RT.,-S¯,1+61

3 +,,16+01! I

13I 13,

ln(I/I) =−ln(I/I) =−ln(1−P/P) =A

< ' *3+! "&=!

<#&=α 10 +6+ X!

<#'= / - / - -4D α + - + - +?

Q 74 41 7/ 41 / ,! -

743 α /! + 1, , , 6+016

- +

α(589.3 #)

◦

3,3 ) /1

−3

23 ) += = +0.6647 ◦

- 6;,/+0 ++4α/γl3

+ +4 α/cl3 γ c ,

<- ,6= l + /! 6, / +0 +

+43 11 [α]

θ

λ! 4/ - / ,1 λ <-;, 1, =

, +, θ ,6+ ,++ +0

+4[α]. +, ;,11 [α]

θ

λ 101 [α]

θ

λ =α/ρl3 ρ

1!

+0 + +4 , * ,-,

,, ;,1 4, ,! - , ,, ,

◦

3 /

−1

1

−1

- +,;,1 ,3

◦

3 /

−1

- 13

◦

,1

6- 1/ - +/!

"(

(50)

-1,1 /0 /1 46

G(n←m) =

i,j

(pi−pj)Gji= (pm/dm−pn/dn) i,j

Gji

pi 1pj 1- ++,-i1j <pi= exp{−Ei/kT}/q

;,6,3 q + -,=P p

m p

n +1/

++,-/31dm1dn1/(pi=pm/dm, !).6+

Gji31XAij 1Bji3-,1,-/

64 11,i 1jP / ;,

Gji=hBν,jie = (h/c0)Bν,ji =Aij/(8c0ν

3)

3 - 1+ ;, ;, -

;,

Gji =hBeν,ji=Aij/(8c0ν

3) = 8 3

3hc0(4ε0) |Mji|2

4 Mji /

|Mji|2 = ρ

|i|μρ|j|2

, +?0.1 μρ +?0.1 + -

1+ ! / , - -,1 64 G

ji

1 Mji 6.+1 + +

Gji/+

2≈

$ !&#"(|Mji/| 2

4 ≈"!""% &$ × )

−30

< 6-16=!

/1 6+ 61 ,, Q1 - ;,

A, S,S,¯ , G

101 6! 64 ;, /

<++.= ;,

G =

/NA≈A/(ν0NA)≈S/ν0 ≈S¯(kT /ν0)

43 ;, ! A,S¯ 1S 11/ 661

4,6 ν0-613 A,

¯

S 1S 616//

4,6 // / - 4,6 ,1- G

1 .

++ - 61 <,/ //6 - /?

/=!

¯

S ,+ / <4

++ , +,=3 +,! , ;,

1 G

+ -,1 ;, ,

+66 +-1 ;, - +/ /1

61!

, -,+1 , ,/6S - -

;,3+, ;,11A, S

¯

S! -+,

+ 10 ;, ,1+/ /1 !

6411, ,1;,G

ji, Beν,ji, Aij,

|Mji| ,1P / 63 ! /1 6+

X A ,1 -,1 X Aij < 663

4 A ,1=! @ , -, / 341 4/ A¯

61 +1 /1 6+ X 4,6!

"*

(51)

,1,1,-A, S,

¯

S,1G664! /

6 , - X,1,3-A, S,S,¯

G

.

%

A,A¯

−1

7

−1 G/

+ 2=

&!&)% $)

A/(7

−1)

ν0/

−1

¯

S

−1

−2

−1

−2 G/

+ 2=

!"&#&)"×10

−2

¯

S/

−1

−2(T /

I)

ν0/

−1

S

G/+

2= 1020 (S/)

ν0/

−1

2

−1

2

−1 G/

+ 2=

!&&) %$)×10

−4

/

2

−1

G

2

+ 2

A, + 6+ / ;,

1,1 - J%(\ & K3 - +,61 , - 61

- /+-1 + -,1- J%*\& K! 64

++6+ J&#K!

$$ -&C%&23-&+,-' (0+-'@23-& 3&2%&+323%+ 3& 5-&=%&+%= @7(+%+

11 , , -

6636+X31/16+X3A31616

6,1-11+! +,11;,-4711,

61 ;,1 1 - 61 - , 1, ,!

, - / 61 ;,1 13

/ - n k3 - + ,/, ,1 +

/! ,/ n k +1 + 1+ - 6+

11 +! ;,13 +1, ;,741/- n 1k -

414! + +1 n k! ?+

++,6101 4++0.! - n1k+

743 + - + ++ ,1;, - + 661

! +-,+.+<#!"3+! &=3εr =ε

r+ε

r

1-+ -1 n! ε

r +1 ε

r /+- εr3

+! 1,/εr=n

2

3ε

r =n2−k2 ε

r = 2nk!

- 1 + ++ - 6,7 +!

6-6, ,;,1 12-6,73

01 ,3 loc3, 11 -, - ++1 01 !

+ Q 013 loc = +/3ε034 +Q!

0161,+/?/+3

- ;,11+ 1!

- 01 / Q?Q -, < ,,

,,? -,4++1 01=/Q1 66/

4,6

εr(ν)−1

εr(ν) + 2

= 1

3ε0Vm

αm(ν)

$)

(52)

Vm ,3 αm + +Q6 < #!"3

'3 +! &=! / + α

m - + +Q6 16 6+

,;,131- /?/+ 126,8,16

+ -160 -4/6 ,!

/16+X -,6+61 11+

161 J&"3&$K< 364=

Cj = 1

4ε0

bandj

ναm(ν)1ν

,, , ,1 61 ,1 j ← i

61 4,6 ν0 - 61!

Cj = NA

3hc0(4ε0)

ν0g(|Mji|2)

4ν0g(|Mji| 2)

++,?4/1,6,/-4,?

6 ;,- 1+ - <g / +,

1+1-,4,12-/,61,,=!

64 / ;,1 + , - 6+ X - / 61 j

?@ ;,J&%K

Aliq=

(¯n2+ 2)2 9¯n Agas

4 n¯ / , - n ,/ 6+ 61!

,1-4/ 1D

<= 61,X 473 !! 2nk+k 2 n2

P

<= 1,6++.1-++.-61

,,P-,g+,1+11/1;,1

+, -g ;,P

<= ν0|M

ji|2 1/1 ;,1 +!

/ ;, 1 -

1 Agas= 8

2C

j! -4 - 61 -

Aliq= 8

2C

j

(¯n2+ 2)2 9¯n

434-1.n,+1/1

6+ X Cj - ;,13 6+ X A -,

1 -+ -!

< = , - ;,

−1

! F, 10 - C

j

Cj =bandjνα m(ν)1ν -1+13 4,

−1

!

$

(53)

&

;, 16/61-

J$K J%!+K! % U, J&&K!

, -* % ,

> ,0

-,1 1;2;3, =n11+n22+n33

- ; ;

</,=-,1

1; 2; 3, i· k= 2 ik

−1

#

-+

∗; ∗;

∗

</,=+ ! !=h1 1+h2 2+h3 3=

−1

3"

h1

∗+h

2 ∗+h3 ∗ !·= 2m= 2

inihi

, / a;b;c

, / α;β;γ 13

+ , / a

∗;b∗;c∗

−1

+ , / α

∗;β∗;γ∗

13

- x;y;z x=X/a $

/ - f f =Ea/Ee %

,, - F(h, k, l) F =

N n=1

fne2i(hxn+kyn+lzn)

&

41 h, k, l

++/ d

>// / θ nλ= 2dsinθ 13 '

1- n

1+3

/ σ

// s

>,/

+ + j,j (

;,6,+ 0

-

1+ =−0

-

6?@- B, D D= e

−2<(· )

2>

*

< =n1, n2 1n3 /! a, b 1c 1!

<#=+ 101 6i· k=ik.

<"=m / 4m=n1h+n2k+n3l!

<$=X 1- /!

<%=Ea 1Ee1/+,1-113+!

<&=N ,6- ,!

<'=λ 4/ -1 1!

<(=1/,64 1+3 1+,1

+! ,6+ j +j.

<*= , - / - ,3<>1 //!

$#

(54)

, -* % ,

6 /, 4,6 qD, kD kD= (ni·6 2)1/3

−1

)

6 /, -;, ωD ωD=kD·c0

−1

)

6 -;, νD νD=ωD/2

−1

6 4,6 νD νD=νD/c0

−1

)

6 +, D D =hνD/kB I

FC + γ3 γ =αV /κCV

1,/ α, M Ecoul =

αNAz+z−e2

4ε0R0

#

1- N

E NE =1N(E)/1E B

−1

−3

"

<+= 1- Nω, g Nω =1N(ω)/1ω

−3

$

6

ρρρ,(ρ

ik) =ρρρ· Ω %

1, σσσ,(σik) =σσσ·

−1

%

1, ρR Ω

1, λ

ik

q=−λλλ· ∇∇∇T @

−1

I

−1

%

τ τ =l/vF &

QX L L=λ/σT U

2 I

−2

'

X AH, RH =ρ+RH(×)

3

−1

- E U (

X E=

ΔT

T U (

X μ,(τ) μ=/T UI

−1

,613 n, p

−3

*

,6

61 /+/ E

B #)

1Q / Ed B #)

+ Q / Ea B #)

/ EF, εF εF = lim

T→0μ

B #)

47 -,3 =E∞−EF B #

47 -,

/, 43 ", k= 2/λ

−1

##

++/

> -, u

k() ψ() =u

k() exp(i"·)

−3/2

#"

/1- ρ ρ() =−eψ

∗(

)ψ()

−3

#"3 #$

2 m

∗

7/ #%

6 μ drift=μ

2 U

−1

#%

6 b b=μn/μp

12, X D =−D∇∇∇n

2

−1

#%3 #&

12, / L L=

√

Dτ #%3 #&

<@= θ, θW I

+,

,+, TC I

O +, TN I

< )= n

i 13c0 +1 - / ,,! qd ;, 2

6 ,?24/ - 4!

< = α ,6 + X3 V ,3 κ +63 CV

+ ,!

< #=Ecoul / + - + 4/ Q+e1 −z−e!

$"

(55)

$$ /0-)+,-' @)(&%+ (&= =3'%523-&+ 3&5'.+2()+

1 - -3 - / + (h, k, l) (h1, h2, h3)

1- >// 8- -+ + (h, k, l) h, k, l h1, h2, h3

1- - ;, -3 {h, k, l} {h1, h2, h3}

+

1- <Q.= [u, v, w]

1- - ;, < u, v, w >

- +1 ,6 ,

! / + -3 +0 13 / ,6 11

6 ,6!

"# (¯110)1 + + h=−1, k = 13l= 0.

839 '.+2() )(2235% +./0-)+

+

-?1

61?1

6?1 P>P

61

8339 %'/(&&;(*>3& +./0-)+ -, +.//%2' -@%'(23-&+

"#

n?-1 n P#P"P $P&

n?-1 n¯

a P

a #P

a "P

a $P

a &

n?-14 nk #1P"1P"2P!!!

8 m

/1 a;b;c;n;d

<,1=

< "=N(E) ,6- - / E,1116 ,!

< $=N(ω) ,6- 614, -;, ω,1116

,!

< %= +16 +1/ ;, +1! q

/ 8, , 1!

< &= 10 ++ P l - +3 vF

+!

< '=λ1 σ 1, + 1!

< (= ,6 ++ 11 ,6+!

- + 12 1,16/1 - +!

< *= +0 ,6 11 ,6+D - nn, n−,(n); - np,

n+,(p)P- 1ndP-+ naP- ,6 1n

i(n2i =n+n−).

<#)= ,1,- ;,U! μ + +!

<# =E∞ / 01J&'K!

<##=" ,1- +3 -+! λ 4/!

<#"=ψ() ?4-,!

<#$= / 161 6,/ !

<#%=,6+ 1+ −1+ 111 1 3+!

<#&= + 8,.1! D 12,X τ -!

$$

(56)

'

/ / 11 J$K

6 J%!K!

, -* % ,

,6- N

,61- C C =N/V

−3

,6

/1 L, NA L=N/n

−1

>Q k, kB B I

−1

<= / R R=Lk BI

−1

, + (x, y, z)

, (cx, cy, cz)3 =1G1t

−1

(ux, uy, uz)3

(v

x, vy, vz)

, , (px, py, pz) =m 7/

−1

#

16,

-, f(c

x) f =

m

2kT

1/2

exp

−mc2x 2kT

−1

#

+1 16,

-, F(c) F = 4c

2

m

2kT

3/2

exp

− mc2

2kT

−1

#

/+1 ¯c,u,¯ ¯v, ¯c=

cF(c) 1c

−1

c,u,v

/Q1 q <= "

/Q1 , p p=∂L/∂q˙ <= "

, ++ = (1/h)

p1q

+66 P, p

4/3 g, d, W, ω, β $

1/

<,,=,6 W, N W(E) =

i

H(E−Ei) %3&

-

1- ρ(E) ρ(E) =1W(E)/1E B

−1

+ -,3

,

/, q, z q =

i

giexp(−Ei/kT) &

63 Q, Z Q=

i

giexp(−Ei/kT) &

<3 6=

< =n , - ,6< ,3+=!

<#=m - +!

<"= -q / p ,! 10 -p3L //!

<$=β ,1- + 4/ 1/ 1++!

,6 -1+1 / /-,- /!

<%= (x) -, < $!#3 +! )'=3 W W(E) ,6

;,, 4/ E!

<&=Ei 1/ -i-,;,,,111

gi 1/!

$%

(57)

, -* % ,

, z, Z

6

+ -,3

,

/1

6

,6 σ3s

+ / + β β= 1/kT B

−1

+, +

θ I '

+,

6, λ λB = exp(μB/RT) (

1+ ρ3σ ρ=

k

pk|

k

k| *

1 PPP3ρρρ ={P

mn} )

Pmn3 ρmn Pmn=φm|ρ|φn )

<'=, +,114,6+3!/! r=hcB/k

6 v = hcν/k D = hcνD/k, E = hcνE/k! +-1

θ, ϑ 1-, 4, +,!

<(= 10++ >!μB +3 #! +!%&!

<*= |

k - ;,, k - p

k +66 -

6! -p

k= 1 - / k +7 - +,3 4- ,!

< )= 101 Pmn - φm!

3 Pmn =

kpk c

(k)

m c(nk)∗3 c (k)

m <+.= X - φm

+ -|

k 6{φ

i}!

$&

(58)

( $

/ J$K J%!3%!K /

/!

, -* % ,

,6- N

<!/! ,3

3-,,=

, - ,63 , n nB=NB/L 3#

< ,=

/1 L, NA

−1

-3 ma, m 7/

- mf, m 7/ "

<,3 -, ,=

mu mu=ma(

12C)/12

7/ $

M MB=m/nB 7/

−1

#3%3&

M

◦

− M−◦ =m

uNA /

−1

&3'

, Mr Mr=mf/mu '

<

, 4/=

Ar Ar =ma/mu '

< 4/=

, Vm Vm,B=V /nB

3

−1

#3%3&

- w wB=mB/

i

mi #

< = 41 L- ,6M +1 +0 - !/! 9,

./: 9, - / ,:! 9, - /: 6/,,

,1 ,1 - / - ! 1,

#! )! <=3+!%"!

"# @ , - 2 ;, "3 n(2) = 33 ,

-(1/2)2 ;, & 31n((1/2)2) = 6! , n((1/2)2) = 2n(2)!

<#= 10 ++ > ,1 11 ,6+

+3 !/! nB n(>)! @ + ,3 + ,1

6,13 n(O2)!

<"= 9-,,: ,! +#! )! <=3+!%)!

<$= mu ;, ,01 ,3 ,3 !! mu = 1 , < "!'3

+! *#=! 13 ,1 - ,01

,!

<%= 10++ +, ,634 m 1V ,!

43 +1/ ;, 101 - , m/n V /n3

n=ini.;,11,+!

<&= ,1 41 9:3 ,-, , -

1+- ! ++ 11!

<'= 9, 4/: 4/: ,1!

, Mr , 9, 4/:! Mr

94/:316Ar 6,1! Mr61

3 Mr

,B =MB/M−◦3 M ◦

− = 1

/

−1

! 11 4/

&!#3 +! '!

$'

(59)

, -* % ,

, - φ φB =VB/

i

Vi #3(

-3, - x, y xB=nB/

A

nA #3*

,6 -3

, -3

<=+, p,(P) #3 )

++, pB pB=yB p

3 γ, ρ γB=mB/V 7/

−3

#3 #3 "

<1=

,63 C, n CB =NB/V

−3

#3 #3 $

,61

, c3J>K cB=nB/V

−3

#3 #3 %

,6 s sB=cB <,1 ,=

−3

#

m, b mB=nB/mA 7/

−1

#3&3 "

,- B=nB/A

−2

#

X ν νB= (nB−nB

,0)/ξ &

-3 ξ ξ= (nB−nB,0)/νB &

1

1/ -1 α α=ξ/ξ∞ '

<(=3VB1Vi,-+++++./! 10

+63!/! " J%K3 ,1 6,1, 474,+/,

10!

<*= 11 + x ,13 1- /, , y 6,1J&(K!

< )= , - +1 ? , 63 W )

5

! 11

+, p

◦ −

W W ) 5

< #! ! <=3+!& '!#3 +! "(

6+! (%=! ,-.+16+34 W )

−3

6

W )) W !

< = 61 10 ++ , >34 ,1 6+01! <?

1=/ 1X,6, 10/+ +,!

< #= V , - ,! A, 16 + - ,

-,1 J&(K!

< "= 10 m ,1 44 12 /D mB

-,>3mA1 -<, ,7/

−1

=! -, -

11 ,/ b - ! , - 7/

−1

1 ,3 11 ,P 43 ,

6- , 7/

−1

6 ,!

< $= ,6 C +-1- ,! ,6

,6n4 +1 1, -,6!

< %=L, M 66-L,?-?,6M! <?

- ,?-?,6 66?

1 L,6 M J #K!= 41 LM ,1

,35, <6= - ,63

< #! "3 +! &*=! + 41 LM

1 c ,1 - ! , ;,

-1 3,/ ,1 6111, , 4;,

! ,1 - ,

−1

<

−3

=3

−1

3

−1

!3-113 ! <+,1 3 =!

$(

(60)

$ $ 27%' +./0-)+ (&= 5-&C%&23-&+ 3& 57%/3+2'

839 7%/35() +./0-)+ ,-' 27% %)%/%&2+

6-<=11 -

4 ,146+1<,+/=+! + /

&!#3 +! '! -41 -,+.+ - !

"# 33

6 412 /<48 ,-,1

;,=D

<= - ! +3

/ ' + ( #) , <// ,6 - "% "'=3

12 6/ /1! /"%!$%#' , +!

<6= 1+- ! +3 +

- + - , /! ,1 1

D - M,!:

+ - +01 ,6 <+ ,6=

,6 <, ,6=! ,1 +01 / ,6

-,++ -

14

3 111 - -

6? $! ,1/ ,66,12 ,61+

,1

12

14

! ,++1361,1/

+ , 6,1D n<= W n<

35

= Y n< 37

=! ,1 /

,66, 12 ,6 16 ,1 D

14

!

,66 -,6+D

14 63

14 7!

/ ,6 11 / ,++3 / /

,6 ;, +, , !

"#

+

1,+ <=

79 >

−

6?'* / <361 =

3+

+3

,, ++

" 2−

"

−2

,-,1,6 / <,01 =

3+

,11 116J&*K! -

+3

1

−2

3,/

41,13 6J&*K3

+++

1

= !

/ ,++ + ,1 -!

611 7!

"# ∗

3 ∗

<,1=

< %=<,1=, -1 6-

−1

!

< &= X 101 ,/ ;,! / - ?

+ - +1,! , - X1+1

;,431#! )! <=3+!%#! nB,01,-nBLQM3

4

ξ= 0 !

< '=ξ∞ ,-ξ L0M34 +!

$*

(61)

.1,6116+ / ,6Q<

#! )! <=3 +!%#=!

