1

.

, 2002 .

2 1- 1.1. .1.2. - .1.3. .1.4. .1.5. .

1.5.1. .1.5.2. .

1.6. . .1.7. .

1.7.1. 1.7.2. Q.

1.8. . 2 - .

2. .2.1. .2.2. .2.3. .2.4. .2.5. .

2.5.1. .2.5.2. .2.5.3. n .2.5.4. .

2.6. .2.6.1. .2.6.2. -.2.6.3. .

2.6.3.1. --.2.6.3.2. + -.2.6.3.3. .

3 - 3.1. .3.2. .

3.2.1. .3.2.1.1. . .

3.2.2. ( ).3.2.3. 3.2.4. .

3.3. .3.3.1. .3.3.2. .

4 - 4.1. .

4.1.1. I .4.2. .4.3. .

4.3.1. .4.3.2. .4.3.3. .

34.3.4. .4.3.4.1.

.4.3.4.2. .

4.4. . 5 -

5.1. .5.2. .

5.2.1. .5.2.2. .5.2.3. .5.2.4. .5.2.5. .

5.3. - .5.4. . .5.5. .

5.5.1. .5.5.2. .

5.6. .5.6.2. .5.6.3. .

6 - 6.1. .6.2. .

6.2.1. . .6.2.2. - .

6.2.2.1. .6.2.3. - .6.2.4. .

6.2.4.1. .

6.2.4.2. .6.2.4.3. .6.2.4.4. ( ).6.2.4.5. (

).6.3. .

6.3.1. .6.3.2. .

6.3.2.1. .6.3.2.2. .

6.3.3. . . 7 - -.

7.1. .7.2. .7.3. .7.4. -.7.5. -.

7.5.1. .7.5.2. .

7.5.2.1. .7.5.2.2. ().

47.5.3. . 8 - -.

8.1. .8.2. -.8.3. .8.4. -.

8.4.1. .8.5. .8.6. .8.7. -.

8.7.1. .8.7.2. .

8.8. - .8.8.1. .8.8.2. . .8.8.3. .8.8.4. .

9 - -9.1. .9.2. .9.3. .9.4. -.9.5. .9.6. 00.9.7. .9.8. .

9.8.1. .9.8.2. .9.8.3. .

9.8.3.1. () .9.8.3.2. ( ).9. 8.3.3. .

9.8.4. . - - . -

.1. ..2. ..3. ..4. ..5. ..6. k .

- . - - . - -

1

5 1.1. .

, . ,

- . : , , , , , , , , , , , . , , , . / . ( 10-10 m) ( 10-14m). ~3 V =511 keV /~5.10-3 , ~8 V ~A GeV =160 /~5.10-5.

: , . , , , - . , - . , .

1.2. - . , ,

, . (1/3)e (2/3)e, e=1,6.10-19C, 6 (): u(up), d(down), c(charm), s(strange), t(truth), b(beauty), . u +(2/3)e, d -(1/3)e. u- d- 2(2/3)e-(1/3)e=1e. u- d-, : -2(1/3)e+(1/3)e=0. , , Z N . , .

- 1.1. , : 3 , , ( ) . , .

6 1.1

*( . )

939,55270,0052 MeV 0 -(1,9131480,000066)1,00898 1838,5 m0

938,2592+0,0052 V 1 (2,7927820,000017)1,00759 1836 m0

, . :

++ ~epn

1/2 = 11,7 . ( ) 1/2,

-. .

1.3. . , , - .

. , , Z, N , N=A-Z.

( ) , N Z. . . 1.1 . , "" .. . N=Z, - - 45 N.

* , ,

: p2/ me= , mp . , 2000 - , .

7. 1.1 ,

, , , . Ca4020 Ca

4820 . Z=const.

, . 214019 Ca 21

3918 Ar .

N=const. , . 21

4019 K 20

4020 Ca .

A=const 45 N Z. ,

- (R ~ 10-10 m). , :

[1.1] 31.ArR 0=

r0=1,2 fm, 1 fm=10-15 m, . , :

[1.2] 1510 VV

- 2.108 t/cm3. [1.1] , : , , .

8 ( ).

1.4. . (kg) ,

, . - , , 1/12 12( ):[1.3] ( ) 12C12 =M

2=22 + m2c4

. , E=mc2 m=E/c2, , p=E/c, V/2, - V/. V :

[1.4] 1 = 931,49 V/2= (931 494,32 0,28) kV/2

[1.5] 1 V= 1,07.10-3 .

: 1993 . , , :

() = (1,007 276 466 6 6 ) (4) = (4,001 506 174 7 15) (197Au) = (196,966 551 3) .

, (Z,A) .

[1.6] (Z,A) [ ] = (Z,A) [ ] - A . V/2

[1.7] M(Z,A) [ V] = M(Z,A) [ V] - 931,49 A. ( )

. :

[1.8] (Z,A) = M(Z,A) + Z.m0 - Be/2

m0 , . , 3V/, 8V/.

9 ? :

[1.9] M(Z,A) = Zm+ (A-Z)mn- B/c2

m mn , . , , . , , , . .[1.10] B(Z,A) = [Zm+ (A-Z)mn- M(Z,A)]c2

[1.11] AB= , . . 1.2 .

. 1.2 =B/A

1.2 , , . : - - .

10

. . , -1, (-1), , AB= , . 1.2.

. 1.3 f=M-A/A

- , f=(M-A)/A=/, . . 1.3. , - 20

11

. 1.4

m, v q B r

[1.12]qBmvr = ,

(F=mv2/r) ( ][ rvmqF

= ). v q , r B

m. , m

, . . . 1.4 ea . :

. , , . . , v,q m.

. E B

:

EqFe = ,

, ][ rvmqFm

= . , : me FF

= , v=E/B, , .

B .

12

-, - - . , .

.

- , .

1.5.2. . q v m B , [1.11] - . 1.5.

. 1.5 -

, - , f.

13

[1.13]qBm

Bqvvm

vrT

222 === , 2

1

B

mq

Tf

==

, q/m . 1 m 0,15 0,8 .

. . + . . , , . : +++ . , , 0=+ . ( RF)

[1.14] )21( fnfRF += ,

n=1,2,... fRF. , e [1.14].

q/m, 162+ 32S++, m=m(16O2+) - m(32S++).

1.5.3. . - Q ( - )

. 1.6 14

281415

2813 SiAl

, - , . .

14

- 28Al(. 1.6):

~eSiAl 28142813 ++ .

28Si -. - 1,782 V. - -, 2,865 V. : E + Emax() = 2,865 + 1,782 = 4,647 V = 0,00499 , 1 V=1,07.10-3 . 28Si 27,98577 . Al2813 27,98577 + 0,00499 =27,99076 .

1.6. . . 1935 .

: , , , . . - . , , . , , :

[1.15]22

4312

332

21 /),()()(),( cNZAZNAZAAmZAZmZAM np ++++=[1.16] ),()( 2

312

32 NZAZNaAZaAaAaB +=

(1) (2) (3) (4) (5)

:(1) - . , . , , . , .(2) - - . , , . . , , , . , .. 2/3.

15

24 RE = , , R- . , [1.1]

324 AE = .

: ~10-5 J/cm2 , - 1014J/cm2. (2)

[1.17] 222

4 cRa == ,

222 /4 cR = [1.15] .(3) - . , ( Q R)

[1.18] 312

3100

22

0

22

453

453

AZa

ArZe

RZeE ===

3 [1.15] 23 / ca= .

(4) - - , . , . , ( ). . , , . , , (3). , . - - . " ", - , - , .(5)

16

. 1.7

E , AZN 2)( . -

. AZN )( = (. 1.7) )( 0 (.. N=Z)

...)0()21()0()0()( 2 +++= ,0= 0)0( = .

22

max )0(21)0(...)0("

21)0(

+=++

AZN

Bmax =const. Amax = const AZN 2)( .(5) . , . . , - - , - . - 163, - - 4, ( 1

21H , 3

63Li , 5

105 B

7147 N ), Z N (54), Z N (49 ).

+=

)(0

)(

A

A

() , N Z , N Z. () . () :

() = 12-1/2 (V).

17

. 1.8

. 1.8 , , . /, . , / .

[1.16] : = 16 V, = 17 V, = 0,69 V, = 25 V.

. , . - , . [1.16].

1.7. .1.7.1. (, , -).

, , =/. , )(p A,ZS , )(n Z,AS - )( A,ZS . , : .

18

[1.19] Sp(Z,A) = B/Z, [M(Z-1,N) + mp - M(Z,N)]c2 = B(Z,N)-B(Z-1,N) = B/Z Z=1. :

[1.20] Sn(Z,N) = B/N. )(p A,ZS =0 )(n Z,AS =0

(Z N N Z ), - . , 0p

19

(200), , - . - .

:

[1.24] Q = [M(A,Z)-M(A1,Z1)-M(A2,Z2)]c2=

= B1+B2-B= AAAAAA ++ )()( 212211 = 0)( > A

= )()( 212211 AAAA ++ . 235U = 7,6 V = 8,5 V. =(8,5-7,6).235= 211 V, 1/1000 , .

:

[1.25] Q = [M(A1,Z1) + M(A2,Z2) - M(A,Z)]c2 =

= B - (B1+B2)= )()( 212211 AAAAAA ++ = 0)( > A :

d + d 3He + n (Q=+3.25 MeV)d + d t + p (Q=+4 MeV)d + t 4He + n (Q=+17.6 MeV)

d 2, t - 3. , -, ( 28 V).

f=(M-A)/A , .. 200 - (. 1.3). , f , , .

