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17 ? 1. () - , , . 1946 . , , . , ( ), , , , , , .. -. : . ? 2. r - I , r I = h I ( I + 1) , h - , I - , 0, 1/2, 1, 3/2, 2, .... Z , N =Z+N. : I=0, A - N Z (: 4, 12C, 16O, 32S, ...); I=1/2, 3/2, 5/2, ... - (: 1, 3He, 7Li, 13C, 31P, ...); I=1, 2, 3 ... A - N Z (: 2D, 14N, ...). I 0 6. , , - , ,
1


Å

B

=

he 2 m ec

,

e me - -

, c - . , , r Å I (. 1).

r r I Å I :

ÅI = I ,

r

r

(1 )

r r H0 Z ) Iz = h mI ,

- , . I r r Å I Z (, -

ÅI z= h mI ,

mI - , mI=(I, I-1,...,-I) - (2I+1) . . 1 I=3/2. , mI , . , , :

Å = ÅI

z max

= h I = gI IÅ ,

(2 )

gI - g-, Å ? =

ÅB he = - , 2 m p c 1836

e mp - . , , , - (p) Å, (n) . ,

Åp = (2.7928456 Á 0.00000011)Å , Ån = -(1.913148 Á 0.0000066)Å .
, (-2 ? 6)Å. , ,
2


. , , (. 1). ? 3. 1. , r r I Å I

r

[1, 2, 4], H0 . (. ?2) , r Å I (. 1):

rr W = - (ÅI H0 ) = - h mI H0 ,

( 3)

.. mI . , . mI = Á1. , , , , :

& W = h H 0 = h 0 ,
a
mI = -3 / 2 mI = -1 / 2
H
0

(4 )

b
3/2 h H0 1/2 h H

0

mI = 1 / 2 mI = 3 / 2

-1/2 h H -3/2 h H

0

0

. 1. : - I=3/2

r H0 ,

b - .
3


. , I=1/2, : +1/2 -1/2. -

r H0 , . , mI Á1, -

r

H1 , ,

r

H0 . , . , r r I Å I , -

r H0 ,
r
r
rr rr dI rr = [ Å I H 0 ] = [ I H 0 ] = [ 0 I ] , dt

r rr N = [ Å I H 0 ]

I Å I (. .2):



0 = - H0 - .
a
H0 H
0

r

r

b
Z I Å

I Å
N

H1

Y

0


X

. 2

Å I : -

r

r H1

r H0

, b -

r H0

-

.

= Const, , (. (3)):

rr W = - (ÅI H0 ) = -ÅI H0Cos .
4


r r , Z ( H0 Z ), XY ,

0 (. 2b), r rr = 0 N 1 = [ Å I H ] . W, .. r . H 1 , , r , N 1 . , , r H 1 . 2. , , . , , , , , , ( 1S0- 10-). [1, 2, 4, 5]. , , , , . , . ( ?Ë), . - , , .. W :

NW = Const e

-

W kT

,

(5 )

k - , - . 5


: +Å -Å. W (2) (3) -Å 0 +Å 0. , 10 W ÅH 0 = << 1 , , 0.01o K kT kT (5) . :
N+ = N- = N 2 N 2

r I=1/2 H0 -

Å H0 1 + , kT Å H0 1 - , kT

N - . N+ N- , . , , ( =2.67ç104 -1 -1) =104 =300 K

2Å H 0 N+ =1+ = 1 + 7 ç 10 - 6 , N- kT
.. 2ç106 7 . , -

r r . , M Z H0 - , (. 3):

NÅ 2 H M Z = ( N + - N- ) Å = kT

0

(6 )

I

N 2h 2 I (I + 1) H 0 M Z = 0 H 0 = , 3kT

( 7)

0 - . , 0 : , , 1 3 0 = 3 ç 10-10 GS.