"#

VII

3/<U =3

−II

3 0

+ / - ,1 - ,Q1

-4D

-,++ ,6

-,6+ ,6

/ ,++ /,63 1,63

/ ,6+ ,6- +< #! )! <=64=

8339 /0-)+,-' @('235)%+ (&= &*5)%(' '%(523-&+

+ + +

+

+ p¯ + ,

+

<

3

2+ =

, / ,

−

+ + <

4

2+ =

, n¯ + <= , e

−

1, , ¯e

6+1<,+/=+<6,+&3+! "=! /

- + 11 11/ ,++ Y3 −3 )P !/! +

+

0

−

3 ! -

6+1 ,14, /3 - ++ 1/

+! ,- 11 - ,, 1/

-,1 J')K!

/ - +1/ , ,16 -4D

,1

/+ , ,// +

;, ;,

0 ,1

"# 14

<,+= 17

3

59

<3 = 60

23

<3"= 20

3 31

< 3+= 29

, 11 - 7< #! #3 +!&#=!

"# 14

7N +→ 17

8O + p → + Y Y¯e

83339 7%/35() ,-'/*)(%

- -3 -, 12 /D

<= ,3 - 13 !

,6 - <4 /= 11 / ,6+3 ,

6/ 1! F,+ - +! / ,6 -

111 / ,++ -,! - , -

+1 611/ 6!

"# ^323 663 +

3

2− 4

<3=3 < #3#?1++ ,=

∗

2 < / 1.1 ,=

< /.1 ,=

•

< /.1 ,3/ -1 =

•

3 < -1=

%)

(62)

4/ -, - + +/ - / ,6 111 <//1

/=3 +D

2−

4 3<4= 2−

! //1 / ?

11J&*K!

+0 - <3 ,3 = 11 //

< #!&!"3 +! "#= +! U6

+01 6// +1/;,, ,6< #!&3 +!#% 1""=!

"# /< 3

1= , +??

<v= 23J = 6= 1/ 8,1,

v= 2 J = 6

2 +

< 2

1= , 1,6??

<6= -, + - ,6 <

63 +6 - / -=! + 11 /

,6+ < /P , 6/ 1=! 9-, ,: <4

,Z= +01 /,+- < <=1 <=64=!

"#

+

33 0.913^63

-,6,1.+7ρ<24=31-,-,1! @+-/

, - ,6 -, - ,+1 -3 /

-3 + <= <=! -3 -, - ,1

<9/ 24:=! -, 12 1/

- J "3&*3' 3'#KD

7 % "# ,

+ ++ 2

, 4, 363

,, ,, / - 3<=

C H

OH C H

H

C OH O

0/,

H3C

HO

H OH

O

+5

C H 3

C O O H

H O H #

< = , 12/ + + + +/,!

.+323321

17

2 ++/, 11

,! ,//1 J $K + - , - +

+6,12,,3,3<=13<=-4

, +?!

<#= +5 Q ,6, +1 + -

++ ,6,+1 61 +- ++!

%

(63)

83C9 1*(23-&+ ,-' 57%/35() '%(523-&+

<= -,+</

/3,311=3, ,! ,6

± <±#=! /4,1 1+1,

3 ;, / ,/ 9: ! #! #! +!&'!

Y>2 →> Y> +>

2 Y>2 W#> ,- , +

<6= 312 6,1/1+1,

;,3 4-4/ /D

2 Y>2 W#> ;,

2 Y>2 →# > -41

2 Y>2 # > 61

2 Y>2 # > ;,6,

,6 ,;,! +1 12

4<4, / /=!

"# 1/ 61 - ;,46

4 - 4

< G#= 2 Y< G#= >2 W> 2 Y>2 W# >

7/+<L+ M=-1-;,!

;,-46,,-,6-

-1 <4 -;,= ;, ±1!

"# < G%=I VII

4 Y<(G%= W< G%= II

2 Y< G#=2 Y< G%=I Y<$G%=2

- +/ , , +1

<;,= 4!

"# I4 Y( W2 Y<%G#=2 YI Y$ 2

−

4 Y% −

Y( +

W

2+

Y<%G#=2 Y$ 2 < G%=

−

4 Y −

Y<(G%= +

W< G%= 2+

Y< G#=2 Y<$G%=2

64/,6-

;, D

"# < G"= 0

<= Y< G#=/ I

24<= W< G&= III

2 <4=3<;=Y/ 0

<=

4 6+ -///3 <=3 +!%$!

./0-)35 -2(23-&: / ;,

0 =

j

νj Bj

4>j 1+1νj+1/,6</

- + - +1,=! ;, +1

4 +6 4D

<= < G#=2 Y<"G#=2 W3 ν<2= W− G#3 ν<2=W−"G#3 ν<3= W+ <= 2 Y" 2 W#3 ν<2= W− ν<2=W−"3 ν<3= W+#

%#

(64)

/ Δnj = nj −nj,0 , - +1, j 1,/ ,

/16 +3 -ξ3,/ ;,

nj =nj,0+νj ξ

.-1+14436,1+1 -4

,110! ,3- <=34ξ W#3Δn<2=W−

3 Δn<2= W−" Δn<3= W +#! <=3 Δn<2= W−

ξ W !

(2'3? -2(23-&: ,? ;,

ννν =0

4<-,=.4A

ij +/,6-

-ij+<+1,=1ννν

,6.4νjk6/,6-j+

k ! @ N

e / +1 /- N

c

6Ne×Ns ! ,3N() =Ns−7<=3/,6 -1+1

Nr3 Ns×Nr ,6 ννν3 11

,+ -! N

e×Nr Q J'"K!

8C9 /-*&2 -, +*0+2(&5% (&= 27% +@%53<5(23-& -, %&2323%+

;, L, - ,6M L ,M <L2/M F3 L;,O

NM=6,16 -/4,++! 4+

-1 L,6 - M! + ,1 611D - +

;, ,1 - , <-4 4,1 , L,6 - M

- L/M=!

, - ,6 ++ ,6 - +01

,6P ++ - ,6 +

- /1 !

+ 11, +! .+ 643 < G#= 23 < G%= I43 !

0 , .! , - ,6

+ ;, 11 - 1+1 +-

16/,!

"# nCl3n<= , - 3, -

n<2= , - 23, - ,

n<24= , - <=24

n<(1/5) I4= , - <=< G%=I4

M<4= -++, 4

cHCl, c<=3 JK , -

ρ<24= 1- ,-,1

</4= 1, -< -=/4

<< G#=/4= 1, -< -=< G#= /4

λ</ 2+

= 1,- < -= /

2+

<< G#=/ 2+

= 1,- < -= < G#=/

2+

/ 10 -, ;, 1;,

n<< G%= I4= W% n<I4=

λ<< G#= / 2+

= W< G#=λ</ 2+

=

[(1/2) H2SO4] = 2[H2SO4]

< +"!"3 +!('!=

%"

(65)

L, - ,-,M 6/,, 6, / + n<=3 n<8=3

n<2=3 ! /, 6/,,! , - +,1

+1 ,, , -, -

!

"# L# -4M +n<2=W#

L)!% - 1,1M +n<= W)!%

L"- M +n<=W"

,,1 6114/ 6/,!

;,pV =nRT 1;,//++3 +1

10 -n,1 1+1 / +< ,- /=3

4 , ,+! A, 16 + - , -,1

J&(K!

8C39 2(2%+ -, (>>'%>(23-&

-4/ ?3 4? ? ,1 + - ///

+J !5K! ++11 -,6 +3 ,1

6+1 <,+/=+ 4, -,+ <+1=!

31 +161 ,6 / / +,

+, ;,1

; ;,,, ;,1

;3 ∞ ;,,, 01,

-1 11 + +

<!!31;,1= + +

- 8,1+ ,

<!!3/ ;,1= ,,6

"# </= 1/ 1/,

CV<-= +- 8,1 ,

Vm<= , - ;,1

U<= / -

2<= /1.1 +,1

2<3 = /1.1

-<;= ;,,,- 1,1.1

<;3∞= ;,,,- 1,1.1 01,

ΔfH−◦<23= 11+ - ;,14

/3 / +3 ;,1 +3 !3 ,1 /

,++31 F7633! 6,11+ +

3! / !

"# V l m3V

s

m, - ;,1 +3!!! - 1+

Sm3S

m + -+3 !!! -+

%$

(66)

16 - /,1 ;,/ 11

J$K1 J%!3 K! 11 - -,1 J !135K1J'$K!

, -* % ,

Q, q B

47 W, w B

/ U ΔU =Q+W B

+ H H=U +pV B

1 T3 I

+,

T

I #

+,

,+, t3θ tG

◦

WTGI−#'"! %

◦

"

+ S 1S W1Q

/T

B I

−1

Q/3 A A=U−T S B $

<Q -,=

F66/3 G G=H−T S B

<F66 -,=

,-, J J =−A/T B I

−1

7-, Y Y =−G/T B I

−1

,- γ, σ γ = (∂G/∂A

)T,p,ni

B

−2

3

−1

;,X X

3<X= X

=X/n

JXKG %3&

+0 ;, X x x=X/m JXKG7/ %3&

+,X β β= (∂p/∂T)V I

−1

+,X α

p αp = (1/p)(∂p/∂T)V I

−1

+63

κT κT =−(1/V)(∂p/∂T)T

−1

+ κ

S κS =−(1/V)(∂p/∂T)S

−1

.+ X αl αl= (1/l)(∂l/∂T) I

−1

,6.+ X α, αV, γ α= (1/V)(∂V /∂T)p I

−1

'

+3

+, Cp Cp = (∂H/∂T)p B I

−1

, CV CV = (∂U/∂T)V B I

−1

< = > Q >0 W >0 / - P ΔU =Q+W!

/ ;, 12 - 1U W bQ Y bW b

12!

<#=+,10169 +,- **)< ?*)=: -4

+0 10 +61 J'%K! 43 *$

th

/ - #))%3

++11"<#))%=- O,-1 O3

?*) - +;,: - 10!

<#))%= ! H)%H"" J'&K! 10 - - +

+ - 1/ 43 ,1 - Q - 0.1 + -

+;,:!

<"=;, L/1 +,M!

<$= , F - Q / -

3 1-, A - !

<%=10++ +, ,6! 43 + - 1+0 ;,

< !$3 +!&= ++1 ,! n , - ,6<

%%

(67)

, -* % ,

- + γ,(κ) γ =C

p/CV

B,? X μ, μ

μ= (∂T /∂p)H

I

−1

+4 , P = dQ/dt @

X3

1 B pV

=RT(1 +B/V+

3

−1

(

1 C C/V

2 +· · ·

=

6

−2

(

1@ a (p+a/V

2 )(V

−b) =RT

B 3

−2

*

X b

3

−1

*

+-3 Z Z =pV

/RT

<+6-=

+ X ,(X ) X = (∂X/∂n )T,p,n

j=

JXKG )

;,X

+3 μ μ = (∂G/∂n )T,p,n

j=

B

−1

<+ F66

/=

11 μ

◦

−, μ◦

B

−1

# +

6, λ λ = exp(μ /RT)

<= a a = exp

μ −μ −◦

RT

3 "

11 + H

◦

− H −◦ =μ −◦ +T S −◦

B

−1

3 #

+

11 + S

◦

− S −◦ =−(∂μ −◦/∂T)

p B

−1

I

−1

3 #

+

<,1=

<%=<,1=#! )3 +!$'=!

<&= X ;,3 , JXK! - ;,

,1 +01!

"# ,- >3 V

<>= WV /n

<'=;, X - +3 + X!

<(= - 9+, X: 6101

pVm=RT(1 +Bp p+Cp p2+· · ·)

<*=/-/1@;,-3/1031

X + a1b 1@ ;,

B=b−a/RT

< )=6++ >4,16+01! 66,11/,

+X -X !

"# +, -24 ;,,, 611

V<243;=31 1/,- , -

, V<243;=!

< = 10++ > ,1 +01! +

101 ;, 6+1/+1-1-,<U3

H3A=!

< #=

◦ −

◦

,1 11! ;,+6!

-11 1,1 #! ! <=3+!&)! @11 +

%&

(68)

, -* % ,

11 F66 Δ

G ◦ − Δ G ◦ −=ν μ −◦ B −1

#3 $

/ <-,= %3 &

X- A3A A=−(∂G/∂ξ)

p,T B

−1

%

=−ν μ

11 Δ

H ◦

− Δ

H ◦

−= ν H −◦

B

−1

#3 $

+ %3 &

11 Δ

S ◦

− Δ

S ◦

−= ν S −◦

B

−1

I

−1

#3 $3 % +

;, Q Q=

aν

'

;,6, K

◦

−, K K−◦ = exp(−Δ G

◦

−/RT)

#3 %3 (

;,6,3

+, Kp Kp =

pνB

ΣνB

%3 *

Kc Kc =

cνB <

−3

=

ΣνB %3 *

K

m Km=

mνB < 7/

−1

=

ΣνB %3 *

-,/ f,p f =λ lim

p→0(p /λ )T

-,/X φ φ =f /p

M k

k, = lim

x→0

(f /x ) 3#)

= (∂f /∂x )x

=0

<,1=

< #=<,1=μ ◦ −

11 ;,6,K

◦ −

11 ;, ,13

11 ,6+01!

< "= 10/;,/ +,1+1-6 /1

-1 - 11 + ++,!

;,10a =λ /λ

◦ −

34λ

◦

−= exp(μ −◦/RT)

! 10-μ

◦ −

1+1

- 11 < #! ! <=3 +!&)=!

< $= /! +, +1

+++ ,6+3 !/! Δ

H ◦ −

1 11 + - -P

#! ! <=3+!%(64 ,6+! Δr +1+ 6Δr

def

= ∂/∂ξ!

< %= ,6 +01- ;, ++!

< &= + <1 / /= ,, ;,1 7B

−1

!

1,7

−1

343 , !

3 7W$! ($ 7B< '!#3 +! "'=!

< '=;, ++/ ;,6,!

< (= ;, ;, , - Q ;,6,3 X Q! 1?

, 1+1 - 11 , +01!

J%!K 1 J'$K 6K

◦ −

1

L11;,6,M! +-6K 1L1

;,6,M!

< *= ;, / 1! 10 /,

;,6, - -,/ K

f3 ! +, Kp ++

K

◦ −

6 ;, K

◦

− ≈ K

p/(p−◦)ΣνB3 1, , K

c ++

1 K

◦ −

6 K

◦

− ≈ K

c/(c−◦)ΣνBP 43 -,/ X

(69)

, -* % ,

X

-1 ,M f f =a /x 3#

-1 M

6 γm am, =γm, m /m

◦ −

3##

6 γc ac, =γc, c /c

◦ −

3##

- γ

x ax, =γx, x )3#

/3

I

m, I Im= (1/2)

i

miz2i 7/

−1

Ic, I Im= (1/2)

i

ciz2

i

−3

X3

φm φm =

μ∗

−

μ

RT MΣ m

#"3#$

-6 φx φx =−

μ∗ −μ

RTlnx ##3#"

+, =−(RT /VA) lnaA #"

<,1=

< *=<,1=;,6,-1,-<16/;,6,

64.1+11=-1,6+1,311K

K

<K

◦ −

K

◦ −

+++=! 4;,6,-11

-4 K

3- 61K

31- 1K !

<#)=M4 +1- ?

+1/, - M4 7/

−1

3

−1

3+!

<# =;, ++ +, +3,6 ,3 !

<##=;, ++ ,!

<#"= > ,!

<#$= > 1+1 , ,3 ! /1 - ,!

, +1 </ - =3 6,

,1,/1!

$ $ 27%' +./0-)+ (&= 5-&C%&23-&+ 3& 57%/35() 27%'/-=.&(/35+

1+- ,65 -,1J'$K!

839 /0-)+ *+%= (+ +*0+5'3@2+ 2- =%&-2% ( @7.+35() 57%/35() @'-5%++ -' '%(523-&

6,1 +1 <,+/=+34, -, +<+1=!

1+

Q

6,

1, <- ,=

1+ 1+

%(

(70)

-

/3 -,<1 →;,1= -,

./ - 8,1

/

,6 <1→ /= ,6

<64 4+=

+ + !+!

+Q3+ <;,1 →/= +

8339 %5-//%&=%= +*@%'+5'3@2+

1+.3 ‡3=

++ ++

;,

1

0 1, ∞

+, ,6 ∗

11 ◦−,◦

83339 ?(/@)%+ -, 27% *+% -, 27% +./0-) Δ

6Δ1/.1;,-+! 11

- ,6+ Δ1 / ++!

"# Δ

H = Δ g

lH=H(g)−H(l) - + -+Q!

ΔH =

$)!&%' 7B

−1

- ))

◦

,1 + +,!

64 ΔH

,

6, ,/ 11!

,6+ ,1 / ! ,

Δ

H

101 ;,

ΔH =

ν H = (∂H/∂ξ)T,p

, +- ;, // , ,

- , ;, 10 - ξ , -

,6 ν !

"# 2</= Y"2</=W#3</=3 Δ H

◦

−=−92.4

7B

−1

ΔS ◦

−=−199

B

−1

I

−1

,10;, +/ +.-!

+1 + - ,6+ 111

+Q 12 - / ;, -11!

! +, +! 1016;,

ΔH ◦

− = ν H −◦

ΔS ◦

− = ν S −◦

ΔG ◦

− = ν μ −◦

+ +- - 6! X -

%*

(71)

−A= ΔG= ΔG ◦

−+RTln

aν

1 11 ;,6, Δ

G ◦

−=−RTlnK−◦

! +1, -

X ;,Q3 +!%'!

+ - ,6!

10- + -,6 / J''K!

+1/;,4,6ν-,6

− !

"# 11 + -6, -/,

Δ H−◦<43/3#*(! % I=W−(*)!"7B

−1

3+/

4</=Y#2</=→ 2</=Y#2<=!

16-1 ,6-

-<,,6-+,111

+,=! +1/ ;, ,6 ν

,6 + !

"# 11 +- ,< =

ΔS ◦ −

</233 #*(! % I= W− %$!" B

−1

I

−1

3+/

/<= Y2</=→ /2<=!

/,631 + ,6 +1

, /,1 / +! +1/ ;,

4 ,6ν - ,6 − !

"# 11 <= / -Q -;,1

ΔU ◦ −

<23 =W&#% 7B

−1

3+/

2<=→ #</= Y</=!

83C9 2(&=('= +2(2%+J !5K1 J'$K

11 + - ,6 > +, T, μ

◦

−(T)

3 , -

+,11113+01-4! 1210111

/Q1!

7 ! 11 -/,,63 4+,/, ,3

<+= - +, ,6 > /, + 11 +,

p=p−◦ 6/1 /6! 11 + 101

μ −◦(T) = lim

p→0[μ (T, p, y , )−RTln(y p/p

◦

−)]

7 # ! ! 11

;,1 ,63 +, ,3 - - +,

,6 > ;,1 1+ 11 +, p =p

◦ −

! 11

+ 101

μ (T) =μ∗(T, p−◦)

7 & , ;,1 , 11 -1

1, 6-,! <+= - ,> 11

m

◦ −

3 11 +, p

◦ −

3 6/ 1, ,! 11

+ 101

&)

(72)

μ −◦(T) = [μ (T, p−◦, m , )−RTln(m /m−◦)]∞

+-,>-,-m +,p=p

◦ −

/ +

μ (m ) =μ −◦ +RTln(m γm /m

◦

−)

<,= ,16+-mP6-

;, + - ,/,! - x ,1 +

mP - ;, x + - m ,/,3 x

◦

− = 1

! ,/

11 - , -1 1, 63 10 -

11 , - 11 + μ

◦ −

12 1+1/

4 m3 c3 - x ,16!

8C9 2(&=('= @'%++*'%+/-)()32 (&= 5-&5%&2'(23-&

++ , - 11 +, p

◦ −

3 11 m

◦ −

1 11 c

◦ −

3 ,/ , +01! +3 6?

,/ +++ / +, ,

p−◦ = )) <W 76=!

+3 43

p−◦ = 0.1 = 100 <= 6=

m−◦ = 1 7/

−1

c−◦ = 1

−3

, - m

◦ −

1 c

◦ −

, +1! , - p

◦

− =

)) 73

1 *(# J !5K31 11 - 6,/ 11!

*(# 11 +, 4,, p

◦ −

W ) "#% <W 31

=! ,- p

◦ −

,16+01!

-,+1/12p

◦ −

161 J'(\ ()K! 4,

- p ◦ −

3 )) !

8C39 3-57%/35() +2(&=('=+2(2%+

+11 +/1-! +

- 1/ , J

+ KW )

−7

1

−3

!

