ＮＭＲの信号がはじめて観測されてから４７年になる。その後、ＮＭＲは１９６０年前半までPhys. Rev.等の物理学誌上を賑わせた。１９６０年代後半、物理学者の間では”ＮＭＲはもう死んだ”とささやかれたということであるが（１）、しかし、これほど発展した構造、物性の

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　ＮＭＲの信号がはじめて観測されてから４７年になる。その後、ＮＭＲは１９６０年前半までPhys. Rev.等の物理学誌上を賑わせた。１９６０年代後半、物理学者の間では”ＮＭＲはもう死んだ”とささやかれたということであるが（１）、しかし、これほど発展した構造、物性の

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9. I S H0 = ωii + ωss ( (9.. H A ( q (0 A = a ( os θ (9..a r ( ± ± i A =± a sinθosθe ϕ r (9..b A a sin e r ( ± ± iϕ = θ (9.. µ 0 γ I γ S a = (9..d 4π A ( q q ( q * = ( A ( q (9..e (0 = { IS ( I+ S + I S + } (9..a 4 ( ± = ( IS± + I± S (9..b ( ± = I± S± (9.. ( q + q ( q = ( (9..d [] q= ( ( H = ( q A q q (9..4 H

9. 07 I S γ I = γs =γ ωi ωs = S = I (9..5 < I + S > (8.4.6 B = ( I + S (9..6 ih0t (0 ih0t (0 e e = ih0t ( ± ih0t ( ± ± i It e e = e ω ih0t ( ± ih0t ( ± ± iωit e e = e * (0 (0 ( ( iwit ( ( iwit ( ( iwit ( = ( ( ( + ( H t A t A t e A t e A t e ( ( iwit + A ( t e [ (0, I + S ] = 0 (9..7 ( ( ( ( ( b = J ( ω I{[,[, I + S]] + [,[, I + S]]} + ( ( ( ( ( + J ( ω {[,[, ]] [,[, ]]} I I + S + I + S ( (, J J (8.4.8(8.4.6 [ I, I ] = I + + [ I, I ] = I [ I+, I ] = I [ AB, C] = ABC [, ] + [ ACB, ] [ A, BC] = [ A, B] C + B[ A, C] [ AB, CD] = ABCD [, ] + CADB [, ] + ACBD [, ] + [ ACDB, ] (9..8 ( ( [,[, I + S]] = IS SI + I S+ ( I + S + ( I + S I+ S (9..9a 4 4 ( ( [,[, I + S]] = IS SI + I+ S ( I + S + ( I + S I S+ 4 4 (9..9b ( ( x y x y [,[, I + S ]] = I ( S + S S + ( I + I + I S (9..9

08 ( ( x y x y [,[, I + S ]] = I ( S + S + S + ( I + I I S (9..9d I = I, I +,..., I I( I + < I ( Sx + Sy > < I > (9..0a I( I + < S( Ix + Iy > < S > (9..0b I( I + < I S > < I > (9..0 I( I + < SI > < S > < ( I+ S + I S+ ( I + S >=< ( IxSx + IySy( I + S > 0 < ( I + S ( I S + I S >=< ( I + S ( I S + I S > 0 + + x x y y (9..0d (9..0e (9..0f / ( ( < b> I( I + < I { ( + S > J ωi + 4 J ( ωi } (9.. 6 d < I + S >= { < I + S > < I + S > 0} (9.. I( I + ( ( = { J ( ωi + 4 J ( ωi } 6 (9.. B = ( I + S (9..4a + + (0 (0 (0 b = J (0[,[, I + + S+ ]] ( ( ( ( ( J ( ω {[,[, ]] [,[, ]]} I I+ + S+ + I+ + S+ + ( ( ( ( ( J ( ω {[,[, ]] [,[, ]]} I I+ + S+ + I+ + S+

9. 09 (0 (0 [,[, I+ + S+ ]] = ( I+ S + IS+ + ( I+ S+ S + I I+ S+ + I+ IS + ISS 4 + I S+ I S + I+ S I S ( ( [,[, I+ + S+ ]] = ( I+ S S+ + I+ I S+ + II+ S + IS+ S I S+ I+ S 4 + (9..4b (9..5a ( ( + + + + + x + + (9..5b [,[, I + S ]] = {( I S S + I I S I I S I S S } (9..5 ( ( + + + + + + + [,[, I + S ]] = ( I S S + I I S I IS ISS (9..5d ( ( [,[, I + S ]] = 0 (9..5e + + d < I + S >= < I + S > (9..6 + + + + I( I + (0 5 ( ( = { J (0 + J ( ω I + J (ωi} 4 6 (9..7 ( q ( q * ( q ( q* / A ( t A ( t τ δqq A ( t A ( t e τ τ + = (9..8 τ аη D R k = (9..9 8π a η