6


r , H0 r MZ .
, , , , . , , , , .
a H0 Z M H b Z

0

MZ M

H1 Y MX M

MY

Y

X

X

r

. 3. M : a - , b - : .

r
MZ -

r

. Z H0

r

MZ , , 1 - . , , , Z=0. , (. (5)), -

r MZ , r H0 . 1

, . , , 2.
7


. , , -

r H0 Z, XY r H1 (1< :
H X = H1 Cos t ,

HY = Á H1 Sin t

(8 )

( m H Á ). , H X = 2H1 Cos t , , (. (8)). , . -

r H1 , , .. -

r H0 . -

M r H0 . , XY M, , , X Y - MX MY (. 3b). .

r

r H1 , -

M T2 , - . ,

r ( H1 )

, - , , - . , r M , M .
8


M . - 2 , 1 / T2 . . 2. 3. , r M , [1,2,4,5]: r r M - M0 rr rM rM dM = [M H] - i X - j Y - k Z , (9 ) dt T2 T2 T1

rrr
i , j , k - , X, Y, Z. :

HZ = H0 ,

H X = H1Cost ,

HY = m H1Sint ,

r H1 (. . 4),

, X 'Y ', ..

M X = u Cos t - v Sin t , M Y = m [u Sin t + v Cos t ],
(9) :

(1 0 )

& u+ & v+

u + v = 0 , T2 v - u + H1M Z = 0 . T2
(1 1 )

M M & M Z + Z - H1v = 0 , T1 T1
=||H- , u v - . 4, (10) r M , Z,

r H1 .
9


v u. v , , . u, /2 , . (9) (11) , . , &&& u = v = M Z = 0 . .
v= u= - H 1T 2 M
2 2 0 2

1 + ( T 2 ) + H 12 T1T

,

H 1 T 22 M

0 2

1 + ( T 2 ) 2 + 2 H 12 T1T = [1 + ( T 2 ) 2 ] 2 M 1 + ( T2 ) + H
2 2

,

(1 2 )

M

Z

0 2 1 T1T 2

.

r 22 T1, 2, H1 H1 T1T2 , 2 2 . H1 T1 T2 = 1 v
2

(12) , v , u . v u . 5. (12) , u v

v

max

M0 = 2

T T

1 2

. -

, v 0 ( ), M 0 T1 . u = H12T1T2
T
ma x



2

2

, .

1 2

=

1 2

1+

2

H

2 1

T1 T

2

.

(1 3 )

10


r 2 2 (13) , H1 ( H1 T1 T2 << 1) T2.

Y

Y' -v

M

Y

M MX u



X

r H

1

X'
. 4. M (XY) (X'Y') . > 0 H 1 .

a

-v

0.6 0.2 -4 -2 u 0.6 0.2 -4 -2 2 4 0 2 4

T

2

b

T2

. 5 : a - , b - .
11


a

-v 0 1 2

T
u 0 2

2

b

1

T2

. 6 : a - , b - .
aT
2

-

r

r H1 -

H Z , = || HZ - . 1 dH Z a = a T2 < , (12) 2 dt . ( a T2 > 1/ 2 ), - (. . 6).

(t)= HZ(t), . , . 6, Q ( 0, 1, 2) v u , .

12


? 4. : [1, 2]. : r r H 0 H1 . . . . , , . , 100 1?20 . . r M , , , r H 0 (. (6), (7) (12)), , r H 0 . , , . H / H 0 . , , . , , . 0.01 5 ç 104 10 200 . ( 500 ) , - : , [2, 5, 6].
13


1. Q- Q- [1, 2], - . 7. , , . . , :
HZ = H
0

H X = 2 H 1Cos t .

- . , (X Y) , , ,



& = -4 S n M X ,

S - , n - , =
V V

- . , -

, , , , (10) :
i=





R

=

4 Sn R

(u Sin t + v Cos t ) ,

R - . :

Uc =
Q =

1 i dt = -Q4 Sn (u Cos t - v Sin t ) c

(1 5 )

1 R c

=

L
R

- , C L - -

. Uc v u U . Uc/U 10-3 ? I0-5. . 14


, , . v u /2, , . , . , Uc, (15), , :
U


= A Sin ( t + )

.