,6/,+1 /- +3 ++

- +3 <3432

−

43 2− 4

3−

4 =3 +! 111

- ,6+01 J( 3(#K!

8C339 7%'/-=.&(/35 @'-@%'23%+

U, - ;, + ++ - ,6

, ,! 6,.3!/!J("\ ('K! +67

+/ 11 , J((3(*K!

8C3339 %,%'%&5% +2(2% 8-, (& %)%/%&29

11? +, - /

+, J $K!

&

(73)

)

1 / 61 +, J !37K J*)K3

4+/! 1/1/+/J* K

1 - +/ - J*#K! / -

,1 76/ J*"K!

, -* % ,

- / -;,X

.

X X. W1XG1t <=

-

.

ξ ξ. W1ξG1t

−1

#

- / rB, vB rB W1cBG1t

−3

−1

"3$

<1, =

- <61 v, vc v W

· ξ /V −3 −1 #3$

, = W ν

−1

B 1cBG1t

- <61 v, v

C vC =νB−11CBG1t 3

−1

,6=3

< =

+1 - mB, nB v=k

cmBB %

1- m, n m=

mB

3 k, k(T) v=k

cmBB <

3

−1

=

m−1

−1

&

X

< =!/! - +,/ p˙W1pG1t3 -4 ,

−1

3- +/

1SG1t ,B I

−1

!

<#= , +013 - ;, ++3 //

;,!

<"= 61 10++ >!

<$= rB v 101 6- ++,3 ,6

,- !3 /, 10! - 12 101

1/,1 ,6+3 !/! v

p = νB−11pBG1t3 !

6101 - - 741 ?1+1

- +01 ;,P ;, - - -4 -

0 - , V ! ,6 1,

11P + 3, 843 21, +,1 ,+, + ,

67 , +34 ++/ 6;,

(dcB/dt)total = (dcB/dt)reaction+ (dcB/dt)transport

<%=6++>!6m,11-,4n-,

,6! 1-101 - +,4++! m6

,6!

<&= k +?.+ - A ,, ;,1 <1

3

−1

=

m−1

−1

, <

3 =

m−1 −1 < 3 , −1 =

m−1

−1

! L,M

,3 6, - ,11 - ,/ - +1 ,/!

k(T) +, 1+1! -;, ;,111

/!

"# 1 k= 10

8.2 3 −1 −1

/<kG 3

−1

=W (!#

k= 10

−12.6

3

−1

/<kG 3

−1

= W− #!&

(74)

, -* % ,

- kuni, kuni(T, cM) v=kunicB

−1

'

,,

/ +, k∞ kuni(cM → ∞)

−1

'

4 +, k0 v=k0cMcB

3

−1

'

>Q k, kB BI

−1

t1

/2 c(t1/2) =c(0)/2

.3 τ Δc(τ) = Δc(0)/e (

-3

-<,= EA, Ea EA=RT

2

1<lnk=G1T B

−1

* /

+?.+ -3 A A=kexp(EA/RT) <

3

−1

=

m−1

−1

*3 )

-;,

-1 + 1, r

1 dAB dAB=rA+rB

σ σ =d

2

AB

2

+1 cAB cAB= (8kT /μ)

1/2

−1

#

64 1>

-;,

- zA(A) zA(A) =

√

2CAσc

−1

- 4> zA(B) zA(B) =CBσcAB

−1

<'=-,,41+1,+cM-

+ ! kuni(T, cM) +Q +, 9+,: 1+1!

/cM(→ ∞) 1+1! 4cM(→0) /+1 -4

+ cM! 10 11 k0!

<(=τ 101 +,6Δc- G - ,

Δc(0)! ,61Qt→ ∞3113

/ ,6<+=! -

,6 1/,1- !

<*=,10/;,

EA=−Rd(lnk)/d(1/T)

, / ,1 - + ;, 101

6! + ;,412 L /M3,

k(T) =A Tnexp(−Ea/RT)

6/ ,1! , + A

3 n3 E

a +, 1+1

+!

/,1-/1++/+

< / - / 6=! L /M E0

/ +-13 6, Ea ,1! ,3 E0

,1 - Q + / -1 !

, 11 +- / /

1 <,=/ - ;,1016!

EA +, 1+1 EA(T) !

< )=A +, 1+1 / A(T) !

< = σ + 13 6, /

/ 1+1! -, 10 +, 1+1 /

3 &! C ,6 !

< #=μ 1,1 3μ=mAmB/(mA+mB)!

&"

(75)

, -* % ,

13

,6

- ZAA ZAA=CAzA(A)

−1

−3

"

- 4> ZAB ZAB=CAzA(B)

−1

−3

"

-;, zAB zAB=ZAB/LcAcB

3 −1 −1 "

- + λ λ=c/zA

++ b $

/ / θ 31 %

12 I

ji Iji=1σ

ji/1

2

−1

&

σji σji=

Iji

2

&

/ '

+66 Pji Pji=|Sji|

2

&3 '

11 + Δ

‡H−◦,ΔH‡ k(T) = kT

h exp

Δ‡S−◦

R

exp

−Δ‡H−◦

RT B −1 ( - , - Δ

‡V,ΔV‡ Δ‡V =−RT(∂(lnk)/∂p)

T

3

−1

11 Δ

‡U−◦,ΔU‡

B

−1

(

/ -

11 + Δ

‡S−◦

3ΔS ‡ B −1 I −1 ( -

< "= ZAA ZAB ,6- > + ,

/ ,3 /4 + -, >! ?61

4!

< $=++bQ11,644+P101

1- ++4,1,-+ 4,1816

!

< %=θ= 0 + 18!

< &= ;, - 1

! i j 1 +1, +3 Ω 1 /P

1σji/1;, <1 +,+1/=1116<1+ ,

+=! / + i=j! >Iji σji 1+1 / -

31 64 I

ji(E) 1σ

ji(E)! F1 +-

X -/ 1+1

kji(T) =

8k

BT μ

1/2 ∞

0

E

kBT

σji(E) exp(−E/kBT)

dE

kBT

4 E / μ 1,1 ! /

6+1 /1σ

ji34 ,1

,- -;, ,1 13 #!

< '=/.,1;,,1,-/J*$K! ,

†

W 1! Pji = |Sji| 2

+66 + i

/j!

< (= ;, Δ

‡H−◦

3 Δ

‡U−◦

3 Δ

‡S−◦

1 Δ

‡G−◦

,1

! ,1 !

64 k1 ;,

k=κ(kBT /h) exp(−Δ‡G−◦/RT)

(76)

, -* % ,

11 F66 Δ

‡G−◦

3ΔG

‡ Δ‡G−◦ = Δ‡H−◦ −TΔ‡S−◦

B

−1

(

/ -

, + q

‡, q‡(T) k∞=κkBT

h

q‡

qA

exp(−E0/kBT) (

-,

κ3γ κ=

k∞h

kBT

qA

q‡ exp(E0/kBT) (

X

, + q˜ q˜=q/V

−3

(

-, +,

+0 kuni(E, J) kuni(E, J) =−

d(lncA(E, J))

dt

−1

*

- ,, ?

E, J

+0 kbi(Et) kbi(Et) =σ(Et)

2Et/μ

3

−1

- 6,?

/ Et

1- ρ(E, J,· · ·) ρ(E, J,· · ·) = dN(E, J,· · ·)/dE B

−1

*

,6<,=- N(E)3W(E) N(E) =

E

0

ρ(E) dE *

1- ρ

‡(E) ρ‡(E) = dN‡(E)/dE

B

−1

*

-

,6- N

‡(E)

3W

‡(E) N‡(E) = E

E0

ρ‡(E) dE *

-

,6- + W(E) W(E) =

a

H(E−Vmax

a ) *

16

KM KM= (k−1+k2)/k1

−3

#)

<X= #3 Kf i −

d

dt =#

−1

#

;,, 13 φ ##

+

8, kf

d[hν]f

dt =kf c

∗

−1

#"3#$

, - τ0 τ0= 1/kf #"

, 41 f =kf B #"

+141 p3diss p=kp B #"

< (= <,1= k - 0?1 ! n

th

1

61 6,+ 4<c

◦

−)1−n

! 6, / ,+

V

◦

− = (c−◦)−1 = (kT /p−◦)

! κ X3 Δ

‡G−◦ = Δ‡H−◦ −T Δ‡S−◦

!

11

◦ −

13 ;, -;, Δ

‡H

3 Δ

‡U

3

Δ‡S Δ

‡G

! 43 - +0 - 11 6/,

, - ;,! - p

◦ −

1 c

◦ −

/ , - Δ

‡H−◦

3

Δ‡S−◦ 1Δ

‡G−◦

!

-, - , ;, - k∞

/ - ,, / +, - 6,

<- 4κ= 1 ,1=

&%

(77)

<,1=

< (=<,1=

kbi=κ

kBT

h

q‡

qAqB

exp(−E0/kBT)

4 q

‡

+ -, - q

‡,qA,qB

+ -, +

, - + >! E0 /

3644,1,! 312

- Q+ - Q+ -!

< *= - ,, + -

6-,4101 / E <1+6/1 ;,,,6,

/, , J != cA(E, J,· · ·)! + ;,

- -47 -;,?;,6, 3?+/?I?

,<I=- 161<=! ,,

/ I.+

k(E) = N

‡(E)

hρ(E)

ρ(E) - - ,3 N(E) ,6 - - ,

4/ E3

N(E) =

i

H(E−Ei) = E

0

ρ(E) dE

1 N

‡(E)

+1/ ,6 - - ! -47 -

16

k(E, J) =κ W(E, J)

hρ(E, J)

Vamax ,- + - 16 a3(x) -, <

$!#3 +! )'= J /, , ;,, ,6 J*%K! -,

- 61J ++/ !

<#)= - - Q

k1 k2

Y <= Y

k−1 k−2

4 Q3 ,63 Q?,6+ +1, <k−2

=!

<# = /Q1 173 ;, 64 ;,3

= (c1, c2,· · · , cn)

T

1 X K

f i

!

<##= ;,,1 φ 101 / * 1116

J%&K! + 101

φ= 1ξ/1t

1n

γ/1t

4 1116 !

<#"= + +, <8,= - -

.1 c

∗

d[hν] dt =−

dc∗

dt =kfc

∗

-,41 -., -Q 6+

8,! +1 p +1 kp! 43

41 6, +!

&&

(78)

$ $ 27%' +./0-)+ 2%'/+ (&= 5-&C%&23-&+ *+%= 3& 57%/35() 63&%235+

111+ 6-,1 J*"K!

839 )%/%&2(' '%(523-&+

, , + !

10,134 4+44 /!

,6 - + - 1 -

!

"# → >Y ,, < ,=

Y>→ Y 6,

Y>Y→ Y , < ,=

8339 -/@-+32%/%57(&3+/+

,6 + ?

! + 3 +4

,1! ++-,1

3 !

"# + +1 41

→ >Y >Y →

+,

>Y

43,-,71/,-;,6,613

4 4 114 L;,M /

>Y =>Y

@ + ,1,+4

- !

"# → >Y ,,

>Y → Y 6,

= Y < ,=

-, ,-, 1/, ;, 10/

- ;,10/ 4!

"# 6- /+,

3 Y3 → 26

14! - , ;,

# 3 W26

10 - /

vC =−1

2

1CCH 3 1t

=k CCH2 3

<,1=

<#$=,1,-,-,6-+34

+1 - +3 , - / +1

/ Lhν - +4-;, ν!

&'

(79)

89 - , ;,

3 W< G#=26

10 - /

vC =−1CCH

3 1t

=k CCH2 3

k

= 2k

!

+3X1014/;,!

114.+;,112;,

16/,! -13X

,1 ;, <- =! 43

+6 , ;, ;,!

"# , - 1/

YY → 2 Y

1 4! ;,

#W 2

1 10 - /

vc=−1

2

1[H] 1t

=k[H]3

6, Y → 2 ;, : ?

< ,7 =3 , ! ?

+ ,1 Q1 , X + A → X + B ;, A = B

1 v

c = −d[A]/dt = k[A][X] (= d[X]/dt = 0)! /3 ,,

→>.3 6, 4,16 : !

&(

(80)

+3 / 161 J !K

J(*\ * 3*&K! 01 - // J*'K3 - 1,

+?/J*(K3-,J**K1-+1

J ))K!

, -* % ,

/3 e

+ /

1 F F =eNA

−1

/,6- z zB=QB/e

/3

Im, I Im = (1/2)

i

mizi2 7/

−1

Ic, I Ic = (1/2)

i

ciz2

i

−3

#

m± m

(ν++ν−)

± =mν++mν−− 7/

−1

"

γ± γ

(ν++ν−)

± =γ+ν+γ−ν− " X

a± a±=m±γ±/m

◦ −

"3$3%

- a(Aν

+Bν−) a(Aν+Bν−) =a

(ν++ν−)

± "

+ + +=−lg<aH+= %3&

, + ψ U '

,- + χ U (

+ φ φ=χ+ψ U

U+ 12 Δψ Δ

ψ=ψ

−ψ U *

< = 10++ >!

<#= -, ,3 6I < ,6+=3 6I

μ<4,116I=,1-/61!

<"=ν+ ν− ,6 - +-,,- ν+>ν−!

"# 2<4=3, ν+= 2 ν−= 3!

m+ m−3 γ+ γ−3 X - !

-

ν+ >

ν− m3 m+ =ν+m m− =ν−m! 10 ,1

- c±!

<$=m ◦

−= 1

7/

−1

!

<%= 11, a+, a− X γ+, γ− +?

,6!

<&=10-+1,1#! "! <=3+!'$! 6+.+

/ ,- -+ ;, < !"! 3+!%= 4?

61 +1 <,+/=+!

<'=ψ

+ -+ 1, /Q- +!

,1 - ! +3- 1,/ + / Q

1 1,r3+1 ,3ψ=Q/4ε0r!

<(= ,- + 101 47 <111 /= -

1 <!! = + / ,/ 1+ + 64 +

! 6, , -χ 6113 12,6!

<*= Δψ , + 12 1, / + ! ,6

;,!

&*

(81)

, -* % ,

F+ 12 Δφ Δ

φ=φ−

φ U )

+ μ

B μB = (∂G/∂nB)T,p,nj=B B

−1

3 Wμ

B−◦ +RTlnaB+zBF φ

,- / σ σ =Qs/A

−2

#

1 + E, U U "

+ 12- Ecell, Ucell Ecell=ER−EL U $

+

,6 - z, n z=|νe| %

</ ,6=

11 + E

◦

− E−◦ =−Δ

rG−◦/zF U &3 '

< )= Δφ + 12 64 + 6,7 + P

,6 - +- +!

< = + - > + + F66 / -

! + L +M3 1 μB3 ,1

1 - + F66 / 1+1 + φ

+! 12 - + - > 64

+ - 12 +1 12 + /

μB−μ

B=μB−◦ −μ

B−◦ +RTln

aB/a

B

+zBF

φ −φ

/ +6 + 1+1/ + -

1+1/ +3 6, +6 ,

aB-3+12644+ -12+!

+3 43 4 1013 ,+

+12+3 ;,6,4/1 >64+

1 + +!

< #= Qs / - -3 A ,-! -

1, 13 / - 1!

< "= 6, , - + ,13 E +1

+ - - 13 !/! - 11 1/

<= < #! "! <=3 +!'"=! + - + 1,1

J*(K!

< $= - 1/,1 ,6+ <-=

1 </=3 1#! - + - ?1 1/

< #! "! <=3 +! '#=! EL ER + - 1!

//3 / , 11 U! / ,

Ecell -Q, 84/,/3/-1;,66/

613 - 1- < -=! -

6- /113 + 12 -!

< %=z<n=,6-6114! +

/3;, |νe|34νe,6-1!

n ,14 , ,- ,6!

< &= ◦ −

1 ◦

6 ,1 11 ! ;,+6!

< '=11+ ,- ! - 1,1 11

1! ΔrG

◦ −

11 F66 / - 1,3

4+-111/1<#! "! <=3+!'"=! ?

1+ ! -,84,/31/

')

(82)

, -* % ,

;,6,1 Eeq Eeq =E

◦

−−(RT /zF)

i

νilnai U %− (

+ <- ?

=

-+ E

◦

− E

eq =E−◦ −(RT /zF)

i

νilnci U %3 *

;,1 5,+ Ej #)

, I I =1Q/1t #

, j, j=I/A

−2

##

-1 , IF IF =Ic+Ia #"

1, kc Ic=−nF Akc

(cB)nB <= %3#$

.1 ka Ia =nF Aka

(cB)nB <= %3#$

-X α, αc αc=−(RT /nF)d(lnkc)/dE %3#%

+ η3E

η η=E−Eeq U

- + b b= (∂E/∂ln|IF|)c

i,T,p U #&

-X kd kd

,B=|νB|Ilim,B/nF cA

−1

%3#'

< '=<,1=-;,6+6,14+11/

<.++6? 5,=1;,6 4+

61!

< (=;,!

νilnai-134ai

-+7/+Pν

i ,6-+;,

13 41,3νi +-+1,1/-!

;,6, + , !

< *= E ◦ −

4 ,1 .+ -

, + 743 6, ! , 1+1 + -

,! ci 13 6/ Q1 ,/

1611 c

◦ −

3,,c ◦

−= 1

1

−3

- ,6 +!

<#)=Ej F+ 12 64 , !

<# =Q /-1 ,/ - !

<##=3 ,1 3dI =·ndA3#!"3 #3+! &!

<#"= IF , ,/ 1|, -3 ,/ - /

1, +1/ Yn

− →

+1,! Ic +

, 1, 1,3 Ia +,1, 1!

> 10 Ic / Ia +! ;,6, +3 Ia = −Ic = I0 <

./ ,= ja =−jc =j0 <./ , 1=! I j /

,3116,6+ 311 ,6+33 !

<#$= ,

−1

! n < z= ,6 -

-1 c

B +3 nB

1 - + >! -,1 kred, kf

− →

k <- kc=

1 kox, kb ←−

k <-ka= 11!

<#%=α αc 6! /,

101 αa = (RT /nF)d lnk

/dE

! + αa = 1−αc!

β31-X3α

i -+i34

-1!

<#&= - + b +;,- 47 - 611!

<#'= - X 8, 111 ! 1?

-3 kd

,B = DB/δB δB 12, <4 1+1=

DB 12, X ->! - J*)K!

'

(83)

, -* % ,

7 + ζ U

<Q +=

1, κ,(σ) =κ

−1

##3#(

u,(m) uB =|vB|/| |

2 U

−1

3#*

1,3 λ λB=|zB|F uB

2

−1

3")3"

1,

-

1, (A

ν+Bν−) =ν+λ++ν−λ− 2

−1

3")3"

+,6 t tB=λBcB/

i

λici =jB/

i

ji

<#(=1,4-1+0 1,! 01/ !

<#*=vB / - >1 | | 01/4 +

1!

<")= , 2

−1

- ,1 - 1,! 1, ;,

κ=λici!

<" = + +- 1,-! 11+

61/zB - -/,6zB31 Q /3

- + 1, - +,3 6, , 4,16;,1

λ(K

+), λ(1/2 Ba2+)

3 λ(1/3 La 3+)

! ;, 1! !

$ $ 3>& (&= &-2(23-& 5-&C%&23-&+ 3&%)%52'-57%/3+2' 1

839 )%52'-57%/35() 5%))+

- <,, = 1,

1, <=! , 84 ,/ Q

?Q! , 84 +

,+, / /3

/ /! +

- /4 61 <+ /= !

8339 )%52'-=%

, ,/ - 13 <= 1,

<,,=1.1<=- 641,

1 1,! ,, -1 !

83339 %@'%+%&2(23-& -, %)%52'-57%/35() 5%))+

+1 61/ , -4/ +D

"# <= |2</=|<;=|/<=|/<= ,<= |,4<;= S4<;= |S<=

,<= |,4<;= I<; = S4<;=|S<=

/ <|= ,1 ,1 + +6,13 11 < =

+ 5, 64 ;,13 1,611 < = +

;,1 5,3 ;,1 5,+ ,1 1!

1

1 4L7 M - *%" J ) K!

'#

(84)

83C9 -2%&23() =3E%'%&5% -, (& %)%52'-57%/35() 5%))

+ 12- ,164

/?11-1/111-?

1 1! + 12 6,1 64 +-

- +! +3 44+-++31

- !

