neutron physics book.pdf

..

-

2004

-

..

-2004

530.145; 539.12

.. . . .: - , 2004. 334 .

" - " 553113" ".

, - - - , . , , - .

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

. -, , - , P - CP -, T -. , - . -, .

, - , - .

.

.. , .. , .. .. , , .. .. .

c .. , 2004 .

1

1.1

1932 17 - " " (Possible Existence of a Neut-ron. James Chadwick, Nature (Feb. 27, 1932) v. 129, p. 312), , , . "... , - , . -, ..."1

1935 ., -, , . . 1939 . - . . - 1942 , . 16 1945 . - , 6 9 , ,

1 1935 .

3

4

. - , . , , , - .

1954 . . , . , , . -, , , , .

, , , ( - , ), .. .

"", . -, , , . . .

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

-

5

(Review of Particle Physics. Euro. Phys. J.,2000, v. C15, no. 14).

(e ) qn = (0, 4 1, 1) 1021e. mn = 939, 56533 0, 00004 , = 1, 00866491578 0, 00000000055 ... mn mp = 1, 2933318 0, 0000005 , = 0, 0013884489 0, 0000000006 ... n = 885, 4 0, 9stat 0, 4syst . n = 1, 9130427 0, 0000005 N . dn < 0, 63 1025 e (CL=90%). n = (0, 98

+0,190,23) 103 3.

, , , , , , .

, - , .

. - - < 6, 3 1026 ( CL=90%). 1520 , , - .

- - . - .

, - , ,

6

. , - , .

n = 1 A ( ) v = p/mn = 2h/nmn = ccn/n 4 / E = mnv2/2 = 0, 08 n = (1, 9130427 0, 0000005)N Z

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

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

,

7

- , . - , .

1.1.1

- -, 1919 . - 14N - . 1931 , , , - 2, (, p), -, , - . 1921 1924 . , - 3, , . , - , . , - .

1930 (. . 1.1), - , . , , , -. - (, 1935 . , - - - -).

2 1931 . ( 1939 .) (, ).

3 Z , - .

8

. 1.1. - -

1932 , - , , , -. , " " (. 1.2).

. 1.2. - . , - ?

, - (. . 1.2, 1.3), , . : "... , , 1 - 0, . , - 9Be 12C -".

. - ,

9

, - 26 , 4,3 . . -, - , , ( ) .

. 1.3.

1.1.2

- k ( - - m), . 1.4.

, k

E, p=0

, k

E , pEi, Pi { Ef=Ei, Pf=Pi

. 1.4. , - ( ) ( )

+mc2 = +E , (1.1)

10

k = k + p. (1.2)

, - ( ).

E2 = p2c2 +m2c4 (1.3)

= ck (1.4)

. . -

- . 4-:

p + k = p + k

, (1.5)

p2 = p20 p2 = m2c2, (1.6)

k2 = k20 k2 = 0, (1.7)

() 4- p k p0 = E/c k0 = /c, . - : - 4- ( - , , ). - :

ab = a0b0 aibi = a0b0 a1b1 a2b2 a3b3,, 4-

ab ab = a0b0 ab = a0b0 aibi. (1.5) :

p p = k k. (1.6), (1.7), -

m2c2 pp = kk,

11

(p (p0,p) = (E/c, 0))

m2c2 EE

c2=

c2 kk cos

= kk(1 cos ).

k k ( -). E = mc2 E = + mc2 (. (1.1)),

k k = kk

mc(1 cos ). (1.8)

k = 2h/, - :

= 2hmc

(1 cos ), (1.9) , , . "" - . , (, , ) . h 0 - , . , (-) -, .