0 a 4a πη τ = = (9..0 6D k R Debye / ( q ( q ( q* τ τ iωτ ( q ( q* τ τ iωτ ( q J ( ω = A ( t A ( t e e dτ = A ( t A ( t e e dτ = J ( ω i e τ τ e ωτ τ dτ = + ω τ (0 (0* π π os θ 6a ( ( = sin θ θ 0 φ( = 4π 0 6 r 5r A t A t d d a ( (* π π sinθosθ 6a ( ( = sin θ θ 0 φ( = 4π 6 0 r 5r A t A t d d a (9.. (9.. (9..a (9..b ( (* π π sin θ 6a ( ( = sin θ θ 0 φ( 4π 0 6 r 5r F t F t d d a = (9.. J J J (0 ( ( a ( ω = r a ( ω = r a ( ω = r τ 6 5 + ω τ τ 6 5 + ω τ τ 6 5 + ω τ (9..4a (9..4b (9..4 (9.. 4 µ 0 γ τ 4τ = ( I( I + ( + 6 4 5 r + ωiτ + 4ωI π τ 4τ Bloembergen + 4ω τ I τ + 4ω τ I (9..5 []Fi m i m i jm j m j m j m j I Im j I I +

9. BPP ( (I + ( = I( I + { J ( ω + 4 J ( ω } 6 4I / I = BPP BPP (9..4 4 µ 0 γ τ τ = I I + τ 6 + + 4π r 5 5 + ωiτ + 4ωIτ ( ( ( (9..6 9. τ 4 µ 0 γ ( I( I + ω 4π 6 I τ = 0.65795 r ω I 9. ω I τ = 0.65795 ω I τ < extremely narrowing

4 µ 0 γ = = ( I( I + τ 4 6 π r (9..7 τ ω I τ > (9..6 αβ βα spin diffusion limit(9..6 < ω > < ω > τ 9. ωτ > 9. ω 4 µ 0 γ τ ( I( I + 4π 6 r ωτ F (q

9. r t r t r e τ τ 5 5 ( 6 0 t ( τ = ( ( + τ = (9..8 τ 0 r r τ 0 = (9..9 D D J ωτ 0 τ 5 + ω τ ( 6 0 t = r ( 6 t r τ 0 6 J (9..0 4 4 r = = (9.. 5 5 r D ( 6 t r τ 0 6 J 6 6 r = = (9.. 5 5 r D µ 0 4 r ( ( 5 r γ I I + 4π 5 6 r D aa / t 4 0 4 r µ 0 N γ I I πr Ndr 6 a r D π ad µ 5 π γ = ( ( + 4 = ( 4π 5 4 4 I S ω ω I S (9.. ih0t (0 ih 0t i( ωi ω S t i( ωi ω t e e = IS I+ S e I S+ e S (9..4a 4 4 (0 = I S (0 ω = 0 (0 = I + S 4 (0 ω ω ω (0 = I S (0 S I = I S + (9..4b 4 ω = ω ω (9..4 ih0t ( ± ih 0t ± iωit ± iωst e e = I± Se IS± e (9..5a

4 ( ± = I± S ( ± = I (9..5b S ± ω ( = ω I ω ( = ω (9..5 ih0t ( ± ih 0t ± i( ωi ωs t = ± ± e e I S e S + (9..6a ( ± = I± S± ( I S ω = ω + ω (9..6b (8.4.6 B = I (0 [, I ] = 0 ( ( 0 (0 (0 (0 (0 (0 (0 {{ ( ω {[,[, ]] [,[, ]]} b = J I + I ( ( ( ( ( J ( ω {[,[, I ]] + [,[, I ]]} ( ( ( ( ( + J ( ω {[,[, I ]]} + [,[, I ]]}} (9..7 (0 b = J ( ω I ωs{ I( S S+ + S+ S ( I I+ + I+ I S} 4 ( ( + J ( ω I IS + J ( ω I + ωs{ I( SS + + SS + + ( II + + II + S} 4 J ( ωi ωs ( < b >= [ < I ( { ( > S S + + J ωi 8 6 (0 ( J ωi ωs ( ωi ωs} ( { ( + J + + < S > I I + 8 ( + J ( ωi + ωs}] (0 (9..8 (9..9 S d < I > = ( < I > I ( < S > S (9..40a II 0 IS 0 d < S > = ( < I > I ( < S > S (9..40b SI 0 SS 0

9. 5 SS ( + (0 ( ( = { J ( ωi ωs + J ( ωi + J ( ωi + ω S} (9..4a 8 6 II I( I + (0 ( = { J ( ωi ωs + J ( ωi + ω S} 8 IS (9..4b, SS SI I S, I S B = I + ( ( ( ( ( ( ( ( + + ( ( ( ( ( + + IS SI, II SS ross relaxation time (0 (0 (0 (0 (0 (0 (0 (0 (0 (0 b = { J ( ω [,[, I+ ]] + J ( ω {[,[, I+ ]] + [,[, I+ ]]} J ( ω {[,[, I ]] + [,[, I ]]} J ( ω {[,[, I ]] + [,[, I ]]} + J ( ω ( ( ( ( ( I+ + I+ I {[,[, ]]} [,[, ]]}} I (9..4 d < I+ > = < I+ > (9..4 SS ( + = { J (0 + J ( + J ( + J ( + J ( 9 6 6 6 (0 (0 ( ( ( ωi ωs ωi ωs ωi + ωs } (9..44 I CS H C (9..4 µ τ τ 4 τ 0 = ( γ C CγH { + + 4π 4 6 5 5 5 r + ( ωc ωh τ + ωcτ + ( ωc + ωh τ µ 0 τ 4 τ = ( γ CH CγH { + 4π 4 6 5 5 r + ( ωc ωh τ + ( ωc + ωh τ } (9..45 } (9..46