1.8. . . 1.9 ( )

A=125 ( ) Z. , ( ) . , . [1.15] :

M(Z,A)=Z(mp-mn)+A(mn-a/c2)+(a/c2)A2/3+(a/c2) Z2/A1/3+(a /c2)(A-2Z)2/A-(A,Z)/c2

[1.26] M(Z,A) = A + Z + Z 2 ( 0),

20

: = 231 /)/( cAaaamn np mmca += 2 /4

)/()/(4 3122

AcaAca += .

Z =const, .. M(A,Z)

[1.27] 0const

=

=AZM ,

[1.28] 0)2(22 131

=+=+=

ZAAaAZaZ

ZM

A

.

[1.29]32

32

31

1

411

12

224

2

Aaa

A

Aaa

AAaAa

aZ+

=+

=+= .

-

[1.30] ZA = 32015,098,1 AA

+* .

Z . ,

Z = A/2,

, . [1.26] [=( 0)] ,

,.. , - ( [1.15]).

- : =0. , + / (). , , -. . 1.9 () (A=135) . , , ( ) 79

13556 Ba .

* Z (mp-mn) . Z [1.27], [1.30].

21

. 1.9 : = 135 () = 102 ()

- : =0. [1.26]. Z ( N) -, - . Z ( N) - , [1.26] . , - , - . 4 - 1

21H , 3

63Li , 5

105 B 7

147 N .

Z=N. , , - .

. 1.9 () =102.- 57

10245 Rh -: +,

CE - ( +-). - , (A,Z) (A,Z+2) - 58

10244 Ru 56

10246 Pd .

2

22

. .

, (109 ). 280, 3000.

. 2.1

(. 1.1) , (N,Z), (Z,N) ( ), , . 2.1. , - , , - , - . , =const, . . 1.9. Z - . , , . - 2.3 .

2. .2.1. .

, - 10-23 s

23

, . , , - , . 109 . 235U 238U , .

, . - 1934 ., - 30, 2,5. :

" : , . ."

:

27Al + 4He 30P + n - 2,7 MeV; 30P 30Si + + + (T1/2=2,5 m)

- 1935 . : - 1903 . , , ( ) 1911 .

, , -:- 1896 . .- 1898 . , .- 1899 . . - -.- 1900 . -.- 1902 . .- 1917 . .- 1928 . , -.- 1930 . -.- 1934 . - .- 1935 . -. -.- 1938 . , .- 1939 . .- 1940 . .- 1962 . .

, , 10 .

2.2. . ,

.

24

, , , , . , .

, , . , . , :

. . t ( 1/ ). t

t. (1-t), 2t e (1-t)2 . t=nt (1- t)n = (1-t/n)n. , n

t

ne

nt = )1(lim ,

t e-t.

2.3. . ( )

. e , t N . N(t) t. t t+dt (dt

25

1 g 226Ra (1/2 = 1620 y). mCi (10-3Ci) Ci (10-6Ci).

, [2.1] [2.2] N , .

2.4. . ,

. [2.1] , N = N0/2 :

[2.3] 693,02ln

21 ==T

[2.1]

[2.4] =693,0

1

)(

)(21

000

00

0

0 TdtetdeN

dtetN

tdN

ttdNt tt

t

======

, 1/2 70% - .

( ) , [2.2]. () . 21

6429 K -- Zn6430 ,

+- (C=Electron Capture) Ni6428 . :

- + +,- EC - -.

, [2.5] + ++= CE .

2.5. .

:

[2.6] nBBBBB 4321 . i , Bn.

2.5.1. . , B3 .

, N01 B1 (N02 =0). B1 a [2.1]: N1 =N01 exp(-1t). (y), (d), (h), (m).

26

N2 . :

[2.7] 2211 NNdtdN = ,

1N1 , 2N2 . N1

[2.8] teNNdt

dN1

011222 =+ .

[2.9] [ ]tt eCeCNN 21 21012 += . , [2.8], .. teN 202

. [2.10] [ ]ttt eCeCNeNtN 212 2101022 )( ++= .

, N2(0)=N02=0, [2.9]. [2.8] 1

12

11

=C

tt eCeNtN 21 2

12

1012 )(

+= .

N02=0 t=0

12

12

=C

[2.8]

[2.11] [ ]tt eeNtN 2112

1012 )(

= .

,

[2.12] [ ]tt eeANA 210112

2222

== [2.2] 1N01=A01.

.

27

tmax dA2/dt=0, a

[2.13] 2

1

21

21

12

12max ln693,0

1)(lnTT

TTTTt ==

.

dN2/dt=0, [2.8] 1N1=2N2, .. . . tmx. ttmax -.

[2.14] ]1[ )(12

2

1

2 12 teAA

=

, . 1 2

.

1. - :

2 >T1 ( 2 < 1) [2.14]

[ ]1)(21

2

1

2 21 = te

AA

, . t, . 110Tt tt ee 12 >> [2.11]

[2.15] teNtN 20121

12 )(

=

teANtA 20121

2222 )(

== ,.. , , . 2.2.

28

. 2.2 T2>T1. () , (b) - , () - , t (d) - ,

2. - :

T1>T2 ( 1> [2.11]

[2.16] teNtN 10112

12 )(

= ,

teAtA 101

12

22 )(

= ,

. [2.1]

[2.17] const)()(

12

1

1

2 ==

tNtN

.

, , - . 2.3. 210Tt .

29

. 2.3 . () , (b) () , (d) - -, .

3. - , ( ):

T1>>T2 ( 11).

[2.18] [ ] [ ]ttt eNeeNtN 2122 11)(2

101

)(

12

1012

== .

210Tt .

2

1012 NN = ,

,

[2.19] const)(1

2

2

1

1

2 ===TT

NtN

.

1N1=2N2 - . , [2.18] . . 2.4.

30

. 2.4 : () - , (b) , (c) , (d)- .

226Ra 222Rn. :

226Ra =1,38.10-11 s-1 (T1/2=1620 y)222Rn =2,1.10 -6 s-1 (T1/2=3,82 d)

, 1g Ra 6,510-6 g (222Rn). 40 .

2.5.2. . 1 N01.

. [2.11]. N3

[2.20] 33223 NNdtdN = ,

2N2 3 2 , 3N3 - 3.

[2.21] [ ]tt eeNNdt

dN21

0112

2133

3

=+ .

[2.22] [ ]ttt eCeCeCNN 321 321013 ++= .

31

- 1, 2 3 ,

[2.23]))(( 1312

211

=C , ))(( 2123

212

=C , ))(( 3231

213

=C .

2.5.3. n .- n

[2.6]. N01, n-

[2.24] [ ] =

=+++=n

m

tm

tn

ttn

mn eCNeCeCeCNtN1

01210121)( ,

C1, C2, C3,, Cm :

)())((.

11312

1211

=

n

nC

...

)())((.

121

121

nnnn

nnC

=

[2.25])()).(()( 121

121

;1

1

1

mnmm

nn

niimi

n

ii

mC

==

=

=

.

, [2.22] [2.23].

. ( ) - , : .

[2.26] 1N1 = 2N2 = .... = nNn N1, N2, ... Nn t.

2.5.4. .

4,5.109 , , , . , ( 15.109 y) . ,

32

. , , . , , , . .

2.1

()

-

()

4n 208Pb 232Th 1,41.1010

4n+1 209Bi 237Np 2,14.106

- 4n+2 206Pb 238U 4,47.109

4n+3 207Pb 235U 7,04.108

, (>200). 12-15 - -, Z , ( ). . 2.5 . - 4, - , 4 4n, 4n+1, 4n+2 4n+3, n (n=58, 59 ). - , . 2.1. , . 2.2 - .

, , 40, 1,28.109 .

33

. 2.5 N

AZ X

, , , . 3 14, .

34

, . , , -. . ( - 10 cm), - . , . , , .. . , , , . . . , .

2.6. .

. , 1, . - :

- - ( )- , .

-. . :

- Z- - - Z - +- Z - Z .

2.6.1. .2.6.2. -.

[2.27] HeYX 4242 + AZAZ (+Q)

- : HeRnRa 422228622688 + . Q>0

[2.28] M(Z,A) > (Z-2,A-4) + M( He42 )

, . , :

[2.29] Q=B(A-4,Z-2) - B(Z,A) + B( He42 ) > 0.

- , [1.19] [1.20]:

35

[2.30] 28,3He)(),(4),(2 42 =>+

BA

ZABZ

ZABMeV

ZB AB - [1.16]. , [2.30] >150. , - , -. - - .

2.6.3. .2.6.3.1. --.

,

np + e- + ~

[2.31] ~eYX 1 ++ +AZAZ Y, ., , . 1930 . . 1956 .

. 2.6 -- - () () .

, , [2.32] M(A,Z) > M (A,Z+1) + m0 ,

m0 . Z , :

36

[2.33] M(A,Z) > M(A,Z+1).

-- - . 2.6 () - -. 2.6 () - . . . , , , . Q , .

2.6.3.2. + -.

. p n + e+ + . :

[2.34] eYX 1 ++ +AZAZ .

--, : , .

[2.35] M(A,Z) > M (A,Z-1) + m0

Z , :

[2.36] M(A,Z) > M(A,Z-1) + 2m0 .

2.6.3.3. . ,

, , p + e-n + . :[2.37] Y)e(X 1 ++ AZAZ .

, . , , -- +-. :[2.38] M(A,Z) + m0 > M(A,Z-1)

, (Z-1)

[2.39] M(A,Z) > M(A,Z-1).

, , +- .

37

+-.

. 2.7 +- . , 2m0c2, , +-.

+- . 2.7 ( ). , , , (~1022 V).

-, -- - , . + 1932 . . , , , , , . , . . 1.1 ( ) , - , . , , - .

38

3

3.1. . ,

: , . , , , - (1 nm). , "", , , . , , .. . , - , . . . , : .

-, - - , . : , , , . , , .

, . , . , , . . , .

(R ~ 10-14 m) . , : , , .

3.2. .3.2.1. .

, . 3.1 . ,

39

"" 2 fm - 600 V.

