Спектроскопия молекулярных взвимодействий. Нелинейные эффекты 985-445-751-6

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. .

Ы . Ы Э

Ы

уч

Г

я я ы . ы [Э ы ]: . — Э . (2,03 ). — .: “Э я БГУ”, 2004. — : http://anubis.bsu.by/publications/elresources/Physics/gorbatsevich.pdf . — Э . я . , 2002. — PDF , я 1.4 . — . я: Adobe Acrobat 5.0 ы . ы .

.К. э .

И «Э

К я

БГУ»

2004

©Г © «Э

.К. -

я

БГУ» www.elbook.bsu.by [email protected]

. .

Ы . Ы Э

И Б 2002

К

Ы

К 535.37

я ы. –

. . ы э

. 150 . ISBN 985-445-751-6.

я ы , 2002. –

.: Б

И -

. , ,

,

.

. ,

, ,

И . 76.

. 4. Б

, .

.: 209

.

, -

С.А.

И .А. емкович

ISBN 985-445-751-6

,

аскевич Б

, ,

© .К. © Б , 2002

, 2002

-

И Л ВИ И ,

, .

-

,

,

. .

.И . 60-

.

. .

.

-

,

-

, .

,

-

. Ф ,

. , ; ,

,

.

3

. -

.

,

,

,

-

. Э

, .

–

, ,

. .

,

, -

. ( )

.

-

. -

, .

. И.

И.

.

,

-

, ,

-

.

4

_

1.

(

) (

) . .

[1, 2]. -

. 1.1.

,

,

[3]. -

, . .

-

– ,

. , [1]. (

)

-

. , 5

W, ∆W

.

.

∆ν a ( f ) =

∆W a ( f ) , ∆W a ( f )

[

]

[4–9]:

1 ∆W a ( f ) + ∆W a ( f ) + ∆W a ( f ) . hc ∆W a ( f ) –

(1.1) -

,

,

-

.

µi ,

αi (

i-

),

, ,

, ( -

∆ν a ( f )

[1]. ), ,

,

-

. . -

[10], ER .

,

,

a (

-

), . , –

n.

-

,

µi :

ER ~ µi . -

[5, 6, 12, 13], 6

ε [10, 11] , i-

(1.2) -

∆ν a ( f )

: hc∆ν

a( f )

(2n + 1) = (n + 2)

2

2

2

2

 a( f )  ε − 1 n2 − 1  n2 + 1  n2 − 1   − 2 C1   + C2 n 2 + 2  + C3 2n 2 + 1 + 2 ε + 2 + n    

(

C1a = 2µ g µ g − µ e cos ϑ

ϑ –

C2 =

(

µ 2g

n2 − 1 . n2 + 2

+ C4

− µ e2

)a

1 3

G µg

) 13 ,

(

C1f = 2µ e µ g cos ϑ − µ e

a

, C3 =

(1.3)

ne 2 f

8πnν 0 a

3

G µe

(

) 13 , )

a

, C 4 = C 4′ α g − α e , , αg

αe –

-

, ν0 – ,

, C 4′ –

, f– . , . -

,

Э

, [12]:

∆ν

a− f

= ∆ν − ∆ν = ∆C a

f

∆C a − f = C1a − C1f =

2 hca

3

 2n 2 + 1     n2 + 2   

a− f

(µ

2 g

2

 ε −1 n2 −1     ε + 2 − n2 + 2  ,  

)

+ µ e2 − 2µ g µ e cos ϑ .

(1.4)

(1.4),

-

( ε ≈ n 2 ) ∆ν a − f ≈ 0 [12]. [13, 14] : 7

,

f (ε, n ) (1.3, 1.4) ,

ϕ(ε, n ) -

hc∆ν a ( f ) = C1a ( f ) f a ( f ) (ε, n) ,

(1.5)

hc∆ν a − f = ∆C a − f ϕ(ε, n) .

(1.6)

∆ν a − f ∆ν a ( f ) ϕ(ε, n) f a ( f ) ( ε, n )

-

[13, 15, 16].

-

[13, 17]. , µ g , µe , ϑ

, ,

,

, . .(

,

.,

[18–20]). -

, , -

, . "

[21–23]

,

–

"

,

,

-

.

N

-

. Э ,

∆ν a ( f )

, .

-

. , ∆ν

kT, a( f )

[22]:

hc∆ν a ( f ) = C1a ( f ) ϕ

(

)

+ C2ϕ

+ C3 ϕ e

+ C4ϕ g

.

(1.7)

C1a ( f ) = ± µ 2g − µ g µ e cos ϑ , C 2 = µ 2g − µ e2 , C3 = −α e , C 4 = −α g , 8

ϕ ϕ

1 2 1 2  ⋅ ⋅ µ , ϕ 6  3 kT   i =1 ri

=∑ N

)

N

1

6 i =1 ri

⋅α,

1  3 I u0 − hcν f I v0 2 = ∑ 6 ⋅ 0 ⋅ α + µ , 0 f + − ν 2 I I hc  n =1 ri  u  v

(

N

e

ϕ

(

=∑

)

1  3I u0 I v0 2 = ∑ 6 ⋅ 0 ⋅ α + µ , 0 r 2 I I + n =1 i u  v  N

g

(

)

, α

r– , I u0(v ) – (

). , ,

-

,

, [24]

-

[21, 22]

-

. , :

2 2 2 µ g (e) µ < U >= − , 3kT r 6

(1.8) ,

, . .

µ g (e)µ ri3

)2  ρ(∆ν) ~ exp− .   2∆ν a − f kT ,

(1.10) σ,

0-0σ=

-

-

:

1 ∆ν a − f kT . h

(1.11)

,

[36–39],

,

, -

. 10

ρ(∆ν)

ρ(∆ν) ,

, (1.11) [30].

,

[33, (1.11) -

36]. ( (1.12),

), < ER >

-

[36], µ g (e) .

1.3.

, -

. τe

τR .

τR ),

τe ( τ e >> τ R , ( τ e exp− , kT   . ,

, , .

, .

-

[79],

 ∆Wsum  exp− ; kT   .

"

-

, -

" ,

, G (E , θ )

, 0-0,

τ e >> τ R ).

ρ(∆ν) .

, [77]. < ∆ν >

–

16

,

, . .

(

ρ(∆ν)

-

G E,

,

σ– ρ(∆ν) .

1 ∞ π 2π 2π < ∆ν >= 2 ∫ ∫ ∫ ∫ ∆ν( E , θ) ⋅ G ( E ,θ) sin θdEdθdα1dα 2 , 4π C 0 0 0 0

(2.5)

π∞

C = ∫ ∫ G ( E ,θ) sin θdEdθ .

(2.6)

00

(2.2), (2.3)

(2.5) < ∆ν a > =

–

 < U g >  µe  cos ϑ − 1 .  h  µ g 

< U g >= σa

: 2

1 ∞π ∫ ∫ µ g E cos θ ⋅ G ( E ,θ) ⋅ sin θdE dθ . C 00

(2.8)

ρ a (∆ν)

-

σ 2g µ e µ 1 = 2 ( cos ϑ − 1) 2 + 2 σ12 ( e ) 2 sin 2 ϑ , µg 2h h µg σ12

=< E

2

> µ 2g − < U g2 (2.9)

G µg

,

G E

(2.9) -

;

Ue ,

:

0-0-

σ 2g = < U g2 > −(< U g >) 2 – ,

Ug

(2.7) ,

,

σa

:

c ∆ν a ,

, >. , -

.

ρ(∆ν) ( µ g , µ e , ϑ , µ , Ra , rs , T ),

.

: , 17

. ,

, :

X=

µgµ 1 , Ra3− s kT

(2.10)

Ra − s – (

-

, ,

).

,

< U g > , σg

(2.11), ,

,

σ1

~ ~ Ug , σ g

~ , σ 1

µgµ Ra3− s

,

-

X

.

Ra3− s ~ , U g =< U g > µgµ Ra3− s ~ , σg = σg µgµ ~ = σ Ra − s . σ 1 1 µgµ 3

(2.11) -

Y=

µ2

rs3− s

⋅

1 , kT

(2.12)

X,

(2.12) rs − s – .

. ,

X 18

Y

-

,

.

Y–

X

-

kT -

( )

. -

,

~ ~ Ug , σ g

~ , σ 1

3%). ~ U g = 15.92 ⋅ {1 − exp[− F ( X , Y )]}.

(

(

~ ,σ ~ σ g 1=

(

(2.13)

).

A + exp − Q 2 ( X , Y )

)

0.199

(2.14)

1 c1 + c2Y + c3Y 2 = + X ⋅ [c4 + c5 exp(c6Y )]. (2.15) F X (2.16) A=b1+b2Y+b3Y2 , 2 2 2 2 2 2 1/Q(X,Y)=d1+d2X+d3X +d4Y+d5XY+d6X Y+d7Y +d8XY +d9X Y . (2.17) (2.14–2.17), bi, ci, di, . 2.1. (2.13) (2.14) 0 ≤ X , Y ≤ 14.5 . 2.1 я

i

ci

1 2 3 4 5 6 7 8 9

–1.598 –2.635 –0.146 0.02696 0.0449 –1.38

~ σ g

0.07429 0.03774 1.235 10-3

, bi

я я (2.13–2.17)

~ σ 1

~ σ g

0.0530 0.0257 –8.1 10-4

0.3975 0.0786 3.13 10-4 8.13 10-4 –4.2 10-2 1.16 10-3 1.14 10-3 2.84 10-3 –7.7 10-5

Ra − s = rs − s

di

~ σ 1

0.3838 0.0367 0.00137 –2.64 10-3 0.0176 –9.67 10-4 5.17 10-4 1.41 10-3 –8.4 10-5

n, , 19

12.

-

Ra − s ≠ rs − s

, ~ ~ Ug , σ g

,

~ ) σ 1 Ra − s ≠ rs − s

G (E , θ ) (

-

n,

-

.

)

, ( Ra − s

,

. .

n = 12. ,

 R  n ≈ 31 + a  . rs   , n 12

,

~ σ 1

~ σ g

(2.18)

Ra − s ≠ rs − s n 12

= rs − s , -

~ Ug

.

,

-

(

),

[77],

. ,

-

, .

0-0-

, . 2.2.

ρ a ( f ) (∆ν) . [38]

ρ (∆ν) a

ρ (∆ν) ( ) f

ρ f (∆ν)  ∆ν  = const ⋅ exp − . a ρ ( ∆ν )  kT 

20

, ,

-

(2.19)

ρ(∆ν) .

-

, . . ( [33, 36–38]). G G µg µe

,

, -

.

, .

:

(

)

 µ 1 1 < ∆ν a >= − < Eµg > µ e − µ g = < U g >  e − 1 ,   µg h h  

(

)

 µg 1 1 < ∆ν f >= − < Eµe > ⋅ µ e − µ g = < U e > 1 − µe h h  σ a( f )

  . 