-

c =h

mc.

m. (1.9) .

c , - , :

e me = 0, 5110 ce = 3, 86 1011

m = 139, 6 c = 1, 4 1013

p mp = 938, 3 = 1836me = 6, 7m cp = 2, 1 1014

12

1.1.3

= 180. , , - ( ), Erec = E mc2, . ("") :

Erec = = ck, (1.10) k = k k. k , (1.8), k = k k,

k =2k2 2kk

mc,

k =2k2

mc

1

1 + 2kmc=

k

1 + mc2k.

k (1.10),

Erec =

1 + mc2

2

. (1.11)

( mc2)

Erec 22

mc2. (1.12)

, , - Erec:

mc2Erec

2. (1.13)

Erec = 4, 3 mc2 = 938 1 , = 47 .

, , , , . , - ,

13

, - , -. , , , Li, Be, B, C, N . , . , , , 1,2 . - - - , , 70 . , -, . .

, ( m) ( M) :

mv2 = mv2 +MV, (1.14)

mv = mv +MV, (1.15)

v, v , ,V .

v,

V =2m

M +mv. (1.16)

, E1 = M1V 21 /2, E2 = M2V 22 /2, M1, M2:

V1V2

=M2 +m

M1 +m. (1.17)

(3, 3 109 4, 7 108 /, ),

m = 1, 15 ...

14

10%. , .

, , - , . - .

1.1.4

, 1932 ., 3 , 1000 , . , en .

, - , - (, ). 1920 - - , - , . - - (, , , ), . , , - , . - 1934 . - , -, , . - , .

15

- , ,, - 10- 26- . - , "" - .

1989 . :

en = (0, 4 1, 1) 1021e, .

1.1.5

1934 . ( , ) - . , - . , -, 13 .

, , - , - . , , - - - , - , , .. W -, ... - = GA/GV , - GA GV , ( ) - . ( ) 2003 .:

= 1, 2695 0, 0029.

16

, - , - . , - , , - ( 2004 . , ) - ( ) .

1.1.6

, , . 30- , ( - - , -, .. ). 1934 , . - () - . , . (1934 .) , - n 1,52 N ( - 1940 . , n = (1, 935 0, 030)N). ? - ( 1928 .) , "-" e, 1/2 m

17

=

eh

2mc=

ec2.

- B,

N =eh

2mpc=

ep2.

, - . , , - , p = 1, n = 0. ,

n = 1, 9 N ,p = 2, 8 N .

- . - . , , - , - :

n = 1, 9; p = +1, 8. (

). - , -(. 1.5), .. , - , , , - .

( , ) , ., - mc

2. , - t h/mc2,

18

p

+

n p n

p n

. 1.5. -

- ct, c . , rN , , :

rN c t = hmc

= c.

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

, , ( -) ( < 1016 ). , , . , u d (up down), eu = 2/3 e, ed = 1/3 e 1/2. - , , , .

-:

(en = 0) (ep = 1)

u u ud d d

19

. , - 1, , , , 1/2. , .

dd1 uu1 1 ( = 1, 0, 1)., 1/2 ( = 1/2, 1/2) d1

2 u1

2.

, ,

n 12

12= C

12

12

11,12 12 dd11

u12 12 + C

12

12

10,1212dd10

u12

12=

=

23

dd11

u12 12

(1)

13

dd10

u12

12

(2)

.(1.18)

Cjmj1m1,j2m2. (1.18) , - 2/3 (1), d- - ( 1), , u- (, , -) ( 1/2). (2) - u-, d- ( 0), . 1/3. , :

n =2

3(2d u) + 1

3u =

4

3d 1

3u. (1.19)

, - , ..

d = 13; u =

2

3,

20

n = 23. (1.20)

(1.19) u d, ..

p =4

3u 1

3d = . (1.21)

(1.20) (1.21),

np

= 23= 0, 67.

- ,

np

exp

= 1, 9132, 793

= 0, 68.

, - , . , .4

1.1.7

() - . - - (), - ( - ). -, - 1964 . -,

4 . , , , . , , , . .

21

40 . - ( - ()).

2004 . , Belle BaBar, , - -, . - - .

- . - - , , .

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

, 1989 ., :

D = (0 0, 4) 1025 ();D = (0, 3 0, 5) 1025 ().