3.1

=h/p

- 8 V 5,1 fm (>R) 200 V 1,9 fm (

40

-, c=197MeV.fm:

12MeV

MeV.fm1001972 ===

Ehc fm .

. 3.2

208Pb ( 248 V 502 V)

100 V 1 GeV. , . . 3.1 . . , . D =arcsin(1,22/D) 16 2,6 fm, 12 2,3 fm. , - .3.3. . 3.2 , 208b, . , , , . , , .

3.2.1.1. . .

ze Ze :[3.1]

d

d =)2(sin4

12 4

2

02

TkzZe =

)2(sin41

4 4222222

TZzc =

)2(sin414

2222

222

Zz

vpc

41

. 3.3

- . - .

z Z , k0=1/40 , , - . [3.1] 42=p2v2. , c, k0 e: =k02/c. (z=1) :

[3.2])2(sin

14 4

222

222

Z

vpc

dd =

( 1/2 v~c) [3.1] . :

[3.3]

=

)2(sin1)2(sin

14

22

2

42

22

222

Mott

cvZ

vpc

dd ,

. , , , 0 . , , Z

42

, =1/137. , . - . f() ,

[3.4] 2Mottexp

)( fdd

dd

=

.

f(), , ( ).

. 3.4

12, 16O, 58Ni 208Pb

- . , .

: - ( . 3.3). .

. 3.4. , . , - . :

= VA = 3)3/4( R

A ~ const .

R R ~ A1/3,

[3.5] R = r0 A1/3 ,

r0 .

( ) . , . , Z

43

[3.6] r0 = 1,05 fm.

. 3.4 . , 90% 10% , , . , , 2,32,5 fm.

. 3.5

.

. 3.5 . r0= 1,23 fm. - .

(. 3.6):

[3.7]aRr

er

+=

1)( 0

. 3.6

, [3.7]

R (R)/(0)=1/2 , . d [3.7]

. 3.7

( )

44

[3.8] 4,49ln2

dda == ,

(d+R)/(0)=1/10. [3.7].

. . 3.7 : , ( A .3.7) ( ). , - . . 3.7 153 V .

3.2.2. ( ). ,

, , 207 - . ( 21T 2.10-8 s) :

[3.9] + , + + , , - . , [3.9] . . , (2,2 .10-6 s) - . , . , . , . , .

. a0 = Z1.

(= cek 20 , - , = /m0c). , 207 - 0.

, (Z=82), (n=1) 0(-)=a0(-)/(207.82)= 3.10-15 m, . . 3.8, , .

45

. 3.8

Au , ( ) ( ).

.

2

2

2

22

02

22 207.6,13207.5,05,0)(

nZ

nZcm

nZcmEn === eV.

En()= 2/93,18 nV, 10 =189 kV, 9=230 kV, 8 =300 kV,..., 2 = 4,73 V 1==18,93 V. n . = 1 , . n=10 230-189=41 kV, 300-230=70 kV,..., 18,93-4,73 = =14,2 V. , -. - , 2p 1s 14,2 V. - Pb 5,5 V, .

, , -, , [3.7]. , () . - Pi

[3.10] 2 = =

N

i 1[Pi - Pi (X1, X2,..., R,..., Xn)]2,

- R. i , , N . .

R(Pb) = 1,17.10-15 2083 m.

3.2.3. .

. +- , Z Z-1. , . , .

46

13622892 U -,

92- 137 . 92 137 . . , , . "" . , . , .

51116 C 6

115 B . :

[1.14] Z +-. N=Z-1 N=A-Z, N = A - Z = Z - 1,

[3.11] A = 2Z - 1.

[1.14] , Z: . , A=2Z-1:

aA-1{(A-2Z)2-[A-2(Z-1)]2} = aA-1[(2Z-1-2Z)2 - (2Z-1-2Z+2)2]=0.

:

[3.12] [ ]22310

20 )1(

53)1,(),( == ZZ

ArekZABZABB 32

0

20

53 A

rek= ,

[3.11]. .

+- +Q , +E

202 cmEQ += ++

, m =0. :

B(A,Z) = [Zmp + (A-Z)mn - M(A,Z)]c2

B(A,Z-1) = [(Z-1)mp + (A-Z+1)mn - M(A,Z-1)]c2,

[3.13] |B| = B(A,Z-1) - B(A,Z) =[M (A,Z) - M(A,Z-1) + (mn - mp)]c2.

[3.14] [M(A,Z) - M(A,Z-1)]c2 = 202 cmEQ += ++ , , [3.15] |B| = +E + 4,5 m0 = +E + 2,3 V.

47

. 3.9

, , 2/3

. 3.9 25 . R0 .

., 6

115 B

, 5116 C .

, 5116 C

6115 B .

3.2.4. . ,

s- p- , r, .. .

[3.16] = rdrVV nn 3* )( , [3.17] rZekrV /)( 20= .

- R. , . r, (r < R) :

[3.18]

=

220

21

23)(

Rr

RZekrV .

:[3.19]

>0 , , N - , - , F

J

. /N ~ 2000, ~ 102-103 , 0,2-0,3 ,

(/N)0 >> .

. 4.2

.

S.

60

I .

. ( I) . , . . 4.2. () . , 1, 2 3, , (). 1 3 z, . : 1, 2 3. 1 3 , :

[4.20]zB

zB

13 = .

( , . 163), , . N. , S, . 3 . , F

,

N, . z-

[4.21]

)1(),cos( +=== II

mzB

II

zBz

zBF Izz

,

[4.22])1(

),cos(),cos( +=== IIm

IIzIz Iz

, , .. 2 .

- , . e , .

61

2 2 I

z - Iz=mI .

2 4, , m m+1, . 4 , ( !). Iz 3, .

2

[4.23] II mBgBU 22. == M.

m m+1

[4.24] 2BgU I= M .

.4.3

2

. 4.3 2 4. . 4.4 . ,

, Isin 100 1000 . .

.4.4: 1 3 4. 1 3 50 cm, . 1 mm. , 100 . 1 8 /cm. 1 m 0,05 mm, 0,01

62

mm. 4 .

[4.25] 2BghU I=== M = 2 2 . , = 2/L . . 4.5 . 2=0,3385 =5,585 Hz. [4.25] g =2,167 = 3,250 , , I=3/2.

. 4.5: 7Li.

- - , ( ), .

. , - - , , . , .

1946 . ., , ( ) 850 cm3 29,8 MHz, 0,71 . 29,8 MHz.

, , . , =/h, . . (1), ( ). , . ( ) , . , , . , , .

63

4.4. . .

V . (x,y,z)

[4.26] = V rdrrrkrV

')'()( 0

[.2] ( ). , . , , , . q, : z=+a/2 z=-a/2. , , . , , , - . , , . , . eeQ = . Q , b (1 barn=10-24cm2), Q b (barn).

. 4.6

),,( zyx

)(rP z .

. ,

( )rP z' . 4.6. [4.25] ( rr ) :

(x', y', z') , (x, y, z)

64

[4.27]

( ) +++= ...'1cos321)'(1'cos)'(1')'(1)( 22320 rdrrrrdrrrrdrrkrV 1 , cos' (3cos2'-1) P0,1,2(cos').

Zerdr = ')'( .

V

rdrr ''cos')'(

eD, , ( 10-7). , )(r )()( rr , . z'=r'cos' 222 zyxr ++= (z'-z') cos', , V . [4.27], , .

[4.28] =V

rdrreQ )1'cos3(')'( 22 .

, z' z r ( z). , ( ):

[4.29] ( )2252 aceZeQ = .

z' (prolate) Q>0, (oblate) Q

65

[4.31] 200 54.

54 eZRRReZeQ == .

z . - , , I z, . q , Q[4.32] Qq = . I :

[4.33] )12(

)1(3 20

+=II

IImQQ I ,

.4.7

Q0 , ),,( zyx , . [4.33] .

, 1/2 0. Q .

, (Z N=2, 8, 20, 28, 50, 82,126) , . . 4.7 Z N. , , N (Z) 5082 82126. - (prolate) .

5

66

-

, , .

, - . :

- - - - - - - - () - (. ).- ,

.

5.1. .

=/ - 8 V, 6 - . , . , 1,5 fm, , 1,4 V, , 1,1.10-26 V.

(

67

, 1932 . , - - -, , , .

. 5.1

: 473Li 3

74 Be

. Z N (Z=N=20).

.

. 5.2

- . 4

62 He ,

363Li 2

64 Be .

. 5.1 473Li 3

74 Be .

, . .

- : 3 (,) 6(n,n) 473Li 3 (n,n) 6 (,)

374 Be .

(n,n) (,) , .. . ,

. 5.2. 4

62 He , 3

63Li 2

64 Be . , -

, 2 462 He , 3

63Li 2 2

64 Be .

. 0+ 2+. - (,) (n,n) , , (p,n) , . , 3

63Li (- + p,n)

.

68

234724 Cr ,

244723V . 5.3. , .

, .

. 5.3

234724 Cr 24

4723V .

.

5.2. . - .

2 , 22 - . . , . , , .

5.2.1. . :

[5.2] B = [mp + mn - M(2H)]c2 = (2,22463 0,00004) V M(2H) = (2,0141017711,5.10-8) ( .1) :(612-6D6) (5D12-C6D6), M(2H) ( 2.10-5 ).

+ 2 p + n, . (2,2240,002)V. .

=1,11 V 8 V , .

. 5.4

5.2.2. .

69

V0 - . 5.4. , . -

[5.3]2

p

np

np mmm

mm += .

, - 0= .

)()(2

2

rErV =

+ 22

2 11dr

udrdr

drdrd

r=

= .

rrur )()( = )(ru : [5.4] )()()(

2 222

rEururVdr

ud =+ .