-

(2.20)

(2.21)

σ g (e)

δEµg (e)

-

:

µ 1 σ a = δEµg µ e − µ g = σ g e − 1 , h µg

(

µg 1 σ f = δEµe µ e − µ g = σ e 1 − , h µe

δEµg (e ) = < Eµg ( e )

)

2

(

)

2

< Eµg (e ) > ρ a ( f ) (∆ν) ,

,

(2.23)

> − < Eµg (e ) > .

,

[33, 36].

(2.22)

ρ a (∆ν)

µ g (e ) .

(1.2) ρ a ( f ) (∆ν) .

-

, ,

21

(2.19) ρ f (∆ν) − , . . σ f = σa . ,

∆ν a− f

38]. δEµg (e )

σ a( f )

(1.11) [33, 36–

(1.2),

, -

. σ f = σa .

~

(1.11)

1 , T

(2.22), (2.23), , . . : ∆ν a − f ~

1 . T

σ a( f ) 0-0-

(2.24) σ a ( f ) (T ) = const .

(2.24) -

: (2.25)

,

, . .

ρ 1.

a( f )

" ,

(∆ν)

" σ f = σa .

ρ a (∆ν)

2.

,

-

ρ f (∆ν)

-

:

. σ a( f ) .

3. 0-0-

, ρ (∆ν) a

, 1–3.

ρ f (∆ν)

,

2.1. 22

. 2.2

-

20

~ Ug

~ σ g

3

1

15

1’

2

2

10

3

2’

4 4’

1 5

5

0 0

3

6

9

3’

5’

12

0 0

15 X

~ U g (a)

. 2.2. ’

6

9

~ ( ) σ

12

15 X

X.

Y=0 (1, 1), 1.45 (2, 2 ), 2.9(3, 3 ), 4.35 (4, 4 ), 14.5 (5, 5’)

µ

~ Ug (X ) ( Ra − s

< Eµg ( e) >

. 2.2 ) ~ Ug G µg

’

3

~ (X ) ( σ g G µ e ).

’

. 2.2 ). G µ g (e) ,

1

(Y=0).

. 2.2,

~ Ug (X ) , . .

~ ~ δE g ( e ) ( σ µ g 1 ’,

-

X

µ g (e) ,

, (

T = const ) X >1 ~ U g (X ) (

(

. 2.2 , .

1 . T µ g ( e) = const )

δEµg (e )

~ , σ g

-

(

X

µ g (e) X.

-

, , ~ σ g

. σ f = σa ,

(2.11), (2.23), (2.24). σa > σ f

,

,

0-0µe > µ g (

-

.

. 2.2).

,

,

0-0(1.11)

(1.12),

,

< Eµg ( e)

-

X

[33, 36], [36], > µ g (e) . [80], µ g (e) ( -

, 24

a ρ (∆ν) ( . . 2.3). a ρ (∆ν) , . -

1.0 0.8

ρ(∆ν)

,

0.6 0.4 0.2

2

1

0.0 -2 0 –3 ∆ν ⋅10

-4

0-0-

. 2.3.

-

2

4

–1

0-0(1), (2). µ g = 10 , µ = 1.7 D;

Ra = 3 , r = 1.6 Å; X = 4.36

. -

, ,

-

σg

-

. . ,

. 2.4 , .

µg ,

(

(

. 2.4,

1, 2).

, σg

,

σg

-

σ g (T ) ,

3–4). . 2.5

.

, 25

1.2

σ g ⋅10–3

–1

σ g ⋅10–3

1.0

–1

5

1.0

4 0.8

4

0.8

0.6

3

0.6 0.4

2

0.2

1

0.0 150

200

250

300

σg

. 2.4.

3

0.4

2

0.2

1 0.0 150

350 T, K

200

250

σg

. 2.5.

-

300

350 T, K -

.

. µ g = 0.5 (1), 2 (2), 3 (3), 5 (4),

. . µ g = 0.5 (1), 2 (2), 3 (3), 5 (4),

10 D (5); µ = 1 D; Ra = 3 , r = 1.6 Å

10 D (5); µ = 1 D; Ra = 3 , r = 1.6 Å

σg .

< Eµg (e ) > , ,

,

0-0-

µ g (e) ,

.

0-0-

. σa( f ) ,

,

,

"

"

-

. 2.3.

Э 0-0, ,

. –1

,

26

-

3⋅10 –4⋅10 , 3

σ

(1.11) 600 –1.

3

–1

. -

, . ρ (∆ν) (

[81]

-

a

),

-

(

.

)

:

I f ν ex , ν reg = const ∫ ε 0 (ν ex − ∆ν )I 0f (ν reg − ∆ν)ρ a (∆ν )d (∆ν ) ,

(

+∞

)

−∞

I f ν ex , ν reg –

; ε 0 (ν ) -

-

,

I 0f (ν) – "

(2.26)

" . (2.26) . ,

(

[82], . . I f ν ex , ν reg

-

) ρ(∆ν)

, . ., 0-0[40, 83, 84].

, , ,

[40, 83, 84]:

< ν f >= const − σ 2

ρ a (∆ν)

dφ(ν ex ) 1 ⋅ , dν ex φ(ν ex )

27

. . – σ. -

(2.27)

φ(ν ex ) – . . 2.6

3-

-N1, 2), 3) -

123 K ( ( 4) [80]. Э

(

. 2.7.

dφ 1 ⋅ ( dν φ

1).

,

[85–87]. 2)

123 K (

6 . 2.7.

, T=223 K (

3) -

0-0-

.

. 2.7,

,

σ a = 535 6 I f,

, ρ a (∆ν)

–1

3-

-N-

,

– 160 – 220

.

–1

.

,

,

–1

< ν ex > ⋅10–3

.

1.0

–1

20.8 0.8

3 1

2

4 20.4

0.6 20.0 0.4 19.6 0.2 19.2 0.0 14

16

18

(3) 3-

-N-

20

24 26 ν⋅10–3 –1

22

(1, 2)

. 2.6.

(4). ν ex =24 520 (1), 22 760 28

, T = 123 K. –1

(2)

,

,

< ν > ⋅10 −3

21

ρ a (∆ν)

1

2

20

-

−1

19

- 18 -

.

3

17 -10

0-0-

-8

-6

-4

-2

0

. ,

dφ 1 ⋅ dν φ

3-

-N-

-

(1), (2) 6 (3). T = 123 (1,2) 223 K (3)

,

τ R >> τ f .

-

. 2.7.

0-0-

. .

2

dφ 1 ⋅ dν φ

-

,

,

,

. ,

–50 º 3,

,

,

τ R ~10

6

,

-N-

, [80],

–10

[50].

. , , ,

. ,

,

, -

10–15 º . 29

ρ(∆ν)

, τ R σ f

σa ρ (∆ν) a

0-0µe > µ g .

σf

,

, -

. 2.2

3-

-N-

ρ f (∆ν) ,

"

" ,

. .Э ,

,

(

σa > σ f

.

(2.22),

(2.23)), ,

, , . . δEµg > δEµe .

,

( σa > σ f )

, 0-03-

-N.

я 0-0-

я

2.2

я σa ,

3–1

1 920 1 440 1 660 32

-N-

σf

–1 ,

540 550 420

2.4.

,

-

,

τR , τ d (1.12, 1.13) [42, 44].

, -

" "

[60–62] [63–65], [66–69].

, :

,

,

. ,

,

– µE0 =

4kT δt , ξ

,

,

G µ

-

δt . :

ξ–

. 34

µE0 = ∫ − µEei cos χΨei (χ, t )sin χdχ , π

0

< U e (t ) >= ∑ < U ei (t ) > . n

< U ei (t ) > –

i =1

i-

.

G µe < U e (t ) >

Ψei (χ, t

-

ψ ie (χ, t ) .

δχ st

,

ψ ie (χ, t + δt ) , ,

-

< ∆ν f (t ) > ,

(2.21).

< (δχ st )2 > = ,

-

G µg

.

δt ,

(2.31)

-

1 < β 2st > . 2

ψ ie (χ, t ) → :

 (δχst ) 2 ξ  1 −∞ i + δt ) = ∫ Ψe (χ − δχst , t ) exp− kT δt d (δχst ) . C +∞   δt , G Eei , :

Ψei (χ, t

  µEei sin χ  µEei sin χ 1 i  δt  . + δt ) = Ψe  χ − δt , t  ⋅ 1 + C  ξ ξ    ,

(2.32) (2.33) ψ ie (χ, t = 0)

ψ ie (χ, t = ∞) ,

,

(2.32) -

(2.33) -

. 36

ψ ie (χ, t = 0) –

(" "

")

.

(

. - 1.0 - 0.5 -

"

,

1.5

~ - ln < U ei (t ) >

.

4

3

) 2

1

. i-

- 0.0

0.0

ψ ie (χ, t = 0)

τ DR

0.5

1.0

-

ψ ig (χ) ,

(2.30).

ψ ie (χ, t ) (2.32), (2.33). ( . . 2.10),

. 2.10. i-

-

µE = 0.01 (1), 2(2), 3.6 (3), 4.8 (4). kT τ DR – ,

.

i e

, , :

 t  < U ei (t ) > − < U ei (∞) > ~i −  . exp < U e (t ) >= =  τi  < U ei (t ) > − < U ei (0) >  r

, τD R – (

.

-

(2.34) ,

τiR

Eei

-

µEei kT ,

,

-

< ∆ν f (t ) > ,

< U e (t ) >= ∑ < U ei (t ) > , n

-

i =1

θ′

Ra − s

, G µe

,

, :

Eei ( R, θ′) =

µe

Ra3− s

-

3 cos θ′ + 1 .

(2.35)

, .

-

,

,

θ′

, . .

-

Eei

. ,

8

 τ iR   D   τR 

−1

K

8

2 6

6

6 5

1 4

4

2

2

4 3 2

3

1 0 0

1

2

3

4

0 0.0

5 µEei kT

-

0.5 (2).

0.8

1.2

t τ DR

. 2.12.

. 2.11.

.

0.4

.

4, 4, 10 Å. . µ e = 0.01 (1), 2(2), 4(3), 6(4), 8(5), µ 10 D (6). e = 2, µ = 1.7 D µg

µe = 2 (1), µg

(3) 38

,

,

.

,

,

-

, .

, .

,

. 2.12. , -

, .

, (2.36),

:

K (t ) =

d   ν t − ν ∞   . ln dt   ν 0 − ν ∞ 

.

(2.36)

,

-

µe .

, ,

, Eei

(2.34),

,

,

, -

. , . , ,

(

)

,

.Э "

" -

. [96]. , , ,

. Э

,

[97]

. [98], 39

-

, . .

-

.Э ".

"

,

∆ν a (2.20)).

Ug ,

0-0-

(

.

-

, .

,

-

, . .

,

,

ψ ig (χ,U g )

,

,

ψ ig (χ,U g ) ,

-

( Ug .

) ,

χ

i-

(2.30))

G E gi (

,

Φ (g−i ) (U ) .

