80 4 r ˆρ i (r, t) δ(r x i (t)) (4.1) x i (t) ρ i ˆρ i t = 0 i r 0 t(> 0) j r 0 + r < δ(r 0 x i (0))δ(r 0 + r x j (t)) > (4.2) r r 0 G i j (r, t) dr 0

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1 x i (t) x j (t) O O r 0 + r r r 0 x i (0) r 0 x i (0) 4.1 L. van. Hove 1954 space-time correlation function V N 4.1 ρ 0 = N/V i t

2 80 4 r ˆρ i (r, t) δ(r x i (t)) (4.1) x i (t) ρ i ˆρ i t = 0 i r 0 t(> 0) j r 0 + r < δ(r 0 x i (0))δ(r 0 + r x j (t)) > (4.2) r r 0 G i j (r, t) dr 0 < δ(r 0 x i (0))δ(r 0 + r x j (t)) > (4.3) G i j (r, t) =< δ(r + x i (0) x j (t)) > (4.4) x i (0) x j (t) G ij (i, j) N G(r, t) 1 N < δ(r + x i (0) x j (t)) > (4.5) i,j i j i = j G(r, t) = 1 N N < δ(r + x i (0) x i (t)) > + 1 N i=1 < δ(r + x i (0) x j (t)) > (4.6) i j self correlation G s (r, t) distinct correlation G d (r, t) ˆρ i ˆρ(r, t) i ˆρ i (r, t) = i δ(r x i (t)) (4.7) G(r, t) = 1 dr 0 < ˆρ(r 0, 0)ˆρ(r 0 + r, t) > (4.8) N

3 r 0 0 V G(r, t) = 1 ρ 0 < ˆρ(0, 0)ˆρ(r, t) > (4.9) ρ 0 δ ˆρ ˆρ(r, t) = ρ 0 + δ ˆρ(r, t) (4.10) < δ ˆρ(r, t) > 0 G(r, t) = ρ < δ ˆρ(0, 0)δ ˆρ(r, t) > (4.11) ρ 0 density correlation function G ρ 0 G(r, t) 1 < δ ˆρ(0, 0)δ ˆρ(r, t) > (4.12) ρ 0 S(q, ω) G(r, t)e i(q,r ωt) drdt (4.13) t = 0 G(r, 0) = 1 < δ(r + x i (0) x j (0) > (4.14) N i,j S(q) G(r, 0)e iq r dr = 1 < e iq (x i x j ) > (4.15) N G(r, 0) = G s (r, 0) + G d (r, 0) (4.16) i,j G s (r, 0) = δ(r) (4.17) G d (r, 0) = 1 N < δ(r + x i x j ) > (4.18) i j

4 82 4 (r ) G d (, 0) = N(N 1)/NV ρ 0 G d (r, 0) ρ 0 g(r) (4.19) g(r) g( ) = 1 g(r) radial distribution function r r G(r, 0) = δ(r) + ρ 0 (g(r) 1) (4.20) S(q) (4.12) ρ 0 S(q) = < δ ˆρ(0, 0)δ ˆρ(r, 0) > e iq r dr = ρ 0 S(q, ω)dω (4.21) S(q) S(q) g(r) r 0 r 0 1 r 4.2 «3/2 β f(v) = exp» βm2 2πm v2 (4.22) x i (t) x i (0) = vt G s (r, t) = 1 N NX Z < δ(r + x i (0) x i (t)) >= δ(r vt)f(v)dv = i=1 β 2πm «3/2 exp» mβr2 2t 2 (4.23)

5 V (r) x i i V (x i ) H = H 0 + V (x i ) = H 0 + ˆρ(r)V (r)dr (4.24) i ˆρ(r) r < ˆρ(r) > V 0 = ˆρ(r)e β(h 0 +H ) dγ e β(h 0 +H ) dγ (4.25) H < δ ˆρ(r) > V 0 χ(r r )V (r )dr (4.26) χ(r r ) β < δ ˆρ(r)δ ˆρ(r ) > V =0 = βρ 0 G(r r, 0) (4.27) χ(r) response function χ(q) χ(r)e iq r dr = βρ 0 S(q) (4.28) < δ ˆρ(q) >= βρ 0 S(q)V (q) (4.29) S(q) ω < δ ˆρ(q, ω) >= βρ 0 S(q, ω)v (q, ω) (4.30)