( ) 0)(2 0222

=+ ruWVdr

ud rR c V(r)=0 : 0)(2 222

= rWudr

ud . W

W=-E, W >0.

u1''+k2u1=0 - rR ,

( )WVk = 022 2 W22 2

= .

:

[5.5] )cos()sin()(1 krBkrAru += - rR . . 5.5

R=2,1fm

.

rrur )()( = r r 0, D=0 =0.

, r=R (. 5.3:

70

[5.7]

=

Ru

Ru 21 lnln ,

)()('

1

1

RuRu =

)()('

2

2

RuRu .

[5.8]WV

Wk

kR == 0)(gcot .

V0 R . , , 2,1 fm R. [5.8] V0=35 MeV. , . [5.8] ,

[5.9]00

~)(gcotVW

WVWkR = ,

W=2,2 V, WV >>0 , . , cotg , /2.

[5.10] ( ) 0202 222 VRWVRkR = ,

pm

VR2222

02

424

= . V0 R=2,1 fm

2

22

0 4 RmV

p

= = 2222 )(

4 Rcmc

p

=

2

22

2

22

MeV.fm.fmMeV

1,2.936197

4 ~ 25 V.

- . u2(r)=Cexp(-r), 1/ , r=1/ 2,7 .

[5.11] 1=Dr = Wmp

= Wcm

c

p2

=

MeV

MeV.fm22,2.936

197 ~ 4,3 fm

, , - , e . , .

(- ) , 1= .

71

effrot J

E2

)1(2 += = 22

2)1(

Dr+ = 22

2)(2

Dp rcmc =

2

22

2

2

MeV.fmfm.MeV

3,4.936197.2 ~ 4,4 MeV.

Jeff = mp/2 ( ), rD . , - , .

5.2.3. .

L

[5.12] LssI pn

++= .

I=1 . . I=1 , ( LSILS + , 2121 + L ). , 1 2 0 1, L 0, 1 2. I=1 :

- ( 1=+= pn ssS ) L=0- ( 0== pn ssS ) L=1- (S=1) L=2 ( -

21121 += I )

, , . , , L=1. L=0 L=2.

5.2.4. . L=0

[5.13] ( )ppsnnspn sgsgM +=+= [4.13], nsg =-3,826084

psg = 5,585691.

z- (+ /2).

[5.14] ( )psnsz ggM += 21 = 0,879804 M. (0,85743764.10-7), , . L =0 ( S=0) I=1 S =1 ( L =1 ).

72

L , L=0 L=2.

[5.15] )()( 13

13 DaSa DSD +=

122 =+ DS aa . )( 13S )( 13D , Sa Da [5.15].

)()( 132

132 DaSa zDzSz +=

)( 13Sz [5.14],

[5.16] [ ]psnsz ggD = 341)( 13 M = 0,56 M D-. z

[5.17] 96,02 =Sa 04,02 =Da . ,

L=0 , . , , p (L=2) .

5.2.5. . ,

, , . L=0 .

eQ = (0,00288 0,0002) eb, , .

4% D-. D- , L=2 () .

, : 1 , , , , , , , .

5.3. - .

. ( )

73

. , .

, (L=0)? , b, "" (b = R = 1 fm) ( - ). , .. LvRmn = (). L=0,

74

- . , , - . . -, -, - .

, o , , (p,p) (n,n). , , , +77 V, , ( ) . .

75

. 5.6 (p,p) (p,n).

5.5. . . 5.6 (p,p) (p,n).

, , . (p,p) , . (p,n) 90. . (p,n) 90.

" " - . , . . , . - - - 1935 . 1947 . . +, -, 0 . 5.6 .

5.5.1. . ,

. . mN mN + m. ,

76

, t [5.18] tE . v~c R=ct , . [5.18]:

[5.19] 130~fm

MeV.fm5,1

1972

==RcEcm MeV

R~1,5 fm ~ 130 MeV. 135 V (273 m0) 139,6 V . , .

,

[5.20]r

egRr

eVrVRrRr //

0 /)(

== ,

g , . . [5.19] , , . r>1 fm. .

5.5.2. .

, , 0,3 fm, . . . . . 5.7 () - .

77

. 5.7 .

. . .

- . , , - . . - mc2 ~ 785V, ~ 0,25 fm. , .

. ( ), "" "" .

5.6. . , , ,

V(r) , , , .

- . - :

- - .

- - .

- - .

, ,

- -. .

, . , : , , , , ,

.

. 5.8

: (),

(b), - (c), (d)

(e)

5.6.1. .-

r - .

78

. 5.8 V(r),

[5.21]

=RrfVrV 0)( .

5.6.2. . - -,

, , . - - . [ ]pr -, -, 21 sBsA

+ -. 21s

, 22s 21.ss . 21.ss

. [5.22] 21

22

212121

2 .2)).((. ssssssssSSS ++=++==

[5.23] ( )21221 21. ssSss = .

[5.24] [ ])1()1()1(2

. 22112

21 +++= ssssSSss .

S=1 s1 = s2 =1/2 4/. 221 =ss , S=0 - 4/3. 221 =ss .

( ) )(. 21 rVss s . Vs(r) , , , - -, 10 - -2 .

5.6.3. .

2% D- S-. V(r), r, .. . , ( )rs . [ ]rs . - - ( )( )rsrs .. 21 [ ][ ]rsrs 21 . . ( )21.ss . V(r)S12, [5.24] ( )( ) 212 2112 ...3 ssr

rsrsS = .

V(r),

79

. S12 [5.24]

( )( )

= 212 2130 ...3 pprrprp

rkU

.

, .

, ( )21.)( ttrVt .

, , , .

[5.25] ( )[ ]21.121 tt + .

[5.26] ( ) ( ) ( )[ ]212112210 .121.)(.)()( ttttVSrVssrVVrV tTS +++++= .

- , , , . , "". 6 () "". "" . , .

6

6.1. .

. N-, , . . , , . , . . , , . . . , . , .

. , . 172

80

. , . , .

, . , . ( ) . . , . - , .

. . : , . , . "" . "" , . "" , "" . "" , . , - - .

, . , . , , .

6.2. . 1948-49 . -

, . , ,

- . . , , , , . , , .

, .

81

. , . , (1038 /cm2). - , ? , , , . , , , .

6.2.1. . . , Z =2, 8, 20,

50 82 - . , Sn (Z=50) 10 . Pb (Z=82), . , N = 2, 8, 20, 50, 82, 126 - .

. 6.1 2

, N Z - , -

. 2, 3, 4,5, 5Li, - 4 ( 6.1)

. 6.2

) - ,) ) N=2.

5He 5Li ,

82

10-22 s - . . 6.1 N () Z () . - . - N Z. .6.2 :

6.1

2 3 4 5 5LiB, MeV 2,2 7,7 28,3 27,3 26,3

() - -, (Rn). 126( 128).

(b) - N. N=50, 82 126 2-3 .

() - N=2. N= 28, 50, 82 126. 2/3, ,.

, (. 4.9).

, . , , , " " , , .

6.2.2. - . ,

, . . , . - . , : , , ( . 3.6 3.8). . . . 6.3 : , - (Woods-Saxon):

[6.1] a

Rr

e

VrV +

=1

)( 0 .

R , a , d a= d/4,4 ( - 3.8)

83

. 6.3 :

,

-.

6.2.2.1.

.- -

[6.2]

+=23NEN N=0, 1, 2,...

. 6.4

-. -

.

( ) += 12 nN , , n (n=1,2,3,...), . 6.2 N, n, ,, .

, . N=2 3, N=4 5 ..

- -

- : - - , . . 6.4 - , -. , .

6.2

84

N n l 2(2+1)

0 1 0 1s 2 21 1 1 1p 6 82 1

220

1d 2s

102 20

3 12

31

1f 2p

146 40

4 123

420

1g 2d 3s

18102 70

5 123

531

1h 2f 3p

22146 112

6.2.3. - .

. 6.5

-

,

( )srVso .)( . s sj += . "" 0 - . 6.5. j, 2/1= j 2/1+= j . 2j+1 , -: j 2 ( 2/1 ) ( 2/1+ ),

( )12212121

21212 +=+

+++

=+ j .

)(rVso , . " " 0 - ( )saE .= . s. ( )22 sj += , [6.3] [ ]222

21. sjs = .

85

[6.4] ( ) [ ])1()1()1(2

.2

+++== ssjjasaE j

.

2/1+= j [6.5] 2

2aE j = , 2/1= j[6.6] ( )1

2

2

+= aE j .

, 2/1+= j 0 , 2/1= j E0, 0 1+ , .. - . ( 12 + ) - . 6.5.

. 6.6 , . 1g j=9/2, 2(9/2)+1=10 50 40, - . 1h11/2, 3s1/2, 2d3/2, 2d5/2, 1g7/2 12+2+4+6+8=32, 50 50+32=82, .

, -, , .

6.2.4. .6.2.4.1. . j

( ), . 7

158O 9

178O ,

. 6.7. 917

8O d5/2. 9

178O I=5/2. 7

158O

1 8 . 1/2 1/2, .

. 6.7 17 19

32

5927 Co , Z=28. f7/2 7/2. .

86

, - . j1 j2 .

6.2.4.2. .,

. . , - (), . .

121126

209831

32126

20882 HBiHePb ++

132 He 126

20882 Pb 1

32 He

, 126

20983Bi

132 He

. 6.8

12620882 Pb + 1

32 He 12620983Bi + 121H

=110.

( 121H ).

126209

83Bi , ,

. =110 - . 6.8. , Bi209 , 2 . , , 209Bi.- () 209Bi - - 1h9/2 - . 6.6. : 2f7/2, 1i13/2, 2f5/2, 3p3/2 3p1/2,

N =5. , g9/2, N=6.

, . 6.6.

6.2.4.3. .