( 90%), -, (1989 .),:

D < 9, 7 1026 (CL=90% ) 10 (1999 .) :

D < 6, 3 1026 (CL=90% )

22

, - .

, - . - - ( ), .. R 1013 , - , - ( e) d, 1025 , d/R 6, 3 1013(. . 1.6). , 4 .

. 1.6. ,

1.1.8

E, -, - . - d, :

d = n E. n . "" , .. -. 1991 ( ).

n = (1, 20 0, 20) 103 3,

23

: (1 = 1013 ), . d 1027 , 108 /, - 103 , . , , - . , , 1021 /. - .

1.2

, - ? , - , , , , . 1934 , - , - , . : , 1947 ., - (-) ( , "" - 1937 . ).

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

, , , .. -

24

, . . , : |1 |2 - (. . 1.7).

P P

e|1

P P

e|2

. 1.7.

E1 E2 ( - ), :

H0|1 = E1|1,H0|2 = E2|2.

H0 . , ? - , , .. V H0, - |1 |2. :

(H0 + V ) = E.

= a1|1+ a2|2. (a1, a2) :

E1 V12V21 E2

a1a2

= E

a1a2

,

25

m|H0|m = Em, m = 1, 2; 1|H0|2 = 0, 1|V |2 = V12. , V 1 2, , .. m|V |m = 0.

(- ),

(E1 E)(E2 E) |V12|2 = 0, (1.22) - , . ,

E(1,2) =E1 +E2

2 1

2

(E1 E2)2 + 4|V12|2. (1.23)

, , , .. E1 = E2 = ,

E(1,2) = |V12|, ,

a1a2

= V12|V12| = 1 ( 1, V12).

, - , : - ("" ). - , - . , , , -, , - ( : ). : - , . - ( ), - , , .

26

- |V12|, . R , - . , , , R, 5, ..

V12 eikR

R,

k =

2mh

= i ( ),

. ,

E(1,2) = geeR

R.

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

E2 = p2c2 +m2c

4 = 0,

( ) :

p2 = m2c2,

k = imc

h=

i

c.

5, (r) exp (r/aB)r( aB = h/

2mEa , Ea )

(|r R|), . R aB (R).

27

, - - , , , - -,

V = ge

mch R

R= g

eR

c

R. (1.24)

. (1.24) , - 1013 , (). - "" , . - . -, g (1.24) - - , .., , (, -, ) , - ( ). ( ) , - - . g2/hc, (1.24), -, ( - = e2/hc, 1/137). g , , , .

: - . , ,

28

: -, , , -, , . .

.

- - . , - , .. , . 1.8.

. 1.8.

:

p = p + k. (1.25)

k ,

p2 + k2 2pk = p

2 .

p2 = p2 = m

2c2 k2 = 0,

pk = 0 (1.26)

E

c2= |k||p| cos , (1.27)

. -, |k| = /c |p| = Ev/c2, E, v , -,

cos =c

v, (1.28)

.., , . ,

29

c/n, n . (1.28)

cos =c

nv. (1.29)

, - "", 1934 . - 1937 . (1958 .).. , .. .. .

30

1. .. . .: -, 1982.

2. .., .. . .: -, 1997.

3. ., ., . -. . 8, 9: . .: , 1978.

4. .. . .: , 1955.

5. Proceedings of the International Workshop on Fundamental Physicswith Slow Neutrons. Grenoble, France, March 811, 1989.Nucl. Instr. and Meth., A284 (1989) 1232.

6. NOBEL LECTURES including presentation speeches and laureatesbiographies. Phisics. 19011921. Amsterdam London New York:Elsevier Publishing Co., 1967.



2

2.1

, - - c = h/mc 1,4 = 1,41013 . 109 c, "-" , . , , .

, o . . - m .

. 2.1.

E hka. :

a = eikar, k2a = k

2, (2.1)

k =2mEh .

31

32

(2.1) 1 , , , ,

ja =h

2mi(aa aa =

hkam

. (2.2)

, - ( -, < v ), j = va, . = 1 j = va.