6 µ 4 τ τ τ = + + + 4 4 5 5 ( 5 5 + ω ω τ + ω τ + ω τ 0 ( γ C CγH { τ 6 π r C H C τ + } 5 + ( ω + ω τ C H H C CH C 9. (9..47 C CH C µ 0 γcγh 9. τ ( I( I + 4π 6 4r ω S <S>=0 I 0 = ( < I > I (0 S (9..48 II 0 IS 0

II S0 IS 0 I 0 9. 7 < I > NOE = = + (9..49 I 0 ( + S IS I C II 0 γ NOE = + γ H C τ 4 τ { + } 5 5 + ( ωc ωh τ + ( ωc + ωh τ τ τ 4 τ { } 5 + ( ω ω τ 5 + ω τ 5 + ( ω + ω τ + + C H C C H (9..50.99 NOE(nulear Overhauser enhanement 9. 4 ω τ.5 C 9. 4 H CNOEτ

8 9. 5 HNOEτ (9..40 d( < I + S > = ( + ( < I > I ( + ( < S > S (9..5 0 II SI 0 SS IS IS(9.. (9..47 γ I = γ S =γ ω I = ω S SS ( + = II ( + J (0 [,[, I + ] (0 (0 (0 (0 (0 (0 (0 (0 (0 (0 [,[, I + ] [,[, I+ ] + [,[, I+ ] [,[, I+ ] + [,[, I+ ] J ( ( ( ( ( + + ( ( ( ( + + ] (0 (0 [,[, I ] + [,[, I ] [,[, I ] + [,[, I non-seular term (9..50 γ I = γ S = γ H ω I = ω S = ω H HNOE

9. 9 NOE H 4 τ ( τ + 5 5 + 4ωHτ = + τ 4 τ ( τ + + 5 5 + ω τ 5 + 4 τ H ωh (9..5 Hω H τ <.5 ω 5 H τ = =.8 ω H τ 0 9. 5 NOENOE H ωhτ <.8 ω H τ >.8 NOENOE Bloembergen, Purell, Pound BPP []Solomon / [] I S N αα N αβ N βα N ββ αααββαββ dnαα = ( W + W + W ( N N + W ( N N + W ( N N + W ( N N I S αα αα 0 S αβ αβ 0 I βα βα0 ββ ββ 0 dnαβ = W ( N N ( W + W + W ( N N + W ( N N + W ( N N S αα αα 0 0 I S αβ αβ 0 0 βα βα0 I ββ ββ 0 dnβα = WI ( Nαα Nαα 0 + W0 ( Nαβ Nαβ 0 ( W + W + W ( N N + W ( N N 0 I S βα βα0 S ββ ββ 0 dnββ = W( Nαα Nαα 0 + WI( Nαβ Nαβ 0 + W ( N N ( W + W + W ( N N S βα βα0 I S ββ ββ 0 (9..5 αβ 9. 6 0

0 9. 6 WN αβ NI = {( Nαα + Nαβ ( Nβα + Nββ } NS = {( Nαα + Nβα ( Nαβ + Nββ } dn I = ( W + W + W ( N N ( W W ( N N 0 I I I0 0 S S0 (9..54 dn S = ( W W ( N N ( W + W + W ( N N (9..55 0 I I0 0 S S S0 N I0 N S0 N I N S II IS SS = ( W + W + W (9..56a 0 I = (W W (9..56b 0 = ( W + W + W (9..56 0 S SN I N Ie NIe NS0 W W0 = + N N W + W +W I0 I0 0 I (9..57 NOE W I = W S

9. d( < I + S > = ( W + W( < I + S > ( I0 + S0 ( W W = + (9..58 αα βα (.4.9 t ( I W = < αα H t βα > e t 0 iw t 0 (9..4 ( ( ( ( A = A ( t { ( IS+ + I+ S} (9..59 ( < αα H ( t βα >= A ( t 4 W ( A ( t e t ( iwit = 4 t 0 ( *( = ( dτ exp( iωτ I A ( t A ( t τ 4 ( = J ( ω I 8 4 µ 0 γ τ = 4π 0 6 r + ωi τ W ( (9..60 t W = < αα H ( t ββ > e t 0 iwit ( ( ( ( A = A ( t { ( I+ S+ } 4 µ 0 γ τ = 4π 0 6 r + 4ωI τ W ( (9..6 (9..58 / (9..5I = / W (0 W0 = J ( I S 4 ω ω (9..6a