. 6.9

87

"" - . 6.9 . ( ) 50, 82, 126 j. , "" g9/2 p1/2 50, - h11/2 s1/2 82 "" 126 - i13/2 1/2 ( . 6.6).

6.2.4.4. ( ).

. . , .

. 6.10 : () ()

, . . 6.10 ( ). . , - "" ,. 1

32 He , 10

199 F , 9

178O .

. . 6.10, ,

. .

. 6.11,

() . , . 6.11.

.

88

, , .

6.2.4.5. ( ).

(3z2-r2) , z ( jmj +=max ). . z ( ), xy (

89

. .

6.3. .

- . 8013050Sn ,

. 6.13. 82. . 6.6 , j=11/2. , "" - . . , 1,2V . , - , . s1/2 h11/2. j1+j2 (11/2)-(1/2)=5 (11/2)+(1/2)=6. - d3/2 h11/2. 4 7. s d , h - , . .6.13 , 2V. -

2+ , Sn130 . , - .

. 6.13 80

13050Sn

, , , .. . "" : 1 V, .

6.3.1. . A

90

. 6.14

(t) ,

),( Y . , = (-)

. ),( Y =0,1,2

= 0 410

0 =Y

[6.9] = 1 cos430

1 =Y ieY = sin

831

1

=2 )1cos3(16

5 202 = Y

ieY = sincos

8151

2

ieY 2222 sin3215 =

=0 00= a0cos(t) [ ])cos(1)( 00 taRtR += - , . "" "" . - 10 V. .

=1 ( ) 10= a0cos(t)

[6.10]

+= cos43)cos(1)( 00 taRtR .

. = /2 . , - , . 10 V. 2+ 1 V.

=2. 20 = a0cos(t)

[6.11] ( )

+= 1cos316

5)cos(1)( 200 taRtR 4 ,

91

. .

: - -. - ( ) . - .. , . xy, . - - . 6.15 .

. 6.15

. - , -

.

, , [6.9]. =2 : =0 - =2 - . 6.15 .

. .

( ) 2 . ,

+= += 2

12

2

nE

[6.12]

+=25NE ,

= nN . ( (5/2) =2) . - 2 , =(-1). - . .

, 2 2 2+2, .. 0+,1+,2+,3+ 4+. , . 1 3 .

. 6.16

72

12452Te

92

. 6.16 () Te12452 (). , . , , . . . , .

6.3.2. . ,

.

6.3.2.1. . 150

93

[6.13])32)(1()1(3 2

0 +++=

IIIIKQQ

=I=2 Q=-(2/7)Q0. . 6.18 , (150

94

, ( ) effJ=

. -

)1(2 +RR , R .

[6.14] )1(2

2

+= RRJ

Eeff

R

R , . . - 0+, R .

[6.15]eff

rot JC

2

2=

E(0+)=0; E(2+)=6 rotC ; E(4+)=20 rotC ; E(6

+)=42 rotC ; E(8+)=72 rotC ; E(10

+)=110 rotC ...

[6.16] E(2+): E(4+): E(6+): E(8+): E(10+)=1:3,3(3):7:12:18,3(3): ... .

[6.16] . . 6.21 Er164 . 2+

91,4 kV, rotC =15,2 V. , , :

. 6.21

164r, .

E(4+)= 20.15,2=305 keV (299,5 keV)E(6+)= 42.15,2=640 keV (614.4 keV),E(8+)= 72.15,2=1097 keV (1024.6 keV), E(10+)=110.15,2=1672keV (1518.1 keV)

.

,

. , . , Er164 , , "" , .

.

95

: , . =170 , , 6 kV. , , 90 kV. (2+)=15,2 kV, Er164 2-3 - , 5-6 - .

, , , . . - "", , ? "" ( 20 V) =v/c 0,2, . 1/5 ! effJE /2= , . = 1.1020 rad/s v~0,002c, - . , , , , "". .

. 6.22

, y

, j , , . 6.22. RjI

+= . , j

, z, jz.

Kj z = . . 6.22 , [6.17] [ ]22222 )1(|||| KIIjIR z +== K z. , K2 = 22 iKK .

effJK

2

22 ,

, - . , , , K, K+1, K+2, K+3,..., ,

96

, . , , .

2:1. - - . : - [6.18] [ ] )12(2)1()2)(1(

2

2

11 +=++== + RCRRRRJEEE roteffRR

,

2 - R=( R +1)-( R -1)=2[6.19] [ ] rotrot CRRCE 81)1(21)1(2 =++= , - . - -.

. 6.23 152Dy. , ,

, , . . 6.24 Er164 , . 6.21. , : , - ,

- - - - .

. 6.23

152Dy6.3.3.

. .

,.. , . . ( ) - . ( ) , . 6.6 . () . 6.25, .

97

. 6.25

,

. , . (prolate) , - (oblate). - mj. , , xy

, . +mj -mj . : (s, d,...) , (p, f, ...) - .

7

-.

7.1. .- - -

. 1903 . - . , 25% - . 1909 . - , . , - .

-. , . - , .

- , Z. Z, , [1.16].

-

98

? , . -. - ( ) . - , .

7.1 ( Q) U232 , - 72y. , Q>0 -, Q0, ..

[7.1] [ ] 0),()2,4()2,4()2,4()2,4(),( 2 >+== ZABBZABcMZAMZAMQ , Q>0 . Q - [1.14] (4,2)= 28,3 V. , Q>0 >140, 200,

N=82 Z=82 (A=212), .

99

7.3. . , -

. Q - , , , -: TTQ += pp = Tmp 2= TMp 2= . MmTT /= . , 2cmT 200 - 98% .

7.4. -. - 4 9 V,

10-7 sec 1010 y. - Nd144 , - 1,8 V, - 5.1015 y.

- , 1911 . - . , - . . (232 218), - :

Th232 - 1,4.1010 y(=4,4.1017 s), T =4,08 MeV

Th218 - 1,0.10-7 s, T =9,85 MeV.

24 . :

[7.3] BTA += lglg .

. 7.2

- .

. 7.2

21lgT Q )(~ T

100

- , - . Z N , . 7.2 , 2 1000 -, - Q. 143

23592 U ( N)

. , , 1000 -, .

7.5. -. . 7.2 -

, 1928 . . , - - . , - , . , - . , - .

7.5.1. . -

, - , . -, . , - , . "" . , . "" , - t )/2( vRt =

pr , ))(2( vmR .

Rm

v2 , f=1/t

- A~220 :

[7.4])10220)(10.67,1.4(4

10.05,142 303/227

34

2

==RmR

vf

= 1021 1020 /s

.

fP= . - .

7.5.2. .

101

. 7.3

-

. 7.3 - .

, , 1/r, (r =R) , - , , -V0. R e - .

cm/ . , . 7.3. , . r =R.

, , : 1) V0, 2) R

102

)(2 EVmip a = , [7.6]

= )(21exp EVmr bII .

, :

[7.7]

= EmriIII 2exp .

III I. , , "", .. I(R) = II(R), a II(R+d) = III(R+d).

[7.8]

=+=+= )(22exp)(

)()(

)(2

2

2

2

EVmdR

dRR

dRP a

II

II

I

III

.

[7.9] P = P1.P2.P3.....Pn =

=

])[(22exp1

EVmr ian

ii ,

ri . ri 0

[7.10]

= ])([22exp ErVmdrP ab

R .

7.5.2.2. (). -

R(r)= u(r)/r

[7.11] - EuurVdr

udm

=+ )(2 2

22

rA

reZkrV =

2

0)2(2)( .

)(

)(ry

eru= .

22 drud [7.11]

[7.12] - 0112

2

22

22

=

+

+ E

rA

drdy

dryd

m

V r, y(r) 22 dryd . m2/ - 1/2m .

103

= ErAm

drdy

2 dEAmryr =0

])/[(2)(

[7.13]

=

= b

REAmd

Ry

by

Rubu

P ])/[(22exp)(2exp

)(2exp

)()(

,

, [7.10].

, ,

[7.14]( ) ( )

+

RmZeE

mZekP

2822exp

20 .

= f

[7.15]E

mZek

2)2(constln2

0 = ,

[7.3].

7.5.3. . .

, Vb r, .

[7.16] 0)(2 2 =+ bVEm .

,

[7.17] [ ] 0)(2sin1cot12

22

2

2222

2

22

2

=+

++

++

rVEm

rrg

rrrr b

R(r) Y(,) :

),().(),,( YrRr = . ( , . 130), , , , .

)1( + . :

104

[7.18] 0)(2

)1()(2)(1 22

22

2 =

++

rRrm

rVEmdr

rdRrdrd

r b

.

)1( + , [7.18] , . = 0 , , .. . 0 , - e

- 22

2)1(rm + ,

32

rmF = (

rvm = rvmF /2=

) ( ) . , . e , , . - , .. - - , .

- 20 , - 1929 . , . -.

. 7.5 Pu23894 . , -. - 0 , - 0+ (= 0), 2+ - = 2 .. . 0+ 0+ 72%, 0+ 2+ 28%, ..., 0+ 8+ 7.10-6%.

. 7.5

- 238Pu 234U. -

- -. - - , - - (

) .

105

8

-.

8.1. . ,

. - , 1935 . . 1934 . - - . -.

-, , 2 10 V, 10-7 s 1015 y, - - =1 =250, 2 V ( Re18775 ) 14 V ( B

85 ),

- 10-2 s ( B85 ) 4.1010 y ( Re18775 ). -

, - .

, : V (. , . 122).

106

e , . - -.

: "" () ""() . , , , , 10-18 m , " " ( , ). , , 1983 . . W Z0 : 80,2 GeV W, 92,5 GeV - Z0. . , , -, .

8.2. -. - [2.33], [2.36]

[2.39].