, ja . . , , :

(2 + k2)(r) = 2mV (r)h2

(r). (2.3)

(2.3), (2.1) , . G(r, r), , r.

(2 + k2)G(r, r) = (r r). (2.4) (2.3) , - , (2.3), :

a(r) = a +2m

h2

G(r, r)V (r)a(r)d3r. (2.5)

- . r , , , - .

33

, () ,

G+(r, r) = e

ik|r r|

4|r r| , (2.6) , -. , - jr

jr =h

2mi

G+(r)

G+(r)

rG+(r)G

+(r)

r

= hk

m

1

(4r)2. (2.7)

, , 4r2, , v/4. , - (2.4) v/4 .

, (2.5)

a(r) = a(r) m2h2

eik|r r||r r|V (r

)a(r)d3r. (2.8)

|r| |r|

k|r r| = kr2 2rr + r2 = kr1 2rrr2 =

= kr(1 rrr2 ) = kr kbr,

kb = kr

r.

, , - , , , - :

a(r) = a(r) +Abaeikr

r, (2.9)

Aba = m

2h2

eikbr

V (r)a(r)d3r. (2.10)

34

Aba . |r| |r|

scat = Abaeikr

r.

d(, ), dN d = sin dd :

d =dN

ja. (2.11)

, , ( - ). r2d

dN = jrr2d

, jr ,

jr =h

2mi

(scat

scatr

scatscat

r

)=

hk

mr2|Aba(, )2|.

,

d =jrr

2d

|ja| =k

ka|Aba|2d, (2.12)

ka = k. a

,

a(r) = a(r) m2h2

eik|r r||r r|V (r)a(r

)d3r + . . .

,

Aba = m2h2

b|V |a+

+

(m

2h2

)2 b(r)

eik|r r|

|r r|V (r)V (r)a(r)d3rd3r + . . .

35

- (), . , - , .. (. 2.2):

. 2.2

( ) - :

Aba = m2h2

b|V |a == m

2h2

ei(kb ka)rV (r)d3r = m

2h2

eiqrV (r)d3r.

q = kb ka .

Aba = m2h2

V (q),

, ,

d =m2

42h2|V (q)|2d.

exp(ikar) exp(ikbr) V (r). ( ) "-" :

dPba =2

h|b|V |a|2(Ea Eb) d

3kb(2)3

, (2.13)

d3kb = k2bdkbd.

36

E =h2k2

2m; dE =

h2kdk

m; kdk =

mdE

h

2

,

k2bdkb = kbmdEbh2

=

2mEbh

mdEbh2

.

-,

dPba =2kbm|Vba|2d

(2h)3.

, , - :

d =dPbava

=m2

(2h2)2vbva|Vba|2.

2.1.1

- , - .

( ) - -, . . -

V (q) =eiqrV (r)d3r.

a = 1/ka RN (RN ), qr 1, :

eiqr = 1 iqr + (qr)2

2 . . .

,

V (q) =V (r)d3r = const = V (q = 0) = V , (2.14)

37

.. a RN ( ). , " " - . , , (2.14) .

, - 1

V (r) = V1(r) + V2(r R), (2.15) R .

Aba = m2h2

(V1 + V2eiqR), (2.16)

, ,

d

d= |Aba|2 = m

2

2h2[V 21 + V

22 + 2V1V2 cos qR

]. (2.17)

kaR 1, qR 1, - (V1 + V2)(r). qR 1 q ( , ) cos qR, .

a R , , , l=0 ( s-). , p , . 2.3, b .

. 2.3

M = pb. -, Ml = h

l(l + 1), -

l 1 -: V (r) =

V (r)(rr)d3r.

38

( p):

bl =hl(l + 1)

p=

l(l + 1).

l = 0, b0 = 0. l = 1 b1 =2 RN , -

l = 0 -. , s-, -. , , RN , - , , ( ). , , , s-. - RN , l = 1 ( p-), 10 .