( WI = J ( ω I 6 ( W = J ( I S 4 ω + ω (9..6b (9..6 ω I ω S ωh NOE (9..57N (9..5 NOEω H τ (9..57W 0 αβ βα 0 ω H τ < (9..5 W 9. 6 S + εε αα αβ αα αβ + ε/ ε/ βα ββ ε/ W αα + εββ ε αα αβ + ε βα ββ ε αα βα ε βα ββ ε W 0 W.5 I x I x u, v > I α >, β > I0 = N S0 > u >= ( α > + β > (9..6a v >= ( α > β > (9..6b < u Ix u >= < v Ix v >= d < Ix > = ( U + 0 U + U < I > x ( U U0 < S > x

9. d < Sx > = ( U U0 < Ix > ( U0 + U + U < Sx > U αβ 9. 7 U = U ' 9. 7 I x d ( < Ix >+< Sx > = ( U + U( < Ix >+< Sx > ( U U = + (9..64 U uuvu t U = < uu H ( t vu > e t 0 iwit U uuvv t U = < uu H ( t vv > e t 0 J (0 (0 iwit (9..4Hq = 0 U < αα αα > < αβ αβ > + < βα βα > < ββ ββ > +< αβ βα > < βα αβ > 0 U

4 < αα αα > < αβ αβ > < βα βα > + < ββ ββ > < αβ βα > < βα αβ > 4 µ 0 γ 9 ( 4 6 π r 0 τ (9..6I = / 9. 4 N 7 O D A eq = V 4 I(I (0 6 (9..a ( ± eq A = ( Vx ± ivy (9..b I(I ( ± eq A = ( V V ± iv 4 I(I xx yy xy (9.. (0 ( = I I ( I + (9..a 6 ( ± = ( II± + I± I (9..b ( ± = I ± (9.. q= ( ( H = ( q A q q A eq (0 = V 4 I(I (0 6 ZZ (9..a ( A ± (0 = 0 (9..b

9. 5 A ( ± (0 eqv = ZZ η 4 I(I q ( q ( q eq (0 ( ( H = η ( A (0 = VZZ { ( } q= 4 I(I + 6 + (9.. (9..4 Ωαβγ ( q ( q ( qq A ( Ω = A (0 D ( Ω (9..5 q [,4] D ( qq Wigner ( iαq D e d ( β e qq = qq iγ q (9..6 [4] d ( β 9. qq 9. d ( β qq q q ± ( os ± β 4 ( ± os β sin β 0 sin β 8 - ( os β sin β - ( os β 4 ± 0 ( ± os β sin β sin β 8 (os β ( ± os β sin β os β sin β os β (os β (os β ( ± os β sin β os β ( os β sin β sin β 8 A eqv ( Ω = ZZ {(os β + ηsin βos α} 8( I I (0 (9..7a

6 A eqv ( Ω = ± ZZ {sin β os β ηsin β os β osα ± iηsin βsin α} I(I ( ± i e γ (9..7b A eqv ( ZZ η η Ω = { sin β + (os β osα + os α ios βsin α} e (9..7 I(I 4 4 ( ± iγ q ( q ( q* ( q ( q* A ( Ω( t A ( Ω ( t+ τ = A ( Ω( t A ( Ω ( t ( τ (9..8 ( q ( q ( q* i ωτ ( q iωτ J ( ω = A ( Ω( t A ( Ω ( t + τ e dτ = A ( Ω ( τ e dτ A (0 ( k =, (9..9 ( q A ( Ω ( k 6eQ eqη A ( A (0 {( V ( } ( q Ω = ( k 5 = ZZ ZZ k 5 4 I(I + V = 4 I(I eq ( η V ZZ ( = + 40 I(I (9..0 (9..7 i J ωτ ( ω = ( τ e dτ (9.. ( q ( q J ( ω = A ( Ω J ( ω (9.. ih0t (0 ih0t (0 e e = ih0t ( ± ih0t ( ± ± i It e e = e ω ih0t ( ± ih0t ( ± ± iωit e e = e B = I

9. 7 ( ( ( ( ( { ( {[,[, ]] [,[ ωi, ]]} b = J I + I ( ( ( ( ( ωi + J ( {[,[, I ]] + [,[, I ]]}} ( ( [,[, I ] = 4I + I( I + I I (9.. (9..4a ( ( [,[, I ] = 4I + 4 I( I + I (8.4.9 d < I > ( = { J ( ω [ 4 ( ] I < I + I I + I I > ( ωi + J ( < [ 4I + 4 I( I + I I ] > < > } I 0 (9..4b (9..5 I < > J τ ( ω = J ( ω = J ( ω = τ + ω τ d < I > = ( < I > I0 I + η eq = ( + ( VZZ 40 I (I τ (9..6 I = I = I η = ( + eq ( V { J ZZ ( ωi + 4 J ( I } 80 ω (9..7 B = I + I = η eq ( ( = + V ZZ {9 J (0 + 5 J ( ωi + 6 J ( ω I} 60 (9..8 9. σ ij (i, j = x, y,