?Ë, .. , , >>1/ :
U g = U cU dt .
0



(1 6 )

(16) Uc Uo , >>1 , :
Ug ~ (u Sin - v Cos ) .

(1 7 )

= 0, v, = /2, u. Q- , , . , , : . , , 100% , ?Ë . 2. - (. 7b) [6]. , , .
15


. 7 - : a - Q-, b - . : 1 - , 2 - .., 3 - .., 4 - .., 6 - , 7 - .., 8 - .., 9 - ..

:
HZ = H
0

H

X

= 2 H 1 Co s t .

, H0 , , p. H Z = H 0 + H p Cos pt , , p 1/T2<

, . , , p. H1< u + jv = H 1T2 M
0


- k ,n



n ( ) k ( )[( + np )T2 - j ] exp[ j ( n - k ) pt ] , (1 8 ) 1 + ( + np ) 2 T22 + 2 H 12T1T2 2 ( ) n

- , n() - p n- , n k - . (18) , = 0 Á n p = 0 , .. :
H0 =

= H 0 - , =

H

p



H0 =

Á np ,

(1 9 )

. 8. (18) , , (19), . [j(n-k)t], , , -

r H1 , , , .

. 8 , , , .
17


, Á np , 100 % . . 8 , . v u , . , , p, v u (. (18)). v u .. .. .. :
U
/

= B Sin ( pt + ) .

, . , , / . . ? 5. . , ( ), ( ) [2, 4]. - , - , . . 2.

18


1. ? Ë , - (. ?4), , . , ,

r

H0 [2, 4].

r

, H0 ( ) r r r H0 , H = - H0 . , , ,
= H 0 (1 - ) ,

(2 0 )

- . (20) , , , ,

r

- - H0 . - :
=
H -H H


= - .

(2 1 )

S0- .

r

H0 . . , , . , : - , ;
19


, ; , . , , , . , . . 9 , (CH3CH2OH) 10-6; (3), (CH2) () . 3:2:1, . , , :

=



+



,

- , - . , , , .
OH CH2 CH3

a
H0

b
H0

. 9 , (CH3CH2OH): a - 10-6 ; b - 10-8.

10-5 , 10 ? 100
20


. , . , . , , , , , , . . 2. , , - (). , : , [2, 4]. . 9b (CH3CH2OH), (10-8), . 9. , . , , , , : , - . , , - , - . - HD, , . , (. . 10).
21










. 10. .

, . , , . HD 2 (I=1/2), 2 . I=1 3 (. 11). , - - ?Ë . -

r H0 ,

r H0 .

, ,

- 12 I1 I 2 , I1 I2 - , a 12 - - , . 12 1000 . - .

. 11. HD.

, . 22


, , , , n I1 I2 (2nI1+1) . , . . (P3), () I=1/2 (I=1/2): '"'", .

r

H0 (. 12). IZ 4 . , .. P . , 1:3:3:1 (. 13). P I=1/2 , , . .

. 12. PH3

23


. 13 P3: a - H; b - P

, . , , - . , . , . 9b: 2 (3) (2) 3 (2ç2çÍ+1=3), 3 4 (2ç3çÍ+1=4). () . , , . . , .

r H0 r H0 ,
.
24




? 6. [1].

r

H0 (4) , , (2) I, Å. , Å, 10-5, , h. ?

r H0 . :

01 02

=

1 Å1 I2 . = 2 Å 2 I1

(2 2 )

I1 I2, Å1 / Å2 ? . , 11H, 7Li, 23Na. 10-6. Å .

r H1 X, -

, Y. Y (. (10)), .. . 0 = Const. , 2 , 2 , , Å2. . , . ?5, , , , . , I1 I2, n I2,
25

r H0 , 1 ,


, I1 2nI1+1 . , . . ? 7. : ; 4000 ; 3ç10-6; 16,2 . . - . 14. 5

r H0 ,
3. -

r H0 . ( 1?5 )

r H0 . 5.