, , - , - , .. . - . . ka,

(r) = eikar =l=0

(2l + 1)iljl(kr)Pl(cos ),

jl(kr) , - kr l :

jl(kr) sin(kr l2 )

kr.

a (kr)1

l=0

(2l + 1)ilPl(cos )l(r),

39

l = sin

(kr l

2

)=

i

2

{ei(kr

l2 ) ei(krl2 )

}

. -

, , - , , . . .

, , x( E = mx2/2 b ), "" mr2/2, r, r =

x2 + b2,

mr2

2=

mx2x2

2r2=

m(r2 b2)x22r2

=mx2

2 L

2

2mr2,

L = mxb . , , -

E :

E =mr2

2+

L2

2mr2.

.

, , :

(r) = (kr)1l=0

(2l + 1)ilRl(r)Pl(cos ), (2.18)

Rl(r) d

2

dr2 l(l + 1)

r2+ k2

Rl(r) =

2mV (r)

h2Rl(r)

Rl(0) = 0,

40

(r) .

h2

2m

1

r2

rr2

r+

L2

r2+ V (r)

= E,

(2.18), = f(r)Ylm, f(r) = R(r)/r.

- Rl(r) ., Rl(r)

Rl(r) =i

2

{ei(kr

l2 ) Slei(kr l2 )

}= sin(kr l

2) +

i

2(i)l(1 Sl)eikr,

(2.19) - . Sl - . (r),

A() =l

Al() =i

2k

l

(2l + 1)(1 Sl)Pl(cos ).

Sl - ( ) l,

Sl = e2il; Sl 1 = 2ieil sin l, (2.20)

, - . (2.19)

Rl(r) =i

2

{ei(kr

l2 ) e2ilei(kr l2 )

}= (2.21)

=ieil

2

{ei(kr

l2 +l) ei(kr l2 +l)

}= eil sin(kr l

2+ l).

, - l - .

41

P (1) = 1,

A(0) =i

2k

l

(2l + 1)(1 Sl) = 1k

l

(2l + 1)eil sin l.

d

d= |A()|2

-

Pl(cos )Pl(cos )d =4

2l + 1ll,

= 4k2l

(2l + 1) sin2 l,

=

l,

l =

4

k2(2l + 1) sin2 l =

k2(2l + 1)|1 Sl|2.

(2l + 1) l. ,

(l)max =4

k2(2l + 1) = 42(2l + 1).

R , - , . , 2 . , 0 /2 -, c .

A(0)

Im A(0) =1

k

(2l + 1) sin2 l,

42

.. =

4

kIm A(0).

.

2.1.2

, - ( -). , : , - . - , " ", , .. .

- (, , - , . . 2.4)

. 2.4. , Er

l. Er, - : . - (1928 .), (1928, 1929).

,

43

. , - "-", r -

Er i2,

Er, > 0. r :

eih (Er i2 )t

2= e

th .

r :

N = N0eth ,

, , ( )

w =1

N

dN

dt

=

h, (2.22)

, , (2.22), = h/ ( ).

- (. (2.19) (2.21))

Rl(r)

r 1

r

{ei(kr

l2 +l) ei(kr l2 +l)

},

Rl(r)

r 1

r

[Al(E)e

ikr Al (E)eikr], (2.23)

Al(E) E:

Al(E) = ileil, Al (E) = (i)leil.

e2il = (1)lAl

Al eilA

l

Al. (2.24)

44

E = Er i/2 ,

Al

(Er i

2

)= 0.

"" -, (2.23) , . , , "" , .

Al Er i2,

Al(E) =

[E

(Er i

2

)]al + . . . (2.25)

Rl(r)

r

[E

(Er i

2

)]aleikr

r

[E

(Er +

i

2

)]aleikr

r. (2.26)

, E = Er i2, Rl(r)

r ial

eikr

r.

- r

4r2jr =4hk

m|ial |2 = 4v2|al|2

h.