8 A (0 = γ ( σ r{ σ} (9..a 6 ( ± A = γ σ ± σ ( x i y (9..b ( ± A = γ( σxx σ yy ± i σxy (9.. (0 = {( BI ( BxIx + ByIy + BI} = { BI ( B+ I + B I + } 6 4 (9..a ( ± = ( BI± + B± I (9..b ( ± = B I B B ib ± ± (9.. ± = x ± y (9..d B i (i = x, y, xy H = γ{( σ r{ σ} BI + σ BI + σ BI + σ BI + ( σ r{ σ} BI + σ y BI y + σx BI x + σy BI y + ( σ r{ σ} BI } = ( A q xx x x xy x y x x yx y x yy y y q ( q ( q (9.. B = B0, B = B = 0 x y (0 = B0 I (9..4a = B I (9..4b ( ± 0 ± ( ± = 0 (9..4 (9.. B = B0, B = B = 0 x y H = γb0( σ rσ I + γb0σx Ix + γ B0σ y Iy (9..5 (X, Y, Z

9. 9 σ X, σy, σz rσ δz = σz rσ δ X = ( ηδ Z δ Y = ( + ηδ Z (9..6 η (0 A (0 = γ δ Z (9..7a ( A ± (0 = 0 (9..7b ( ± A = γ ( δx δy (9..7 q ( q ( q H = ( A = γ ( δ B I + δ B I + δ B I (9..8 q X X X Y Y Y Z Z Z B x, B y, B A (0 ( q (0 A ( Ω Ω (0 A ( Ω = γ δz {(os β + ηsin β os α } (9..9a 8 ( ± A ( Ω = ± γ δz {sin β os β η sin β os β os α ± iη sin β sin α} e γ (9..9b ( ± η η iγ A ( Ω = γδz { sin β + (os β osα + os α iosβsin α} e (9..9 4 4 η A ( Ω = A (0 = (+ (9..0 J ( q ( k γ δz 5 k= 0 ( q Z B = I η ( ω = γ δ ( + J ( ω (9.. 0 ( ( ( ( ( ( ( {[,[, ]] [,[ ωi, I ]]} b = J I + (9..4 i

0 0 B0 d < I > γ = δz( + η J ( ωi{ < I > < 0} 0 > (9.. B = I + 6 η = γ B0 δz ( + J ( ω I (9.. 40 d < I+ > = (0 (0 (0 ( ( ( ( ( { < [,[, ]] {[ J I J,[, I ]] [,[ + + +, I+ ]]} > < > } η = γ B0 δz ( + {4 J(0 + J ( ωi} (9..4 40 : =7:6 δz = ( σ σ η = 0 (9.. (9..4 = γ B0 ( σ σ J ( ωi (9..5 5 = γ B0 ( σ σ {4 J (0 + J ( ωi} (9..6 90 C 9. 4 J H = JI S J /, J J J

9. 4 ISS JIS mj S / γ m s = S, S+,,S IS i J 0S i I τ ei J τ Ji( t Ji( t+ τ = exp( (9.4. τ ei (0 i Ji ( Ji( t Ji( t e ωτ τ ω = + τ dτ = Ji ( t + ω τ e ei (9.4. IS i P i J ( t = PJ (9.4. i i τ ei iτ e J (0 i ( ω = PJ i τ e e + ω τ (9.4.4 H = Ji (( t IxSix + Iy Siy + I Si = Ji ({ t I Si + ( I+ Si + I Si+ } (9.4.5 i i S (0 i ISi = (0 i A = Ji ( t (0 i = I + Si (0 i A = Ji ( t (0 i (0 i = I Si + (9.4.6 A = Ji ( t (9.4.7 B = I (0 (0 (0 (0 (0 b = J ( {[ i ωi ωs i,[ i, I]] + [ i,[ i, I]]} (9.4.8 i

d < I > (0 SS ( + (0 II ( + = { Ji ( ωi ωs ( < I > I0 Ji ( ωi ωs ( < S > S0 } i = ( < I > I + ( < S > S II 0 IS o (9.4.9 P = I S J τ e = SS ( + II + ( ωi ωs τe J τ e = I( I + IS + ( ωi ωs τe i i (9.4.0a (9.4.0b SS =0 I SII 0 ( + < I >= I0{ } ISS ( + 0 (9.4. I S I 0 B = I + (0 (0 (0 (0 (0 (0 (0 (0 b = { J i (0{[ i,[ i, I+ ]] + Ji ( ωi ωs{[ i,[ i, I+ ]] + [ i,[ i, I+ ]]}} i J τ e = SS ( + { τ + } (9.4. + ( ω ω τ I e I S /, J SS H = J( IxSx( t + IySy( t + IS( t = J{ IS( t + ( I+ S ( t + I Si( t} (9.4. S e (0 = I ( = I + ( = I (9.4.4a