6,1 ++ | + 12P ,

+1 + -1!

,12-12,-1-,3;,1

5, +3 Ej3 ++ 4 , - 12 +

+161+/1./! -;,6,61

5,3 ,1 ,74 5, +! 61/ <3 - +3

+, <== +1 Q 6Q

6, - <;,1= 5, + - - ,

,1 + 12! - - ,3

1 16,+ 611, ;,6,/+!

8C9 2(&=('= @-2%&23()-, (& %)%52'-57%/35() 5%)) '%(523-&

- , 84 ,/ / - ;,6 -

1 613 + 12 - F66/

- 6;,

ΔrG=−zF Ecell,eq

,/5,+//6!

7++,3ΔrG/ 1Ecell +! -4

ΔrG +1 Ecell /! ;,6,+ - /

Ecell,eq=E−◦cell,eq−

RT zF

i

νilnai

4ai-+7/+1νi

,6-+;,4-< %1 &3+!')=!

8C39 2(&=('= %)%52'-=% @-2%&23() 8-, (& %)%52'-57%/35() '%(523-&9

- 3661 11+3101

11 + - + <-?= - -

1/ <=11 /1

;,! +4.1-,1/!

11 1/ - +,1 ,-

+

,1,1 42 /4-,/3-1 11 +,- )

5

<#! ! <=3+!& =! 1;,6,41

1/

|2 | +

z+ |

1

z++ (z/2)

2</=WY z +

1/6661E<

z+

G=36,1-6,161!

11 1/ 101 ;,, ,!

- ,/ + ;,,1?;,, 3J* ) K!

'"

(85)

8C339 &-=% 5(27-=%

1 ++1 ,/

, 84! ;,6, +, + , + ,1!

+1/ 1P

+1,1</=.1<=! 14

+1/1,4,+1,13

.1-3 1311 ,/.,!

84 - / < += +3 / 84 -

1 < / 1= < + 1=3

.1-1<+1= 6.,1,1

</ 1=!

/6 , ,,3 +

1 1,/ 1/ 1 1,/ /3 / 1

1,/ 1/ 1 1,/ /! 1 -,3 11

/6 + / < += ,1!

11- +3 J*&K!

8C3339 %<&323-& -, @J )#K

;,+ 101 - -1/ ,D

+ = −lg(aH+) =−lg(mH+γ

m,H+/m−◦)

4 aH+ - 1/ ,3

+

<;=3 γ

m,H+ ?

X-

+

<;=6mH+! 11m

◦ −

6

;,

7/

−1

! +101 - ;,6,11+13

6 ;, /11 10!

- + + 11 ;, ++ - + -

9+1-,: J )#K3,/-,6-,-,

1 ,! - +

,6,11 1,- 1!

+1-,-+,-4,-3

74 - J )"KD

|2 |>,23

− |

/|/

++ - ;, +

E=E−◦ −RTln 10

F lg[(mH+γH+/m

◦

−)(m

Cl−γCl−/m−◦)]

4 E + 12 - E

◦ −

11 + - /|/

1! ;, 6/1

−lg(aH+γCl−) =

(E−E−◦)

(RTln 10)/F + lg(mCl−/m

◦

−)

, - E 1 ;, −lg(aH+γ

Cl−) 61 +

mCl−/m−◦ = 0! ,-γ

Cl− ,1,/ >?F,// J )$K 61

6?C7! −lg(a

H+) ,11101+<=34 /0

+ 11! , + )!)) −lg(aH+γ

Cl−)−◦3

1 ±)!))" +3+!

-+11+6,2,+++;, ?

,1/+,1631++6->?F,//

'$

(86)

-lg(γ

Cl−)! ;, /,

0.17/

−1

! 116,2,11;,1 5,+

,1 ;,1 5,! 113 +<=3 63 6,

/,,1 ,!

+,/,/;,15,43;,3

;,1 5, +3 Ej3 + J )#K! , - + +-1

,/ |2 13 6, / <

+

?= 13 +

- <1EG1+= ,, - +! , /-?

/ -,1 , ,/ !

3+-,-+131-,6;,?

,3 + , - +1, 671 +116

,67 -+!

-, - 1121;,,?/ , J )%K!

'%

(87)

1 /61 J !?K1

J )&\ )*K! Q 161 J )K ;, ,

J K!

, -* % ,

+0 ,- a

, a, s a=A/m

2

7/

−1

,- , -> n

#

161, - > n

#

,- , -> n

σ

"

,- ,(

σ)

=n

σ/A

−2

"

->

,- ,(

σ)

=

i

−2

+, a, σ a =A/N

a

2

$

+, a

, σ a =A/N

2

$

01

,- / θ θ=N

a/N

$

/ θ 13

0 t, h, δ

7 -<, τ, δ, t

-=

,- γ, σ γ = (∂G/∂A

)T,p,ni

−1

3B

−2

-

0

= (∂G/∂A)T,p,ni

−1

%

6 / - LD LD=κ

−1

&

12,

/

,6?/ Mn Mn=

i

niMi/

i

ni 7/

−1

?/ Mm, Mw Mm=

i

niMi2/

i

niMi 7/

−1

z?/ M

! M!=

i

niMi3/

i

niMi2 7/

−1

1 X s s=v/a '

1@ λ B

11 1@ β, B B

1@?7 A

B

,- +, =γ

0−γ

−1

(

< =,6+1/,-46+1+-+,!

m 1/ - 166!

<#= , - n

1+1 /1 ,- #! )3

3+!$'! <"= , - n

σ

1 1+1 ,1 10 + - F66

,-! / , - > ,- - > ,

4,1++ 46,7+4/,/,+F6611/,-!

'&

(88)

==323-&()'%5-//%&=(23-&+

,++1++-, ! +-1+

6 +16 ,++ !

"# Q/ - - A

, - 161 ,6 n

, - 161 2 n

<2= n<23=

+, > a<>=, a

,++σ ,1 ,- ++ F66,-!

"# ,- , n

σ

<F66,- ,= ->

/ , -

1 1+1 + - F6611/ ,-!

43 4;,3

"#

1

"#

<1 +1/n

σ()

1 n

σ()

=36101

4<J !K=!

()

1 ,-

- >4 + + 1+ ->P ,-

,-

= 0 !

()

,- ->3

+ 1,1 1+- >P ,- ,-

=

ii= 0!

+- + <,,= 116+1/,++ 1!

"# ,- -+ γ

- 64 + γ

6 - ;, 111 6,- ,, +1/

P , ,8.!

"# - ++ s

(= ˆs

) =S

/A

-4/ 66 ,11 D

/,

+ +

+Q + - Q/

<,1=

<"=<,1= J !K3 11 +!''!

<$=N a

,6 - ,<N

a =Lna

=3 N

,6 -161 ,

01! 10 ++ >!

<%= ;,3 Af - 0!

<&= / J K J )*K / / J )*K LD ++

F,?+ - 1, + /3 #! "

+!&*!

<'= 103 v - 1 a - - -

-,/! 6-/1XJsK3-1,11

X s

◦

31- 1,1/ X Js

◦

KPJ !K - -,1!

<(= 103γ 0

, ,-1 γ -1,-!

''

(89)

$ $ *',(5% 2'*52*'% F G

839 3&>)%;5'.+2() +*',(5% (&= C%52-' =%+3>&(23-&+

" 1<hkl= ,1 +- ,- <hkl= 6,7+!

- ?;, ,- 1/1 chkld! U 1/1 JhklK

?;, 1< hkl >!

8339 -2(23-&+ ,-' +2%@@%= +*',(5%+ 8,-' 3=%()) 2%'/3&(2%= 0*)6 )(2235%+9

++1,-<-/-?/+1-641=4

/ <hkl= 41 +1 - / 4??1 - <h

kl =

-+-1<h kl

=- +! +1/ ,,-

<hkl= Wn(h

kl) × <h

kl =

4 n, 41, - 4!

"# <'%%= ,- - - 134< = 11 < ))=

1+- 1/1 + &< =×< ))=!

- +.,- 3,/ 1+

1+1 4?1 - <h

$k$l$ =3<h

%k%l%

= <h &k&l&

=D

<hkl= Wa 1

λ(h$k$l$ = Ya

2

μ(h%k%l% = Ya

3

ν(h&k&l&) !

- a

+ 1+ X - <hkl=

?1.3 ,6+λ, μ1 ν -Q -#

, -!

"# < )3(3'=,- - - 13 4< =1 1+ Q/Q///

4/ < ¯1= < ))=3 1/1

< )3(3'= W[(15/2)15(111) + (1/2)1(11¯1) + 22(100)].

83339 -2(23-&+ ,-' +*@%')(2235%+ (2 +*',(5%+

.D #,+46 1, 2 6,7?7,64#

61,20 1 =m111+m1221 2 =m211+m2223,10/

M =

m11 m12

m21 m22

,;, +0 ,+! -

/3 ,+ 1, 4,6 !

@1D ,+661i

b1

a1 ×

b2

a2

Rα◦34i

1 ,+ i + - + ,+ <+ -1++1= α

/ ,6 6<+ 1++1 4α= 0=!

"# 671 461 ,+ ,1/ -

;,! ,+ 61/1

1 1

−1 1

,4

;, @16 <

√

2×√2)$% ◦

1+<#×#=!

'(

(90)

83C9 /0-)+

1,2 #,6

∗

1, ∗

2 #+,6

1, 2 #,+6

∗

1, ∗2 #+,+6

$ #+

hk #1

hkl "1

M - ,+

z ++1,

,-θ ,- /

'

6 +,

Δφ(

47 -, /

λ

-+

φ(

47 -,

'*

(91)

11 / 11

J$K1 J%!K! , -++

6-,1 J**K!

-4/ ,1 10D <m=3 <t=3 , <V=3 <A=3

1 <ρ=3 +1 <v=3 / <l=3 <η=3 +, <p=3 - - - <g=3 ,6

.+ X<α=3 +, <T=3 ,-<γ=3 +1- ,1<c=3 -+

<λ=3-;,<f=312,<a=3X <h=31,<k=3

+0 + +, <cp=3 12, X <D=3 - <x=3

-X <kd=3 +6<μ=3 1, <κ=31 /8,.1<B=!

, -* % ,

8,.<- ;, X= JX, J JX =A

−1

1XG1t JXK

−2

−1

, 84 qV,

.

V qV =1VG1t

3

−1

84 qm,

.

m qm =1mG1t 7/

−1

-X kd kd W <q

m/A)(1c/1λ)

−1

7/

−1

2

−1

#

843 , P =1QG1t @

+4

8, Jq Jq=/A @

−2

1, G G=/ΔT @I

−1

R R= 1/G I@

−1

1, λ, k λ=−2Jq/(1TG1l) @

−1

I

−1

X - - h,(k, K, α) h=Jq/ΔT @

−2

I

−1

12, a a=λ/ρc

p

2

−1

12, X D D=−Jn/<1cG1l=

2

−1

3 η η=−τxz(∂Vx/∂z)

−1

"

6,7 κ κ=−τ

xx(∇∇∇ ·)

−1

"

12, X D

D

=Jxc−1(

1T /1x)

−1

2

I

−1

< =8,.-,,-3JN3144,161

, ,73 -2,,/,-! ,1/.+,3

JN1t3-,-/3,-01,-,,+1,-+,1

,-.+, +1,++,68,.3JN3

JNt =C(u/4)t = (u/4kT)pt3 C ,6 - ,3 u / +13

k >Q T 1+,! ,/, <6=

+1 +,- ,- / )

−6

- 1!

<#=c , !

<"= #!#3 +! $Pτ !

()

(92)

$ $ 3/%&+3-&)%++ 2'(&+@-'2 1*(&2323%+: *(&2323%+ -, =3/%&+3-&

, -* ,

1,6 ( ( =ρvl/η

, ,6 Eu Eu= Δp/ρv

2

,1,6 F r F r=v/()

1/2

F-,6 Gr Gr=l

3gαΔT ρ2/η2

@6,6 W e W e=ρv

2l/γ

,6 M a M a=v/c

I,1,6 Kn Kn=λ/l

, ,6 Sr Sr=lf /v

, ,6 F o F o=at/l

2

O ,6 P e P e=vl/a

/,6 Ra Ra=l

3gαΔT ρ/ηa

, ,6 N u N u=hl/k

,6 St St=h/ρvcp

, ,6- F o

∗ F o∗=Dt/l2

-O ,6- P e

∗ P e∗ =vl/D

-F-,6- Gr

∗ Gr∗=l3g

∂ρ

∂x

T,p

Δxρ η

-, ,6- N u

∗ N u∗ =kdl/D

3#

,6- St

∗ St∗=k

d/v

-1 ,6 =η/ρa

1 ,6 Sc Sc=η/ρD

4 ,6 Le Le=a/D

/ 1,6 Rm,(m Rm=vμκl

-O,6 Al Al=v(ρμ)

1/2/B

,6 Ha Ha=Bl(κ/η)

1/2

4/ ,6 Co Co=B

2/μρv2

< =;, ++ + - ,J&(K!

<#= 41 ,6 16Sh 41,1- ;,!

(

(93)

(94)

(95)

(96)

*+

- < = 1+1 F - - @/

1 ,<F= *&) J"K! -, 6, - %

- - 1+1 ;, < !#3 +! $=P

D +3 13 73 7/3 3 13 - ;,

,3 ,, +,3 /3 , - ,63

3+! 10- 6,/"!"3+!('! %

.+1+1,-+4-6,3/,+1/

64 + ;, 6, , - ;, , J"K! ,

11, /- -% !

- ,- + ;,!

+++ , - < "!#3 +! (&= +++ 11

,< "!$1 "!%3+!(* 1*)=! 43-++1 1+0.3

% *#3 6,1 ,1,+ ,6,+ - , <"!&3

+! * =! , 1 ,+ ,6,+ ,1 +0

1 %!

11 ,- 6,1 1/<4 +0

4 +++=! @ + - 7/ + ,3

11 10 , - ,!

(%

(97)

+6 + - ,

/1 /1 /,/ +! !"1

!$3 +!%1 +!& +/ -6 - ,!

%

$ ! ,

, +

,, 1

1 +, I

7/ 7/

/

, - ,6

(&

(98)

-4/ 10 - , 1+1 F -

@/1 ,<F=J"K!

(/@%'%<6D =

+ , 43 - / + 1,

0 /3 - //6 , ?3 +1 + ,,3 4,1

+1,64 1,-;,#× )

−7

4+-/<*

th

F3

*$(=!

5(&=%)(<6D 1=

,, / 13 - ,

1 ;, %$)× )

12

Q 1 -< G&("=

4+1 < & th

F3 *'*=!

6%)C3& <6D I=

73 , - +,3 - G#'"! & -

+, - + + - 4< "

th

F3 *&'=! 1

63)->'(/ <6D 7/=

7/ , - P ;, - ++ -

7/<" rd

F3 *) =! 2

/%2'%<6D =

/ - + / ,, 1,/

G#**'*# $%( - 1< ' th

F3 *("=!

/-)%<6D =

, - ,6 -

)!) # 7/ - 6? #! @ ,13

,6+01 3,3 33+3 +01/,+

- ,+< $

th

F3 *' =!

103 ,11 ,6,1 - #3 /,1

3-1 !

"#

-1

2 6, &!)##× ) 23 1

2 ,3 #!)$$× ) 23 1

- /- #"&!)$/

- /22 - $'#!)(/

- /

2+

2 -$) ! ( / / - *#!*'

- 0.91 - (#!((/

- −

- %$(!%( / / -−96.49

-+ -;, %× )

14 Q

/ -6, **!% 7B

+0- + 1D -

+ , /.,!

1

3 *$

th

/-6#))%311110-7

- +01+ +3 #! #3+!%%!

2

7/ ,3 101 , 101

6 , + .+ ,+11 - , !

1016,-< ++ -7/=! -3

10 -7/ ,1, 1, J "\ %K!

('

(99)

+%5-&= <6D =

1 1,-* *#&" '') +1-1+1/

64 +0-/,1 -,? "" < "

th

F3

*&'=!

10 ,11 +, - ) I3 ,+,61

67611! -;,- + -;,11 ,1-61

- -;, - 1, 13 6,

1 ;, <3 ***=!

((

(100)

%

- ! , "# % ,

+/ 1

−1

W

1/

2

−2

W

-;, Q Q

−1

#

- 7/

−2

+,3 +

−2

W

−1

7/

−2

/3473 5, B W

2 7/

−2

+43 8, @ B

−1 W 2 7/ −3 / ,6

+3 U B

−1 W 2 7/ −3 −1 -3 Ω U −1 W 2 7/ −3 −2

1, Ω

−1 W −2 7/ −1 3 2

+ -1 U

−1 W −2 7/ −1 4 2

/ 8, 46 @6 U W

2 7/

−2

−1

/ 8,.1 @6

−2

W 7/

−2

−1

1, U

−1 W 2 7/ −2 −2

,+, 1/ ,

◦

"

,, 8, , W

, ,

−2

W

−2

3<1= 6;, >;

−1

$

-1 1?

,1

66113 / F B 7/

−1 W 2 −2 $

1;, B 7/

−1 W 2 −2 $

<1 ;, 1.=

7

−1

%

< = 1 11 ,! - +

+6 - ,1/ / + - 11 ,! +

16,14+++ 161-

6!

<#= /, -;,1 - /,,

−1

3 +

−1

3,16,13

1 +14 Q! ,Q6 ,1 - -;,

+1!

<"= ,+, t101 ;,

t/◦=T /I−273.15

, - , +, 1/ ,3

◦

3 ;, 73 I!

◦

/ 63 + 64

◦

/ !

◦

I3 16

◦

3 / ,1- ,- 1+,!

<$=>;,3 /31 11- - -/,1/, J"K!

<%= @ , - +1 ,6 -

, - ,63 : 101 ++

,1 Q1 - ,1 +01 +Q1 1!

73 W

−1

3 ,1 + 9<Q= ,:3 W

−1 ≈ 16.67

(101)

6 / +- 11 ,P ,!

%

- ! "# % ,

X @@

−1 W 2 , 3 +13 −1

/,

−1

W

−1

−2

W

2 7/

−2

+34,6

−1

131 7/

−3 +0 , 3 7/ −1 , −3 # , 3 −1

+3 + B I

−1 W 2 7/ −2 I −1

+3 B I

−1 −1 W 2 7/ −2 I −1 −1 +

+0 +3 B I

−1 7/ −1 W 2 −2 I −1 +0 + / B −1 W 2 7/ −2 −1

+0 / B 7/

−1

W

2

−2

/ B

−3 W −1 7/ −2 ,- −1 W 7/ −2

8,.13 @

−2 W 7/ −3 1, @ −1 I −1

W 7/

−3

I

−1

7

2

−1

12, X

1 W

−1 7/ −1 /1 −3 W −3 , −2 1, −1 W −3 7/ −1 3 2 1, 2 −1 W 7/ −1 3 2 −1 + −1 W −3 7/ −1 4 2 +6 −1

W 7/

−2

01/ U

−1

W 7/

−3

−1

/ 01/

−1

.+, <^1γ = 7/

−1

W 7/

−1

6611 F

−1 W 2 −3

< = 41 L4,6M ;, L+ 4/M! 41+1 ,

1 ,

−1

,1 1,/1!

<#=41L, M66-L,?-?,6M!

@ 66/, ;,6 1+LM!

(102)

#

-4/ +0.J"K ,1 1,+ 1,6,+ - ,!

*# , ) −1 1 ) −2 ) −3 ) −6 ) −9 ) −12 + + ) −15 - ) −18 ) −21 Q+ Q ) −24 *# , ) 1 1 ) 2 ) 3 7 ) 6 / ) 9 // F ) 12 ) 15 + ) 18 ) 21 Q S ) 24

0 6 +1 <,+/= + + 64 +0

,6!

"# 737

@ +0 ,1 ,63 6

1 +44, ,-+!

"#

3 W< )

−2 = 3 W ) −6 3 −1

W< )

−6 = −1 W ) 6 −1

UGW UG< )

−2

=W ) 2 UG G1 3 W ) −3 G< ) −3 3 = W −3

+0.6,1431+0.661+,1+0.!

"# +3

- ,+ ,6,+ - , -

7/3 7/3 +0.3 ,1 11/ +++

+0 / 16/!

"# /3 7/P/3 77/

< = 11Q1 -4/ +0

6 ,+3 ,1 - /3 1/,1 - +0

- ,+ J'K!