6 (q 0) (4.21) q 0 ρ 0 S(0) = < δ ˆρ(0)δ ˆρ(r) > dr = 1 V < ( ) 2 drδ ˆρ(r) >= 1 V < (δn)2 > (4.31) N δn = N < N > < (δn) 2 > N = ρ 0 k B T κ T (4.32) κ T 1 ρ ( ) ρ = 1 p T V ( ) V p T (4.33) S(0) = ρ 0 k B T κ T (4.34) q 0 sum rule 4.3

7 g(r) r g( ) = 1 h(r) g(r) 1 (4.35) total correlation function S(q) = 1 + ρ 0 (g(r) 1)e iq r dr (4.36) structure factor L.S.Ornstein F.Zernike direct correlation function c(r) 1914 h(r) c(r) + ρ 0 c( r r )h(r )dr (4.37) S(q) 1 + ρ 0 h(q) = 1 1 ρ 0 c(q) (4.38) c(r) 0 c(r) S(q) 4πr 2 (g(r) 1) = 2r πρ 0 0 dq q sin qr S(q) (4.39) S(q) g(r) (4.37) (1) HNC Hypernetted Chain 1957 h(r) c(r) = ln[1 + h(r)] + βu(r)

8 86 4 u(r) (2) PY Percus Yevick 1958 ln[1 + h(r) c(r)] = ln[1 + h(r)] + βu(r) ln h(r) c(r) HNC c(r) (4.37) c(r) h(r) σ c(r) PY ρ η πσ 3 ρ/6 1 h c(r) = (1 + 2η) 2 6η(1 + η (1 η) 4 2 )( r σ ) + η 2 (1 + 2η)2 ( r σ )3i (r < σ) = 0 (r < σ) S(q) = 1 N < e iq r i j > (4.40) i,j r i j x i x j q form factor a V = 4πa 3 /3 ω n V/ω 4.4(a) S(q) = 1 nω 2 dr 1 dr 2 e iq r 1 e iq r 2 = 1 nω 2 = 1 nω 2 a π 0 0 2πr 2 sin θdθdre iqr cos θ 2 [ ] 2 4π (sin qa qa cos qa) (4.41) q3

9 q = 0 1 P (x) S(q)/S(0) ( ) 2 3 P (x) = x 3 (sin x x cos x) 2 (4.42) x = qa q z q q n r r r y x (a) (b) (c) 4.4 a 4.4(b) P (x) = 2 1 J «1(2x), (x qa) (4.43) x 2 x J 1 (x) l 4.4(c) P (x) = 1 x Z 2x 0 sin y y dy x 1 P (x) 1/x 1/q «2 sin x, (x = ql) (4.44) x i j r i j = x i x j ( ) [ ] 3/2 3 P 0 (r ij ) = 2πa 2 exp 3r2 ij i j 2a 2 i j (4.45) 0 < (r i j ) 2 > 0 = a 2 i j S(q) = 1 < e iq r i j > 0 = 1 n n q 2 a 2 /6 κ S(q) = 1 n n 0 di n 0 ij dj e κ i j = 1 nκ n 0 i j e 1 6 q2 a 2 i j (4.46) di[2 e κi e κ(n i) ] nd(x) (4.47)

10 88 4 x nκ = na 2 q 2 /6 =< s 2 > 0 q 2 < s 2 > 0 na 2 /6 x D(x) D(x) 2 x 2 (e x 1 + x) (4.48) Debye s scattering function x 1( D(x) 1 x/3 x 1 D(x) 2/x < s 2 > 0 q 2 1 q 2 S(q) I(q) q 2 I(q) q Kratky s plot 4.5 q S(q) q 1 q 2 I(q) 2/q 2 q 2 (1-R 0 2q 2 /3) rod-like 0 R 0-1 l p -1 q Guinier range 4.5 submolecular range θ λ = 1.6A k 0 = 2π/λ ε 0 = 2 k0/2m 2 300K 1/2 (k 0, s) n > s s = ±1/2 k 0 ψ 0 = e ik0 r / L 3 L 3

11 L k, s' d k 0, s n> 4.6 j j ψ 0 2 v = v L 3 = k 0 ml 3 (4.49) v = k 0 /m θ k ε = 2 k 2 /2m k k 0 q ε ε 0 ω ω = 0 (k, s ) n > 2π/L dω (k, k + dk) k 2 dkdω (2π/L) 3 = ml3 k 8π 3 dωdε (4.50) 2 d 2 σ dωdε (4.51) dωdε v = hk/m k 0 ds = 1 4.7

