5. NMR µ = γ I µ = γ I r H D 0 I r I r { I 3 I r r µ γγ 3( )( ) = } (5..) zb 0 µ 0 γγ I r I r 0( γ z γ z) { I 3 I r r 3( )( ) H = B I + I + } (5..) (5..) z z µ 0 γγ D = ( + + + + + ) 3 r H A B C D F (5..3) r θφ AB CDF A = I I ( 3cos (5..4a) B = ( 3cos θ)( I+ I + I I+ ) = ( 3cos θ)( IzIz I I ) (5..4b) 4 3 sn cos φ * C = θ θe ( IzI+ + I+ Iz ) =D (5..4c)
56 3 sn φ * = θ I+ I+ =F (5..4d) 4 B I = I + I, I + I, I I I m Im, > / trplet state, >= >,0 >= { β > + β > }/, >= ββ > 0 snglet state 0,0 >= { β > β > }/ β > > β > A B I I 5. / µ 0 γ, γ B0 3 = + ( 3cos (5..5a) µ 0 γ,0 3 = ( 3cos r (5..5b) µ 0 γ, γ B0 3 = + ( 3cos (5..5c)
5. 57 0,0 = 0 (5..5d) γ = γ = γ r = r 5. A +B secular part,0 >, >,>,0 > (3.4.)k + k I( I + ) k( k + ) = (,0, ) = γb 0 ( 3cos θ) (5..6a) = (,,0 ) = γb 0 + (3cos µ 0 3γ = 3 (5..6b) (5..6c) Pake r lne-shape g( ) g( ) d +d r r θ θ+dθ snθ d θ g( ) d snθdθ, >,0 > g( ) d = g( ) 6cosθsn θdθ snθdθ g( ) (5..7) cosθ g( ) ( + ) (5..8a),>,0 > g( ) ( + ) (5..8b) g( ) ( + ) ( < < )
58 g( ) ( + ) + ( + ) ( < < ) g( ) ( + ) ( < < ) (5..9) 5. / (5..9) 0.3 5. Pake 0KHz
5. 59 g( ) Pake r =.58Å rgd lattce cos θ /3 τ c T T 3 C / 3 C > β > β > ββ > 3 CA β β ββ µ 0 γγ γ B0 3 = ( γ + ) / + (3cos (5..0a) µ 0 γγ γ B0 3 = ( γ + ) / (3cos (5..0b) µ 0 γγ γ B0 3 = ( γ ) / (3cos (5..0c) µ 0 γγ γ B0 3 = ( γ + ) / + (3cos (5..0d) > β > β > ββ > µ 0 γγ H = ( β ) = γb0 + 3 ( 3cos r µ 0 γγ H = ( β ββ ) = γb0 3 ( 3cos r (5..a) (5..b) > β > β > ββ > 3 C
60 µ 0 γγ C = ( β ) = γb0 + 3 ( 3cos r µ 0 γγ C = ( β ββ ) = γb0 3 ( 3cos r (5..a) (5..b) 5. 3 5. 3 H 3 C (5..0)(5..) γ = γ β > β > 5. ρ n V (x, y, z) W= ρn ( xyzv,, ) ( xyzd,, ) τ (5..)
5. 6 V V V V V V 0 0 0 0 0 0 0 V( x, y, z) = V + ( ) x+ ( ) y+ ( ) z+ {( ) x + ( ) y + ( ) z x y z x y z V V V + ( ) 0xy + ( ) 0 yz + ( ) 0zx} x y y z z x (5..) W = ZeV0 µ + [ Vβ Qβ + Vβ δβ r ρndτ ] (5..3) 6 β = x, yz, e Z Ze = ρ dτ (5..4) n µ = ρn x d τ (5..5) x x, y, z V = ( ) (5..6) x 0 (5..3) β (3 β β ) n d Q = x x δ r ρ τ (5..7) V 0 V β = V ( x x ) (5..8) 0 β V (5..3) HQ = Vβ Qβ (5..9) 6 β
6 A x, y, z Qβ A β = β δβ = Q e(3 x x r ) (5..0) xβ δβ (3 x r ) ( I Iβ + IβI) 3 δ β I Wgner-ckart I z m Im > Im > m C ( I ) Iβ + IβI < Imη e (3 xxβ δβr ) Im η >=< Imη (3 δβi ) Im η > C (5..) β β η (3 x x δ r ) ( I Iβ + IβI) 3 δ β I C m = m = I z < IIη (3 z r ) IIη >=< IIη (3 I I ) IIη > C = CI(I ) (5..) ) eq =< IIη e (3 z r IIη > (5..3) eq C = I ( I ) (5..4) Q I eq 3 HQ = V { ( I I + I I ) I } (5..5) 6 I(I ) β β β δβ β (X,Y,Z)Z
5. 3 63 eq HQ = { VXX (3 IX I ) + VYY(3 IY I ) + VZZ(3 IZ I )} (5..6) 6 I(I ) V + V + V = 0 XX YY ZZ eq HQ = { VZZ(3 IZ I ) + ( VXX VYY )( IX I Y )} (5..7) 4 I(I ) eq = V ZZ (5..8) η = ( V V )/ V (5..9) XX YY ZZ HQ = eqq {3 IZ I( I + ) + η ( I I + + )} (5..0) 4 I(I ) q η η = 0 0 l l = 0 s l = p l = d l = 0 s l I z z x = y ( z x ) = (3 z r ) y Q 5. 3 IB 0 γ eqq Bo I Z + H = + {3 I I( I + ) + η ( I + I )} (5.3.) 4 I(I ) XYZ
64 η =0 z Z z θ y Y I = I cosθ + I Z z x snθ η =0 (5.3.)xyz eqq H = γb0 I z+ { (3cos θ )(3 Iz I( I + )) 4 I(I ) 3 3 + snθcos θ( I z( I+ + I ) + ( I+ + I ) Iz) + sn θ( I+ + I)} 4 (5.3.) (0) m () m () m 3eqQ Q = I(I ) (5.3.3) (0) m = m (5.3.4) 0 () θ m = Q( ){ m 3cos I( I + ) } (5.3.5) 3 () Q 4 m θ θ θ 80 4 = m{cos sn (8m 4 I( I + ) + ) + sn ( m + I( I + ) )} (5.3.6) m m m m ( m m ) = θ m 0 Q ( m (3cos ) = + ) (5.3.7) (3cos θ ) I = 0 0 Q 5. 3 (3.5.) 3/ 3:4:3
5. 3 65 5/ 5:8:9:8:5 // θ m m () Q 3 3 m = sn θ{ ( 7cos θ)( m m) I( I + )( 9cos θ) + ( 3cos } 8 4 0 (5.3.8) () Q m 0 3 = sn θ( 9cos θ){ I( I + ) } (5.3.9) 6 4 C Q eqq = (5.3.0) h MHz 6π CQ Q = (5.3.) I(I ) Q