*#

,

(210)1 W< )#$= 1

76 I 76

(210)2 W< )#$= 2

6 /6

(210)3 W< )#$= 3

/6 F //6

(210)4 W< )#$= 4

6

(210)5 W< )#$= 5

+6 +6

(210)6 W< )#$= 6

.6

(103)

% ,

-4/ , + - 6, /Q1 F J"K

, ,1 +++ ! +0 - ,3

, 3P /3 UP 737! - ? ,3

4- +1/ ,3 / +'3+! #*!

9:7

9;:77

9<:=77

# #

◦

9*>2<7+

#

9*>27<77+

#

9*>:=<777+

- 92

3

927 −3

3

2

92/#927

3

)#

9ln e9(1/2) ln e

2= 1

9*2>6+ln 2749

ln

√

104≈2?2826@;4

# A*9 e·2A+ =2?:762B:8;*2=+×27

−19

C

=2?::78;<<:*6<+×10

−27

)# 6;

*=ma(

12C)/12

+ =20 6;

# / 92<86 =

92?=@8@B<B7:@2*7:+×27

11

< = .+ - / , - ,

6+1 4,11 -+! 11

7 ,64 1,6 3,-+1! 43

4 ,16 !

<#=,-,-+1/ ,.31+1

, - + e <- = ma(

12

) NA <- ,01

,=34 11 6.+3 +%3 +! )*!

<"= 13 46 31 ,01 ,3 46,3

- ,! 61 +0 .+

/ !

<$= /1 6- , ! >,,6!

<%= ,, -/++ ;, ?,1!

,,34,116-613

/ <)!) ' #)#)*( *%=

2 ,

3

−2

!

*#

(104)

& )$

11 11 , 101 +1, - +4 - , 4,

, -3 ,/ - , 161 6/ ! +3

7 / T - + -m / +1 v 101 6;,

T = (1/2) mv2

6, , - 7/ 5,3 101 6;,

J = kg (m/s)2 = kg m2s−2

4 - < G#= 1! - 5,3 B3 +

+1 6- +1, -, 7/

2

−2

!

< =-,! 1/-

- , - ,- ;, ,6,1- ;,6;,

;,3 , 13 / ;, 64 , ,

<,1/ , -= / ;, 64 ;,!

7/ ,41617/1-

;,!

, - - , - ,

4+ +01 - ;,;,3, A- !

*"

(105)

'

-,1 + 101 + ;,3 ,1

,/4,+Q1 01-! +36

.+ - - - ,3 +

+1-+ 6- +1-M63 ,

,! , + .+

- 3me3 - ,01 ,3 ,Wmu=m(

12

/12)31

+ / - / e3 , ,!

- ,/ ,+ ;, ,/ 4, ,- +

,,+Q1016,,,61

, , /! @ + ;,

,1 , , 11 +3

,65 ,31 - / 41 +.+

1+1! - ,/ , , , -

/ , - , +1

- + ,! > +-6 + +,

4,/ ,!

, + ;, /Q1 , ?

<U=3 <= ,01 , <,=31 ,<,=3

164J"K! +1, ,1< /3

e= , - + 12 < U=! 1 -

6? #,131, -,1 ! ,

101 ! 43 + ;,?

-,1 ,1 ,/ ,3

1+6 !

,

! ' % ,

/ U UW !&)# '& %"< $=×10

−19

B 13 , W !&&)%"( (&<#(=×10

−27

7/ #

,01 ,

/ , , ,W !$*% *'( ')& * <)&=×10

11

"

< = / ;,1 +/ ,/ +

6- U,,!

<#= 1 ,01 , - ,!

16614 +0 .+ -/,71

<7= /1 <=!

<"= , - , , 101 , 4,1 16

- 61 / <)!) ' #)# )*( *%=

2

, 3

1

−2

! ,,661 - +3 - 74 !

$$ 2-/35 *&32+ F G 8+%% ()+- +%523-& $ @$

+, /,+- + ,1,/ 4, +

! ?1 , -4-,

- ,3 !! ;,,! 0 , 64

+ 6! -,- 1+1P 6116

,+ 1 ,, 43 ,1 ,6 - +!

*$

(106)

64 01 , 6.+16 - ;,

Eh=2/mea20=e2/4ε0a0 =mee

4/(4 ε0)

22

-,+1/ ,, ,1

+ - ! , , -

+J#)K161-,1/+ %3+! )*!

, , - , -;, ;,1 ,3

, , - ! 111

7 ,/, - + !

me 9@?27@;<6:*2:+×27

−31

)#

# # e 92?:762B:8;*2=+×27

−19

!

) 92?78=8B2:<*2<+×27

−34

C

*#+

# a0 98?6@2BB627<*2<+×27

−11

# &# Eh 9=?;8@B==2B*B8+×27

−18

C

/Eh 96?=2<<<=;6:878*2:+×27

−17

a0Eh/ 96?2<B:@26:;;*B;+×27

6

−1

6

Eh/a0 9<?6;<B668*2=+×27

−8

4

/a0 92?@@6<82::*;=+×27

−24

4

eEh/ 9:?:6;:2B<6*8B+×27

−3

%

Eh/ea0 98?2=667:=6*==+×27

11

A −1

ea0 9<?=B<;8;7@*B;+×27

−30

!

ea

2

0 9=?=<:8826=*;@+×27 −40

!

2

D e

2a2

0/Eh 92?:=<BBB6B=*2:+×27 −41 ! 2 2 C −1 st D e

3a3

0/Eh2 9;?67:;:282*6<+×27 −53 ! 3 3 C −2 nd D e

4a4

0/Eh3 9:?6;8;<7<*22+×27 −65 ! 4 4 C −3

#E /ea

2

0 96?;8782B=6*67+×27

5

# e/me 92?<8=<72@7*2:+×27

−23 C −1 ; #D e

2a2

0/me 9B?<@27;::7*2;+×27 −29

C −2

< ==h/2;a0= 4ε0 2/m

ee2;Eh =2/mea20.

<#= , , - +1 - /3 +1 ,3 ;,

+ -0 ,, αP

cG<,- +1=Wc/a0Eh=α

−1 =

"'!)"%*** <$&=!

<"= ,- /1+ 4> /3μB!

$$ 7% %1*(23-&+ -, 1*(&2*/ 57%/3+2' %?@'%++%= 3& 2%'/+ -, '%=*5%= 1*(&2323%+

*+3&> (2-/35 *&32+

, ;, - ;,, - 1,1 ;,! ,

/.+11,1/E

∗

311,11r

∗

31,1

m

∗

3/ 1,1/Q

∗

31 /, 1,1/, J

∗

4 1,1 ;, / 6;,

E∗ =E/Eh, r∗ =r/a0, m∗ =m/me, Q∗ =Q/e, J

∗ =J/

(107)

1,1 ;, - , ;, ?

+1/,! 1/-.+/;,-1,1;,

;, +01 + 1++ - ;,

<,/+01.+-/1/-17?

/3 1,1 ;, 1=! + T1/ ;, -

1/ 3.+1 ,,+ ;,3

−(2/2me)∇∇∇2rψ(r, θ, ϕ) +V(r)ψ(r, θ, ϕ) =Eψ(r, θ, ϕ) <#=

r, θ,1ϕ1-31+∇∇∇r1∂/∂r,∂/∂θ,

1 ∂/∂ϕ! 4- 1,1;, ;,

−(1/2)∇∇∇2r∗ψ(r∗, θ, ϕ) +V∗(r∗)ψ(r∗, θ, ϕ) =E∗ψ(r∗, θ, ϕ) <"=

4 ∇∇∇r∗ ∂/∂r

∗,∂/∂θ

3 ∂/∂ϕ! 6 ,6,/

1,1 <1= ;, - , <,1= ;, ;, <#=

;,<"=!

01 - ;,, , ;, - 1,1

<1= ;,3 ;, 13 -,1

, e, me,, Eh31 a0 1++- ;,! 61 +0

1 +-/+6-17/! +,

,,4.+ -,- ,1 ,

- 1,1;, 67 , - , ;, ,/ ;,< =!

-, , , ,1 6,

, 6- 11,1 ;, ,;,!

+6 ;, , < =! < /, ,

4,1 -4 , 6- h 3 = h/2 , 7/

+6 64 h1 != ++6.,1 /,1

61,,16-+;,44/

;, ;,, 36, + 1,- 01,1

Q 1! + Q , - ;, L.+1

,M3 !! , - 1,1 ;,3 67 , -

/ ;, ,!

, , , e, me,, Eh3 a0

;, :34 ! 4,16 ,

/ ;, e3- ;, me3! 12

64 ;, , <"=3 -,1 <#=4

-,1 ;, ,! <"= ;,

1 1,1 ;,3 101 ;, < =3 <#= ;,

,, <11= + ;, 44 -,!

3 , , - - ,

63 6, , L!,!M L,M - ,! , ,1

-41! -,3 5, 4,1 - 4 L M -

,3 LFM 6- F ,!

"# 1/, ;,6,61 / re31

1/ De3/

re= 2.1a0 re= 2.1 !,!

De= 0.16Eh De= 0.16 !,!

*&

(108)

(

U, -1 + ;,3 ++1L;,- M3

- +1 - 101 , 11 +

663,e<+=! ,31 ,1,

,!

$ $ '(523-&+ 8'%)(23C% C()*%+ 3%)=+ %H53%&53%+9

,,3,?-?,6-x< 1,-=3

-w31,-ϕ<#! )3+!$'-;,=3

.+1 - 6 64!

, ' "#

+ e )

−2

+ 6,1 -6? ".+1

,?-?,6 - xW ! e

+ )

−3

+ w W#!"

,+ -, +- 1

,1 ,1! -;, ,1 , - LM 4,

1 - + - - +13 !/! ,?-?,6 -3 -

, -! 6/, ,1 ,1 /

- ;, -, 101! , - +++ ,

+-1!

"# -wW !%× )

−6

W !% /G7/!

,?-?,6 -x W"!'× )

−2

W"!'e x W"'G!

6+ ++4 ;,,,

-7ρ<=W#!& /1

−3

34 ++ ;,?

- w<= W#!&× )

−6

!

+ - ,/ 11 - ;, -

6 +! , M - 74 #!&× )

−6

6/,,

,1 11!

.+,++.;,-ρ//1

−3

1wG10

−6

;,,

,3 -4 - - - 1, ;,,,

++ !) /

−3

! , , - ,1 61 74

/1

−3

31,6+-1,/++<+1/

66= +- -!

$ $ %@'%5(2%= *+(>%

11/.6 e163,e<V /V= </e6,=,1

11! A,-/6 6111 6- + ;,36, ,!

"# -wW)!% e36, )!%e<m/m=!

6e,16,164,! 61/16/

- /+ , - e 11! ,/ 4,1

x<

13

=W ! e3 ))x 6+-1xGe61/+< -.+

&!"3 +! # =!

*'

(109)

-, 6 64 -,1 ,3 6,

,61+1! 16- )

−9

1 )

−12

61 -! +-413 6-1- )

12

1 - )

18

! ++ ,1 - + + ,13

1 - + + ! *$( 41 6 ++1 - )

12

- )

18

J 'K! ,/ ++3 ++63++ 17 41,1, ++

1 3,//1 + 61 ,6,

6/,1! , ,1 +16 ?+6

;,,+G<++=34,6/,,! ,

,//1+ <+ -,1 /G/3 /G/3+/G/ !=!

, ' "# (

++,11 ++ )

−2

;, +3 e

++,13 ++3 10

−3

+ 1.1 1+1 G

+ 1

6? " -6'

' ++ /G/

++ ++ )

−6

, , #)++ G

++,11 ++ )

−8

+,

% ++

++6 ++6 )

−9

;,11 - Q G

, ϕW #) ++6

++ ++ )

−12

, 67/,1 , - +G

- -,1 6ϕW $) ++

++;,1 ++; )

−15

-G 1

+ +1 + 3+3 + +!

$ $ &32+ ,-' )->('327/35 1*(&2323%+: &%@%' 0%) (&= =%530%)

013+,1,3+/,6

4 +/ + ;, 101 - / - ! 1+1

+,1 - ;, -,- /

F(t) =A

−δtcosωt=A

[

(−δ+ω)t

]

,- 1+/X δ 1/,

-;, ω +4- ,

−1

! 43 + +3 +3

1 13 < #! +! "3 "!$3 +! (* "!'3 +! *#=3 ,1 - , -

1 +1, δt ωt3 +! , ;, δ ω +1

, +G 1G3 +! +3 +3 13 13

66,/ - + - ,6 !

01-,1/3/+41/+,1

< 01= ,, +1 11 + / - -

+4 P - +4 P03 - 01 F - 01 F0! +4

++ ;, - 01 +,1 <4 01 ;, +1

= 10 +4 01 ;, ,

! 610/01 1+41/

LF = ln(F/F0)3 L

P = (1/2) ln(P/P0)

-(P/P0) = (F/F0) 2

LP =LF! ;, 64

-LF = ln(F/F0) +3 LP = (1/2) ln(P/P0) +

*(

(110)

63 >3 -;, ,1,6,+ 163 1>3 ,14 011

+4 ,1 ,/11 / 1/

LP =/(P/P0) >= 10/(P/P0)1>

1

LF =# /(F/F0)>= 20 /(F/F0) 1>

64 +-4 - +/ ;, +?

1/ ;,! @

LF =(F/F0) += 2 /(F/F0) >= ln(10) /(F/F0) +

//

1 >= 101>W(1/2) ln(10) + ≈ ! % #*" +

+ 61,1! 16,13+ 11/3

+, - ,3 6/ - +4 +0! ,

LP =n1>+ ) /(P/P0) =n!

;, +4 101 , 63161 +3,Q1

6 -4!

, , ,

01 LF = ln(F/F0) = ln(F/F0) +W# /(F/F0) >W #)/(F/F0) 1> −" +4LP = (1/2) ln(P/P0) = (1/2) ln(P/P0) +W/(P/P0) >W ) /(P/P0) 1> $−&

< =F0 -01 ;,34 ,16+01!

<#= - ,011 ,1+,1/

Lp31 -+, p0 W#) !

<"= +3 4L

F = 1 +3F/F0 W≈#!' ( #( (!

<$=P0 - +43 ,1 +01! - G# ,11 10

LP=LF!

<%= -, +41,1+4 1/

LW31 -+4 P0 = 1 +@!

<&= +34 LP = 1 >W )1>3 P/P0 = 10P1 4LP = 2 >W#) 1>3P/P0= 100P

!

**

(111)

(112)

(113)

(114)

$

! ,6 / +1 <,+/= +! / 64

1/ ,6 ,1 + <!/! #!"= <!/! #3"=! 43 J%!K

1 - /! @ / +1 6-0

/0 1/ - ,6 Q +1 /! -

1/ - / ,6 1/ +1 /,+ - 6,

/3 ,/ + <6, + =! 4

-,1/6 1741+;,11

+,1 6,1!

"# #%'"!$# '"& #%'"3$# '"& )!#%'"$# '" &× ) 4

)3#%' "$# '" &× )

4

"# %'"!$# % "# %'"3$# '

#! ,,-+;,46.+11,,

,65 ,! + , ,1 +01!

/,1- ,6 +1-4

"# l=J5.3478−0.0065,5.3478 + 0.0065K

l=%!"$'(<"#=

+ / - , 11 [a−b, a+b]!

11 ,1 ,1 /

[a−b, a+b] , , /1/- , b2σ34

σ 11 , 11 < + (3+! $*=!

+3 a(c)3 / - , c 11 + ,1

++ /0 1/- a! 11

- / b + σ 01/- a!

"! - <!/! π3 W

√

−1 = +1

<,+/=+36, -,6 <!/! ;,,,6=

,1 +1 <+/= +3 + ;,!

$! -+0 -,<!/! 63 3/3 +3 313 Δ3∇∇∇3!!!=

6 +1 +36, - / -, <!/! f(x)3F(x, y)3!!!=

+1 +!

%! + +< +3+IW−lgK != +1 +!

&! - +/,+ </! 3 3!!!3 +313 !!!3 Σ3 Π3Δ3!!!3 1g3 >

23!!!= +1<,+/=+4 + 6-

,3 ,/ - +1 + +

+- + /,+!

)"

(115)

'! U1 +161 +!

"# -3 01 3+

1 + ,1 1/,1 -+1/ !

"# r =||

;, 6+161 -?- +!

"# ËËË3ÌÌÌ

U Q1 43

→

1

1,643

S,T!

)$

(116)

"

,

+3>&+ (&= +./0-)+

;, W

;, =

1 ;, ≡

;, 610

def

=3:=

++ ;, ≈

+ ;,

+1 =

++ ∼,∝

1 3++ →

0 ∞

<

/ >

;,

/ ;,

,

, /

-@%'(23-&+

+, Y

, −

+, , ±

, +, ∓

a,+1 6b a b, ab, a·b, a×b

a111 6b a/b3ab

−1

3

a b

/,1 -a |a|

a +4n a

n

;, - a31 - a

2+b2 √a

3a 1/2

31 √

a2+b2

3

a2+b21/2

n -a a

1/n

3 n √

a3

, -a a3a

/ -a<;, a/|a|-a= 03)-a= 0= /a

n - n!

6 X3 n!/p!<n−p=! C

n p3

n

p

, -ai

ai3

iai3

n i=1

ai

+1,- ai

ai3

iai3

n i=1

ai

,*&523-&+

-x x

- x x

/ - x x

/ -x x

< =@ ,+11 13 -/D a·b!

)%

(117)

- ,

- x x #

/ -x x #

+6 - x x

+6 -x x

+6 / - x x

+6 -x x #

+6 - x x #

+6 / - x x #

+6 / -x x #

6 -, /

.+ - x +x3

x

/ a-x /ax "

, / - x x3/e x "

/ )- x /x3/10 x "

/ #- x 6x3/2 x "

/ / x x

/ +- x x

/ <n/m=

1 - / n/m−<n/m=

1

/ x Δx=x<0= −x<=

0 -f f

- f(x) x a lim

x→af(x)

1 - f 1fG1x3f

3<1G1x=f

#1 1- f

2f G1x

2 3f

n -f

nf

G1x

n

3f (n) + 1- f ∂f /∂x3∂xf3xf

12 - f 1f

12 - f bf $

0 1- x

.

x31xG1t

+

/- f(x)

f(x) 1x3

1xf(x)

I7

ij W

1 -i=j

0 -i=j

? ijk W

⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩

1 -ijk +, - #"

123= 231 = 312= 1

−1 -ijk +, - #"

132= 321 = 213=−1

0

1 -, (x)3

f(x)(x) 1x=f(0)

<16,=

<#= - + -,3!! arcsinx + -sinx!

<"= + x!

<$= ,113 #! 3+!%%!

)&

(118)

- ,

, +-,3 (x)3(x)3(x)3

1 -, (x) = 1- x >03 (x) = 0 - x <0!

/ -, (x) W

tx−1

−t

1t

(x) W<x−1=Z -/ , -x

,- -,f g f∗g=

f(x−x)g(x)1x

5-/@)%? &*/0%'+

;, - −13

√

−1

+- z=a+ ib z=a

/ +-z=a+ ib z=b

1,, -z=a+ ib3 |z|=

a2+b21/2

6,,-z=a+ ib

/, -z=a+ ib /zP</ z= Wb/a

+ 5,/ -z=a+ ib z

∗ =a−ib

C%52-'+

→

a

+ - a

x3a

y3a

z

, x3y3z %33 "

+1, ·

+1, × (∧ )

6+3 1+ ∇∇∇=

x∂/∂x+

y∂/∂y+

z∂/∂z

+ + ∇∇∇

2,=∂2

/∂x2+∂2/∂y2+∂2/∂z2

/1 - 01 V /1V3∇∇∇V

1/ - 01 13∇∇∇ ·

- 01 3∇∇∇ ×3<,=

/(2'35%+

- Aij

+1,- 34 < =

ik =

j

AijBjk

,

- ;,

−1

+-

Ì 3

+ 5,/ -

∗

5,/ +-

H

3 †

34

†

ij =A∗ji

<5,/ -=

- ;,

i

Aii3

1 - ;, 13||

+%2+ (&= )->35() -@%'(2-'+

p q <5,/= p∧q

p q <15, /= p∨q

/ - p3 p ¬p

p +q p⇒q

p ;, q p⇔q

A B A⊂B

)'

(119)

- ,

,- A 1B A∪B

-A 1B A∩B

x 6/ A x∈A

x 6/ A x /∈A

A x Ax

A 6, B A\B

)(

(120)

(121)

(122)

1/6-11, ,1+

#))# J#)K < =1 -#))$ +?