,

iΦ (g−i ) (U )

-

. j+1

Φ (gj ) :

Φ (gj +1) (U )

(U )

, , ,

j

1 +a ( j)  U′ = ∫ Φ g (U − U ′) ⋅ exp− dU ′ , C −a  kT  40

.

n–1

U g + µ E gi cos χ .

,

-

,

-

(2.37)

a – j+1,

. (2.37) n–2

( i-

)

Φ (g1) (U ) = Φ (g−i ) (U ) .

Ψgi (χ,U g )

,

1  U  ⋅ exp−  , C  kT 

(2.38)

ψ ig (χ,U g )   µE gi 1 i i cos χ . = ⋅ Φ g (U g + µE g cos χ) ⋅ exp C   kT G G µg µe

(2.39) , . .

Ψ ie (χ,U g , t = 0) = Ψgi (χ,U g ) . (2.32)

Ψ ie (χ, U g , t ) . < ∆ν f (∆ν a , t ) >

(

(2.40)

(2.33),

-

(2.31)

)

< U e U g ,t > ,

(2.20)

(2.21).

< ∆ν f (t ) >

∆ν a .

,

, .

. 2.13 < ∆ν f (t ) >

∆ν a .

f ∆ν eq ,

ρ f (∆ν ) . 2.13 ,

-

.

∆ν > ∆ν ∆ν a < ∆ν f a

f

, , 41

-

-1.0 -1.3

< ∆ν f > ⋅10–3 1 2

, , . . µe > µ g ,

3

-1.6

6 4

-1.9

5

-2.2 0.0

-

[98].

–1

, -

< U e (t ) >

0.1

0.2

0.3

0.4

-

µe < µ g –

0.5

t τ DR

, (

.

(2.21)). -

. 2.13.

. a ∆ν = −1.01 (1), −1.18 (2), −1.38 (3), −1.86 (4), −2.11⋅103 –1 (5). ∆ν eqf = −1680 -1(6). Ra = 4, rs = 4Å.

.

( µe > µ g )

2.14

. 2.14

( µ e < µ g ),

µ g = 3, µ e = 4, µ = 1.7 D

.

,

[98–100],

,

. .

-

, (

G µg

G µe

,

-

).

( ∆ν a < ∆ν eq f )

, . .

-

, .

,

< U e (t = 0 ) > < U e (t = ∞ ) > .

< U e (t ) > ,

( , 42

-

, µe < µ g ,

,

).

,

-

. , . (

.

-

(2.21)). -

, .

(

)

. 2.14 f ∆ν a → ∆ν eq

K t = 0, ∆ν a (

1).

, . .

1

, .

-

. 2.14 ,

∆ν a , . .

-

. , ,

. 2.11.

µ E ∆ν f

K 7

0.4

3 1

6

τ′R τ DR

2 0.3

5

1

4

2

0.2

3 2

0.1

-2.2

-2.0

-1.8

-1.6

-1.4

∆ν a > ∆ν f

∆ν a < ∆ν f

K

-1.2 -1.0 -0.8 ∆ν a ⋅ 10 −3 −1

7

0.4

3 1

6

1 2

0.3

5 4

0.2

2

3 2

0.1 1.2

. 2.14.

τ′R τ DR

1.4

τ ′R (2)

1.6

1.8

K (t=0) (1) ∆ν a .

2.0 2.2 ∆ν a ⋅ 10 −3

−1

ρ (∆ν) (3). a

-

µ g = 3 (a), 4D ( ); µ e =4 ( ), 3D ( ). R = 4, r = 4Å, T = 300 K, n = 12, µ = 1.7 D. 44

,

τ′R . 2.14 ),

. ,

,

f ∆ν eq

( . τ′R

,

-

,

.Э .

-

, ,

-

τD R

, .

-

, , ,

. , . -

[98] .

,

,

4183

τR

-N, ,

,

.

. 2.14 -

, [98].

, K (t = 0 )

. . 2.14 µe < µ g . ∆ν a

, .Э

,

45

τe ∆ν a ∆ν a

-

, .

f ∆ν eq

< U e (t ) > (

)

-

( µe > µ g .

). , ,

, ,

,

-

kT,

"

" ,

-

. , ,

,

.

2.5.

, . . -

. τe

τg

τR ,

, -

t ex [1, 101].

,

, ,

,

,

,

[101–108].

[1, 101–105, 109, 110] 1) τ R > τ R ,

,

-

τ ex > τ R ,

( [102, 103].

, )

,

,

t ex

[102, 103], ν ast

47

-

ν stf ,

ν ast

.

ν stf ,

(

a ν ast = ν ∞a − ν ∞ − ν ∞f

(

)τ

ν stf = ν ∞f + ν ∞a − ν ∞f a ν∞

ν ∞f –

0-0,

[110, 112]:

τe τR , ⋅ + τ τ + τ e g R g

)τ τ+ τ

⋅

g

e

0-0-

g

(2.41)

τR . τ R + τe

(2.42)

, .

(2.41) ,

(2.42)

,

-

, ,

-

. .

, ,

.

-

, , –15 º

4-

(~ 400–500 [109],

[108]. -

-N–1

) [109].

, "

"

-

. ,

,

.

, -

48

.

(

[113]. )

.

-

. [109, 110, 114],

, . 0-0-

[1],

(

)

:

 t  a( f ) a( f ) ) ⋅ exp − g (e )  , ν a ( f ) (t ) = ν ∞ + (ν 0a ( f ) − ν ∞   τ  R 

ν 0a ( f ) –

0-0-

)

(

t = 0 , τ Rg ( e) –

-

, )

(2.43)

(

-

t=0

. , .

.

t1

, . , .

τ Rg ( e) ,

t′

n-

)

( (

-

) (n–1)-

(2.43),

. (2.43),

t, .

t n − t n−1

( n 49

) -

< ν a > ·10–3

20

,

–1

(

) -

.

2

,

1

-

19

τe

18 2

4

τg ,

-

τg

6

I, . 2.15.

(1) (2)

/

-

2

. . 2.15. < νa >

-

-

.

2)

(

a : ν 0a = 20 000, ν ∞ = 18 000,

; τ e = 0.01, τ R = 0.1 , σ = 4⋅10–16 ~300

ν ex = 17 500

1)

( .

–1

–1

, .

–1

,

.

( 0.01 .

50

) -

3.

_ -

,

,

. , S1-S0– T1-S0-

,

[115].

,

,

[116],

S1-S01,2

,

S1-T1-

, .

,

.

, , -

, ,

S0-S1 ( ∆ν S ) , . . ,

T1-S0 ( ∆ν T ).

, ,

-

.

3.1.

. 3.1.

G µg

G , µe

S1

G µT

T1 51

.

-

Z

K E G ∆µ T G µT

G µg θ

G µe

G ∆µ T⊥ G ∆µIIT

ϑ

ϑT α2

Y

α1

X

. 3.1

G E,

-

G µg .

, ,

G (E , θ )

S0

,

, -

G µg .

α1 ,

Z,

0

G E,

2π. , -

,

-

:

1 G G ∆ν S = − (∆µ S ⋅ E ) h G 1 G ∆νT = − (∆µT ⋅ E ) h 52

S1-S0 -

,

(3.1)

T1-S0 -

.

(3.2)

G G G G G G ∆µ S = µ e − µ g ; ∆µT = µT − µ g ( . . 3.1). (3.1) (3.2) , : 1 (3.3) ∆ν S = E ⋅ µ g cos θ − µ e ⋅ [sin ϑ sin θ sin α1 + cos ϑ cos θ] , h 1 ∆ν T = E ⋅ µ g cos θ − µT ⋅ [sin ϑT sin θ sin(α1 + α 2 ) + cos ϑT cos θ] . (3.4) h (3.1) , ∆ν S G G ∆µ S . , ∆ν S E G ∆ν T , . . E, G G ∆µ S ⋅ E = const , G ∆µT , , ∆ν T , G G ∆µ S ∆µT . -

{

{

(

}

)

Γ(∆ S , ∆ T ) .

∆ν T ,

}

< ∆ν T > =

A(∆ν S ) =

:

∆ν S ,

1 1 G G − ( E ⋅ ∆µT ) ⋅ G ( E , θ)dΩ . ∫∫∫ A(∆ν S ) Ω ( ∆ν ) h

∫∫∫ G ( E , θ)dΩ

Ω ( ∆ν S )

∆ν S ; Ω(∆ν S ) –

(3.5)

S

–

,

, ∆ν S = const .

(3.5)

-

:

π 2π   ∆ν s 1  × < ∆νT > = θ G , ∫∫ A1 (∆ν S ) 0 0  µ g cos θ − µ e ⋅ [sin ϑ sin θ sin α1 + cos ϑ cos θ] 

×

µ g cos θ − µT ⋅ [sin ϑT sin θ sin(α1 + α 2 ) + cos ϑT cos θ] µ g cos θ − µ e ⋅ [sin ϑ sin θ sin α1 + cos ϑ cos θ]

1   1 × 1 + ∆ν s2  4 + 4  ⋅ sin θ dθ dα1 . C  B 53

∆ν S ×

(3.6)

π 2π

A1 (∆νS ) = ∫

∫

0 0

  ∆νS G , θ ×  µ g cos θ − µ e ⋅ [sin ϑ sin θ sin α1 + cos ϑ cos θ]   

1   1 × 1 + ∆νS2  4 + 4  ⋅ sin θ dθ dα1 , C  B

B = µ g sin θ − µ e ⋅ [sin ϑ cos θ sin α1 − cos ϑ sin θ], C = µ e ⋅ sin ϑ sin θ cos α1 . , G ∆µT ∆ν S < ∆ν T > , G G ∆µIIT ∆µT⊥ 3.1). (3.5) :

G ∆µ S (

.

.

 1 1 G G  ∫∫∫ − ( E ⋅ ∆µIIT ) ⋅ G ( E , θ)dΩ + A(∆ν S ) Ω( ∆ν ) h S   1 G G (3.7) + ∫∫∫ − ( E ⋅ ∆µ T⊥ ) ⋅ G ( E , θ)dΩ . h  Ω ( ∆ν S ) G < E (∆ν S ) > , ∆ν S = const ,

< ∆νT > =

, (3.7)

:

∆µIIT 1 1 G G⊥ ∆ν S − − < ∆ν T (∆ν S ) >= ( E ⋅ ∆µ T ) ⋅ G ( E , θ)dΩ . (3.8) ∫∫∫ ∆µ S A(∆ν S ) Ω ( ∆ν ) h G ∆µT⊥ Γ(∆ν S = const, ∆νT ) . S

, Γ(∆ν S , ∆ν T ) ,

∆ν T

G(E,θ)

, , , . .