10 10 11.

r H0 . -

r H1 , , -

. -

1. 5 . 0= H0 , , -

r

, H0 . . , , .

26




+

1

H
0

2

3 N


H H
1

0

3
H
p



S


4

5

p

6

7

8

9

10

1

. 14. - . : 1. , H1 ( AFG3021B; ; - 0,01; . ). 2. ( ). 3. . 4. p ( ). 5. ( ): ) .. ; ) ; ) () ; ) . 6. . 7. p ( 3-36; 3-63/1). 8. ( 5-54). 9. ( ). 10. ( 11). 11. ( 1-48).
27


r (. ? 4). H0 p -

, -

5, 7. ,
H0 = Á np , n = 0, 1, 2, ...

, (, , ), - . ( n=2 ..).
c = o Á kp , k = 0, 1, 2, ....

= Hp/ p. 0 / (2) 16200 , p/(2) 6 . :
0 = = 16200 (n = 0, ); 2 2 0 p = - = 16194 (n = -1, ); 2 2 2 0 p = + = 16206 (n = 1, ). 2 2 2

:
16200 16194 c = 16206 2 16138 16212 k = 0 k = -1 k = 1 k = -2 k = 2

, 2 ( ) . , 4 p. (u v) 9 p. , 7, 8,
28


5-54; . 9 11 (). 5 - , , . 0 . ( ) . , ; ( ).

AFG 3021B

4

5

6

7

1

2

3

. 15. AFG 3021B

1. 2. 3. 4. 5.

[1]. , . [3] (Recall). [5] (Recall). [2] (On - ). [6] (Frequency/Period - ,
29


[4] ). 6. [] [] [4]. 7. [7] . 8. [1]. , , 16200 , , . ; , , - , 16200 .

1. 2. - 1. .
2 2 2

= 2 - 1 n , ( ) . ( ). 2 n 2. 3 - 6. 3. - , . , - .

. 2

30


1. M M : ? ? 2. ? 3. : v u? 4. ? 5. ? , ? 6. ? , . 7. p1/2. 1 2 3 4 . . - .: , 1957. .. . - .: , 1963. .. . - .: , 1973. ., ., . . - .: , 1962. 5. .., .., .. . - .: , 1972. 6. -. - .: , 1964. 7. .. . T. 1. - M.: , 1974. . . . . 1 1. : ) - (Z - , - ) : I = 0, Å = 0. )
31
15 7

N -


. , , . - , . . , ( ) , . , ~3 , ~1 . , , . , , , : 00 = ( j1 j2 0 | m1m2 0) j1m1 j2m2 ,
m1m2

j1m1 j2 m2 - , j1 j2 - , m1 m2 - Z. , , j1m1 j2 m2 . . 16 . . , j - m
j m (. 16a).

32


a

m

1

b

m

1

m2 m1 = - m
2

m

2

|m1 | = |m2 |

. 16. : a - m1 = - m2; b - |m1| = |m2|.

(l1 = l2) , : s1=-s2. (m1=-m2) ( ) m1-m2. , , , , ( ), . ( ) . . 1937 . :

rrr j = l+s ,

rr r Å j = Ål + Ås , Ål = gl l , Å s = g s s . r r r r

. 17 r r r s ), ( l ) ( j ) ( (), - r rr Å s , Å l Å j

33


. 17. Å

r
s

Å

r

Å l .

r

j - , -



r j

.

gl gs ( gl = 1, gS=5.5886; gl = 0, gS = -3.8263), -

Å j j rr . l s r

r

r

j .

r r rr j . Å s , Å l Å j r r r r

j . Å j* Å j j , (). . 17,

s 2 = l 2 + j 2 - 2ljCos(lj) , l 2 = s 2 + j 2 - 2sjCos(sj) .