- - Q- = [Ma(A,Z) - Ma(A,Z+1)]c2- Q-[8.1] + - Q+ = [Ma(A,Z) - Ma(A,Z-1) - 2m0]c2 Te+ Q+

EC - QEC = [Ma(A,Z) - Ma(A,Z-1)] - ?

--. , -, - , Q. , 1914 ., , - . - Tmax. , -,, , ( , 1927 ). . . , -, . . 8.1 Bi212 , .

107

. 8.1

212Bi 208Pb. ( V)

6,203+1,793+3,203=11,199.

( V)

2,248+8,948=11,196.

-, . - - , 13 (n p + e-). , ,

(1/2) . , , .. . C14 , , :

C14 ( 0) N14 ( 1) + -( 1/2). .

? .

He6 , -. , .

, - , . (1/2) , , .

8.3. . , ,

, 1931 . , , . - [8.2] eN

AZN

AZ ~eYX 11 ++ + ; eNAZNAZ eYX 11 ++ ++ ; eNAZNAZ YeX 11 ++ + .

, , ( ~e ), - ( e ).

108

(, , , ,...), .

. 8.2

W, - . 8.2. : d u W- , .

- . Q (Q = T + T = Tmax). (Q =T).

8.4. -. - -

. E , . .

1934 . -. , , - , . , , 20 - . , .. :

[8.3] )(22

ffifi EV = .

fi , 2.2, Vfi V (i) (f) , , :[8.4] rdVV iffi

= * .(f)=dn/dEf ,

109

, -, - . dn dEf.

V, [8.3] . XO , , . , XO , ( = V, A, S, P, T): V - ; - -; S -; P- -; - . . 50- (V-)-. , , , , , , V-. , - , , (V-) 5% (S-).

8.4.1. . p q.

, . V, p pdp + , ( dp)

[8.5] 324h

dpVpdne=

h ( ) e , dn . , q qdq + [8.6] 3

24h

dqVqdn = ,

, V,

[8.7] 62222

2 )4(h

dpdqVqpdndnnd e

== .

Vfi , i, , , . XO

110

g

XOgV = . :

[8.8] rdOgV iXeffi ***=

, V

[8.9]).(1)(

rpi

e eVr

= ).(1)( rq

i

eV

r

= .

1 V 1,4 V/. /

1-3fm10.5~MeV.fm

MeV197

4,1 ==c

pcp ,

[8.10]V

rpirpiV

re1...).().(11)( 2

2

+

++=

V

rqirqiV

r 1...).().(11)( 22

+

++=

.

" ". [8.11] fiiXffi MgrdOgV == * ,[8.12] = rdVM iffi .

, , . , dp dq ,

[8.13]( )

f

fi

dEdqdppq

hMg

d 226222 42 = .

f=Ee+E=Ee+qc, dq/dEf =1/c . , , , d p pdp + [8.14] dpqCpdppNd 22)( == ,

g, , .

111

22732

1fiMgc

C = . Q

[8.15]c

cmcmcpQc

TQq e2

042

022 ++==

[8.14]:

[8.16] dpcmcmcpQpcCdpTQp

cCdppN e

22

042

0222

222

2 )()(

++== .

, , , , , .

d=c2pdp, ( d=dTe), c2pdp=(Te + m0c2)dTe, [8.16] :

[8.17] eeeeeee dTcmTTQcmTTcCdTTN 220

220

25 )()(2)( ++= .

. ( 1) . , , . , [8.12] . [8.10] , -, . "" [8.10], - , - .. , fi - , fi 1, fi 0.

. 8.3

- [8.16] - -- +- 64Cu.

[8.16] : N(p)=0 =0 N(p)=0 = max( ) - . 8.3. , - ( ) . -- +- 64Cu,

112

, . +- - - [8.16], -- - . - . , - . , . , . - F(Z',p), . Z' .

- fi, , . , [8.16], p2(Q-Te)2, , .

-, .." " S(p,q), . (p2 + q2).

[8.18] dpqpSMpZFTQpCdppN fie ),(),()()(222 = , 733

2

2 cgC = .

8.5. .

[8.19] ),()(),( max45

02

0

222max

efi

p

efi TZfcmMCdpTQppZFMC == .

f(Z',pmax),

[8.20] = max0

2275

0

max )(),(1),(p

ee dpTQppZFcmTZf .

, f (Z',Temax). .

. ( ),

5

20

maxmax const),(

=

cmTTZf ee .

- f(Z',Eemax) T1/2,

.. , .

113

[8.21] 2max

21const),'(2ln

fi

e

MTZffT == .

fT1/2 , [8.21].

. 8.4

- fT1/

. 8.4 fT1/2. -

, lg(fT1/2). lg(f.T1/2) 3 23, . 8.4

lg(fT1/2) 3 5 , lg(fT1/2)=3 - . 0+0+ , . 3-4 - lg(f.T1/2). , 3 5 -lg(fT1/2).

8.6. . -, [8.18]

, . .

[8.18] :

[8.22]),(

)(~ 2 pZFpdppNTQ e .

, - e, . , (Kurie). ( Q) -, .

,

[8.23]),(),(

)(2 qpSpZFp

dppN

114

. S(p,q), , . . 8.5 () S(p,q).

. 8.5

S(p,q)

8.7. -.

8.7.1. .

r=0, , . .

, . 2 1/2 (S=0) (S=1). . , , =0 I=|Ii- If|=0. , (=1) . -. iI

fI

1 += fi II ( )

I=0, 1. Ii = 0 If = 0 ).

, , )1(= .

[8.24] I = 0, 1 . HeH 33 NO 1414 ,

0+0+. . LiHe 66 0+ 1+, ,

-. n p 1/2+ 1/2+, I=0 . " ",

115

.

, - - -.

8.7.2. . [8.24] ,

. , . , [8.24] - . - [8.24] . .

I=0, 1 I=0, 1 2 -. ON 1717 (1/2-5/2+).

I=2,3 NeNa 2222 (3+0+).

, -. CaK 4040 . 1015 4- 0+, .

8.8. - .8.8.1. .

1942 . Be7

[8.25] e7-7 Li)eBe( ++ .

- - , , QEC = 0,864 keV . Li7 .

[8.26] 3,5722

)(222 2

2

2

2

2

222

=====Mc

QMc

TQMcE

Mp

MpT ECEC eV,

116

Mc2 =7,931 MeV. , , 40- . . 8.6. Be7 S. Li7 , 100 200 V, , . , , 3,5 kV.

. 8.6

, Li7 48 V. , . - , = (56,6 1,0) V,

.

, . 1953-56 . [8.27] p + ~e n + e+

, .

( ), 100, 1013 /m2s , . - 511 V. Cd114 - 9,1 V . . - Cd114 (n,) - 510 s , . 1 m3 . . , [8.27]

= 9,4.10-44 cm2,

(Clyde Cowan) (Fred Reines). 1974 . 1995 ., .

117

- (~10-24cm2). 10 !

- , , , .. , , . CCl4 . ,

[8.28] ( ~ ) + AreCl 3718-3717 + .

, , , ~ .

- . ( ~ !), , . CCl4 1500 m 10 [8.28]. , , , - . 1 , . 10 , . , - , , [8.28]*. 1998 . , , . , , , - , - . 400 .

8.8.2. . . -

, : , 1/2, , . .

, -

e TcmTTQ +++= 2 (T + T = max) ,

T. n + ( ~ )p + e-.* .

118

- Q ( ), . . - . m=0 max , m0 - . 8.7.

. 8.7

- -

, - .-

187Re (2 kV), (1010 y) . -

e~eHeH -3231 ++ 18,6 kV 1/2 = 12,6 y. ( 1 106 ) . 10 V -, , -, , .

. 8.8

- . - , -, 37 V.

1980 . m 55 V -

. 1980 . ()

119

37 V 14 46 V - . 8.8. - - , . , . 5 V. (2002 .) , m 5 V.

, ? ( ). , , , , - , .. , ( ). , - . . ( ) m~510 V . - , .

8.8.3. . , , ,

, , . , . . - , ( 1956-57 . - ). 60- .

[8.29] ||||

.sp

spH

=

+1 -1, . 1958 . , . , "",.. , . , -. " ", r r; - ; + . , ( +) . xy, (-).

120

, p , -( ) ( ) . , , .. . , , -- . +- - , - "" "", +- . . .

8.8.4. .

( ). , . . , . , . , . 50- , .

, (parity). ( ), . (charge) . "" , (time reversal). -, - - - - , .

- 1956 . . , ( 967 m0 1/2=10-8 s).

+ + + + + -

=(-1)(-1)(-1)=-1, (-1), -=(-1)(-1)=+1

+ + + 0 . . , - - . , .

121

, + + , +, , .

. 8.9

, . ) ) , .

- . - , - . 8.9. -.

, , , -. Co60 :

[8.30] Co6027 ( 5-) Ni6028 ( 4+) + e- ( 1/2) + ~e ( 1/2).

, , - . , ( ), ( ). ,

22 ),(),( = rr , (-).

.8.10

()

().

- ()

.

. 8.10 (). . Co60 .

122

, (0,01 ). -, . . , . 8.9 . . 8.10 (). ( ) 40% , 6 . . . 8.10 () -, 10-14 s -. - - . . , .

. 8.11

.

- - , . . 8.11. , . ,

[8.31] I = A(1+ cos), , , 100%, - , . , =0 =180 . .

. 8.12

-, -

-

.

. 8.12

123

Co60 . , - , . , , , . -, ( ), . , 33 27 , , . , - -. -, , , : . , - - , -.

, 0, 10 20( )01020 21~ KKK ( )02010 21~ KKK + . - -.

9

9.1. .-

- . - - , - , .

- - . . -, , . .

. - - . , - , -. - - .

, , . , : {u () d ()}, {s() c ()} {b () t()} .

124

9.2. . - - 10

kV 58 V , - "" , - , . - - - - 1 nm 2.10-4 nm ( 5 V).