α2 = 54

,

π . 2

∆ν S [115]. G G µ g , µe

G µT

Γ(∆ν S , ∆νT ) : < ∆ν T > ∆ν S

,

< ∆ν T (∆ν S ) > = c1 ⋅ ∆ν S + c2 ,

1)

c1

-

c2 –

∆νT

2) Γ(∆ν S = const, ∆νT ) σT ,

: (3.9)

∆µIIT ; c1 ≈ ∆µ S

,

∆ν S

, ∆ν S . Γ(∆ν S = const, ∆νT ) : c1 , c2 σT . 3.1 S0-T1

№ /

∆ν S

S1-T1

S0-T1

S1-T1

0
+ 3000 . (7, 7’ ) (8, 8’ ); 26 500 –1 (7’, 8’ ). T = 300 K; µ g = 2.6, µ e = 4, µ T = 4 D; k g0 kf

=

km0 = 0.2 ; α g = α m = 0.1 . ϕ max – k ph

,

-

< τ df ( ph ) (

. 3.3, >

1, 1’ 7–7’ 8–8’,

( . ( ( . 3.2, < τ df ( ph ) >

. 3.2,

2, 2’). . 3.2). 7–7’).

8–8’). , . , 59

ϕ df -

ln( I )

0

< ν > ⋅10–3,

20.6

–1

3’

20.4

4’

-2 20.2

2’ 1’ 2

-4

-6

1 0

5

10

15

20.0

3

19.8

4

19.6

20 t, c

0

< ν > ⋅10–3,

2.0

(2, 2 , ),

10

15

20

t, c

. 3.3. ’

5

(1, 1’, ), -

–1

1.5

(3, 3’, ), ’

(4, 4 , ),

1.0

(5, 5’ , ) ν ex = 22 000 (1–5) 26 500

. (1 –5’ )

–1

5’

0.5

’

5

0.0 0

ϕ df

ϕ df ϕf

ϕ ph (

5

10

15

20

t, c

(

. 3.3,

5–5’’

. 3.2).

3–3’), (

-

-

’

4–4 ). I df I ph

(

5–5’’).

. 3.3,

, [127].

. 3.4

( (

2) 303 . 60

1)

-

1.0

< ν > ⋅ 10–3,

19.8

I (ν) , ε(ν) , . .

I df

–1

4

0.16

If

19.6 19.4

0.5

2

3 19.2

1 0.0 15

17

0.14

5

19

21

6

19.0 23 25 20 ν⋅10–3, –1

0.12 23 24 ν⋅10–3, –1

22

( ); ν ex = 22 600 (4)

(1),

. 3.4. (3)

21

(2) –1

-

. (5) -

( ); (6). C = 3⋅10–5

/ , T = 303 K. –1

17 500

-

( ). : .

, .

( (

. 3.4, 4).

,

5)

. 3.4 -

. , , 1.

, , S1

0-0"

"

. 0-061

:

-

0-0-

, . . . . 3.1).

kg (

S1–T1

,

,

-

T1– S10-0-

k e ), -

(

( )

,

.

,

S10-0-

,

, . kg

ke -

I df I f (

. 3.4,

6).

.

(

.

. 3.5),

-

, < ν df > ⋅ 10

–3

ln( I df )

0.0

19.4

1

-0.5

. -

19.2

5

1

-1.0

2

19.0

6

-1.5

( ( 17 500

3 4

-2.0

. –1

18.8

: -2.5 0.0

0.2

t,

0.4

18.6 0.6

0-0-

(5, 6) . ν ex = 22 370 (1, 5), –1 (4, 6). 21 290 (2, 3), 20 540 ν reg = 21 450 (1), 20 270 (2), 18 150 (3), 17 820

).

(1–4)

. 3.5.

–1

(4). C = 3⋅10–3

/ , T = 303 K 62

. 3.6);

,

-

km ,

ke

1-

;

-

,

.

I,

< τ df > , c

.

1.0

< τ df > .

0.5

,

0.8

-

τ df

-

,

3 1

0.4

0.3

0.2

.

0.0 14

0-0-

0.4

2

0.6

-

16

18

20

22 –3 ν⋅10 ,

0.2 –1

.3.6. -

:

(

.

(1) (2,3), t = 0.041 (2) 1.08 (3). ν ex =21 220 –1. C=3⋅10–5 / , T=303 K

-

. 3.5, 3.6). ,

-

. 268

(

.

,

. 3.7). ,

-

: 1) , 2)

(

. 3.7,

, (

1, 2); 3)

3); , . 3.7,

-

(< τ >

-

). , , T1-

T1– S1(

.

ke , . . (3.13)).

I ph I df

63

I df ,

.

< τ >,

.

.

-

1.1

1.0

1

0.8

2

S1-

1.0

,

0.6 0.4

T1–

0.9

3

S0-S11-

0.8

0.2 0.0 14

16

18

.3.7.

20 ν⋅10 (1, 2) 22–3

-

0.7

.

–1

,

-

(3)

-

. t = 0.082 (1) 2.42 (2). T=292 K, ν ex = 22 140 –1. = 3⋅10–5

1(

, ,

/

.

-

. 3.1). 1 . 3.2, ,

-

.

2 ↑

. 3.2

3,

.

↓

,

.

~

, -

< ν f > − < ν df > ,

. "+"

< ν f > − < ν df > .

, .

,

" ", 1, 2 3. 64

"−" -

я

νf

ν df

ν ph

↓

↓

↓

m

↓

↓

↓

e

↓

↓

↓

↓

↓

1

2

3

я

ν ex ↓

ν f − ν df

+↓ − ↓ − ↓ +↓

↓↑

3.2. , ,

я

ν reg ↓

ϕf

ϕ df

ϕ ph

τ df

τ ph τ df

~↓

↑

↓

↓
⋅ 10–3 ,

22

24

ν ⋅ 10–3 ,

–1

3’’

20.0

0.00 12

–1

/

0.03

0.0

28

ν ⋅ 10–3 ,

0.06

–1

I df

–1

2.5

I ph

21.0

6’

20.5

7’ 8

20.0

2.0

6

1.5

7 8’

19.6

19.5

19.2

19.0 0.0

20

22

26 28 –3 ν ⋅ 10 , –1

24

. 3.8. (1’’, ) (2–2’’, ) (2, ; 3, ), ’’ ’’ (2 , ; 3 , ). (4–4’, ) ’

0.2

0.3

0.5 0.4

t, c

(1, ), (1’, ), (1’’’, ); ν ex = 23 700 –1.

(3–3’’, )

(2’, ; 3’, ) (5–5’, )

. (6–6’, ),

-

(8–8’, ). ν ex = 21 500 (4–8) 23 500 –1 (4’–8’ ). –1 3 000 . T = 300 K; µ g = 2.6,

(7–7 , ) 3’’ , 7

0.1

1.0

7’

k m0 = 0.2, = 5, α g = 0.1, α m = 0.5 µ e = 4, µ T = 4.3 D; ϑ = 20 , ϑT = 29 ; kf k ph 0

0

k g0

67

ε (ν ) ,

1.0

.

ϕ

.

ϕ max

I (ν) ,

1.0

1.4

5

0.8

< τ >, 1’ 1’’

. . 1’’’

0.8 1.2

1

0.6

2’ 2 2’’

0.4 0.2

24

26

0.5 12

ν ⋅ 10 ,

< ν > ⋅ 10–3 ,

1.0

0.0

28

–3

20.8

4’

0.2 0.8

22

16

18

20

22

24

ν ⋅ 10 , –3

21.0

< ν > ⋅ 10–3 ,

I df

–1

6’

3

–1

2.0

I ph

7’

20.6

3’

20.4

14

–1

–1

3’’

1.5

4

0.4

1.0

0.0 20

5’

0.6

2.0

1.5

20.2 1.0

20.0

19.8

7

8’

8

6

19.6 20

22

24

26

ν ⋅ 10–3 ,

. 3.9. (1’’, ) (2–2’’, ) (2, ; 3, ), (2’’, ; 3’’, ). (4–4’, )

19.4 0

28

0.5 2

4

6 t,

–1

(1, ), (1’, ), ’’’ (1 , ); ν ex = 23 700 –1.

(3–3’’, )

(2’, ; 3’, ) (5–5’, )

. (6–6’, ),

(8–8’, ). ν ex = 21 500 (4–8) 23 500 –1 (4’–8’ ). 3’’, 7 7’ 3 000 –1. –1 ’ ’ ’’ ν ex = 21500 (4–8) 23500 (4 –8 ). 3 , 7 7’ 3 000 –1. T = 300 K; µ g = 2.6, µ e = 4, µ T =4 D; ϑ = 200, ϑT = 300;

-

(7–7’, )

k g0 kf

k m0 = 0.2, = 5, α g = 0.1, α m = 0.1 k ph

68

-

T1-

-

0-0-

, I df

ke . Э

I ph (

,

,

8–8’).

. 3.9, 3.

,

, 0-0-

,

T1-S0. Э

, ,

(

.

,

3–3’’).

. 3.10,

-

T1– S1( . ke > k m , . . km

, . 3.10,

(

, . . 2’).

. 3.10, ke > k m ,

2’’),

0-0-

, 1, 1’’,

( .

4–4 , 5–5 , 0-0-

(

. 3.10),

-

: < τ ph >

. ,

-

S0-S1 T1-S1-

, -

ke

.Э < τ df >

-

. 3.10).

, ’

ν ex

.

,

’

,

. . , , 69

ε(ν) ,

1.0

.

ϕ ϕ max

. 1

2.5

1.0

.

2.0

0.8

0.6

1.5

0.6

, 1’’ 1’

. 1’’’

5’

0.8

6.0

4.0

5

2’’ 2

0.4

I (ν) ,

1.0

0.4

0.5

0.2

2.0

’

2

0.2

4’ 4

0.0 20

22

24

26

28

0.0 12

ν ⋅ 10–3 ,

(1, ),

(3–3’’,

. (2–2’’,

21.0

-

–1

) (2’’, 3’’). (4, 4’)

α g = 0.1, α m = 0.1

k g0 kf

= 0.2,

< ν > ⋅ 10–3 ,

20

22

ν ⋅ 10–3 ,

24

3’

3

-

3’’

20.0 22

24

26 ν ⋅ 10–3 ,

28 –1

k m0 = 0.2, k ph

,

-

. ,

–1

–1

20.5

(5, 5 ) ( ). ν ex = 21 500 (4–5) 23 500 –1 (4’–5’). 3’’ 3 000 –1. T = 300 K; µ g = 2.6, µ e = 3.5, µ T = 3.5 D; ’

ϑ = 250, ϑT = –150;

18

) -

(2, 3), (2’, 3’)

16

–1

. 3.10. (1’, ), (1’’, ) (1’’’, ); ν ex = 23 650

14

,

. 3.2 ( G G µ g , µe 70

G µT ).

3.3

-

,

[128–136]. -

.

-

,

,

,

-

,

,

,

0-0-

.

,

T1,

-

0-0-

[137]. < τ df >

. 3.11 .

-

, , , .

,

S1-

, –

,

, 71

< τ df > ,

I df ,

.

.

0.4

-

1

3

[138]. ,

1 0.3

, -

0.5

2

.

, S-S(

0.2 16

20 –3 22 ν ⋅ 10 , –1

18

) [128–131, 139],

0

-

. 3.11.

–5

T1-

, -

(1, 2). / (2).