, ( ), /h,

|al|2 = 1hv

, (2.27)

v = hk/m . (2.24) (2.25), :

e2il = eilalal

E Er i2E Er + i2

.

45

e2il(0) eila

l

al,

e2il = e2il(0)E Er i2E Er + i2

= e2il(0)1 i

E Er + i2 , (2.28)

eil = eil(0)E Er i2(E Er)2 + 24

.

l(0) . |E Er| , l l(0).

l = l(0) arctg 2(E Er). (2.29)

, , . , , :

A() =1

2ik

l

(2l + 1)

[(e2il(0) 1)

iE Er + i2

e2il(0)]Pl(cos ). (2.30)

- , . , - .

d

d=

1

4k2(2l + 1)2

2

(E Er)2 + 24[Pl(cos )]

2. (2.31)

E = Er 2 , - ( E = Er),

d

d=

1

k2(2l + 1)2[Pl(cos )]

2. (2.32)

46

-, . , ( ) - .

l = (n+1

2) + l(0), (2.33)

n .

2.2

, , - . , . , , - , 8 /. - , , , - , , .

( - 1934 -) 2,23 (.. 1 /)

, - 3H (8,5 , 3 /) 4He (28 , 7 /), - , , .. . , - ( 2D 1/2 , 3H 1 , 4He 6/4 ). - , , , . -

47

. - ( ). (.. ) .

2.2.1

-

2(r) + 2h2

[E V (r)](r) = 0, (2.34) ( m/2 ). E . - l = 0, = R0(r)/r

d2R0dr2

+m

h2[E V (r)]R0 = 0. (2.35)

V0 a:

V = V0 r < a,V = 0 r > a.

E = W , W > 0 , d2R0dr2

+m

h2(V0 W )R0 = 0 r < a, (2.36)

d2R0dr2

mh2

WR0 = 0 r > a.

, R0 = r - r = 0 r r. :

R0 = A sin kr r < a,R0 = Be

r r > a, (2.37)

48

k =

m(V0 W )

h(2.38)

=

mW

h. (2.39)

R0 lnR0. r = a,

k ctg ka = , (2.40)

ctg ka = WV0 W

WV0

(2.41)

, . , ctg ka ,, ka /2. , ka = /2 (W = 0), ..

V0a2 =

h22

4m. (2.42)

" ", . , - .. n- ka = /2 + n. 2,2 - . l = 0. , - . (2.42) :

V0 =2

4

2cpa2

mc2, (2.43)

cp . - "" , .. - - ( 2, 8 ),

49

V0 0, 014mc2 13 . . 2,23 , - 21,4 ( , ka = 3/2, V0 = 9h22/4ma2 = 117 ). - .

, - ( ). , . -,

Cer

R0(r) . . 2.5.

. 2.5. -

1/ , , - , c , . (1/ a),.. "-" :

1

=

hmW

= cp

m

W 4, 3 .

, R0(r) r > a. R0(r) - r < a, C exp(r) .

50

r = 0 , , r > a.

R0(r) =

2er (2.44)

- .

R0(r)(2.37), A B. , B - C, , , a, :

B =

2

(1 +

1

2a

). (2.45)

2.3 -

, , . -, - , .

s-

d2R0dr2

+2

h2[E V (r)]R0 = 0, (2.46)

. r a E V (ka 1),

d2R0dr2

2h2

V (r)R0 = 0 r a (2.47)

d2R0dr2

+2

h2ER0 = 0 r a. (2.48)

51

r, (ka 1), , -, r 0. - E, - .

R0(r)R0(r)

r0

= (2.49)

. E, r a - ( ) E = |W |:

R0 = Cer, =

2|W |h

. (2.50)

, R0/R0 = , .. = .

R0 = B sin(kr + 0),

r = 0

ctg = k=

|W |E

. (2.51)

,

=4

k2sin2 0 =

4

k21

1 + ctg20,

=4

k2 + 2=

2h2

1

E + |W | . (2.52) . , -

V (r), , , - ( ). - , , ( 2), |W |

52

. , .