, - i f. - , R R (R Recoil-)

i = f + + R, ppR +=0 .

, . =

[9.1] 222

22 McE

MpT RR

==

0 ,

[9.2] 22

0 2McE

ETEEEE Rfi

+=+== 02 022

=+ EEMcE

- [9.2] :

+= 202 211 McEMcE .

0 V, 2~ GeV, , .

[9.3] RTEMcEEE = 02

20

0 2~ .

, . 191Ir - 129 V

[9.4] ( ) 2625 10.5~10.931.191.2 10.29,1 =RT V. - -.

...36.4.2

3.124.2

1

2

111 ++=+ xxxx

125

9.3. . - ,

. , - . , .

, , , . .

, 4 ( ) . , . , , , . - . - - : . . 9.1 () ().

. 9.1 () (). - E

B

P

-r . - .

z , D0=q.z. , S i, 0 = iS. z D(t) = D0cos(t), (t)= 0cos(t). . 9.1 , z . , , BE

P , . , z.

:-

sin, r z, .. , .

. . , " ", .,, 1965, . 300-304 603

126

- f = i(-1)L. . B

, )()( rBrB = . B

, - . , , - .

-

[9.5] 034

003

4

0 31

41

31 D

ckD

cPe

==

[9.6] 054

003

40

31

431 M

ckM

cPm

== .

D0 0 . 1/2 0/4=k0/c2, 0 .

- . L=1,2,3... . L=1 -.

2L (L=1 , L=2 , L=3 , ...) .

1. 2L mX ,

mY , (, . 605)

9.1

2),( mX m=0 m=1 m=2

=1

38 sin

2 316 (1+cos

2) -=2

158 sin

2cos2 516 (1-3cos

2+4cos4) 516 (1-cos

4)

2. : L - (EL) (-1)L L - (ML) (-1)L+1

9.4. -. -

, . . , . .

127

. - - , , , , . - , , , . .

, 1 ( )

[9.7]21

== RWL ,

R , 2/= e . - 100 V8 V, , . -,

MeVMeV.fm197

Epcc

p=== .

- 1 V ~100 R~6 fm, [9.7] e ~10-5. .. , - - - .

- L+1 L:

. 9.2 1/2 , - .

[9.8] 51 10~ +L

L

WW ,

:

[9.9]32 1010~

)()(

MLWELW

L

L .

. 9.2 - 1 5. , ( ) . - , -

128

, , .

-. ,

if ILI += .

L [9.10] fifi IILII + .

. :

[9.11] ( )Lf

i 1= L

[9.12] ( ) 11 += Lf

i

L .

, [9.10], . - , . , - .

: 3/2, - 5/2. L [9.10] 1, 2, 3 4. , 1, 2, 3 4. , - 1, 2, 3 4. ~100 (R2~2/3) - 1 V :

W(1):W(2):W(3):W(4) = 1:1,4.10-3:2,1.10-10:1,3.10-13.

- 1 2. . :

W(E1):W(M2):W(E3):W(M4) = 1:2,3.10-7:2,1.10-10:2,1.10-17.

, , 1. , . - , .

- , -, , . ( -) .

. >10-6s,

129

. 10-6

130

-, K, L M. , - . - L1, L2 L3.

. 9.3 203Hg. - -, K, L M. , - . L M , L3. - (0.07%) L- . - 279,16 V. 279 , ( -279), - . . 9.4 155Eu155Gd, . -, 155Eu . 3 - (60, 21 18,8 V), LMM- , , 155Gd.

. 9.4

155Eu. K, L M 3 -, LMM- .

(ICC=InternalConversion Coeficient),

-:[9.14]

NNe=

:

[9.15] )1(1

+=

+=+= ee .

, L-

321 LLLL ++= .

131

[9.16] ...+++= MLKtot .

-. , -. ,

1. Z3, , -.

2. - ( -).

3. L. , - , -.

4. - (n>1). ~ 1/n3, K/L ~ 810.

5. - , .

. 9.5

(Z=40).

. 9.5 - (Z=40).

, - .

- , . , .

- - 1022 V .. , , -. . .

9.6. 00. - -.

, - .

132

. , 1 1 . . , , . - , , . - 1,022 V - -.

9.7. .

, , . - . - 10-1410-16 s. - , , , , 178mHf 31 . (), . , . , , IT(Isomeric Transition).

. 9.6

80Br. .

. , 79Br 81Br,

- 80Br 82Br - 18 , 4,4 34 . - - - , - . 9.6. I, , - 18 m. II, 4,4 , 80mBr. - , -. -, 18 , - 4.4 ( 14 - - 1.5.1).

, , , .

133

. 9.7

87Y 87Sr.

, 3. . 9.7 SrYZr 878787 . 14 2,83 1/2 9/2

( 4). .

9.8. .9.8.1. . -,

, 1958 . -.

. - ( - [9.1]) , . /~ , . - . - ( ), . 2TR.

- 129 V 191Ir (- [9.1]:TR =5.10-2 V, /~ = 1,05.10-34/1,3.10-10 s ~5.10-6 eV. 1,3.10-10 s . , - - - . 9.8.

50- . , - . - v

. 9.8

-

/~ , , .

134

.

[9.17]

+= cos10 cvEE

-. , R 104 cm/s. . . , . 191Ir 10000 -, .

. 9.9

, - ,

. 2. , , 20 mm/s, , 100 mm/s. . 9.9 , . -. - . , . - : - , - . . 9.9 2 , .

- - . /0. 191Ir 3.10-11, 93 V 65Zn, =5.10-11 V /0 = 5.10-16! 65Zn 3.10-4 mm/s, ,

135

, . 90 60

. - - - , , , .. , , , , . 1961 .

9.8.2. . - ,

( ) (. ). , . , , , .

. 9.10. - - , , , . , . - , [9.17] , . "" , . -. :

. 9.10

(), , (), 2.

[9.18] %100% 0

=N

NN . , (77 ). (4 ). ( ) -

136

-. - -, , .

9.8.3. .-

. . -, .

9.8.3.1. () . ,

. . s-, .

WQ , ( ). . (R/a0)2=(10-15/10-10)2~10-10, . ,

[9.19] [ ]2220

2

|)0(|10

RRZeEEE == , . 14,4 V 57Fe 0,1% - , 119mSn 23,8 kV 0,01% - .

, ,

[9.20] 22 |)0(||)0(| , ( IS)[9.21] [ ] 2222

0

2

.|)0(||)0(|10RRZeE ==

137

. 9.11

, () ().

(IS= Isomeric Shift) 10-12 V, . .9.11, ( ) -. , v=.

s- , . :

[9.22] [ ]2220

2

|)0(||)0(|10 == R

ZeE

.

9.8.3.2. ( ). ,

B

, . B

, , [4.22] [4.21]. :

[9.23] ( ) IIzzB BMmBmIIIBBBBBW ====== ),cos(. .

138

. 9.12

: , .

, mI , 2+1 , 2I+1 . . ( )

30 (300 000 Gs). . 9.12 57Fe 3/2 1/2, . , mI = 1, 0, .

/ ~ 10-12 10-10, , . Fe2O3 . - - - =33 . , , . . 9.12 57 , .

9.8.3.3. . ,

z ( z ) ( , - [.19])

[9.24] QW zzQ = 41 ,

22

zzz = - z, Q

( , - [.25]). [4.32] m

139

[9.25])12(

)1(341 2

0 +=

IIIImeQW IzzQ ,

. 9.13

z .

, m . . 9.13 3/2 1/2 . 4 3/2 . , . . ,

Q0. Q0 .

9.8.4. .

1960 . , , - .. . , . , , , / v=gH/c, g .

[9.26] gHcEE

cvE 2

00 == ,

, .. .

162

0

10~ =cgH

EE = 1 m.

14,4 kV 57Fe, /~3.10-13. , 22,5 m. 1/100 . .

140

0EE = (4.9020.041).10-15

4,905.10-15 45 m. - . 10 - , 1919 . .

: ii kp

= ff kp = ( )rkii ie

.= ( )rkif fe .= .

[.1] fi ppq

= fi kkq = .

. .1 , )2/sin(2/ ipq = /=ip , q ( ) )2/sin(/2 =q , , ( )pq . e .

. A.1

141

, , V(r). .. " ", i(initial) f (final) :

[.2] ,22

ffi dE

dnV =

fdE

dn ,

[.3] ifiV

ffi rVrdrVV )()( ==

. . . , [.1] -a , -, , .

. A.2

. F'. [.3]

[.4]

==V

rkirkififi rderVekkFV if

).().( )(),( ,

[.1] [.5] ==

V

rqifi rdrVeqFV

)()( ).( .

, F'(0)=1, .. 1. V(r) ( )rZe , r - , ( )rp , . ( )rp , 1')( = rdrp . . .2 ., - r

142

dQ . r [.6]

rrrdrZek

rredQkdV p

==

)(2

00

V(r), dQ , .. , .

[.7] rdrrr

kZerV p = )(

)( 02 .

[.6] [.4] :

[.8] =

= rdrdrr

reZekr

rrZekrderdqF prqip

rqi )()()( ).(20

20).(

rrs = :

[.9] )(4)()( 2

20

).().(

20 qFq

Zekrdersds

eZekqF rqipsqi == .

= sesdI sqi /).(1 - : I1= - 4/q2. [.9] :

[.10] rderqFrqi

p = ).()()( - - - . - )(qF

( )rp . . :

).(4)(' 202 qF

qkZeVqF fi

== ( ipq

143

2R

[.14] = rdrrR p )(22 , - [.12] rdr 24

= rdrrR p )(4 42 . [.14] , , 1')( = rdrp . [.14] [.13] , , F(q) .

, - 1.

( )rp , , . , - .

.

. .1

, (..1).