–3

C = 5⋅10 (1), 4⋅10

,

(3)

-

, (

. . 3.11). -

S-S-

(

, , ,

,

). , ϕf ,

0-0-

τ ph .

-

∆ν s , ϕ ph ,

[140]: 72

: -

τ 0d –

1 ket = d τ0

9000ln 10 ⋅ Φ 2ϕ0d d  R0  ⋅  = I ( ν ) ε a ( ν ) ν − 4 dν , 5 4 6 ∫ f 128 ⋅ π n Nτ0 R  R 6

S1-

-

; R0 – ;n–

;N– ; I df (ν) – ; ε a (ν) – ,

ϑda –

(3.23)

Φ 2 = (cos ϑda − 3 cos ϑ dr cos ϑar ) 2 , ; ϑdr

; ϕ 0d – ;R– ;Φ – :

(3.24)

ϑar –

, .

, , . . .

, –

0-0-

. (3.24) k et = k

0

:

∞

∫ ε a ( ν ) I f ( ν ) ⋅ ν 4 dν , d

1

(3.25)

0

k0 –

, )

-

( ν ex

.

ν reg

+∞ 1 +∞  0 d I ph (ν ex , ν reg ) = ⋅ ∫ ε (ν ex − ∆ν S ) ∫ I 0ph (ν reg − ∆νTd )ϕdph + C −∞  −∞

73

:

]

+ I 0ph (ν reg − ∆νTa )ϕaph × ρ(∆ν dS )ρ(∆ν aS )d (∆ν dS )d (∆ν aS ) . ; ∆ν dS

C–

∆ν aS ,

(3.26)

∆νTd

∆ν Ta – -

; ρ(∆ν S ) – 0-0-

( σ =800

,

); ϕd(a) ph –

–1

),

-

(

(3.11) (3.16, 3.17, 3.19),

∆νTd(a) .

(3.26)

∆ν dS

∆νTd

∆ν aS


⋅ 10–3,

∆νTa

-

(3.9). . 3.12

. εa ( ) ,

∆ν d(a) S

,

(

–1

1) -

20

1.0

1

0.8

3

2

19

0.6 0.4

-

(

2).

-

S 1-

18

.

0.2 0.0

-

17 20

22

24

26

28

30

ν ⋅ 10–3,

32 –1

.

. 3.12. (1, 2). (3). k = 0 (1) k 0 = 0.5 (2) 0

. -

. : 74

+∞  t  1 +∞  0 d d d 0  ε ν − ∆ ν ν − ∆ ν ϕ I ph(ν ex ,ν reg ,t) = ( ) I ( ) exp − d  + ex S ∫ ph reg T ph ∫ C1 − ∞   τ ph  −∞ 

 t  + I 0ph (ν reg − ∆νTa )ϕaph exp− a ρ(∆ν dS )ρ(∆ν aS )d (∆ν dS )d (∆ν aS ) . (3.27)  τ ph 

τ dph , τ aph

1–

∆ν S

–

ϕ ph

∆νT

; (3.13, 3.16–3.19).

τ ph

,

, . . 0.

:

X d (k df + k gd + k 21 ) − X a k 21 = 1 ,

X d k 21 − X a (k af + k ga + k 21 ) = 0 ,

Xd, Xa –

(3.28)

S1;

k12 , k 21 –

,

-

(3.25); k df (a ) , k gd (a ) –

.

(3.28)

, X = d

Xa =

k af + k ga + k 21

(k df + k gd + k 21 ) ⋅ (k af + k ga + k 21 ) − k12 k 21

,

(3.29)

k12 . (k df + k gd + k 21 ) ⋅ (k af + k ga + k 21 ) − k12 k 21

(3.30)

(3.29) (3.30)

:

ϕdph

=

k af + k ga + k 21

⋅ , k dph + k md (k df + k gd + k 21 ) ⋅ (k af + k ga + k 21 ) − k12 k 21 k dph k gd

75

(3.31)

ϕaph

=

k aph k ga

k aph + k ma

⋅

k12 , (k df + k gd + k 21 ) ⋅ (k af + k ga + k 21 ) − k12 k 21 τ dph( a ) =

(3.32)

1 . k dph( a ) + k md ( a )

(3.33) -

(3.16–3.19). . 3.13 < τ ph >
,

. Э

0.25

.

3 0.20

km

2

’

3

2’

0.15

, -

.

’

1

0.10

1

"

0.05 12

16 18 –3 ν ⋅ 10 ,

14

20

" "

22

, ".

–1

-

. 3.13.

,

. ν ex = 22(1,1 ), /

’

3

.

–1

25(2, 2 ), 31⋅10 , (3, 3’); k0 = 0(1–3), 0.5 (1’–3’)

2, 2’)

(

-

(

3, 3’) -

.Э

, T1-

,

-

. , .

76

1, 1’),

(

. -

[129, 134, 141–143].

-

,

. P (ν ex , ν reg ) P(ν ex , ν reg ) =

0 Pph

C2

⋅

+∞

∫

−∞

ε

0

:

(ν ex − ∆ν dS )

+∞

∫ I ph (ν reg − ∆νT ) ⋅ ϕ ph (∆ν S , ∆ν S ) ×

−∞

0

d

d

× ρ(∆ν dS ) ⋅ ρ(∆ν aS ) ⋅ d (∆ν dS ) ⋅ d (∆ν aS ) ,

C2 = I ph (ν ex , ν reg ) ⋅ C (

d

a

(3.34)

0 . 3.26); Pph –

-

. (3.34)

,

-

, ,

0. -

:

P(ν ex , ν reg , t ) =

+∞  t  P 0 +∞ 0 ⋅ ∫ ε (ν ex − ∆ν dS ) ∫ I 0ph (ν reg − ∆νTd ) ⋅ ϕdph ⋅ exp−  × C3 − ∞  τD  −∞

× ρ(∆ν dS ) ⋅ ρ(∆ν aS ) ⋅ d (∆ν dS ) ⋅ d (∆ν aS ) ,

C3 = I ph (ν ex , ν reg ) ⋅ C2 (

(3.35)

. 3.34).

. 3.14

P ) P0

(

,

. (

. 3.14,

1) 77

P P0

1.0

-

. Э 2 1

0.8

3 4

.

5

,

0.6

6 0.4 0.0

, -

,

0.1

0.2

0.3

0.4

t,

P ) " P0

(

; ν ex = 31 (1, 6), 25 (3, 4), 22⋅103 –1 (2, 5); ν reg = 13 (2, 4, 6) 22⋅103 –1 (1, 3, 5) . 3.14.

,

-

" ,

"

".

, -

. "

",

,

-

. .

(

. 3.14,

,

-

, S-S,

-

3, 4) . ,

(

. 3.14,

2, 5).

. (

), . ,

, 6G (C = 2⋅10

/ ), -

S-S0.33 – .

–3

, 78

0.25 . -

-

[128–130, 141]. , . . ,

,

0-0-

. 6G (

)

,

(

)

, ,

,

0-0.

,

.

(3.13)

, kn

S1.

S16G S1-

-

,

. . 3.15, 3.16

( (

1)

2)

6G -

[138]. , (

. 3.17

(

2)). -

(

1)

6G , 6G

, , , S1T1-

.(

.)

, , 79

-

.

1.0 I,

.

.

I,

1.2

.

2

1.0

0.8

0.8 0.6

0.6 0.4

1

0.4

2

0.2 0.0 12

14

16

18

1

0.2

20 22 ⋅ 10–3 –1

0.0 13

. 3.15.

15

17

21 –3 23–1 ⋅ 10

19

. 3.16.

(1) (2)

(C = 4⋅10–3 6G (C = 4⋅10–3

(1) (2)

/ ) / )

0.28 .

(C = 2⋅10–3 6G (C = 2⋅10–4

/ ) / )

. 3.15, 3.16

,

,

-

.

.

,

,

, . (

-

)

(

6G)

,

. .

,

, R > 2R0 .

-

.

N -

, : 80

ϕdf ϕddf = ϕdf ⋅

=

k df

k df

+ kg + ∑ N

+ k nd

keti

,

(3.36)

i=1

(km + ke + k ph )

 R0   – ⋅  d-a  r  i  ; rid-a –

1 keti = d τ0

k g ke

N   ⋅  k df + k g + ∑ keti + k nd  − k g ke i=1  

.

(3.37)

6

i-

-

. :

∑ keti N

ϕaf ( df ) = ϕdf ( df ) ) ⋅0 ϕaf ⋅

0

i=1

k df

+ k g + k nd

+∑ N

.

(3.38)

keti

i=1

ϕaf –

. -

.

ε(ν) ,

1.0 0.8

.

1

2

0.6 0.4

, , (3.37, 3.38),

ϕadf ϕddf

-

0.2

-

0.0

, =

ϕaf ϕdf

17

19

. . 3.17. 6G (1) .

81

21

23 25 ν ⋅ 10–3

(2)

–1

-

-

-

. (3.37) (3.38). , . .

,

. < ϕddf >

[140].

-

. .


< ϕdf ((adf) ) >

, . :

< ϕdf(df) >= ξ0

ξ1 –

;
N=0 +

< ϕaf(df) >=

1

> N =1 –

< ϕdf(df) > N=1 ,

< ϕaf(df) > N=1 .

0

(

1

)

(3.39) , , ; -

1

( 1

< ϕdf ((adf) ) > N = 0 –

-

) , (

(3.37, 3.38), < ϕdf ((adf) )

3 R 2 d (a) > N =1 = 3 ∫ r ⋅ ϕ f ( df ) ⋅ dr . R 0 C ≈ 0 ϕdf

 3π C  1 − ⋅  , (k ph + ke + k m )(k f + k g + k n )  4 C0  ke k g

ke k g π . 2 (k ph + ke + k m )(k f + k g + k n )

< ϕadf >≈ 0 ϕdf 0

ϕdf

0

ϕaf –

(3.41) -

. (3.41) < ϕadf >

C  

<
>

C,

= β, β = 1.

,

-

.

200 Ǻ,

.

,

, 0.3

)

ϕ df

1.0

(

ϕf 2

0.8

1

1

0.2

0.6 0.4

0.1

2 0.0

10-4

0.2

10-3

10-2 Ca,

0.0

10-4

10-3

/

. 3.18. ( )

(1) 83

10-2 / Ca, ( ) (2)

, .

, (3.37, 3.38), 50 Ǻ).

(

-

,

, < ϕdf ((adf) ) > . . 3.18.

, 0.5

, . . 3.18 ,

(

( ,

.

ke > k ph , k m , k e (

(3.44) , b k e ). ; ( ). b

(3.47)

(

-

b < k e ),

,

,

-

, ke,

, . . X 2 τ imp (3.53)

,

t < τimp

(3.43),

(3.54).

-

∆ν S

0-0-

. 91

1.0

.

I,

I, ε,

. 1.0

. .