(0 A = JS ( t ( 9. 4 A = JS ( t + ( A = JS ( t (9.4.4b b ( ( ( ( ( b = J ( ω {[,[, ]] [,[, ]]} I I + I (9.4.5 ( J ( ω = ( J S ( t S ( t + τexp( iωτ dτ (9.4.6 + Sω s τ τ SS ( + τ S+ ( t S ( t + τ = S+ ( t S (exp( t iωsτexp( = exp( iω τexp( (9.4.7 τ S τ J SS ( + τ (9.4.8 ( ( ω = ( J + ( ω ωs τ d I < > = ( ω I < > J ( ( I I 0 J τ = SS ( + + ( ω ωs τ (9.4.9 (9.4.0 Sτ τ SS ( + τ S( t S( t+ τ = S( t S(exp( t = exp( (9.4. τ τ SS ( + τ J J S t S t i d J (9.4. (0 ( ω = ( ( ( + τexp( ωτ τ = ( + ω τ (0 (0 (0 ( ( ( ( ( { (0[,[, ]] ( I {[,[, ]] [ b = J I+ + J ω I +,[, I ]]}} (9.4. d < I+ > (0 ( = { J (0 + J ( ω I } < I + > (9.4.4 J τ SS ( { ( ωi ωs τ = + τ + } (9.4.5 +

4 9. 5 ω K Kħ Ω K H = Ω I K (9.5. K K K τ (9.4.0(9.4.5 S, ωs, J K, ωk, ΩK τ = τ = τ ΩK τ = K( K + + ( ωk ωi τ ΩK τ K( K { τ } ( ωk ωi τ (9.5. = + + (9.5. + 9. 6 Shimiu Fujiwara[5] Makor MaLean[6]Grant [7][8,9] / AX (9..54(9..5 N = N + N + N + N β (9.6. t αα αβ βα β N t 0 N = Nαα Nαβ Nβα + Nββ (9.6. [5] dn = ( W + W N (9.6. I S

9. 7 5 ( WI WS = + (9.6.4 Grant [7]multiplet asymmetry relaxation II SS IS time(9..56,, W0, WI, WS, W 9. 7 / / / / J 5 N ross orrelationgoldman[0] / I S J I H = ( ω I + ω S + JI S + H ( t + H ( t I S DD SCA S I (9..7 (0 8π (0 A CSA = Y ( γ ( σ σ ( θ, ϕ (9.7.a 5 ( ± 8π ( ± A CSA = Y ( γ ( σ σ ( θ, ϕ 5 ( ± 8π ( ± A CSA = Y ( γ ( σ σ ( θ, ϕ 5 (9.7.b (9.7.

6 θ = β, ϕ = α, γ = 0(9..4 (9.. A A A (0 4π a (0 DD Y = ( ( ( θ, ϕ (9.7.a 5 r ( ± 4π a ( ± DD = Y ( ( ( θ, ϕ 5 r ( ± 4π a ( ± DD = Y ( ( ( θ, ϕ 5 r (9.7.b (9.7. (9.. I S * ih Zt ih Zt + + + + ( = ( DD + CSA = + + + + + + + + H t e H H e K L L M M N N P P (9.7. H = ( ω I + ω S (9.7.4a Z I S (0 K = I Y d(s + (9.7.4b ( L = I+ Y d ( S + exp( iωit (9.7.4 M = ISY d i t (9.7.4d ( + 6 exp( ωs (0 + exp{ ( ωi ωs } N = I S Y d i t ( + + 6 exp{ ( ωi ωs } (9.7.4e P = I S Y d i + t (9.7.4f µ 0 π γγ I S r d = (9.7.5 4π 5 B0 ( σ σ = µ 0 ( γ 4 S r π (9.7.6 H * 0 JIS = (9.7.7 i * * (8.4.6 r { B [ H 0, ρ ]} S = / / I ( l l I = I ( + S ( l l I = I ( S l =, + (9.7.8

9. 7 7 ( ( l l l ( ( l l l I = I + I, IS = ( I I (9.7.9 B = I B = I S B = S d < I >= A ( < I > I 0 B < I S > E ( < S > S 0 (9.7.0a d < I S >= C < IS > B( < I > I0 (9.7.0b d < S >= A ( < S > S0 E( < I > I 0 (9.7.0 ( q ( q (0 ( ( q Y Y τ = Y δ exp( τ τ q q 6( + A = Dτ { + + } + ωiτ + ( ωi ωs τ + ( ωi + ωs τ B = Dτ } { + ωi τ E = Dτ + } { + ( ωi ωs τ + ( ωi + ωs τ 6( + 6 C = Dτ + } { + ωiτ + ωsτ 6( + A = Dτ { + + } + ωsτ + ( ωi ωs τ + ( ωi + ωs τ (9.7.a (9.7.b (9.7. (9.7.d (9.7.e 6 D = γiγs r (9.7.f 0 d ( ( ( < I >= ( λ + η ( < I > I0 µ ( < I > I0 E( < S > S0 d ( ( ( < I >= µ ( < I > I0 ( λ η( < I > I0 E( < S > S0 (9.7.b 6( + 6 λ = ( A + C = Dτ { + + + } (9.7.a + ωiτ + ωsτ + ( ωi ωs τ + ( ωi + ωs τ