12 90 4 θ dω (ε, ε + dε) δ V (r) = 2π 2 b j δ(r x j ) (4.52) m E.Fermi x j j b j j scattering length m 4.8 j x j a j 4.8 µ = g n µ n s µ n = e /2m g n = g j x j A j (r) = µ (x j r) x j r 3 (4.53) V (r) = [ e 2m j e c [ p A j(r) + A j (r) p ] + e ] 2m e c σ A j(r) (4.54) µ e = (e /2m e c)σ m e σ 4.9

13 = g n B s = g B s j x j 4.9 dω W (nk 0 s n ks ) 4.50 M.Born W (nk 0 s n ks ) = 2π < n s 1 L 3 V (q) ns > 2 δ ( 2 k 2 2m + E n 2 k0 2 ) 2m E n (4.55) V (q) V (q) dr V (r)e iq r (4.56) q = k k 0 d 2 σ dωdε = k ( m ) 2 <n s V (q) ns> 2 δ( ω + E n E n ) (4.57) k 0 2π ω 2 k 2 /2m 2 k 2 0/2m δ P n = e βe n /Z w s (n s ) d 2 σ dωdε = ns P n w s n s k ( m ) 2 <n k 0 2π 2 s V (q) ns> 2 δ( ω + E n E n ) (4.58) V (q) = 2π 2 m b j e iq x j (4.59) j

14 92 4 d 2 σ dωdε = k P n w s < n s b j e iq x j ns > 2 δ( ω + E n E n ) (4.60) k 0 ns n s j j b j b d 2 σ dωdε = k k 0 b 2 nn P n <n j e iq x j n> 2 δ( ω + E n E n ) = AS(q, ω) (4.61) A A (N/2π )(k/k 0 )b 2 S(q, ω) S(q, ω) = G(r, t)e i(q r ωt) drdt (4.62) b i b j = b 2 δ i j + b 2 (1 δ i j ) (4.63) b i b j = (b 2 b 2 ) δ i j + b 2 (4.64) d 2 σ [ ] dωdε = A b 2 S(q, ω) + (b 2 b 2 ) S s (q, ω) (4.65) G s (r, t) ω dσ dω = d 2 σ dω = AS(q) (4.66) dωdε S(q) = 1 + ρ 0 g(r)e iq r dr (4.67)

15 ˆρ(r) = ρ 0 + δ ˆρ(r) d 2 σ dωdε = A[ρ 0δ(ω)δ(q) + S(q, ω)] (4.68) S(q, ω) = 1 ρ 0 < δ ˆρ(0, 0)δ ˆρ(r, t) > e i(q r ωt) drdt (ω 0) (4.69) 4.3 k dr' r k 0 r' O E = E 0 e i(k r- t) τ I 0 d I I I = I 0 e τd (4.70) τ turbidity Lord J.W.S.Reyleigh α ρ τ = 8π 3 ω0 4 c 4 α 2 ρ (4.71) 0

16 ω 0 c 0 C ρ = /cm 3, n 1 = 2πρα = n D λ 0 = 5890A τ = /cm τ 1 = 115km ε τ = ω4 0 6πc 4 0 [ ( ) 2 ε k B T ρ 2 χ T + k BT 2 ρ ρc v ( ) ] 2 ε T (4.72) χ T c v λ 0 = 2π/k 0 ω = c 0 k 0 c 0 k 0 n θ ε n = ε/ε 0 ε 0 c = c 0 /n λ = λ 0 /n ω r E in E in (r, t) = E 0 e i(k 0 r ωt) (4.73) k 0 E 0 = 0 r ε ε(r, t) = ε + δε(r, t) δp(r, t) = δε(r, t)e in (r, t) (4.74) r δe δe(r, t) = k2 0 4πɛ 0 r (r δp(t)) r 3 e i(k r ωt) (4.75) δp δp(t) = δε(r, t) E 0 e iq r dr (4.76) q k k k r k = k 0 e e r/r