0.8

0.8

2

4

0.6

0.6

1

0.4

1

0.4

2 0.2

0.2

3 0.0 0.0 0.2 0.4 0.6 0.8 1.0 t, c

0.0

-

. 3.22. . 19 000 –1 (2, 4); –1 . ex = 23 000

reg

12

= 23 000 –1. ex = 1.2 (1, 3), 0.03 c (2, 4)

24

28

–1

-

. 3.23.

ex

(1)

( τex > τ df , τ ph )

. 3.22 ( τ ex τ df .

. 3.24

< τ df > 1)

( (

,

2). 92

-

-

0.40


,

df

0.30

< τ df > ,

2

0.35

0.25

0.30

1

0.20

0.25

3

1

3

0.15

0.20 0.15 12

14

16

18 ⋅ 10–3,

2

0.10 12

20 –1

14

16

18 20 ⋅ 10–3, –1

. 3.24. (1, 3) (2) –1 . b = 0.01⋅kph (1, 2), b = 50⋅kph (3); ν ex = 23 000 ( ) 18 200 ( )

( b = 0.01 ⋅ k ph ).

-

, ,

.

(

. 3.24 ).

3,

.

.

. T1-

.

, , T1-

,

, .

. . (

) , . 93

,

(

.

. 3.24 ). . 3.25

< τ df >

.

b

,

,

-

, , 1, 1’).

(

, -

,

’

(

2, 2 ,

. 3.25). . -

1’–3’,

( .

. 3.25), -

. . .

,

, ,

0-0-

.Э

-

. 3.26, ).

. 3.26

-

( , .

-

. (

-

) 94


,

df

0.25

3’

18.0

3

17.5

1 0.20

< > ⋅ 10–3,

18.5

1

2

16.5

2’

16.0

2 5

3

6

4

17.0

1’

–1

0.15 0.10 0

15.5 15

50 100 150 200 250 300 b k ph

19

21

23

⋅ 10 , –3

. 3.25.

25 –1

. 3.26. b k ph .

= 20 000 (1, 1’), 17 000 (2, 2’), 23 000 –1 (3, 3’). ν reg = 17 000

(1,3,5) (2,4,6) . b/kph = 0.01 (1,2), 50 (3,4), 500 (5,6)

ex

’

ex

17

–1

.

’

= 1.2 (1–3), 0.03 c (1 –3 ).

. (

.

-

’

. 3.26,

3, 3 ).

,

, .

,

. . ,

.

95

4.

-

,

-

, .

, .

–

, S0-

. .

4.1. -

–

,

. . -

[140, 144]. , [145].

, 96

, [145, 146]. – 2–, (–CH2–)n, –CH2O–, –H2C–S–CH2– [147–150], [152–156], [151]. – 2– . [152, 155]. ,

-

, ,

[153– 155].

-

, .

,

[157]. [158],

[153, 159–161]. –( 2)n–.

n > 4, [160],

n = 1, 2, 3 –

[162].

-

, . :

-

, ,

–

, . [163]. ,

–

-

[164–167]. -

[168]. ,

[169] (3-

-

) .

97

,

-

. [169], (1014–1015

–1

)

,

.

4.1.1.

,

. 4.1

. , ,

,

. 4.1

.

S1

Tn k gd

Tn

S1 k ga

T1 bd

k df kmd

k af

ba

d k ph

k et(1)

S0

k

a m

T1 k

a ph

S0

ket( 3)

ket( 2 ) . 4.1.

: k et(1)

"d"

k et( 2) –

, .

-

-

T1-

, ;

"a"

-

k et(3) –

( )

( T1b

d (a)

S1-

).

=

d (a) σ d ( a ) (ν ex ) ⋅ I ex d (a) hν ex

98

,

(4.1)

σ d (a) –

d (a) , I ex –

d (a) – , ν ex

.

S1-

, -

, . . , . ,

-

, . ,

, .

-

,

, . 4.1,

( ),

[170, 171],

(1 − X ) b − X (1 − X ) k − X (1 − X )X k − (k + k )X

:

d

Xd . d k f >> k gd

d

d

a

d (1) et

Xa– k ga

-

a

(1) et

a ph

a m

, " d d kf a

= 0,

= 0.

(4.2)

S1(4.2) ,

>> k af .

"

T1-

, -

,

T1k et( 2) (

,

.

. 4.1),

,

.

. 4.2 (

(

1)

-

2)

, (4.2). : ϕd =

X d k df

(1 − X d )b d 99

.

(4.3)

ϕd , X a

1.0

-

, 2

1

, b d ( a ) (4.1).

0.5

, -

. 4.2

,

0.0

10-1

1

10

. 4.2. (2)

. ket1 = 100k df

ϕ0

ϕa –

a b d k ph (1) -

. ,

ϕ d = ϕ 0 ⋅ X a + ϕ a ⋅ (1 − X a ) ,

: (4.4)

,

-

(T1)

.

, , ,

. ,

T1(4.2)),

k df >> k gd ,

( k et(1)

,

>>

-

k df -

ϕ0 = 1 ,

ϕa = 0 .

, ,

, . -

[172, 173] –

. ,

. 4.1. T1

(

{i, j}, , k ga >> k af 100

k df

>>

S1 k gd ,

S1

).

T1 0

: -

i, j

1,

, . ,

(4.2),

-

Yi j {i,j}

:

Y11k df + Y10 ket(1) − Y01 ⋅ (k ph + k m + b d )= 0

b d ⋅ (1 − Y01 − Y10 − Y11 ) + Y11 (k ph + k m ) − Y10 ⋅ (k df + ket(1) )= 0 Y01b d − Y11k df = 0

(4.5)

(4.5)

:

Y00 + Y01 + Y10 + Y11 = 1 . S1Yi j

T1-

:

X d = Y10 + Y11 ,

X a = Y01 + Y11

(4.6)

(4.5), (4.6) k et(1) >> k df .

,

(4.4)

,

(4.6). , (4.2)

(4.5).

, "

T1-

,

"

. (4.2)

"

, "

k et(1)

, . .

"

"

, (

) 101

(1 − X ) a

,

-

k et(1) . , -

, . ,

[172, 173]

, ,

.

,

, . ,

, (4.5).

, ϕ0

, (T1)

(4.4).

ϕa

-

: ϕa =

k df

k df + k gd + k et(1)

;

ϕ0 =

k df

k df + k gd

.

(4.7)

(4.7) , T1-

.

ϕet ,

1-

-

: ket(1) ϕet = (1) . ket + k df + k gd X = a

b d ⋅ ϕ et

b d ⋅ ϕ et + k aph

: .

(4.4), (4.7) – (4.9) . ,

(4.8)

(4.9)

, -

102

,

-

. я

4.1.2.

,

[202]. , , . ( k df >> k gd ),

( k ga >> k af ), . . 0.

-

, ,

"

". . -

Yi j Y01 = b

a

⋅ (1 − Y01 − Y10 − Y11 ) − Y01 ⋅ (k aph

+b

d

) + Y10 ket(1)

+ Y11 (k df

: + ket( 2) ) ,

Y10 = b d ⋅ (1 − Y01 − Y10 − Y11 ) − Y10 ⋅ (b a + k df + k et(1) )+ Y11k ph , Y11 = Y01b d + Y10b a − Y11 (k df + k aph + ket( 2) ) , Y00 + Y01 + Y10 + Y11 = 1 .

S1Yi j

(4.10)

T1(4.6). , . ,

– –

τ ex τ ex . ,

-

.Э

T1, . . ,

.

T1-Tn-

,

,

, [174]).

S0-S1-

(

, .

S0-S1., ,

. . 4.3 1.0

-

d f d 0

τ

b

-

k et(1) (

1 3

0.5

. 4.3). 4

,

10–5

10–3

10–1

101 a b d k ph

b d k aph , -

. 4.3. b d . k et(1) = 1010 (1,4), 109(2), 108

(4.1); -

–1

(3). b a = 0(1–3), ba = bd (4). k et( 2 ) = 0. k df = 108

-

,

2 0.0

d

–1

104

< τ df > τ 0d

τ 0d –

,

.

,

.

-

. : T1-

,

,

,

, S0: τ1 –

S1-

. ,

τ2 –

T1-

). -

τ1 < τ 2 . ,

, < τ df > .

, τ df

,

-

T1-

( ,

,

T1(

. 4.3,

, ,

4). (

-

. 4.4).

, T1-

,

, , . . k et(1) ~ k et( 2) .

S0bd (

-

1’–3’).

. 4.5

. 4.5

,

1- n-

, ,

, .

(

.

. 4.5,

1–3). 105

-

< τdf >

1.0

τ0d

1.0

< τdf > ϕd , d τ0d ϕ0 1’

1 1 0.5

0.5

2 2 3 0.0

10-5

3 10-3

10-1

0.0

101 a b a k ph -

10-1

(1–3) (1’–3’) b d . ket( 2) ket(1) = 0 (1,1’), 0.01(2,2’), 0.03(3,3’). ket(1) =109, k df = 108 c −1

0.01(2), 0.1(3). ket(1) =109, k df = 108 c −1

-

я

,

, . "

101 a b k ph

. 4.5.

a =0 (1), b a . b d k ph

я

10-3

3’

d

. 4.4.

4.1.3.

10-5

2’

" . .

X d (θ)

bd

,

: b (θ) = d

d σ d (ν) ⋅ I ex d hν ex

⋅ cos 2 (θ) .

θ -

(4.11) -

: 106

I II = C ⋅ 2πk df

π

∫ X d (θ) cos

0

2

(θ) ⋅ sin(θ)dθ ,

π

I ⊥ = C ⋅ πk df ∫ X d (θ) sin 3 (θ)dθ .

(4.12)

0

C–

. . 4.6 (

1)

, .

-

, . .

. τ1

τ2 . τ1 –

{1,0}

{1,1}

, ,

,

τ2 –

T1-

. (S0) ( ):

, ,

f ex →{1,0}  →{0,0} " 1. {0,0} 

hν

hν

f ex et ex {0,1}  2. {0,0}  →{1,0} →  →{1,1}  →{0,1} " " .

hν

hν

hν

ks

"

. θ

{1,0}. , cos θ . T1-

,

2

-

cos θ . 4

{1,1} , , 0.5.

107

{1,1} [175–183].

0.70

,

P

,

0.65 0.60

2

-

1

2/3

0.55

, 0.50 0.45 0.0

0.1

0.2

t τ 0d

0.3

, -N-

[175]. 4-

-

-

. 4.6.

-

, . k df = 108, 6

d

9

(1) et

a

6

P = 0.49 0.25 [178]. 4-N-

-1

a = 10 , k = 5⋅10 , b = 5⋅10 , b = 0 c , k ph τ ex = 10–10, ∆t =10–7 c. (1) (2).

~ 0.6

-

[178]. , :

τ1 ;

1) 2)

0.5

τ2 .

-

2/3

-

, ,

, ,

0.5.

,

, ,

, 2/3,

, -

( τ1 < τ 2 ), . (

)

108

0.70

P

-

1 2

0.65

.

- 0.60

3

0.55

4

{0,1}. - 0.50 -

-

0.45

0

-

10

20 n

-

. 4.7.