8 η = B = Dτ } { + ωi τ µ = ( A C = Dτ { + + + ωsτ + ( ωi ωs τ + ( ωi + ωs τ µ,, + ω τ + ω τ + ( ω ω τ + ( ω + ω I S I S I S τ 6 } (9.7.b (9.7. (9.7.4 ( λ η = + (9.7.5a ( λ η = (9.7.5b B = I + B = S I + d < I+ >= A < I+ > B < S I+ > (9.7.6a d < SI + >= C < SI + > B < I+ > (9.7.6b ( + 6 6 = τ + + + + + + ωiγ + ( ωi ωs γ + ωsγ + ( ωi + ωs γ A D {4( } ωi τ (9.7.7a B = Dτ {4+ } (9.7.7b + ( + 6 = τ + + + + + ωiγ + ( ωi ωs γ + ( ωi + ωs γ C D {4( } (9.7.7 d ( J ( ( ( < I+ >= i < I+ > ( λ + η < I+ > µ < I+ > (9.7.8a d ( J ( ( ( < I+ >= i < I+ > ( λ η < I+ > µ < I+ > (9.7.8b

λ 9. 8 9 ( + 6 = Dτ + + + + + + ωiτ + ( ωi ωs τ + ωsτ + ( ωi + ωs τ {4( } ωi τ (9.7.9a η = Dτ {4+ } (9.7.9b + µ = Dτ + ωsτ (9.7.9 µ (9.7.4 ( λ η = + (9.7.0a ( λ η = (9.7.0b 5 N[]I 5 N S Hσ σ = 60ppm r = 0.0nm ω I π = 50.06MH (.8 0ns(9.7.4 ( 7.5 ( ( + = ( 9. 8 Redfield [](8.. dm dm dm x y M = x M = γ BM ( M M0 = γbm y y

40 x Redfield H 000µs [] τ > SlihterAilion[] >>τ Redfield[4,5] Jones[5] I S H = H0 + Hrf + HDD H 0 (9..ω B H rf i t i t i t i t Hrf I ( I e ω I e ω = ω S ( S e ω + + + ω + + S e ω I I B ω = γ ω = γ B S S H DD H DD q= ( ( = ( q A q q B 0 B x IS ω U = exp( iωti exp( iωts (9.8. r = ω + H UHU ( I S

9. 8 4 UH U 0 = H0 UH U = ( I + S rf ωi x ωs x H = {( ω ω I + ω I } + {( ω ω S + ω S } + UH U (9.8. r I I x S S x DD (0 (0 = exp( iωti exp( iωts exp( iωts exp( iωti ( ± ( ± exp( iωti exp( iωts exp( iωts exp( iωti = exp( ± iω t ( ± ( ± exp( iωti exp( iωts exp( iωts exp( iωti = exp( ± i ωt q ( q ( q H = ( ω I + ω I + ( ω S + ω S + ( A exp( iqωt (9.8.a r I I x S S x I I q= ω = ω ω (9.8.b ω = ω ω (9.8. S S ω tan Θ I I = ( ωi (9.8.4a ω tan Θ S S = ( ωs (9.8.4b R = exp( iθ I exp( iθ S I exp( iθ I I exp( iθ I = I osθ + I sinθ y y y x exp( Θ i I I exp( iθ I = I osθ I sinθ y x y x exp( iθ Iy I± exp( iθ Iy = Ix osθ I sinθ ± ii y S y 4 ( q ( q = p p β p p= 4 R R C V exp( i t (9.8.5

4 V = I S, β = 0 0 0 V = I S, β = ( β β V V V V V V V + I S = I S, β = ( β β + I = I S, β = β + I = I S, β = β I = I S, β = β + S = I S, β = β S = I S, β = ( β + β 4 + + 4 I = I S, β = ( β + β 4 4 I S S S (9.8.6 I = ( I + I β ω ω (9.8.7a S = ( S + S β ω ω ( q C p 9. (9.8.7b H = β I + β S (9.8.8a r0 I ' S ' 4 q ( q ( q rdd p p β p q= p= 4 H = ( A C V exp( i texp( iqωt (9.8.8b Hr Hr0 HrD D = + (9.8.8 i i H rdd = exp( Hr0t HrDD exp( Hr0t i i exp( H r0tv p exp( Hr0t = Vp exp( iβ pt 4 ( q ( q ( q rdd p p β p q= p= 4 H = ( A ( t C V exp( i texp( iqωt (9.8.9