17 I I = (ɛe 2 /2)c = ε/µ E 2 /2 < > I(e) = 1 ( ) 1/2 ε0 < δe 2 > 2 µ 0 = 1 ( ) 1/2 ε0 k (k E 0 ) 2 2 µ 0 (4π ɛr) 2 < δε(r 1 t)δε(r 2 t) > e iq (r 1 r 2 ) dr 1 dr 2 k 4 sin 2 θ 1 = I 0 (4π ɛr) 2 < δε(r 1 t)δε(r 2 t) > e iq (r 1 r 2 ) dr 1 dr 2 (4.77) I 0 (ε 0 /µ 0 ) 1/2 E 2 0/2 z k x θ 1 y θ 2 z θ 4.12 sin 2 θ 1 xz yz sin 2 θ 2 (sin 2 θ 1 + sin 2 θ 2 )/2 = (1 + cos 2 θ)/2 Rayleigh ratio R θ Ir 2 I 0 V (1 + cos 2 θ) (4.78) V R θ = 1 ( ) 2 1 k 4 < δε(0, t)δε(r, t) > e iq r dr (4.79) 2 4π ɛ ε ρ δε δρ δε(r, t) = ( ) ε δρ(r, t) ρ ε 1 ε + 2 = 4π αρ (4.80) 3

18 R θ = 1 ( ) 2 ( ) 2 1 ε k 4 < δ ˆρ(0, t)δ ˆρ(r, t) > e iq r dr (4.81) 2 4π ɛ ρ T G(r, t) R θ = Kc S(q) (4.82) K c S(q) P (θ) R θ /R θ=0 = S(q)/ S(0) (4.83) R θ Kc = 1 < e iq r i j > (4.84) N i,j 4.13 I(e, ω) 1 ( ) 1/2 ε0 δe(r, t)δe (r, 0)e iωt dt (4.85) 2 µ 0 R θ (ω) = 1 k 4 ( ) 2 ε 2 (4π ɛ) 2 ρ 0 S(q, ω) (4.86) ρ

19 λ q r 0 e iq r δε(r, t) = ε 0 α i δ(r x i (t)) (4.87) i e iq r 1 I ( = k 4 ɛ ) 2 0 sin 2 θ 1 I 0 ɛ (4πr) 2 j <αj 2 > (4.88) < α i α j > < α 2 i > Rayleigh s scattering formula k 4

20 98 4 sin 2 θ (1 + cos2 θ) θ τ I ( tot ɛ0 ) 2 ρ0 α 2 = C I 0 ɛ r 2 λ 4 (4.89) α 2 < α 2 i > /N C ρ λ S(q) x i i c q c S(q, c) S(q = 0, c) = RT M K T 1 c ( ) c = crt π T M K T (4.90) ( ) c π T (4.91) isothermal osmotic compressibility c M K 1 T = crt (1/M + 2A 2 c + ) (4.92) A 2 q c 0 S(q, c = 0) P (θ) S(q, 0) = S(0, 0)P (θ) = MP (θ) Kc R θ = 1 MP (θ) + 2A 2c + (4.93) c 1 M ( < s2 > q 2 + ) (4.94)

21 < s 2 > B.Zimm 4.90 N 0 Ω N 1 n N 0 Ω = nn 1 + N 0 δφ = δ «nn1 = Ω nn0 Ω 2 «δn 1 < (δn 1 ) 2 >= k B T/( µ 1 / N 1 ) T N 1 dµ 1 + N 0 dµ 0 = 0 µ 1 = N 0 a 3 π = n a 3 φ 2 π 0 N 1 N 1 N 1 N 1 φ <(δn 1 ) 2 >= k BT N 1 a 3 n φ K T (4.95) φ 2 0 K T S(q = 0) =<( R δφ(r)dr) 2 > /φω = (nφ 0 ) 2 <(δn 1 ) 2 > /φω S(q = 0) = k BT a 3 φk T = crt M K T (4.96) α, β

22 100 4 i, j α i t x α i (t) ˆρ α i (r, t) δ(r x α i (t)) (4.97) 4.15 V a 3 Ω V/a 3 a (α, i) < ˆρ α i (r, t) >= 1/Ω ˆρ α i (r, t) = 1/Ω + δ ˆρ α i (r, t) A B A r t ˆφ A (r, t) = α ˆρ α i (r, t) i A < ˆφ A (r, t) > dr = φ A φ A = n A N A /Ω A B φ A = f A n A A N A A ˆφ A (r, t) = φ A + δ ˆρ α i (r, t) (4.98) α G αβ i A i j (r, t) < δ(r + xα i (0) x β j (t)) > = < ˆρ α i (r, 0)ˆρ β j (r + r, t) > dr G αβ i j (r, t) = 1 Ω + < δ ˆρ α i (r, 0)δ ˆρ β j (r + r, t) > dr