- F,+ J (K < =3 - 1!

11 , /0 1// +!

' ,

/ μ0 $× )

−7

−1

<101=

+1 -/ ,, c0 #** '*# $%(

−1

<101=

ε0 = 1/μ0c

2

0 (!(%$ ('( '!!!× )

−12

−1

3# +1 Z0=μ0c0 "'&!'") " " $& !!! Ω #

- ,,

7 h &!&#& )&*"< =× )

−34

B =h/2 !)%$ %' &(< (=× )

−34

B

hc0 !*(& $$%& <"$=× )

−25

B

,+/ GF/(c0)

3

! && "'< =× )

−5

FU

−2

"

47 / /θW sin

2θ

W )!### %<'&= $3%

/ e !&)# '&%"< $=× )

−19

me *! )* "(#&< &=× )

−31

7/

+ mp !&'# &# ' <#*=× )

−27

7/

, mn !&'$ *#'#(<#*=× )

−27

7/ mu W , !&&) %"((&<#(=× )

−27

7/ &

/1 L, NA &!)## $ %< )=× )

23

−1

' >Q k3kB !"() &%)%<#$=× )

−23

B I

−1

1 F =Le *!&$( %""("<("=× ) 4

−1

/ R (!" $ $'#< %=B I

−1

Q- , #'"! % I<101=

, - 1/3 Vm ##!' ) *( <$)=

3

−1

(

p W )) 73tW )

◦

11 + ) "#% <101=

0?,, α Wμ0e

2c

0/2h '!#*' "%#%&(<#$=× )

−3

α−1 "'!)"% *** <$&=

>1, a0 W $ε0

2/m

ee2 %!#* ''# )(< (=× )

−11

/ Eh W

2/m

ea20 $!"%* '$$ '<'%=× )

−18

B 16/ R∞=Eh/2hc0 !)*' "'" %& (%#%<'"=× )

7

−1

>/ μB =e/2me *!#'$ ))*$*<()=× )

−24

B

−1

/ μe −*!#($'&$ #<()=× )

−24

B

−1

1O g?- - ge= 2μe/μB −#!))#" * ")$ "' (<'%=

-

, / μN=<me/mp=μB %!)%) '("$"<$"=× )

−27 B −1 < = −1 W −2 W 2 −2 P −1 W 2 B −1 −1 !

<#=ε0 Z0 6,1 -101 , - μ0 c0!

<"= , - ,+/ 11 F,+ J (K!

<$=@ 47 / /θW3sin 2θ

W 1@6/+!

,6- 12/ ,1 sin

2θ

W < + )J (K=!

, / J#)K 61 ? , sin

2θ

W = 1−(mW/mZ)23

;, mW 1mZ 3+3 - @

±

1 S

0

6!

<%= F,+ J (K / mW = 80.425(38) FUGc 2

03 mZ = 91.1876(21) FUGc 2 0!

11 , sin

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BB B:?@2@@2=<*2:+ B?:;*2:+ 2>6− M7?8;87B=6=*6<+K B< BB?@2B;7@B*2:+ 6;?BB*6<+ 7M

<7 B@?@2:8662*67+ =@?:2*=2+ 7M <6 <2?@2:B77;*66+ <?B;*66+ 7M

;8 B@ B<?@2<;;B@*67+ 87?:@*B+ ;>6− M6?27:=77*=+ M;2?;*;+ <2 <7?@2:6@2*;+ =@?;2*B+ ;>6− M6?6B78:6*=+ M6:?6*;+ ;: N B< BB?@67;<<*B+ 7?;88*;+ 7M

<7 B@?@2:;B@*=+ 6?6<:*27+ 7M <6 <2?@2;=<87*6<+ 22?8@;*;2+ 7M

<; <6?@2=2;B*=+ 22?877*2@+ @>6M −7?@B7::@*;+ M68?@*2+ <= <;?@2287<*;+ 8:?@<B*28+ 7M

<: <8?@27:28*8+ 2B?6B@*=2+ 7M

;B , <8 <=?@22B@6=*6B+ B6?2B*6+ 8>6− M2?;8;;828*<+K M6B?:*2+K <BF <:?@7@2<8<*6<+ 6B?<;*6+ ;>6− M6?B82<2<*6+K M2;?;8*8+K ;< <= <;?@2;=6:*=+ 7?8:*2+ 7M

<: <8?@7@6:=B*68+ @?<:*2+ 7M

<B <:?@7<<<2:*68+ B?77*2+ @>6M −2?7@;:7;7*2;+K M;;?8*67+ << <B?@78:2:B*68+ <6?8<*2+ 7M

;@ P <@ <<?@78<=<8*6:+ 277 2>6− −7?2;B=28=6*;=+K =7 O @7 <@?@7=B766*6=+ 82?=8*=7+ 7M

@2 @7?@78:=;=*6;+ 22?66*8+ 8>6M −2?;7;:6*6+ −2B?:*;+ @6 @2?@787;<:*6;+ 2B?28*<+ 7M

@= @;?@7:;2==*6:+ 2B?;<*6<+ 7M @: @8?@7<6B8*;+ 6?<7*@+ 7M

=2 @; @6?@7:;B:6*6=+ 277 @>6M M:?2B78*;+ −;6?7*67+K

=6 / @6 @2?@7:<27*=+ 2=?BB*;2+ 7M

@= @;?@787<:B*67+ @?6;*27+ 7M

@8 @=?@78<=7:*67+ 28?@7*@+ 8>6M −7?@2=6*2+ −6?6*2+K @: @8?@7=:B<7*67+ 2:?:<*2+ 7M

@B @:?@7:7672*67+ @?8:*8+ 8>6M −7?@;;8*2+ M68?8*2;+K @< @B?@78=7:@*67+ 6=?2@*6:+ 7M

277 @@?@7B=B:*:+ @?:B*67+ 7M

=; @<K @B?@7B628*=+ *:+M

== , @: @8?@7B:7=*@+ 8?8=*2=+ 7M

@< @B?@786<B*B+ 2?<B*;+ 7M

@@ @<?@78@;<8*66+ 26?B:*2=+ 8>6M −7?:=2;*82+K MB?@*=+ 277 @@?@7=62<@*66+ 26?:7*B+ 7M

272 277?@788<28*66+ 2B?7:*6+ 8>6M −7?B2<<*:7+K M=8?B*6;+ 276 272?@7=;=<<*66+ ;2?88*2=+ 7M

27= 27;?@78=;7*=+ 2<?:6*6B+ 7M

=8 , 27; 276?@7887=*;+ 277 2>6− −7?7<<=7*6+

=: 276 272?@78:7B*;+ 2?76*2+ 7M

27= 27;?@7=7;=*8+ 22?2=*<+ 7M

278 27=?@787<;*8+ 66?;;*<+ 8>6M −7?:=6*;+ M::?7*22+K 27: 278?@7;=<=*8+ 6B?;;*;+ 7M

27< 27B?@7;<@8*=+ 6:?=:*@+ 7M

227 27@?@7828;*26+ 22?B6*@+ 7M

#$

(136)

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=B %# 27B 27:?@787@;*:+ 82?<;@*<+ 2>6− −7?22;:B@:8*28+K 27@ 27<?@7=B8:*;+ =<?2:2*<+ 2>6− −7?2;7:@7:6*66+K =< ! 27: 278?@7:=8<*:+ 2?68*:+ 7M

27< 27B?@7=2<;*:+ 7?<@*;+ 7M 227 27@?@7;77:*;+ 26?=@*2<+ 7M

222 227?@7=2<6*;+ 26?<7*26+ 2>6M −7?8@=<<:7B*<=+K 226 222?@76B8BB*;7+ 6=?2;*62+ 7M

22;F 226?@7==72=*;7+ 26?66*26+ 2>6M −7?:66;77@6*<B+ 22= 22;?@7;;8<:*;7+ 6<?B;*=6+ 7M

22: 228?@7=B8:*;+ B?=@*2<+ 7M

=@ 22; 226?@7=7:6*=+ =?6@*8+ @>6M M8?86<@*6+ MB8?@*<+ 228F 22=?@7;<B@*=7+ @8?B2*8+ @>6M M8?8=7<*6+ MBB?7*<+K

87 226 222?@7=<66*8+ 7?@B*2+ 7M

22= 22;?@76B<;*;+ 7?::*2+ 7M

228 22=?@7;;=B*;+ 7?;=*2+ 2>6M −7?@2<<;*B+

22: 228?@72B=8*;+ 2=?8=*@+ 7M

22B 22:?@76@88*;+ B?:<*B+ 2>6M −2?7727=*B+ 22< 22B?@72:7<*;+ 6=?66*@+ 7M

22@ 22<?@7;;22*;+ <?8@*=+ 2>6M −2?7=B6<*B+ 267 22@?@762@<8*6B+ ;6?8<*@+ 7M

266 262?@7;==22*6@+ =?:;*;+ 7M 26= 26;?@786B=8*28+ 8?B@*8+ 7M

82 262 267?@7;<666*6:+ 8B?62*8+ 8>6M M;?;:;=*;+ −::?@*28+K 26; 266?@7=62:7*66+ =6?B@*8+ B>6M M6?8=@<*6+ −<8?;*2@+

86 267 22@?@7=76:*22+ 7?7@*2+ 7M

266 262?@7;788<*6@+ 6?88*26+ 7M

26; 266?@7=6B22*67+ 7?<@*;+ 2>6M −7?B;:@=B<*<+ 26= 26;?@76<2<<*2:+ =?B=*2=+ 7M

268 26=?@7==6=2*67+ B?7B*28+ 2>6M −7?<<<8782;*=;+K 26: 268?@7;;7=@*67+ 2<?<=*68+ 7M

26< 26B?@7==:28*2@+ ;2?B=*<+ 7M 2;7 26@?@7:666@*62+ ;=?7<*:6+ 7M

8; 26B 26:?@7==:<*=+ 277 8>6M M6?<2;6B;*<=+ −B2?7*27+ 8= Q 26= 26;?@78<@8=*62+ 7?7@86*;+ 7M

26: 268?@7=6:<*B+ 7?7<@7*6+ 7M 26< 26B?@7;8;78*28+ 2?@276*<+ 7M

26@ 26<?@7=BB@@*@+ 6:?=77:*<6+ 2>6M −7?BBB@B:;*<=+ 2;7 26@?@7;87<@*22+ =?7B27*2;+ 7M

2;2 2;7?@787<6<*2<+ 62?6;6=*;7+ ;>6M M7?:@2<:2@*;@+ −22?=*2+ 2;6 2;2?@7=28=:*28+ 6:?@7<:*;;+ 7M

2;= 2;;?@78;@=8*@+ 27?=;8B*62+ 7M 2;: 2;8?@7B667*<+ <?<8B;*==+ 7M

88 ! 2;; 2;6?@78==B*;+ 277 B>6M M6?8<676=:*;=+K −7?;88*=+K

8: 2;7 26@?@7:;22*B+ 7?27:*2+ 7M

2;6 2;2?@7878:*;+ 7?272*2+ 7M

2;= 2;;?@7=87=*;+ 6?=2B*2<+ 7M

2;8 2;=?@78:<=*;+ :?8@6*26+ ;>6M M7?<;B@=;*2B+K M2:?7*;+K 2;: 2;8?@7=8B2*;+ B?<8=*6=+ 7M

2;B 2;:?@78<66*;+ 22?6;6*6=+ ;>6M M7?@;B;:8*67+K M6=?8*=+K 2;< 2;B?@786=6*;+ B2?:@<*=6+ 7M

#%

(137)

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8B - 2;<F 2;B?@7B27<*=+ 7?7@7*2+ 8M M;?B2;:=:*B+ M=8?7*67+K 2;@ 2;<?@7:;=@*=+ @@?@27*2+ B>6M M6?B<;7=88*@+ M67?7*27+

8< ! 2;: 2;8?@7B2=7*87+ 7?2<8*6+ 7M 2;< 2;B?@78@<:*22+ 7?682*6+ 7M 2=7 2;@?@78=;8*;+ <<?=87*82+ 7M 2=6 2=2?@7@6=2*=+ 22?22=*82+ 7M

8@ 2=2 2=7?@7B:=<*;+ 277 8>6M M=?6B8=*8+ −8?<@*=6+

:7 2=6 2=2?@7BB2@*;+ 6B?6*8+ 7M

2=; 2=6?@7@<27*;+ 26?6*6+ B>6− −2?7:8*8+ −:;?7*:7+ 2== 2=;?@277<;*;+ 6;?<*;+ 7M

2=8 2==?@268:@*;+ <?;*2+ B>6− −7?:8:*=+ −;;?7*;7+

2=: 2=8?@2;22;*;+ 2B?6*;+ 7M

2=< 2=B?@2:<<@*=+ 8?B*2+ 7M 287 2=@?@67<<B*=+ 8?:*6+ 7M

:2 2=8K 2==?@26B==*=+ 8>6

:6 2== 2=;?@22@@:*=+ ;?7B*B+ 7M

2=BF 2=:?@2=<@=*;+ 2=?@@*2<+ B>6− −7?<2=<*B+ −68?@*6:+ 2=< 2=B?@2=<2<*;+ 22?6=*27+ 7M

2=@ 2=<?@2B2<7*;+ 2;?<6*B+ B>6− −7?:B2B*B+K MB?8*<+K 287 2=@?@2B6B6*;+ B?;<*2+ 7M

286 282?@2@B6@*;+ 6:?B8*2:+ 7M

28= 28;?@6667:*;+ 66?B8*6@+ 7M

:; " 282 287?@2@<=:*;+ =B?<2*:+ 8>6M M;?=B2B*:+ @7?;*27+K 28; 286?@6266B*;+ 86?2@*:+ 8>6M M2?8;;7*<+K M6=2?6*62+K

:= 286 282?@2@B<@*;+ 7?67*2+ 7M

28= 28;?@67<:6*;+ 6?2<*;+ 7M

288 28=?@66:2@*;+ 2=?<7*26+ ;>6− −7?68B6;*;8+K M26B?7*;7+K

28: 288?@66267*;+ 67?=B*@+ 7M

28B 28:?@6;@8B*;+ 28?:8*6+ ;>6− −7?;;B6:*88+K M2;8?7*;7+K 28< 28B?@6=272*;+ 6=?<=*B+ 7M

2:7 28@?@6B782*;+ 62?<:*2@+ 7M

:8 28@ 28<?@68;=;*;+ 277 ;>6M M6?72=*=+ M2=;?6*<+

:: 28: 288?@6=6B<*B+ 7?78:*;+ 7M

28< 28B?@6==78*=+ 7?7@8*;+ 7M 2:7 28@?@682@=*;+ 6?;6@*2<+ 7M

2:2 2:7?@6:@;7*;+ 2<?<<@*=6+ 8>6M −7?=<7;*68+K M687?B*67+K 2:6 2:2?@6:B@8*;+ 68?=B8*;:+ 7M

2:; 2:6?@6<B6<*;+ 6=?<@:*=6+ 8>6− M7?:B6:*;8+ M6:=?<*62+ 2:= 2:;?@6@2B2*;+ 6<?6:7*8=+ 7M

:B & 2:8 2:=?@;7;2@*;+ 277 B>6− M=?2B;*6B+ ;8<?7*67+K :< " 2:6 2:2?@6<BB8*=+ 7?2;@*8+ 7M

2:= 2:;?@6@2@B*=+ 2?:72*;+ 7M

2:: 2:8?@;76@7*;+ ;;?87;*;:+ 7M

2:B 2::?@;67=:*;+ 66?<:@*@+ B>6M −7?8:;<8*26+ M;8:?8*6@+ 2:< 2:B?@;6;:<*;+ 6:?@B<*2<+ 7M

2B7 2:@?@;8=:2*;+ 2=?@27*;:+ 7M

:@ 2:@ 2:<?@;=622*;+ 277 2>6M −7?6;2:*28+

#&

(138)

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B7 P 2:< 2:B?@;;<@8*8+ 7?2;*2+ 7M

2B7 2:@?@;=B8@*;+ ;?7=*28+ 7M

2B2 2B7?@;:;6;*;+ 2=?6<*8B+ 2>6− M7?=@;:B*2+K 2B6 2B2?@;:;B<*;+ 62?<;*:B+ 7M

2B; 2B6?@;<67B*;+ 2:?2;*6B+ 8>6− −7?:B@<@*;+K M6<7?7*=7+ 2B= 2B;?@;<<8<*;+ ;2?<;*@6+ 7M

2B: 2B8?@=68:@*;+ 26?B:*=2+ 7M

B2 - 2B8 2B=?@=7B:<6*6<+ @B?=2*6+ B>6M M6?6;6B*22+K M;=@?7*67+K 2B:F 2B8?@=6:<6B*6<+ 6?8@*6+ B− M;?2:@6*=8+K M=@6?7*;7+K B6 & 2B= 2B;?@=77=6*=+ 7?2:*2+ 7M

2B: 2B8?@=2=7;*;+ 8?6:*B+ 7M

2BB 2B:?@=;667=*6B+ 2<?:7*@+ B>6− M7?B@;8*:+ M;;:?8*6@+K 2B< 2BB?@=;:@<2*6B+ 6B?6<*B+ 7M

2B@ 2B<?@=8<28=*6B+ 2;?:6*6+ @>6M −7?:=7@*2;+ M;B@?;*;;+K 2<7 2B@?@=:8=<<*6B+ ;8?7<*2:+ 7M

B; 2<7 2B@?@=B=::*;+ 7?726*6+ @−

2<2 2<7?@=B@@:*;+ @@?@<<*6+ B>6M M6?;B78*B+ M;2B?7*67+K

B= G 2<7 2B@?@=:B7:*8+ 7?26*2+ 7M

2<6 2<2?@=<678*;+ 6:?87*2:+ 7M

2<; 2<6?@8766=6*;7+ 2=?;2*=+ 2>6− M7?22BB<=B:*@+ 2<= 2<;?@87@;6;*;7+ ;7?:=*6+ 7M

2<: 2<8?@8=;:6*;+ 6<?=;*2@+ 7M

B8 , 2<8 2<=?@86@88*;+ ;B?=7*6+ 8>6M M;?2<B2*;+ M62<?7*67+K 2<BF 2<:?@88B878*;7+ :6?:7*6+ 8>6M M;?62@B*;+ M67B?7*67+K

B: 2<= 2<;?@86=@2*;+ 7?76*2+ 7M 2<: 2<8?@8;<;<*;+ 2?8@*;+ 7M

2<B 2<:?@88B=B:*;7+ 2?@:*6+ 2>6− M7?7:=:82<@*:+K 2<< 2<B?@88<;8B*;7+ 2;?6=*<+ 7M

2<@ 2<<?@8<2=8*;+ 2:?28*8+ ;>6− M7?:8@@;;*=+ M<8?:*6<+ 2@7 2<@?@8<==8*;+ 6:?6:*6+ 7M

2@6 2@2?@:2=B@*=+ =7?B<*2@+ 7M

BB 2@2 2@7?@:78@2*;+ ;B?;*6+ ;>6M M7?287B*:+K M<2?:*@+K 2@; 2@6?@:6@6;*;+ :6?B*6+ ;>6M M7?2:;B*:+K MB8?2*@+K

B< 2@7 2<@?@8@@;7*B+ 7?72=*2+ 7M 2@6 2@2?@:27;8*=+ 7?B<6*B+ 7M 2@= 2@;?@:6::;*;+ ;6?@:B*@@+ 7M

2@8 2@=?@:=BB=*;+ ;;?<;6*27+ 2>6− M7?:7@86*:+ 2@: 2@8?@:=@;=*;+ 68?6=6*=2+ 7M

2@< 2@B?@:B<B8*8+ B?2:;*88+ 7M

B@ % 2@B 2@:?@::882*;+ 277 ;>6M M7?2=<28<*<+K M8=?B*2:+K

<7 &# 2@: 2@8?@:8<2=*=+ 7?28*2+ 7M 2@< 2@B?@::B86*;+ @?@B*67+ 7M

2@@ 2@<?@:<6:6*;+ 2:?<B*66+ 2>6− M7?878<<8=@*<8+ 677 2@@?@:<;7@*;+ 6;?27*2@+ 7M

672 677?@B76<8*;+ 2;?2<*@+ ;>6− −7?8:7668B*2=+K M;<?B*:+K 676 672?@B7:68*;+ 6@?<:*6:+ 7M

67= 67;?@B;=B8*;+ :?<B*28+ 7M

<2 67; 676?@B6;6@*;+ 6@?86*2+ 2>6M M2?:6668B<B*26+K 678 67=?@B==26*;+ B7?=<*2+ 2>6M M2?:;<62=:2*26+

<6 67= 67;?@B;76<*;+ 2?=*2+ 7M

67: 678?@B===@*;+ 6=?2*2+ 7M

67B 67:?@B8<<7*;+ 66?2*2+ 2>6− M7?8@68<;*@+K 67< 67B?@B::;:*;+ 86?=*2+ 7M

#'