9. 8 4 9. C p (q q 0 ± ± C C 0 ( q ( q ( q (0 C C ( q (os Θ os Θ sin Θ sin Θ sin( Θ Θ I S I S I S sin Θ sin Θ ± + I S (sin ΘIsin Θ S os ΘIos ΘS {sin( ΘI + Θ S sin Θ sin } I ± Θ (os S Θ os I ΘS os Θ os I ± ΘS 4 8 8 {sin( ΘI + Θ sin sin } S ± ΘI ΘS 8 (os Θ os I Θ os os S ± ΘI ΘS 8 C ( q (0 C q C ( (sin Θ I os Θ S + os ΘIsin ΘS {os( ΘI + Θ os } S ± ΘS (os Θ sin I ΘS ± sin Θ S 4 4 {os( Θ os } I + ΘS ΘS (os Θ sin I Θ sin S ΘS 4 4 C ( q (0 C C q C ( 4 ( q (0 C 4 (os Θ I sin Θ S sin I os S + Θ Θ {os( Θ I + Θ os } 4 S ± Θ I (sin Θ os I Θ sin S ± ΘS 4 {os( ΘI + Θ os } S ΘI (sin Θ os I Θ sin S ΘS 4 4 (sin ΘI sin Θ S os ΘI os ΘS + {sin( ΘI + Θ S ± sin Θ sin } I ± ΘS 4 8 C 4 (os Θ os Θ + ± os Θ ± os Θ 8 I S I S {sin( ΘI + Θ sin sin } S ΘI Θ (os S Θ os I ΘS + os Θ os I ΘS 8 8

44 d ρ r q ( q ( q ( q = ( ( exp[ ( ] exp( exp( dτ τ i βp + qω τ Cp Cp iβpt i β p t 0 q p, p ( q q ( q ( q = J ( β ( [,[, ]] p + qω Cp C p Vp V p ρr qp, < > I ' (9.8.0 d < I ' > = ( q q ( q ( q r{( ρr ( t ρ0 ( ( [,[, ]]} J β p + qω C p C p Vp V p I qp, = < ( b> b 0 (9.8.a ( q q ( q ( q b = J ( β ( [,[, p + qω Cp C p Vp V p I]] (9.8.b qp, d < I ' > = ( II < I' > Iρ0 ( S IS < ' > S 0 ρ ρ ρ ρ ρ (9.8. (9.8. II, IS ω I ω I ω ω S S I S βiτ, βsτ β p 0 H 5 τ τ τ ρ = K( II + + 6 + ω τ + 4ω τ IS ( K ρ ω τ Θ = Θ = π (9.8. τ = τ + (9.8.4 + 4 µ 0 γ K = ( I( I + (9.8.5 4π 5 6 r IS [6] ρ 5 τ τ ( = + = K τ II IS + + ρ ρ ρ + ω τ + 4ω τ (9.8.6

45 (9..6 Θ Θ = Θ βs βi = ωe Θ, ωe τ τ = K{ [sin Θos Θ + sin Θ ] 4 ρ 4 + ωτ e + ωτ e τ + [os os + sin sin Θ Θ Θ Θ + ( ω0 + ωe τ + ( ω0 ωe τ τ τ + sin os + sin sin ] 4 4 Θ Θ Θ Θ + ( ω0 + ωe τ + ( ω0 ωe τ 4 τ 4 τ + 4[sin Θos Θ + sin Θsin Θ + ( ω + ω τ + ( ω ω τ 0 e τ τ + os + sin ]} 8 8 Θ Θ + (ω0 + ωe τ + (ω0 ωe τ 0 τ S e I [5] M. E. Rose, Elementary heory of Angular Momentum, John Wiley, New York, 957. 97. N. Bloembergen, E. M. Purell, and R. V. Pound, Phys. Rev. 7, 679(948. I. Solomon, Phys. Rev. 99, 559(955. 4 M. Mehring, High Resolution NMR in Solids, Springer-Verlag, Berlin, 98. 5 Hiroshi Shimiu and Shiuo Fujiwara, J. Chem. Phys. 4, 50(96. 6 E. L. Makor and C. Malean, J. Chem. Phys. 4, 454(965. 7 C. L. Mayne, Donald W. Alderman, and David M. Grant, J. Chem. Phys. 6, 54(975. 8 L. G. Werbelow and D. M. Grant, Adv. Magn. Reson. Ed. J. S. Waugh, Vol.9, 89-99, Aademi Press, New York, 977. 9 R. L. Vold and R. R. Vold, Progr. NMR Spetrosopy, Vol., Pergamon Press, 79(978. 0 M. Goldman, J. Magn. Reson. 60, 47(984. L. E. Kay, L. K. Niholson, F. Delaglio, A. Bax, and D. A. orhia, J. Magn. Reson. 97, 59(99. A. G. Redfield, Phys. Rev. 98, 787(955. C. P. Slihter and D. Ailion, Phys. Rev. 5, 099(964. 4 D. C. Look and I. J. Lowe, J. Chem. Phys. 44, 995(966.

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