23 G αβ i j α β t = 0 A G αβ i j G AA (r, t) = G αβ i j (r, t) =< ˆφ A (0, 0) ˆφ A (r, t) > (4.99) α,β i j A A G AB (r, t) I(q, ω) = k k 0 α,β i,j b α i b β j Sαβ i j b α i S αβ i j (q, ω) Gαβ i j (r, t) S αβ i j (q, ω) = (q, ω) (4.100) α i G αβ i j (r, t)ei(q r ωt) drdt (4.101) G I(q, ω) = k b α i b β αβ j S i j k (q, ω) Ω αβ i j αβ b α i b β j δ(q) δ(ω) (4.102) i j ω = 0 I(q, ω) = k k 0 b2 αβ i j b α i bβ j = b 2 + (b 2 b 2 ) δ αβ δ i j (4.103) S αβ i j (q, ω) + (b2 b 2 ) α,i S αα i i (q, ω) + elastic term (4.104) 4.5 I(q) = αβ i,j b α i b β j Sαβ i j (q) (4.105)

24 102 4 S αβ i j (q) (α, i) (β, j) G αβ i j (r, 0) < δ(r + xα i (t) x β j (t)) > (4.106) ˆρ α i (r, t) = 1 (4.107) α,i δ ˆρ α i (r, t) = 0 (4.108) α,i t < δρ α i (r) >= β dr Sαβ i j (r, r ) V β j (r ) (4.109) β,j V β j (r ) r (β, j) S β 1/k B T S r r δv (r) (α, i) (β, j) χ 4.29 < δ ˆρ α i (q) >= β βj S αβ i j (q) V β j (q) (4.110) α <δ ˆρ α i (q)>= β βj S 0 (q) αβ i j V β j (q) (4.111) ( S 0 ) αβ i j

25 < δ ˆρ α i (q) >= β βj S 0 (q) αβ i j V β j (q) β 1 χ βγ j l < δρ γ l γ,l (q) > +δv (q) (4.112) χ βγ j l (β, j) (γ, l) χ 0 δv (q) α i δv δv (q) = [(Ŝ0 ) (1 + ˆχ Ŝ)]αβ αβ,i j i j V β j (q)/ αβ,i j ( S ˆ0 ) αβ i j (4.113) < δ ˆρ α i (q) > S S Ŝ(q) 1 = ˆQ(q) 1 ˆχ (4.114) Ŝ(q) = 1 1 ˆQ(q) ˆχ ˆQ(q) (4.115) ˆQ ˆQ Ŝ0 (Ŝ0 e) : ( t e Ŝ0 )/( t e Ŝ0 e) (4.116) e t e Q αβ i j (q) = S0 (q) αβ i j ( ) S 0 (q) αγ i l S 0 (q) δβ mj / S 0 (q) αβ i j (4.117) γl δm αβ,i j random phase approximation RPA S 0 (q) αβ i j = 1 Ω δ αβj ij (4.118) RPA J ij e κ i j κ (aq) 2 / J ij J i j = 1 κ (2 e κi e κ(n i) ) (4.119) j

26 α i j J i j = n 2 D(x) (4.120) i j x nκ = na 2 q 2 /6 D(x) 4.48 A B A B τ α i b α i = A τ α i + B(1 τ α i ) (4.121) (α, i) A 1 B 0 χ αβ i j = χ { τ α i (1 τ β j ) + (1 τ α i )τ β j } (4.122) I(q) = (A B) 2 τi α τ β j Sαβ i j (q) (4.123) αβ,i j RPA 5.43 I(q) = (A B) 2 S(q) (4.124) S(q) 1 G(q)/W (q) 2χ (4.125) G W G(q) = SAA 0 + SBB 0 + 2SAB 0 (4.126) W (q) = SAAS 0 BB 0 [SAB] 0 2 (4.127)

27 S 0 SAA 0 = 1 J i j τi α τj α Ω α i j SBB 0 = 1 J i j (1 τi α )(1 τj α ) Ω α i j SAB 0 = 1 J i j τi α (1 τj α ) Ω α i j (4.128) A B RPA A B n A A N A n B B N B Ω = n A N A + n B N B 4.17 S 0 AA = N A Ω S 0 BB = N B Ω S 0 AB = 0 e κ i j = n A φd(x) i j e κ i j = n B (1 φ)d(y) i j (4.129) D(x) x < s 2 > A q 2 = n A (aq) 2 /6 y < s 2 > B q 2 = n B (aq) 2 /6 S(q) 1 = 1 n A φd(x) + 1 2χ (4.130) n B (1 φ)d(y)