(139)

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<; 67@ 67<?@<7;<=*;+ 277 @>6− M=?227:*6+ −82?:*28+K <= 67@K 67<?@<6=2:*;+ 2>6−

<8 % 627K 67@?@<B2;2*@+ *8+M

<: , 666K 666?72B8B78*6B+ 7M

<B ( 66;K 66;?72@B;7B*6@+ ;>6*−+ M2?2B*6+ M22B?7*27+

<< , 66:K 66:?768=76:*6B+ 7M

<@ % 66BK 66B?76BB=B7*6@+ ;>6− M2?2*2+ M2B7?7*677+

@7 6;6F 6;6?7;<7=@8*66+ 277 7M

@2 6;2K 6;2?7;8<<*6+ 277 ;>6− 6?72*6+ −2B6?7*87+

@6 6;;K 6;;?7;@:6<*;+ 8>6M 7?8@*8+ ;::?;*<+

6;=F 6;=?7=7@==B*66+ 7?778=*8+ 7M

6;8F 6;8?7=;@666*62+ 7?B67=*:+ B>6− −7?;<*;+K =@;?:*:+K 6;<F 6;<?787B<;8*66+ @@?6B=6*27+ 7M

@; 6;BK 6;B?7=<2:B;*62+ 8>6M M;?2=*=+K M;<<?:*:+

@= 6==K 6==?7:=2@<*8+ 7M

@8 % 6=;K 6=;?7:2;B6B*6;+ 8>6− M2?:2*=+ M=67?7*2;7+

@: ! 6=BK 6=B?7B7;=B*8+ @>6− 7?;B

@B ) 6=BK 6=B?7B76@@*:+

@< ! 682K 682?7B@8<7*8+

@@ " 686K 686?7<6@B7*87+

68;K 68;?7<=<2<*;+ B>6M :B7?7*<77+

277 ( 68BK 68B?7@87@@*B+

272 / 68<K 68<?7@<=68*8+

276 68@K 68@?27276*22+

27; - 6:6K 6:6?27@:@*;6+

27= , 6:2K 6:2?27<B8*22+

278 6:6K 6:6?22=28*67+

27: # 6:;K 6:;?22<;2*2;+

27B 6:=K 6:=?26=B;*;7+

27< & 6:8K 6:8?2;777*;6+

27@ / 6:<K 6:<?2;<<6*;=+

227 6B2K 6:B?2=;@:*=2+

222 ,# 6B6K 6B6?28;=<*;:+

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(140)

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1+1/1+1 67/,1 +16

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1/,1.+6434,,++.!

"# ! 4/ λ- -4 -1, /

λ≈5.896×10−7 , λG≈5.896×10

−7

]/T 101 ;,< '!#3 ,1/ +! "%=

1 [W [DW )

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λG[ W<λG=<G[= ≈<%!(*& × )

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= < ) 10

=W %(*&

λ≈5896 [

"# #! +, +,- #)

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=≈ '!%

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1 1

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ν(−^) =T0()−T0(^)≈3156

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/ -/,1+ .1 / ,

ΔE=hc0ν≈<&!&#& × )

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B =<#!**( × ) 8

−1

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6 ;,< '!#39/:3 +! "'= U ≈ !&)##× )

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B3 B ≈< G)! &) ##=U3

ΔE≈6.269×10−2/)! &)##

U ≈)!"* " U

/6Eh =

2/m

ea20 ≈$!"%*'B3 B≈< G$!"%*'=Eh < "!*!

+!*$=31 , / / ,6

ΔE ≈6.269×10−2/4.3597Eh≈1.4379×10−2Eh

/ /

ΔEm=LΔE ≈(6.022×1023

−1)(6.269×10−2

B)≈37.75 7B

−1

3 7DW $! ($7B3 7BDW< G$! ($= 73

ΔEm≈ <"'!'%G$! ($=

−1 ≈

*!)#"7

−1

- - ΔE ΔEm X L ,63 6,

12 - ! .+ - X ,1

7 1- 167!

"# $! 1,3 3- 101 6;,

=κ/c

4 κ 1, - , , 1, - +, ?

c ! 1, - ,, +1

−1

1

−3

P - + κ<I= ≈ '!"* × )

−5

−1

c<I= ≈)!)))%))

−3

! 1, 6,1 -4

≈(7.39×10−5

−1

=G<)!)))%))

−3

= ≈ )! $'(

−1

1 3

W $'!(

−1

2

3

W ))) 3

! +, - 63

4 ?11

-= 1000κ/c

43 - + + ;,3 6,

- + ;, +1 ,! +03 ;, ,

, , - 1,

−1

2

3 κ , , -

1,

−1

31 c , , -

−3

!

1 -4 , - ;, ,,3 ,1 11! ;, = κ/c3

4 + + ;,3 , ,! - 11

64 , , ,16

/<

−1

2

=W

1000 κ/(

−1)

c/(

−3)

"#

(144)

"# %! ,-)! #%-,>m

) ≈953

/-b /

6 <

-2

364=

b =n /m)≈(0.125/953)

/

−1 ≈

)! " 7/

−1

,?-?,6 , ++ /

x =n /(n)+n )≈n /nS=b M)

4 ,1n n

) !

- 44 (!) % /

−1

3

x ≈0.131 7/

−1 18.015

/

−1≈2.36

/G7/W )!))#"&

;, ;,1 1+1 - bB W )))nBGMS3

x ≈ b M)/1000

! 43 , - ;, ,, 6,

- + ;, +, ,P +0

,1b , m

)

1M

)

1,,7/

−1

3/31/

−1

+!

4-4/ 1;, 4,13- +3

x = (b G 7/

−1)(M

)/

/

−1)/1000

"# &! +/ /,+66 ,1.+?

,1 / - , / 1+

,, - , ! +/ 6,

/ ,+6 - χm3 , / 1+ m

6 ,

χm=χVm=μ0NAm2/3kT

?Q1 ,3 ,3 F, , < '!"3 +! $"=3

;,6

χ(ir)m =χ(ir)Vm=NAm2/3kT

/- m31.+/ ,- >/ μB3

m/μ = (3k/μ0NA)1/2μ−1(χmT)1/2

1 ?Q1 , 1F,

m/μ = (3k/NA)1/2μ−1

χ(ir)m T

1/2

3,/ ,- -,1μ , k, μ031NA/+%3+! )*3

4

m/μ ≈0.7977χm/

3

−11/2[T /

I]

1/2 ≈2.828χ(ir) m /

3

−11/2[T /

I] 1/2

+ - + ,! , -;,

.+1 11

-m/μ ≈2.828 (χmT)1/2

4 ,13 - ;, ,,3 χm T

- ,+6 +, ,

3

−1

1 I3

+314 ,1<6,1=,+6101,/

/ ;,101 4?Q1 < '!"3+! $"=!

2

@ , b 6, - +6 -, - ,/ mB 31

mS - ! mB -;, ,1 !

#! )3 %3 +!$(!

""

(145)

"# '! , F, , - /

√erg cm

!

1, -7 <= < '!" 64=! 10 - -7

+ / - 3+1 - +

- - 1! - , ,63

4 / +1, - , 1! ,

1 dyn = cm g s−2= 10−5N = 1 4ε0

Q2

(10−2m)2

-4 < '!"=

Q2 = 4ε0×10

−9 N m2=

μ0ε0×10−2 A2m2 =

c−02×10−2 A2m2

1 ,

Q= 1

10c0

A m = 10

ζ C

4 ζ ,6ζ =c0/(cm s

−1) = 29 979 245 800

< '!#1'!"3 +! "%1

$"=! , W G(2.997 924 58×10 9)

!

"# (! ,F,,-01/

√

erg cm cm−233

Fr cm−2! + - 64 -7 ,6

4,1

−2

W < ) 5

Gζ=

−2

! 43

−2

, - 01

/ ! 01/

1 Fr cm2 =

1 4ε0

×105

ζ

C m2

+' 4ε0×10

−9 N m2 = (10/ζ)2C2

3,

105C

4ε0ζm

2 =ζ×10− 6N

C

,1

−2

Wζ×10

−6

U

−1

!

"# *! , F, , - +Q6

3

D - /

+Q6

3

3 01 - G

2

+1, 1+ - < '!"3

+! $"=! +1/,- +Q6 61 -4D

1 cm3 = p

E =

(10/ζ) C 10−2m

ζ10−6V m−1 =ζ

−2105m2C V−1

,

3 = (105/ζ2) m2C2J−1

3 - 10 - ! ;,

/3 /! / / 64 , -

3

1

, !+Q6,

3

,F,

,(10

5/ζ2) m2C2J−1

!

"$

(146)

%

64 / - - - , +1/ ,!

.+ - , - 6 / +1/ !

+ ;, /3-41 11 6<=! ,

/3 -41 ,3 ,3 F, ,3 ,<,=3 , ,3

4 - ,! ζ , -

/ - ,6#* *'* #$% ()) Wc0G<

−1

=!

, -? , 6,1 + ,

,/1! @ +3 , +-1 ? ,! 43

-,646-,10,3 6,

!

, ,3 , F, ;,1 - -,

116,1/-7<=

, - / <>= / , - ,! / +

;,13-,6!

$ε0 = k

−1

es 6 4/ W /

1/2

W

3/2 /

1/2

−1

3

kes = 1

−2

/ W , + - , < '!"

64=! 6,16/116-,-/!

- μ0/4=kem > 6,/ >W1 1/2

W

1/2 /

1/2

−1

31

kem = dyn Bi−2= 13 , + - ,!

, -4/ 43 - + - -3 , - /D

- W 10

−15

- - / "! - +1 10

−15

3 /

/ , 13.1×10

−15

! 1X, + -

+Q6 α! @ α '!(

3

F, (17.8×10

5/ζ2) m2C2J−1 ≈

3.53 ×10−9m2C2J−1 ! 3

+1 +

(105/ζ2) m2C2J−1 , - +Q6 < .+ *

'! =! - / <4 W / ,1P - 10?

3 / DW ,1=3 / ++ +1/ +

74<4 /≈,1=! /,1-,

4 % 1/ ;,13-, +11!

, "# % ,

< ,=

</ ,= W )

−2

6 <,= a0 W$ε0

2/m

ee2 ≈%!#* ''# )(< (=× )

−11

]/T [ W )

−10

W W )

−6

W W )

−9

., ^ ≈ !))#× )

−13

- - W -W )

−15

W#!%$× )

−2

- - W # W)!")$(

1 W" - W)!* $$

W '&) 1W &)*!"$$

, W (%#

"%

(147)

, "# % ,

<,1=

, , ≈ !$*%*'( ')& * <)&=× ) 11

+ + ≈ "!)(%&'(× )

16 / !! ≈ *!$&)'"&× )

15

/ W#** '*# $%(

;, < ,=

2

6 W )

−28

2

≈ $)$&!(%&

2

W ))

2

W )

4

2

'

,6 < ,=

3

W

3 W )

−3

3

#

61 λ W )

−6

1 3

JW K

6 < = W %(!*('"

3

/ < = /< = W"!'(% $ # 3

/ < I= /< I= W$!%$& )*# 3

α

1 < ,=

1/

◦

W(/180) 1≈ < G%'!#*%'(= ,

W<G ) ())=1 JW < G&)= ◦

K

W<G&$( )))=1 JW < G"&))= ◦

K / / W(/200) 1≈ < G&"!&& *(=

7/ < ,= 7/

/ <F,= / W )

−3

7/

<,= me ≈ *! )*"(# &< &=× )

−31

7/

,01 ,3 DW ma<

12

=G # ≈ !&&) %"( (&<#(=× )

−27

7/

,31

/ γ W /

3 < = W / W )

3 7/ +,1<1,+= W)!$%" %*# "'7/

+,13 W)!% 7/

,<1,+= Q W#(!"$* %# /

,<= Q<= W" ! )" $'& (/

/ / W&$!'*( * /

< =!! 61/.,- !"36,-,166!

<#= , - !

"&

(148)

, "# % ,

1 < ,3 F ,=

, - /Eh ≈#!$ ((($ "#& %)%< &=× )

−17

, W&)

, W"&))

1 ≈(& $)) "

≈" %%&*%# $

16/ W )

−13

,

−2

11 - gn W*!()&&%

−2

-

-/<F ,= F W )

−2

4 < ,= W 7/

−2

%

1 <F,= W /

−2

W )

−5

, Eh/a0 ≈(!#"('## %< $=× )

−8

7/?-3 7+1 7/-W7+ W*!()&&%

"

5, < ,= B W 7/

2

−2

/<F ,= / W /

2

−2

W )

−7

B

<,= Eh W

2/m

ea20 ≈$!"%* '$$ '<'%=× )

−18

B

16/ WEh/2≈#! '*('# )*<"(=× )

−18

B U We·1U ≈ !&)# '& %"< $=× )

−19

B

3

W4.184 B

3

*

W$! (&( B %

◦

15 ≈$! (%% B

+ W ) !"#% B

> , >, W )%%!)& B

<"= 101 - ?1 +?1

111 ,61 - 1, 7+ ,/ ,

1/ #$D))D)) 7!

<$= ,6 1 ! *&'3

11 41,13 + *))1 6- 10 -

1! + *))!) ,1 "&%!#$# *( '* ≈ " %%& *#%!*( 1

6 )!%") + ,! 101 - 1D "*)3(&

;, "&%!#% 1P '%>-'3(& ;, "&%!#$#% 1P (.(& ;,

"&%!#$#) 1! 10 +1 F/ ! /

61 - / "&% 13 + - "&& 1P +

16 $ 6, 16 ))3 16 $))! @

"#)) ,1 + +3 6, ,

11- "#1 ,! ,/ ++

≈"! %%'× ) 7

! -, 113 +10-,1

,1 1!

<%= ++ -.1 ,+ ++!

"'

(149)

, "# % ,

+ < ,= W

−2

W 7/

−1

−2

+ W ) "#%

6 W )

5

W< ) "#%G'&)= ≈ ""!"##

/ W "!%*% ×*()!&&%× )

−2

≈

-, ""!"##

+,1+;, + ≈ &!(*$'%(× )

3

4 < ,= @ W 7/

2

−3

+ +4 + ≈ '$%!'@

+4 W'"%!$*( '% @

B

, B W 7/

2

−1

F , / W )

−7

B

, - :=h/2≈ !)%$%' &(< (=× )

−34

B

η

, W 7/

−1

+<F ,= W )

−1

+ W

ν

,

2

−1

7<F ,= W )

−4

2

−1

7 < ,= I

1/

◦

W<%G*= I &

1/ ,< ,=

◦

W I &

, B I

−1

,, W$! ($ B I

−1

JW

I

−1

K

<&=T / ◦

W<*G%=T /I! 3,+, t11 +,

;,

/ ◦

=T /I−273.15

+, tF , +, t ;,

F/ ◦

= (9/5)(/ ◦

) + 32

"(

(150)

, "# % ,

m

, B I

−1

W 7/ 2

−2

I

−1

+, W$! ($B I

−1

W J th I

−1

K

'm

,

3

−1

/ DW 'm- /

1 #'"! %I ≈##!$× )

−3

3

−1

1/Vm

,

−3

+ / DW GVm - /

1 #'"! %I ≈$$!&

−3

'

6;, < ,= >; W

−1

, W"!'× )

10 >;

- (

/< ,= F W B7/

−1

W

2

−2

1 W)!) F

!

< ,= W B7/

−1

W

2

−2

= 0.01 *

%

+ < ,=

,3 F,

−1

DW < )Gζ=≈"!""%&$× )

−10

)

6 <,= > W )

, eEh/ ≈&!&#" & ' (#<%'=× )

−3

,6 < ,= W

-7 <,3 F,= DW < )Gζ=≈"!""% &$× )

−10

)

, <6,6= > W )

+ / <,= ≈ !&)# '& %"< $=× )

−19

≈

$!()" # × )

−10

<'= 9/: ,-, - ,1 , - , ,

1! ,/12-12/38/1-16,

- /6/11!

<(= ,T/3 3+1 + +, ^ γ 1! W#!%(× )

−4

7/

−1

!

<*= -T/ ;, !

< )=ζ ,6ζ =c0/(cm s

−1)

W#* *'* #$% ())!

"*

(151)

, "# % ,

ρ , −3 W −3 ,3 F, −3

DW < ) 7/ζ

=

−3 ≈

) "!""% &$) *%#× )

−4

−3

, ea

−3

0 ≈ !)( #)# " '<*"=× ) 12

−3

'φ

< ,= U W B

−1 W 7/ 2 −3 −1 ,3 F, −1

Wζ× )

−8

U W#**!'*# $%(U )

L

−1

M e

−1/4

ε0 ≈ !$"* *&$ $%< "=× )

−7

U

, e/4ε0a0 WEh/e≈ #'!# "($ %<#"= U

W !))) "$U

W !))) "") U

(

< ,= Ω W U

−1 W 2 7/ −3 −2

W !))) $*Ω

W !))) $*% Ω

F,

−1

Wζ

2×10−9 Ω≈

(!*(' %% '('× ) 11Ω

)

κ σ

−1 W 7/

−1 −3 3 2 F, −1

W<10 11/ζ2

=

−1≈

) ! # &%) )%&× )

−10 −1 W 7/ −1 −2 4 2

F, DW <10

9/ζ2

= ≈ ! # &%) )%&× )

−12

)

* "

, U −1 W B −1 −1 W 7/ −3 −1 ,3 F, −2

DW ζ×10

−6

U

−1

W )

#!**' *#$ %(× ) 4 U −1 L −2 M e

−2/4

ε0 ≈ !$"* *&$ $%< "=× )

−5

U

−1

, e/4ε0a

2

0 WEh/ea0 ≈

%! $# #)& $#<$$=× ) 11

U

−1

< =, ;,7 - + ,/+Q6 -,1

,3 ,/ P ,//1 , 10

, - + ;, ,3 -

+ ;, +1 , ,

+1 , !

(152)

, "# % ,

* E

αβ3q

αβ , U −2 W B −1 −2

W 7/

−3

−1

,3 F,

−3

DW ζ×10

−4

U

−2

W )

#!**' *#$ %(× ) 6 U −2 L −3 M e

−3/4

ε0 ≈ !$"* *&$ $%< "=× )

−3

U

−2

, e/4ε0a

3

0 WEh/ea 2 0≈

*!' ' "& (#<("=× ) 21

U

−2

μ

, W

,3 F, DW <10

−1/ζ

= ≈ )

"!""% &$) *%#× )

−12

16 W )

−18

≈

"!""% &$) *%#× )

−30

LM3 1+/ e ≈ !&)# '& %"< $=× )

−21

, ea0 ≈(!$'( "%" )*<'"=× )

−30

!

αβ

αβeQ

, 2 W 2 ,3 F, 2

DW <10

−3/ζ

=

2 ≈

) "!""% &$) *%#× )

−14

2

L 2

M3;,1,+ e

2 ≈

!&)# '& %"< $=× )

−23 2 , ea 2

0 ≈$!$(& %% #$<"*=× )

−40 2 / α , B −1 2 2 W 2 W 7/ −1 4 2 ,3 F, 3

DW <10 5/ζ2

= B −1 2 2≈ ! # &%) )%&× )

−16 B −1 2 2 ) L 3

M3+Q6, 4ε0

3 ≈

! # &%) )%&× )

−16 B −1 2 2 L[ 3

M 4ε0 [

3 ≈

! # &%) )%&× )

−40 B −1 2 2

, 4ε0a

3

0 =e2a20/Eh ≈

!&$( ''' #'$< &=× )

−41 B −1 2 2 - #

<= /

, −2 W −2 ,3 F, −2

DW < ) 5/ζ

=

−2 ≈

"!""% &$) *%#× )

−6 −2 ) C# $ < *=

< ,= W B

−1 −2 W U −2 W @6 −2

/, <,3F,= F W )

−4

, /ea

2

0 ≈#!"%) % ' $#<#)=× ) 5

< #= , - , F, , - 1+ ,, + ?