)(rj . r , )(rj rd . , - r [.1] ArArB rot)()( == , r

[.2] '')'(

4)( 0 rd

rrrjrA

V

= .

[.2] ,

[.3] ...)'.(1/'1

/1'

13 ++== rrr

rrrr

rr

,

144

[.4]

++= ...)'()'.(1)'(14)( 30 rdrjrrrrdrjrrA VV

.

( ), - , . )().()..( jrrrjrjrr

= ,

. )()..(2 jrrjrr = , [ ])(

21)..( jrrjrr

= [.4]

[.5] ( )rr

rA =

30 1

4)( .

:[.6] [ ] rdrjr

V

= )'('21 . )(rj ,

)()()( 2 rrr = v , 22)()( vrerj = . )( vr mp pmL /

. L

rvmL p =

.

2)(re

[.7] rdrLrme

Vp

= )()(*2 . Lz, z-

[.8] rdrLrm V

zp

z = )()(*21 .

.1. . ,

[4.15], [.3]

[.1]

+++=

==...

!211),,(

3

1,5

3

130321

jijiij

iii xxQr

xqrr

qkxxxV

q, pi Qij

., , . , 1965 ., . 168-171.

145

[.2] =V

rdrq )( =V

i rdrrp )( =

Vijij rdrrxxe

Q )()3(1 2 q , Ze , i d, Qij .

.2. . (

), . :

[B.3] rdYrrEMV

= ),()(),( . ,

[B.4] =

=Z

kkkk YerEM

1),(),(

. ),( EM (2+1) ,

[B.5] )0,0(4 EMq = )0,1(3

4 EMpz= )0,2(

516 EMQzz= .

, Yr

, = z - =m . , .

, =(-1) =2, .

. IIm

I Im , -

, , ..II (mmax=I)

[.6] IIEMIIQ ),( = , Q

[.7] IIEMIIQ )0,2(= .

: I

.

, , , ( z')

0=ijQ ji. .

146

[.8] yyxx QQ = ,

0=++ zzyyxx QQQ ,

[.9] zzyyxx QQQ == 21

.

,

[.10] =V

zz rdrrzQ)()3( 22 .

, - - )0,2( EM .

.3. .,

, . , ( , z' )

[.11] =V

rdrzQ )3( 220

)(r . 2= x'2+y'2,

[.12] 2

2

2

2

2

2

1cz

by

ax =+

a=b

[.13]

=cza 1 .

[.14] +

==

2)(1

0

22222 )2(22)3(czac

c

drzzddzzeQ ,

drd 2= z' "" -..1.

[.15]

( ) ( )2222252

158 acZeaccaeQ == ,

. .1

147

)(r 23

4 caV = Ze. , .. ,

20acR += , R=c-a

0RR= ,

[.16] 2054 ZRQ = ,

, . Q -: Q > 0 (prolate) Q < 0 (oblate).

. .2

(x',y',z') , (x,y,z) -

.4. . ( z) .

(x',y',z'). z SLJ

+= - . , x ' - . .2.

(x,y,z) 0, :

++

++=

zz

yy

xxzyx )0()0()0()0(),,(

[.17] ...)0(...)0(2)0(21

2

22

2

2

22 +

++

++

zz

yxxy

xx

E -

rdzyxzyxW ),,(),,( = =

148

= +

+

++ rdzzyyxxzyxrdzyx )0()0()0(),,()0(),,(

rdz

zyx

xyx

xzyx

++

++ 2

22

2

2

22 )0(...)0(2)0(),,(

21 + =

[.18] = WC + WD + WQ +...

, .

zyx)0(,)0(,)0( , e

. ,

z, y , z. ,

[.19] 0)0()0()0(222

==

=

zyzxyx.

2

2

2

2 )0()0(yx =

,

s- , - .0, ..

0)0()0()0( 22

2

2

2

2

=+

+

zyx

[.20] 2

2

2

2

2

2 )0(2)0(2)0(yxz =

=

.

( ) =

+

= rdz

drzzyxrdz

dyxz

zzyxWQ

222

222

2

22 )0(3),,(

41)0()(

21)0(),,(

21

222 zyxr ++= ,

[.21] QrdrzzyxW zzV

zzQ == 41)3)(,,(41 22 .

2

2 )0(zzz = z.

: - . , - s -e. - e(0), WQ

149

[.22] 2)0(3

2 rW eQ = ( - CGS) 20

)0(61 rW eQ = ( ),

. WQ, . , .

[.18] (x',y',z') . .2. z z'.

z = z'cos - y'sin, (x=x')

[.23] rdrzyyzzyxWV

zzQ += )cossin6sin'3cos3(),,'(41 22222 (z') [.24] 0),,( =

V

rdzyxzy .

,

[.25] =+== rdzyxyxrdzyxxrdzyxy ),,()(21),,(),,( 2222 += rdzyxzr ),,()(21 22

[.23], WQ :

( ) rdrzrzzyxWV

zzQ

+= 222222 sin23cos3),,(21

[.26] ( ) ( ) ( )1cos3813),,(1cos3

81 2

0222 == eQrdrzzyx zz

Vzz

Q0 , [.10]. [.26] Q0, zz.

.5. . Q0 -

(x',y',z') ..11. , . Q, , , , z ( J

).

- . [.21] [.26]

[.27]2

1cos3 20

= QQ [.21] [.26] , .

.6. k . , I

, (2I+1)

150

, .. (2I+1) :

II EMmQ Im)2(Im)( = . . ( [.7]) - I: Q=Q(mI =I), I

)1(

cos2

+= III .

, cos [.27]

[.28]112

211

)1(3

21)( 0

2

0 +=+== I

IQIIIQImQ I

[.29]

+= 1)1(3

21)(

2

0 IImQmQ II ,

[.30])12(

)1(3)( 2

0 +=

IIIIm

QmQ II .

I , . 6.20. .

[.31]

+= 1)1(3 2

0 IIKQQ .

. ( )

[.32])32)(1()1(3 2

0 +++=

IIIIKQQ .

I=

[.33])32)(1(

)12(0 ++

=II

IIQQ .

Q

[.34])1()12(

81

0 +=

IIeQW zzQ

m

151

)1()1(3

12)1(2

811

)1(3

81)(

22

++

+=

+= II

IImIIeQ

IImeQW IzzIzzmQ I =

[.35] )12(

)1(341 2

0 +=

IIIImeQ Izz .

I=0 I=1/2. , z'. I=0 . - . . , Q00, . I=1/2 cos=1/ 3 (3cos-1)=0. . , , I0. .

.

, .. . 2 z ,

[.1] zz TTTTTTT ,)1(,2 +=

zzzz TTTTTT ,, =

sH , ,

, sH , [ ] 0, =zs TH (p,n) t=1/2

tz=1/2.

[.2] pptz 21= nntz 2

1=

+= zTeQ 21 .

[.3] =

=A

iitT

1

=

=A

iizz tT

1)(

, .. .

[.4] ( )2

221

2)()( AZAZNZnNtpZtT zzz ===+= .

eZQ = e

152

[.5] zzz TTA

eQTTT ,

2,

= ,

[.4] - zt . , Q zT

sH .[ ] [ ]zss THQH ,, = (t=1/2) ,

22ATZN

153

, , . L ( (-1)L), S-, -,

L + S + T = 1, 3,...- .

, - . , , +, - 0. . . : ++, +, 0 - +2, +, 0 -.

, . . ( sj += ), , ( . .1)

. .1

sz ( )

[.1] zsz Msgg +=

, zzz sj += . jmj jz == (mmax=j)

[.2]( )[ ]

zs M

sggjg

+= zs s

j

,

. sz , sj . js

,

j

, .. jj

/ . s j ( )jsss j ,cos= . ( ) ( )jsjsjs ,cos.. = ,

(hadrons) , .

154

( ).s (6.3),[.3] ( )

2).()(.

2222 sjssssjs

+=+=+= js

[.4]( ) j

jsjj

jjss j

2

222

2 ||2. +== .

zs [.4] ,

[.5] jjj

ssjjsz )1(2)1()1()1(

+++++= ,

j

jmjj jz === max . j=+1/2 (=j-1/2) 2/=zs , j=-1/2 (=j+1/2) )1(2/ += jjsz . [.2] zs

: , , 0=ng

j=+1/2[.6]

nsn MMg 91,12

1 == j=-1/2[.7]

nsn MI

IMgII

191,1

)1(2 +=+=

, 1=pg : j=+1/2[.8] ( ) ( ) psp MIMgI 29,2121 += += j=-1/2[.9] ( ) ( ) psp MI IIMI IgI 129,21121 +=+ = 586,5=psg 826,3=nsg , , I=j.

.

[8.20] , , ( ) .

e=m0c2+Te, a emax,

155

[E.1]

=

max

0 0

2

0

2

20

maxmax ),(),(

pee

e cmdp

cmp

cmEEpZFEZf .

, , , Z =0, F(Z',p) .

[E.2]5

20

max

0 0

2

0

2

20

maxmax ~),(

max

= cmEcmdpcmpcm EEEZf e

pee

e ,

. p2c2 = E2 - m02c4

[E.3] maxmax

2/1

2max

420

2

max

2

max )(1

max

20 e

e

e

e

ee

eE

cm e

e

EdE

EE

Ecm

EE

EEI

e

= .

maxe

e

EEx = max

20

eEcma = xdxaxxI

a = 1 222)1( .

, , .. emax>>m0c2 (=0,511 MeV), 301~)1( 2

1

0

2 dxxxI = . [E.4]

5

20

maxmax

301

),0(

=

cmE

Ef ee

[E.5]

5

20

max

const

=

cmEe .

, . , , . 9,3 152Eu, . .1. 960 keV, -, - 152Sm. , (-)

- ( 1/2) + 152mEu( 0) ( 1/2) + 152Sm*( 1). .1

152mEu ().

, - ()