28 106 4 q 0 S(0) 1 = 1 n A φ + 1 2χ (4.131) n B (1 φ) K T RPA A n A = n B n B = 1 A D(x) B D(y) = 1 S(q) 1 = 1 nφd(x) + 1 2χ (4.132) 1 φ x < s 2 > 0 q 2 1 D(x) 2/x = 2/ <s 2 > 0 q 2 S(q) = A q 2 + κ 2 = S(0) 1 + q 2 ξ 2 (4.133) A κ A 2nφ <s 2 = 12φ > 0 n 2 (4.134) κ 2 1/(1 φ) 2χ <s 2 nφ = 6φ > 0 a 2 ( 1 2χ) (4.135) 1 φ φ 1 κ 2 12(1/2 χ)φ/a 2 1/2 χ κ ξ κ 1 RPA a 2 ξ RP A = κ 1 = ( 12(1/2 χ)φ )1/2 = (φτ) 1/2 (4.136) Θ τ = 1 Θ/T 1/2 χ = ψτ (1/2 χ)a 3 ξ φ 3/4 τ 1/4 (4.137)

29 H D b H = cm (4.138) b D = cm (4.139) D H χ 0 A = B I(q) = 0 A B SAA 0 (q) = N 1 ( nn n2 D(x) = 1 1 ) nd(x) N SBB 0 (q) = 1 nn n2 D(x) = n N D(x) SAB 0 (q) = 0 (4.140) x na 2 q 2 /6 G(q) = nd(x) W (q) = (1/N)(1 1/N)n 2 D(x) 2 S(q) = 1 N ( 1 1 ) nd(x) (4.141) N D(x) N D nd(x) (N D /N)(1 N D /N) 1974 A B SAA 0 = 1 nn N(n 1)2 D(x) nd(x) SBB 0 = 1 1 = 1 nn n S 0 AB = N nn α J i j = E(x) j (4.142)

30 E(x) E(x) (1 e x )/x (4.143) G(q) = nd(x) + 2E(x) W (q) = D(x) E(x) 2 S(q) = 1 {1 (1 e x ) 2 } n 2(x 1 + e x (4.144) ) B B A B 4.19 correlation hole 4.19

31 A B S 0 AA nd(x) SBB 0 1 nn 2N (1 + e κn ) = 2 n (1 + e x ) SAB 0 1 nn 2N J i j = 2E(x) j (4.145) S(q) = 2 {1 + e x (1 e x ) 2 } n x 1 + e x (4.146) block copolymer A B 4.20 A n A B n B n = n A + n B A a B b n A = na n B = nb a + b = 1 x (aq) 2 n/6 nn Ω S 0 AA = 1 nn (an)2 D(ax) N = na 2 D(ax) S 0 BB = 1 nn (bn)2 D(bx) N = nb 2 D(bx) S 0 AB = n 2 [D(x) a2 D(ax) b 2 D(bx)] = ne(ax)e(by) (4.147) ns 1 (q) = D(x) a 2 b 2 D(ax)D(bx) E(ax) 2 2nχ (4.148) E(bx) 2

32 110 4 a = b = 1/2 S(q) = n 4/[D(x/2) D(x)] 2nχ (4.149) x 4.21 nχ = 10.5 x = 3.78 microphase separation (a) (b) (a) B m f A n (b) A m f B n g 4.22 a b

33 α D m R(m) m R(m) D m f m (α) m τ F (m/m ) (4.150) m ( α) 1/σ z- α α α α(> 0) I(q) = w m I m (q) (4.151) m 1 I m m g m (r) I m (q) = dre iq r g m (r) (4.152) f m w m mf m m g m (r) = 1 ( ) r g rd D R(m) (4.153)

34 112 4 R(m) D g(x) I m (q) = q D Ĩ(qR(m)) (4.154) I(q) = (mf m )q D Ĩ(qR(m)) = m 1 τ F (m/m )Ĩ(qR(m))/qD (4.155) m 1 m 1 qr(m) qm 1/D m = m x x h(z) I(q) = h(qr z )(m ) 2 τ /q D = q (3 τ)d h(qr z ) (4.156) h(z) 1 x 1 τ F (x)ĩ ( zx 1/D) (4.157) z 1 h(z) 1 z 1 h(z) z (3 τ)d (1 x 2 ) F (z) I(q) =< m > w F (qr z ) (4.158) I(q 0) = R (3 τ)d z = (m ) 3 τ < m > w ( α) γ (4.159) enhanced low-angle stattering ELAS qr z 1 I(q) q (3 τ)d (4.160) q D τ d D τ σ (3 τ)d (FS) (3 τ)d

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