Q1 1+ 6/;,13D

(ir) = 4

(153)

, "# % ,

C#

46< ,= @6 W B

−1

W U W 7/

2

−2

−1

.4 <,3F,= W )

−8

@6 JW F

2 K

*

,

−1

1 <,3F,= W< )

3/4

=

−1

"

<= /

,

−1

/, <,3F,= F W )

3 −1 " μ , B −1 W 2

,3 F, / F

−1 W ) 2 W ) −3 B −1

> / μB :=e/2me≈ $

*!#'$))* $*<()=× )

−24

B

−1

, e/me := 2μB ≈ !(%$() *)< &=× )

−23

B

−1

, / μN := (me/mp)μB≈

%!)%)'(" $"<$"=× )

−27 B −1 / ξ , B −2 W 2 2 2 7/ −1

F, / F

−2

W )B

−2

, e

2a2

0/me ≈'!(* )"&&)< "=× )

−29

B

−2

χ3κ

,

,3 F, %

χm , 3 −1 ,3 F, 3 −1 W ) −6 3 −1 & *

, W U

−1

W 7/ 2 −2 −2 F, 2 −1 Wζ

2×10−9

≈(!*('%% '('× ) 11

)

, W )

−9

< "= + 13 ,1 , - H

(ir) = 4

H3, H

(ir) = 1

H = (103/4)

−1

< '!"3 +! $"=! F, , 3/, 1

;,,!

< $= >/ μB 11 > <>!!=3 6, 11!

< %= + ,+6 ;,1 - , F, , ,

- χ

(ir) =χ

G$ P , 4χ

(ir) W )

−6

3χ W$× )

−6

< '!"3+! $"=!

< &= + ,

3

−1

,, + ?Q1 ,+6

6/ ;,1 χ

(ir)

m =χmG$ P ,3 - + - χ (ir)

m W −15× )

−6

3

−1

3

4 L− % /++M3χmW− !((× )

−10

3

−1

<'!"3 +! $"=!

(154)

% " " $

A< !#3 +!$= ;, - / ,, ,14 +

;, ,3 +, -, , <=3 7/ <7/=3 <=3

+ <= - /3 ,3 +! ;, -

-es64+4/Q1 1Q2,,31-0

/ -

2

em 64 1, - / 11 12 +1/

, I1 1I2 ,,3

es = Q1Q2/4ε0r 3

1 2

em = (μ0/4)I1 11×(I2 12×)/r 3

4 + 11, +1 <4 ||=r=! +

;, ε03 <- + - ,,=3 101

,

ε0 =

107/4c 2 0

7/

−1

2 ≈

(!(%$ (' ( '×10

−12

2

−1

B

−1

3 + ;, μ03 / <- +6

,,=3,

μ0 := 4×10

−7

−2 ≈

!#%&&"' )& $×10

−6

−2

! 12 ,ε01μ0 12, ,1,!

674,ε0 1μ0 1- , /61+- ,

/ kes 1kem 16;,- ,1;,

1,1 64! ,- μ0 , - 10 - +< "!"3 +!('=!

,- ε0 , -

ε0μ0 = 1/c20

4 c0 +1 -/ ,,< + %3+! )*=!

/3-4/ ,1 J $ K1 J $#K3 ;,-

1 /- 64

= k

Q1Q2

r3

1 2

=

k

k2

I11 1×(I212×)

r3

4 kes3kem k - /

k2·kes/kem =c20

1, - 16 -,

1 ;, , /! 11

, < ,= , </ ,= F,

1 - ,! k3kes1 kem , /

-4/ 6!

$"

(155)

% ) ,

k ζ

−1

kes 1/4ε0 ζ

2

−2

#

kem μ0/4 (1/ζ

2)

2

−2 α2

"3$

< =ζ ,6 ζ =c0/(cm s

−1)

W#* *'* #$% ())3+! "%!

<#=1/4ε0 Wζ

2×10−11

−2

2

−2

<"=μ0/4 W10

−7

−2

<$=α 0,, α

−1 =

"'!)"% *** <$&=< + %3+! )*=!

6 6,1/4'!$3 +! $& - + /?

/ ;, 64 ! +, F,

k =c0! /,3 / / - ;, /

'!$3 +1 - / ,, , c0 F, ! +

64 F, / '!$!

==323-&()'%/('6+

839 7% %+* +.+2%/

,36, <=3/</=3 11<=-/3

1 3+! -736 <

-1

364= - ,

/ 1,1 -, ,! + /

- + ,,3 + - - W /

−1

!

103 W< )Gζ= < + ' '! =! kes W

-/ 10 / 63 ;, W/

1/2

, , /

1/2

, - /! 67 -7 ,

,1- - ,- /!

8339 7% %/* +.+2%/

,3 6, /1 -/31! 6<6

>= - / , - , 1,1 -,

6 ,! / +1 , - > 84

13 + ,, - <- + /= - 1G!

10 > W ) ! kem W - / 10

/ - / 63 ;, > W

1/2

, ,

1/2

,- ,! 6/6,1+ +

, - ,!

83339 7% (*++3(&+.+2%/

F, , 1, 1! +

1 ,

1 >=ζ

−1

k

= 1

1 k

= 1

3, - k 11 6c0 /

.4 / 6! 6, k

+1 .- t 1x=c0t!

1

L-7M363-,-/4,//16F,//J $"K3,/

411+1! L,6M ,1- ,- /!

$$

(156)

83C9 7% (2-/35 *&32+ +.+2%/

- , J *K < "!*! +! *$=3 / / , -

/e3,,-eEh/34Eh17

1116#3//,-63a0301//,

Eh/ea03/8,.1,-/ea

2

0!

, ,11 "!*! '!#3 +! *$ "%! ,3

k= 13-4 k

= 1

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= 1k =α

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8C9 -&;'(23-&()3I%= 1*(&2323%+

, $ 1,1 10 - ε0 μ0 6, - +

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/ ;,- ,3,3 F, 1, D

D(ir) = 4D

H(ir) = 4H

χ(ir)e = χe/4

χ(ir) = χ/4

4 ,++ <=3 - / ?Q13 , - ?

+1/ ;, L?Q1M , ++1

LQ1M 1616!

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- / ,+6 '!$3 +! $#! + ε /

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, E = 1

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Q

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ea0

(Q/e) (r/a0)2

!

3

,-+1-/ ,+-0,,3

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, - k= 1!

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=k Q1Q2

/r 3

=Q1Q2/4ε0r 3

=Q1Q2/r 3

+ ,1 Q1/1+ ,,D

φ=kQ/r φ=Q/4

ε0r φ=Q/r

64 01/ +D

=−∇∇∇φ =−∇∇∇φ =−∇∇∇φ

11, / 16,ρ ,,<F, 4=D

∇∇∇ = 4k

ρ ∇∇∇ =ρ/ε0 ∇∇∇ = 4

ρ

1+ - /16,D

= ρ1V =

ρ1V =

ρ1V

,11+ ,,D

φ=k /r

3 φ=

/4ε0r

3 φ= /r3

/ - /16, 01D

E=Qφ− +· · · E=Qφ− +· · · E =Qφ− +· · ·

1+ 1,1 01D

=α +· · · =α +· · · =α +· · ·

+QD

=χ /4

k

=χ ε0

=χ (ir)

,+6 +D

ε= +χ ε = +χ ε= + 4

χ (ir)

1+

1 D

= /4k +

=ε0 +

(ir)= + 4

=εr /4kes =ε0εr

(ir)=ε r

+ - + + 13 A3+ dD

C=εA/4

k

d C=ε0εA/d C =εA/4

d

64 , ,,D

1 2

=

k

k2

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r3

2 =

μ0

4

I111×(I212×)

r3

2 =

I111×(I21 2×)

c2

0r3

/ + 1, , ,,D

1=

k

k I

1/r 1=

μ0

4

I1/r 1=I1/c0r

64 / 8,.11 / +D

=∇∇∇ × =∇∇∇ × =∇∇∇ ×

/ 8,.11, , ,,<>? 4=D

1=

k

k I1×/r

3

1=

μ0

4

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3

1=I1×/c0r 3

< = 1;, 1+ 1!

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∇∇∇ ×= 4

k

k ∇∇∇ ×=μ0 ∇∇∇ ×= 4 /c0

, /8, 1D

1=I1×/k 1=I1× 1=I1×/c0

/ 1+- , + -D

=I/k =I =I/c0

/ + ,1 / 1+,,D

=k

×/r 3

=

μ0

4

×/r 3

=×/r 3

/ - /1+/ 8,.1D

E=− E =− E=−

/ 1+1,1 / 8,.1D

=ξ+· · · =ξ+· · · =ξ+· · ·

/QD

=χ =χ =χ

(ir)

/ ,+6 +6D

μr= +χ μr= +χ μr= + 4χ

(ir)

/ 01/

1 D

=/4k

−

=/μ0−

(ir) = −4 =/4μrk

=/μ0μr

(ir) = /μr

1,D

=κ =κ =κ

-?1,- -, V n 41/+,/D

L= 4

kem

k2 μrn

2V L=μ

0μrn2V L= 4μrn 2V /c2

0

1 1,4D

∇∇∇ × +1

k

∂

∂t = 000 ∇∇∇ × +∂/∂t= 000 ∇∇∇ × +

1

c0

∂ ∂t = 000

64 01 /1/ +D

=−∇∇∇φ−1 k

∂

∂t =−∇∇∇φ−∂/∂t =−∇∇∇φ−

1

c0

∂ ∂t

.4 ;,D

∇∇∇=ρ ∇∇∇=ρ ∇∇∇

(ir)= 4 ρ

k∇∇∇ ×−∂/∂t= ∇ ×∇∇ −∂/∂t= ∇∇∇ ×

(ir)− 1

c0

∂ (ir) ∂t =

4

c0

k∇∇∇ × +∂/∂t= 000 ∇ ×∇∇ +∂/∂t= 000 ∇∇∇ × +

1

c0

∂ ∂t = 000

∇∇∇= 0 ∇∇∇= 0 ∇∇∇= 0

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1

c2

0 ∂2

φ

∂t2 =−4ρ

Δ−

k

k2 k

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∂t2 =−4k

Δ−ε0μ0 ∂2

∂t2 =−μ0 Δ−

1

c20

∂2 ∂t2 =−

4

c0

∇∇∇+

k

k k

∂φ

∂t = 0 ∇∇∇+ε0μ0 ∂φ

∂t = 0 ∇∇∇+

1

c0

∂φ

∂t = 0

/ 1- 1D

U/V = ( +)/2 U/V = ( +)/2 U/V =

(ir)+

(ir)/8

- 1/ 84</=D

=k × = × =

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/ / Q4<Q?-=D

=Q( +/k×) =Q( +×) =Q( +×/c0)

$(

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(161)

(162)

+ , / ,! 6-3 +

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< =,6117,-1/ 16,

+1 ,16, !

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, -* ,

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i=1

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i=1

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1/2

(

Y =AX1a1X2a2· · ·XNaN y=Ax1a1xa22· · ·xNaN uc,r(y) =

N

i=1

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<= -6,;,3X36116+66

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6 , - ;, X

i ,+1 a

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i ,1 74

!

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!

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(165)

(166)

66 <41 -1 - - /,+ - 41

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6! +1 413 , LM-

! 66 ,1 + ;, ,1 - +6 +1

11 6- ;,<!/! Ei - Q/3#!%3

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6 61?1,6

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++

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(173)

A , ;,1,+

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Q ++

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(175)

12

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^ ^?+ ++

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F ,,, /

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(177)

(178)

(

[1] ,- 61 / - A,

<= 1!3 ! !F! & &3# D −"(3 *')! <6= #11!3 ! !,! >,4313 *'%!

<= "1 1!3! !@2! & &3% D −"&3 *'*!

<1= !!@2! ++1 −0 - 11 A,!

& &3% D"'−$ *'*!

<= !!! ++1 −03/ 61

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<-= B!71 !+! ++1 −03 / 16

1 1,- ! "D 103 /

6 -/ +! & &3% D # "− # (3 *'*!

</= ! I71 B!! I! ++1 −03 / 16

1 1,- ! $D / /! & &3

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<= !!>,4 B! D/, ! & &3$&D' −*)3 *'&!

<= !! ++1 −,! & &3

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:11: 13 6,1

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<7= I!B! 1! ++1 U−6 1/ I!

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& >743 -13 13 *((!

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<= , % D U! &37/ D

I 7I73 43 *((!

<1= ! 1! 7/+> -*E > BF>& 7T71h3 >,1+3 **)!

<= I!I,,! & I13

73 ** !

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& HIJK (3 , ! !!!!−#% < ? ('− =

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[5] 113

/Q- 11Q3 F34Q1

<= " −)D **#3 A, 1,−)D F++

<6= " − D **#3 A, 1,− D +1

<= " −#D **#3 A, 1,−#D 11 1+

<1= " −"D **#3 A, 1,−"D

<= " −$D **#3 A, 1,−$D

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1

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<= " −(D **#3 A, ,− (D ?

,+

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1

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1 /

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<+= " − "D **#3 A, ,− "D +

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J# K B! ,! - F,+ /! & $ 8$93

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! U 133 *$&!

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(181)

J#'K F! Q6/! '& %%%& "

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(182)

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(183)

J%'K ! ! ! ! @/! 11 11 - +/

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(184)

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5

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(185)

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(186)

J )*K ! ??/! ,1/ D /

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(187)

J ##K I!B! !1 !!!! /

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++ - **'! & &3')D# '\#"%3 **(!

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( $! , - **%!

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! !!! / @/ +

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-133

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(188)

J "(K B!!!1!U! ,;,1,+

-115

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-201

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16/3 **)!

''

(189)

(190)

!

, 2"! ,

3 A3α +

>3 B3β >

Γ3 3γ / F

Δ3 δ

3 E3 +

S3 Z3ζ Q S

3η H3η 3m3

Θ3ϑ3 ϑ3θ

3 I3ι

I3 3κ K33 7++ I #

3 3λ 61

3 M3μ ,3 <=

3 N3ν ,3 <=

Ξ3 ξ ^

3 O3o

Π3 3π +

3 P3ρ

Σ33 σ3 / #3 "

3 T3τ ,

3 Y3 ,+3+

Φ33 φ ϕ3φ + #

^3 X3 χ

Ψ3 3ψ +

Ω3ω ω / $

< = ;,6+,1Fm!1F7+,?

- η +! -3 ;,

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<#= 7++3 / + <

1 LM+/=!

<"= - / ,1F7 -41!

<$= < = / +,1 / !

'*

(191)

(192)

" #

(193)

(194)

, - ,63 "

3"

("

(195)

($

(196)

)

2 92 927

−3

927

−5 ≈

@?<:@6;×10 −6 ≈

B?877:6×10 −3 ≈

2?=87;<×10 −4

2) 927

3

92 927

−2 ≈

@?<:@6;×10 −3 ≈

B?877:6 ≈7?2=87;<

2 927

5

927

2

92 ≈7?@<:@6; ≈B87?7:6 ≈2=8?7;<

2 9272;68 9272?;68 92?72;68 92 9B:7 ≈2=?:@8@

2 ≈2;;?;66 ≈7?2;;;66 ≈2?;;;66×10 −3 ≈

2?;28B@×10 −3

92 ≈2?@;;:<×10 −2

2 ≈:<@=?B: ≈:?<@=B: ≈:?<@=B:×10 −2 ≈

:?<7=:7×10 −2 ≈

82?B2=@=

.+ - ,- 6D ≈)!*(&*#" ≈ ""!"##

,L / W 2×10

−7

3 +! "(!

(197)

(198)

hν = hc ˜ ν = kT Em = NA E ˜ ν ν E Em T − 1 Eh − 1 − 1 − 1 b = ! × 10 4 "# $$# × 10 − 5 % "$ × 10 − 4 $!!# %%! × 10 − 6 # ## × 10 − 3 "! $$ × 10 − 3 $%" ! b = %%%! #$ × 10 − 5 ### &# × 10 − 10 $%! ## × 10 − 9 ! "%& × 10 − 10 %& %% × 10 − 7 !% & # × 10 − 8 $ % × 10 − b = !& %$ !& & × 10 9 #$ !& & % % #&$ $%%# $ #% × 10 4 b = "&#!!$$ $ " × 10 8 &#& %# $ % × 10 − 2 #$"! %$ %&#& !! #& $! × 10 4 Eh b = $ $# #! #"$ × 10 9 $%! $$ %" #!!&& # !&! %! $ × 10 5 − 1 b = "%!% $ !&# &# × 10 6 ##& !% × 10 − 3 &%# $ × 10 − 2 %"&" × 10 − 4 &% &&! & − 1 b = %$ !! &$" !% × 10 7 #$ #! × 10 − 3 $%%# $& × 10 − 2 !% #& × 10 − 3 $"$ !&%" b = &#! &%! # &"% ##$ × 10 4 %"& #! × 10 − 5 "# %$% × 10 − 5 %## "! × 10 − 6 "%$ $ % × 10 − 3 " & × 10 − 3 b = )(* * ) + , -+ ) *+ ,+) -+ + '( )+ +) */++ ( ( (+ #1 ! '( ) + (+) ( +* ( ) ) + ( !1 & '( ) *++ + ) + )++/ ( ) (+) b = !& %$ − 1 b = #$"! % $ − 1 ( *+ + ( )+ ) (1 aJ ) h b = 10 − 18 J 6 . 626 069 3 × 10 − 34 Js b =1 . 509 190 × 10 15 s −

1 b=1

. 509 190 × 10 9 MH z − 1 (1 cm − 1 ) hc

„ e e « b=

(199)

(200)

Changes made to the draft of the Green Book (GB) dated 2005/JUL/03

Listing prepared for the GB Reviewers by Jăurgen Stohner

just@ir.phys.chem.ethz.ch

As of 26 October 2005

1 General Matters

The entries in the table of section display changes applied to the 2005/JUL/93 draft of the Green Book which has been distributed at the Beijing Meeting 2005 (IUPAC GA) Only those changes are listed which go beyond corrected typos and changes of the layout Some of the changes have been made in response to pre-reviewer’s comments.

Please note that a line numbering has been introduced to facilitate your work For technical reasons, tables etc are not line-numbered; however, lines in tables can easily be named by the proper keyword An empty page can show a single numbered line, but this is for technical reasons and will not appear in print.

The Subject Index is missing Indexing will make the electronic version of the manuscript almost unreadable The index will be prepared when all points raised by the reviewers are discussed and settled This will be the very last step of editing the GB manuscript.

1 Reference to theNotes in the Tables is now consequently written as ‘see note x’ instead of ‘see

footnote x’ The term footnote is reserved for real footnotes to running text, as for example in section 7.1

2 Nucleă has been replaced by nuclei in the whole manuscript. 3 A consistent writing of sums with the lower index

i

instead of

i or

has been introduced for entries in the tables of the whole manuscript (where applicable). 4 After receiving the new IUPAC periodic table (now dated October 2005), the Secretary of

Commission II.1 was contacted about the new atomic weights The minutes of Commission II.1 from the Beijing Meeting were received and the few corrected atomic weights have been considered in section 6.2 After completion of the II.1 manuscript we will receive a copy to complete the now incomplete citation [123] in the submitted draft The atomic weights in section 6.2 are now consistent with those appearing in the new IUPAC periodic table.

5 Please note an error in the Commission I.1 Beijing Minutes: Based on a misunderstanding, it

was stated that the GB draft dated 2005/JUL/03 needs anupdateof the fundamental constants

and the atomic masses or weights (chapters and 6) By the time of the Beijing meeting, both chapters in the distributed draft were up-to-date (which can be seen by inspecting the list of references cited) The year of publication of ref [107] in the draft is misprinted and should read 2005 and the fundamental constants are therefore the most recent (also currently

1

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