( ,

.

. 4.7). -

.

,

1.7⋅10–9 (1), 1.5⋅10 (2), 1.2⋅10 (3), 10 (4) –9

–9

–9

, (

.

. 4.6,

-

2).

4.2.

,

, -

, . -

-

[184–190]. , .

S1 → S0

, . 4.1.

109

, . .

.

S1 ,

-

,

. ,

,

-

.

i

{i, j}, j

( i) 0

(j).

-

1,

,

(T1) .

Yij [189–190]:



(1 − Y01 − Y10 − Y11 )η0a b a + b d 

(

)

 ket(1)  + Y11k dph − Y01 k aph + b d η1d = 0 , d d (1) k f + k g + ket 

(1 − Y01 − Y10 − Y11 ) ⋅ b d ⋅ η0d − Y10 (k dph + b a η1a ) + Y11k aph = 0 ,

(

)

Y01b d η1d + Y10b a η1a − Y11 k dph + k aph = 0 .

η0d η1a

=

=

k gd

k df + k gd + k et(1)

k ga

k af + k ga + k et(3)

,

η1d

=

k gd

k df + k gd + k et( 2)

(4.13)

η0a

,

=

k ga

k af + k ga

,

.

T1(4.13) b d (a)

-

(

) ,

, ⋅(k aph + kma ), T1-

i-

,

,

-

:

b d ⋅ < ϕiet > +b a < X i >= d , i = 1, 2, 3,..., n . (b ⋅ < ϕiet > +b a ) + k aph + k ma

(4.22)

(4.23)

ϕiet –

ik ga

(4.22) >> k af .

. -

, , i-

-

, .

ϕiet ,

,

–

) : 121

, Xi (i = 1, 2,..., n). ( ϕiet

ϕiet

= k df

+

kiet

kiet

+∑∑

klet δ lj l =1 j =1 n ml

ml –

l-

N = ∑ mi .

δ lj = 1 ,

n

i =1

l ≠ i.

i = 1, 2, 3,..., n ,

,

(4.24)

,N–

-

j-

l-

δ lj = 0 ,

, . . , T1-

.

τ df

S1-

:

τ df =

1

k df

+∑∑

.

kiet δ ij i =1 j =1 n mi

ϕiet , X i

(4.25)

τdf ,

2N ,

.

,

mi

,

ξi .

, , . . δ ij = 1 (i = 1, 2...,

, n, j = 0, 1, 2..., mi).

,

δ ij , Xi

< ϕiet

.

.

>,

,

ϕiet

(4.23), (4.24) mi , 1 0 < Xi > ,

< ϕiet >

(4.23)

δ ij < ϕiet > 122

< Xi > ,

Xi

ϕiet .

(1 − X i ) , -

< Xi > – . (3.4),

-

τ df ψ (τ df , b d , b a ) ,

S1bd bd

ba , .

-

ba

. bd

ba

,

.

4.3.2.

ψ (τ df

ϕ

d

ϕ0d

1.0

ϕd / ϕ0d

ϕd

, d

a

, b ,b ), ∞

=

∫τ

0

d

:

ψ (τ d , b d , b a ) dτ

∞

τ 0d ∫ ψ (τ d , b d , b a ) dτ

ϕ 0d

0

1

.

(4.26) τ 0d –

-

2

0.8

. ,

3

0.6 0.4

, ,

0.2

0.1

-

5

4

0.0

-

1

10

-

bd . Ca = 10–4(1), 5·10–4 (2), 1.5·10–3(3), 4.2·10–3(4), 3·10–2 / (5)

. -

( b a = 0 ).

100 a b d / k ph

. 4.17.

.

: R0 = 50Å, 200 Å,

R = -

123

– 6 Å.

. 4.17 b .

,

d

,

, . . .

,

n: . [175–183,

, ,

,

205]. . [206–209], 0–2⋅10

24

./(

10–3

⋅ )

, -

/ .

-

.

2

. .

, 10–4 – 10–2

, . 4.17. 10–2 ,

/ ,

/ , . .

, . . -

-

,

-

. , 1−

ϕd ϕ 0d

, [140]:

= πβ exp(β 2 ){1 − φ(β)},

π Ca 2 1 4π 3 β= ⋅ , exp(− x 2 )dx . R0 , φ(β) = = ∫ 2 C0 C0 3 π0 β

124

(4.27)

(4.27)

, Ca

a

, ,

[140], . -

. "

"

b →0 d

Ca ,

bd ≠ 0

, Ca . Ca :

(

-

Ca

(

-

))

Ca = Ca ⋅ a1 + a2 ⋅ arctg a3 ln(b d ) + a4 ,

(4.28)

a1 = 0.518536; a2 = 0.407771; a3 = – 0.495768, a4 = 0.781215.

-

. , (3.23)

k et

< Φ2 > =

2 . 3

, ,

-

(3.6), 0.845 ( ) [140].

-

, , .

0.845 ,

, (

, , ,

, . 125

), -

1, 2, 3..., n))

(

k iet

− δk

et

( ri − ∆r > r > ri + ∆r (i = {r ,ϑ da ,ϑ dr ,ϑ ar } -

.

)< k < ( et

k iet

+ δk

et

),

δk et kiet

0.9

1

1.1

8

1 6

0.8

2

4

0.7

3

2 0 0.0

0.2

4

0.4

0.6 0.5

0.8 1.0 τ d / τ 0d

0.6

3

2

10–3

10–2

10–1

1 a b d / k ph

. 4.20.

. 4.19. .b a=

d

a k ph

S1= 0.01(1,3) 30(2);

10–2(1,2) 1.93·10–3

b d . =10–3(1), 3·10–3(2), / (4) 10–2(3) 3·10–2

/ (3)

τd .

S1-

-

, (

, τd .

. S1. 4.17

) -

,

-

bd )

(

-

.

Ca = 10 −2

,

,

b

b d / k aph = 0.01

/ ,

d

/ k aph

Ca = 1.93 ⋅10 −3

ϕd = 0.437 .

S1( .

2, 3,

, < τ df > = 0.482 ,




, .

– < τ df > = 0.623 . 127

-

= 30 /

. 4.19). -

, -

(2.9),



∞

I df (t ) =

t 

∫ exp− τd  ⋅ ψ(τ ∞

∫ ψ(τ

0

d

)dτ

: d

) dτ d .

0

~d ϕ < ~τ d >

. 4.20 d d ~ d = ϕ , < ~τ d > = < τ > , ϕ < τ0d > ϕ0d

bd .

.

~d ϕ < ~τ d >

(4.29)

d

ϕ 0d

< τ 0d > –

-

, .

, ,

, ,

.

-

, .

ϕd

. 4.21 ba (

bd

ba

1–3).

ϕd

,

, S0-

. , , , .

, -

,

,

:

 b a   C a′ = C a ⋅ 1 − a .  b + k aph    128

(4.30)

1.0

ϕd ϕ0d

3’

1.0

3

0.8

ϕd ϕ0d

4’ 4

’

’

2 0.5

1

2

2’

0.4

’

1

3

3

0.6

2 1’

1

0.2 0.0

10–1

0.0

1 10 d a b / k ph

10–1

1 a b / k ph

10

d

. 4.22.

. 4.21. a b d . b a k ph = 10–1 (1, 1’ ), 1(2, 2’ )

a b a . b d k ph =1 (1, 1’), 10 (2, 2’), 30(3,

10 (3, 3’ ). -

3’) (1–3)

-

(1’–3’ ); Ca = 10–2

/

100 (4, 4’). -

C a′ (4.27, 4.28). 1’–3’). (

. 4.21 ( b

d

b

(1–4)

(1’–4’); Ca = 10–2

/

. 4.21)

1–3

a

, -

. (4.30)

"

" ( .

. 4.22). Э

. –

.

,

, .

, ( ).

, . 129

(4.30)

, -

ϕd ϕ0d

1.0

, ,

3

0.8

b

d

b

a

.

4

-

, b ~ bd . a

0.6

5

0.4

1 2

0.2

. 4.23. 0.0

10-1 1

-

102 103 104 a b d / k ph

10

. 4.23.

,

b . b / k = 0(1), 5(2), 50 (3). d

a

-

T1-

a ph

b a / b d = 0.5(4), 2 (5)

.

,

,

S0– T1-

,

,

-

. , -

.

, . .

,

S0-,

– k et(1)

k et( 2)

T1-

( ). ,

, , S0– T1ϕ dS Ca T1-

: ϕTd

ϕ d = ϕ dS ⋅ ϕTd .

(4.31) -

(4.27, 4.28) T1-

CaT :

.

C aT = C a − C a , 130

(4.32)

Ca –

(4.28).

ϕ dS

, :

ϕ dS

(

ϕTd

. 4.17),

ϕTd

( , ,

,

.4. 24).

(

,

T1,

, 4.3.1.

k et( 2) < k et(1)

,

(

. 4.25).

, ,

(

,

-

> k et(1) – k et( 2) < k et(1)

k et( 2)

. 4.26),

. 4.27).

, ,

S0-

, , T1k et( 2)

>

. k et(1) ,

1.0

1

ϕ d ϕ 0d

, . .

2 3

0.6

2

S01

0.8

0.8

0.4

0.6

6 7

3 0.0

10

1

2

10 10 a b d / k ph

3

10

4 5

0.2

0.4

–1

-

-

ϕTd ϕ 0d 1.0

0.2

,

10–1

1

10 102 a b d / k ph

103

. 4.25. ϕd bd . –3 –3 –2 Ca = 10 (1,5), 3·10 (2, 7), 10 (3, 4, 6) / , k et( 2) k et(1) = 10(5, 7), 10–1(1, 2, 6), 10–2(4), 10–3(3)

. 4.24. ϕTd bd . Ca = 10–3 (1), 10–2 (2, 3) / , ( 2) (1) k et k et = 0.1 (1, 3), 0.01 (2) 131

ϕ d ϕ 0d

1.0 0.8

0.7

1

ϕ d ϕ 0d

0.6 0.5

2

0.6 0.4

3 4

0.2

5

0.0

0.4

0.2

2

0.1

10–1

1

10 102 a b d / k ph

0.0

103

. 4.26. ϕd bd . Ca = 10–3(1), 3·10–3(2), 10–2 (3, 4, 5) / , ket( 2) ket(1) = 10–1 (1, 2, 4), 10–2 (4), 10–3(3). , -

10–1 1

10 102 103 a b d / k ph ϕd

. 4.27. Ca= 10–3(1), 3·10–3(2) k et( 2) k et(1) = 10.

bd .

/ , -

S0. (4.31, 4.32),

T1(

1

0.3

, . . ,

-

. 4.27). 4.3.4

я

я

я

[26–31] [26, 28],

-

, [26].

0-0-

.

,

,

, 132

-

.