j 2 + l2 - s2 lCos (lj ) = , 2j
34


j 2 + s 2 - l2 sCos(sj ) = . 2j

r r j Å
(. 17):

j*

Å j* = [gllCos(lj) + gs sCos(sj)]Å ,

r r (l j ) - l j , (sj ) -
s j . ,

r

r

Å j* = g




l

j 2 + l2 - s2 j 2 + s2 - l2 + gs Å ? = 2j 2j gl + g s l2 - s2 = + (gl - g s ) jÅ ? . 2 2 j2

j = I Å j* = Å I , I Å I - . s=1/2,
r r

r

r

ÅI =

r

l(l + 1) - 3 / 4 r gl - gs + (gl - g s ) I Å ? . 2 I ( I + 1) 2

I , , mI h (|mI| I ). I Å I Z max ( ), , :

Å=

l(l + 1) - 3 / 4 gl + gs + (gl - g s ) IÅ ? = g I IÅ ? . 2 2 I ( I + 1)

gl = 1, gs = 5.5886 gl = 0, gs = -3.8263 , .

35


1 I =l+ , Å= 2 1 I I =l- , Å= 2 I +1

Å

1 + g l ( I - )Å ? , 2 3 - Å p,n + gl (I + )Å ? . 2
p,n

Åp,n , , . , rr s l l . , p1/2 (l = 1, I= 1/2) Å = 0.64Å ( Å = -1.91Å).
13 6 C (Å = 0.70Å).



15 7

N . ,

13 15 6 C ( 7 N ) () p1/2,

6C (1s1/2)4(1p3/2)8(1p1/2)1 (. [7]). ( I = l Á 1/2) (. [7]), , , . , 6 C 7 N . . , . - . , , , , . . (.: .. . - .: , 1967, . 13, . 2 . 116, . 2). , -
36
13 15

13


, , . - . 2 1. , , , .. [1, 2, 4]. . , - . r H , r r H 0 . H Z :


H Z = H0 Á



Å

I 3 ri

(3Cos2i - 1) ,

(I)
r

ri - , i - ri r H 0 . (I), , , ~ H . - , , r H 0 . , , , , , . , .. - , . H .
37


, , , H ( t ) . , , , . - , . . , , , : t T1 1 . I > 1 / 2 , . . r H 0 . - , , . , .

r

HI (. (12)).

=

1 . T2

(II)



=
*

1 1 + H = * , T2 T2

(III)

T2 - , , , 2 (III) , (III). , 38


, -, , (10-3?1) . , . , - .. , - , . 2. T1 T
2

, , ( ) . , , . , ,
2 n( 0) = H (t )

2 c , 2 1 + 0 c2

(IV)

c - , , ?Ë [1, 2, 4]. (c ~ / , - , - ). , , , - 2 (. (II)). - 1 . 1 0, , , . w, 1, 0 , :
w~ 1 2 c 2 ~ n(0 ) = H ( t ) . 2 T1 1 + 0 c2

(V)

, T1 T2 (V),
39


0 c . , - T1 T2 :
4 c 1 3 h 2 4 c = + , 2 2 T1 10 r06 1 + 0 c2 1 + 4 0 c2 5 c 2 c 1 3h = 3 c + + , 2 2 T2 20 r06 1 + 0 c2 1 + 4 0 c2
2 4

(VI)

r0 - . (VI) , 0 c << 1, .. ,
1 1 3 h 2 4 = = c. T1 T2 2 r06 (VII)

, 1 2 - . c (.. ) 1 2 . (VI) (VII) , 2 , .. 1 2 . , H ( t ) , (V), 1 2. 1 2 :
2 1 4 N p Å = T1 kT 2

,

(V III)

Np - 1 3, Å 2 - . Np , 3 . - , , .
40


, 1 10-5 . 2 << 1, 2 1, .. .

41


3 ,
1.





H2O


-

2.



C2H5OH

O
3. CH3COOH

4.



(H)2P(H)O

5.



(CH3O)2P(H)O

6.



(2H5O)2P(H)O

. 3 - 6 .
42