. b = 0. a

I 0f (ν)

" 0-0-

. 4.28). ρ(∆ν)

ν ex bd d I (ν ex , ν r , b ) = C τ 0d

τ 0d ∞

. νr

:

∫ ∫ I f (ν r − ∆ν) ⋅ ε

0 −∞ d

0

0

× τ ψ (τ ,bd′ )d (∆ν)d τ d , d

C=

ε 0 (ν )

" (

τ0d ∞

∫ ∫ ρ(∆ν) ⋅ ψ(τ 0 −∞

-

d

,bd′ )d (∆ν)d τ d ,

bd′ = b d ⋅ ε 0 (ν ex − ∆ν) . (4.33) δ δ

. 4.29 . :

∞  ∫ I (ν ex , ν r )ν r dν r  δ < ν >=  0∞  I (ν ex , ν r )dν r  ∫  0

(ν ex − ∆ν) ⋅ ρ(∆ν) × ,

 ∞   ∫ I (ν ex , ν r )ν r dν r   −  0∞     d  ∫ I (ν ex , ν r )dν r b  0

-

bd

   . (4.34)    d b →0

,

. .

bd′ ,

, 0-00-0-

.

133

, bd

-

ε 0 , I 0f ,

1.0

.

0.8

.

0.2

δ < ν > ⋅10 −3 ,

–1

4 0.6

0.1

1

2

5

3

0.4

2

0.0

0.2

1 0.0 13

15

17

21 23 ⋅10-3,

19

"

. 4.28. "

-0.1 –1

-

1

. 4.29. bd .

(1)

102

10

δ ex =19(1), 20(2), 21(3),

22(4), 23⋅103 (5)

(2)

,

103 a b d / k ph

–1

,

= 500

–1

.

.

(

. ,

. 4.17)

δ

, .

δ

d

( я,

я

я

bd I (ν ex , ν r , b , t ) = C d

τ 0d ∞

∫∫

I 0f (ν r 0 −∞

1).

.

я

я

,

я

b . 4.29,

,

:

− ∆ν) ⋅ ε (ν ex − ∆ν) ⋅ ρ(∆ν) ⋅ e 0

-

−

t τd

×

× ψ(τ d ,bd′ )d (∆ν)d τ d C=

< τd >

+∞ τ0

∫ ∫ ρ(∆ν) ⋅ ψ(τ d

−∞ 0

d

,bd′ )d τ d d (∆ν) .

(4.35)

(

d

, 134

). .

4.30,

. 0-0-

(

. 4.30,

, -

2) bd

, . . ,

S1-

.

-

. (

. 4.31).

(

(

1),

3). ,

-

, .

(

, P0 = 0.5)

:

τ d τ0d

0.35 0.30

1

0.5

2

0.3

3

0.1

δ < ν f > ⋅ 10–3,

–1

1

0.25 0.20

2 -0.1

0.15

3

0.10

-0.3 16

.

17

18

19

ν ⋅ 10–3,

20

0.0 0.2 0.4 0.6 0.8 1.0 1.2

t / τ 0d

–1

19(2), 22·103

δ

. 4.31.

4.30. . ν ex = 20(1), –1 (3), σ = 500 –1

3

19·10

135

–1

ν ex = 22(1), 20(2), (3), σ = 500 –1

(

)

I II ν ex , ν r , b d = C1 ⋅ 2π

(

)

I ⊥ ν ex , ν r , b d = C1 ⋅ π

π +∞ 2

∫ ∫ I f (ν r − ∆ν) ⋅ X 0

−∞ 0

π +∞ 2

0

τ0d

X d (θ, ∆ν, b d ) = C1=

(θ, ∆ν) ⋅ ρ(∆ν) ⋅ cos 2 (θ) ⋅ sin(θ)×

× d (∆ν)dθ ,

∫ ∫ I f (ν r − ∆ν) ⋅ X

−∞ 0

d

∫ε

0

d

(θ, ∆ν) ⋅ ρ(∆ν) ⋅ sin 3 (θ)d (∆ν)dθ,

(ν ex − ∆ν) ⋅ τ d ψ (τ d ,bd′′ )dτ d

0

τ0d

,

τ 0d ∫ ψ (τ d ,bd′′ )dτ d 0

1

+∞

∫ ρ(∆ν)d (∆ν)

, bd′′ = b d ⋅ ε 0 (ν ex − ∆ν) cos 2 (θ).

(4.36)

−∞

θ–

-

, X d (θ, ∆ν) – θ

0-0(4.36)

,

, X d (θ, ∆ν)

cos 2 θ ,

.

θ

θ.

S1, , -

0.5.

, (

)

, S0-

,

.

,

S1-

3⋅10–2

,

. 18

( 136

R0 = 50 Å),

-

/ -

n-

S1 → S 0

.

-

,

T1.

θ

,

-

S1cos 2 θ , 0.5

. ( ∆ν ), bd′ = b d ⋅ ε 0 (ν ex − ∆ν) cos 2 (θ) ,

0-0-

, .

.

-

. 4.32

, . , -

. 4.32

, ( (

1–2), 3). Э

, 0.65

P

0.64

4

0.62

0.63

0.60

3 0.60

P

0.58

2

0.56

0.58

0.54

1

0.52

0.55

0.50 14

16

18

20 –3 ν ⋅ 10 ,

10-1

1 10 102 103 104

–1

a b d / k ph

. 4.32. .b

a k ph

d

2

b .

= 5(1), 10(2), 10 (3),

10 (4); νex = 22·10 3

3

-

. 4.33.

d

–1

, σ = 700

C a = 3·10–3

–1

137

/

. (

.

-

. 4.17).

0.5.

,

νr ,

P .

0-0-

(

. 4.33). . 4.32,

-

.

0-

,

0, -

( (

), (

)

)

. .

-

,

,

θ,

.

,

,

: τ0d

X d (θ, ν ex , b d , t ) =

∫ε 0

0

(ν ex − ∆ν) ⋅ e τ0d

∫ ψ(τ

d

−

t τd

⋅ ψ(τ d ,bd′′ )dτ d

,bd′′ )dτ d

.

(4.37)

0

. 4.34

,

S1, , .

X (θ, ν ex ) d

. 138

,

-

Xd ,

1

.

1 2 3 4

0.5

−

0

π 2

π 2

0

θ

. 4.34.

. t τ0d = 0(2), 0.5(3), 1 (4).

a=

3·10–2 (2–4), 0

/ (1)

-

,

S1-

,

, -

. (4.36)

(4.37) -

:

I II (ν ex , ν r , b , t ) = 2π ⋅ C2 d

π d + ∞ τ0 2

∫ ∫ ∫b

−∞ 0 0

d

⋅ε

0

(ν ex − ∆ν) ⋅ ρ(∆ν) ⋅ I 0f (ν r

− ∆ν) ⋅ e

−

t

τd

×

× ⋅ψ(τ d ,bd′′ ) cos 4 (θ) ⋅ sin(θ) d (∆ν)dτ d dθ , I ⊥ (ν ex , ν r , b , t ) = π ⋅ C2 d

C2 =

+ ∞ τ0

π d + ∞ τ0 2

∫ ∫ ∫b

−∞ 0 0

d

⋅ε

0

(ν ex − ∆ν) ⋅ ρ(∆ν) ⋅ I 0f (ν r

× ψ (τ d ,bd′′ ) ⋅ cos 2 (θ) ⋅ sin 3 (θ)d (∆ν)dτ d dθ ,

∫ ∫ ρ(∆ν) ⋅ ψ(τ d

−∞ 0

d

,bd′′ )d (∆ν)dτ d .

. 4.35, 4.36 139

− ∆ν) ⋅ e

−

t

τd

×

(4.38)

0.75

0.9

P

4

0.70

P

6

0.8

0.65 0.60 0.55 0.50

3

0.7

2 1

0.6

5 4 3 2

0.5

1

0.45 13 14 15 16 17 18 19 20 ν ·10–3, –1

19

(1, 2)

22 23 –3 ν ·10 , –1

-

–1

23·103

–1

ex = 19·10

(1–3)

, -

3

σ = 700

21

. 4.36.

. 4.35.

ex =

20

,

100 (3, 4). d a , b k ph = 103(1,4)

100

(4–6). ν reg = 16·103

–1

,

a b d k ph = 10(3, 4), 102(2, 6)

103(1, 5), σ = 700

a , b d k ph = 10(2,3),

-1

–1

.

, . ,

.

140

1.

.

. . , 1972. 264 .

2.

:

/

1989. 319 .

3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37.

.

. .

.:

-

.:

,

. . 1960. . 8, № 6. . 777–786. ., . . .: . . 1961. 305 . . . // . . 1961. . 10, № 6. . 717–726. . . // . . 1964. . 16, № 5. . 821–832. Liptey W. // Z. Naturforsch., 1965. V. 20a, № 11. P. 1441–1471. . // . .: , 1968. . 179–206. . ., . ., . . // . . 1968. . 24, № 6. . 901–909. . . .: . . 1960, 250 . . ., . . // , 1961. . 74, № 1. . 3–30. . . // . . 1962. . 12, № 5. . 557–564. . . // . . 1965. . 19, № 3, . 345–353. . ., . . // . . 1964. . 16, № 2. . 351–359. . . // . . 1962. . 12, № 3. . 350–358. . . // . . 1962. . 12, № 4. . 473–478. . . // . . . . 1960. . 24, № 5. . 587–590. . . // . . 1962. . 13, № 2. . 192–199. . . // . . 1962. . 13, № 1. . 43–51. . . // . . . 1962. . 7., № 8. . 920–298. Abe T. // Bull Chem. Soc. Japan. 1965. V. 38, № 8. P. 1314–1318. . ., . . // . . 1973. . 34, № 5. . 902–906. . . // . . 1975. . 38, № 4. . 803–805. . . // . . 1975. . 38, № 5. . 1034–1035. . . // . . . . 1973. . 37, № 2. . 284–289. . ., . . // . . 1970. . 29, № 6. . 1082–1086. . ., . . // . . 1971. . 30, № 2. . 275–278. . ., . . // . . 1971. . 32, № 2. . 424–427. . ., . ., . ., . ., . . // . . 1976. . 46, № 1. . 64–69. Galley W.C., Purkey R.M. // Proc. Nat. Acad. Sci. USA. 1970. V. 67, № 3. P. 1116–1121. . ., . . // . . . 1972. . 16, № 6. . 1017–1022. . . // . . . 1976. . 25, № 3. . 480–487. . . // . . 1972. . 33, № 1. . 42–50. . ., . . . .: , 1964. 240 . . . .: . . 1967. 276 . . . // . . 1976. . 40, № 5. . 940–942. . . // . . . . 1973. . 37, № 3. . 615–618. . .,

. . //

.,

141

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143

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.

. 1988. . 65,

. . //

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. 1987. . 62,

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" //

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. . //

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148

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3.3. В

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55

71

3.4. З ......................... 149

85

4. 4.1. Н 4.1.1. М 4.1.2. К 4.1.3. Д

я

я

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96

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4.2. Н 109

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............................................... 4.3.1. М ................................. 4.3.2. .............. 4.3.3. К .............. 4.3.4. я я я .......... .......................................................

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