- 2,5 . (2030%). - (2.52) W = 2, 23 2

2, 3 , 20, 5 .

1935 , . , -, ( S = 1 ), (- S = 0), , :

=1

4s +

3

4t. (2.53)

1/4 3/4 , , ( 4 : 3 - Sz = 0,1 Sz = 0 ). Wt Ws, :

=h2

m

3E +Wt

+1

E + |Ws| . (2.54)

(E Wt, |Ws|) |Ws| , t Wt. ,

34t

1 + Wt

3|Ws|

|Ws| =14t Wt 34t

.

2 : 1 =1024 2.

53

20, 5 Wt = 2, 23 t 4h2/mWt 2, 3 ,

|Ws| = 68, 3 .

s =WtWs

t = 75, 1 . (2.55)

, : - , , , .

Ws, .. , - . , - .

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

=h2

2m

3E +Wt

+5

E + |Wq| . (2.56)

Wq , E 200400 , 1,5 , .

54

2.4 1. V0 d

V (r) =

{ V0 r d0 r > d .

:

R0 +2m

h2(E V0)R0 = 0,

R0 +K

2R0 = 0,

K2 = k2 + 2; k2 =2mE

h2; 2 =

2mV0

h2.

:R01 = A sinKr.

r R0 = C e

i0 sin(kr + 0).

"" -, 0 , :

KctgKd = kctg(kd+ 0),

tg(kd + 0) = kD, KctgKd = K/tgKd D1 (- ),

D in tgKd = tgKdK

.

tg0 =kD tgkd1 + kDtgkd

.

kd

55

kD , .. Kd (/2 + n),

tg 1tg kd

1kd

1,

, 0 /2. ,

Kd = /2 + n = (2n+ 1)

2(2.57)

. k2Dd

56

2.

R0 = ei0 sin(kr + 0) = e

i0 sin 0(cos kr + ctg0 sin kr),

kr 0R0 ei0 sin 0

(1 r

a

)= ei0 sin 0

(1 +

kr

tg0

).

a tg0

k= 1

k ctg0 , , R0 0.

3. V0 d

2 = 2mV0/h2, , - , ( i), - (2.2)

0 = 4d2

(1 th d

d

)2.

() d thd 1,

0 = 4d2.

D =

th d

1 0,

tg 0 k(D d) kd,

..

a = tg0k

= d.

:

0 =4 sin2 0

k2=

4

k2

(1

1 + ctg20

)=

4

[k2 + 1a2(k)

].

k 0 0 = 4a

2 = 4d2.

57

4.

S- R0 0, ..

R0 =i

2(eikr S0eikr) =

= sin kr +i

2(1 S0)eikr.

R0 :(d2

dr2+ k2

)R0 =

2mV (r)

h2R0; R0(0) = 0.

S0

e =

k2|1 S0|2, (2.60)

( )

r =

k2(1 |S0|2). (2.61)

S0 = exp (2i0), R0 = ei0 sin(kr + 0) r = 0. S0

R0 d . ,

f(E) d R0/R0,

f(E) = ix1 + S0e2ix

1 S0e2ix ,

x = kd = d/

58

R0 -, f(E) r = d r d. , f0 h - ( ). h = 0 , , f(E) = f0, r = 0 |S0|2 = 1. .

Er, f0(Er) = 0, . r e . f0(E) E Er E = Er,

f0(E) =

(f0E

)

E=Er

(E Er) + . . . ,

e = 2x(f0

E

)E=Er

, r = 2h(f0E

)E=Er

,

r =

k2re

(E Er)2 + 2/4 ,

= e + r.

e = 4|Ares + Apot|2,

Ares =1

k

e/2

E Er i2 () ,

Apot =1

keix sin x

() . Apot - .

,

e = 4|Apot|2 = 4k2

sin2 kd 4d2.

( -), r = d R0(kd) , ..

R0(kd) =i

2(eikd S0eikd) = 0,

S0 = e

2ikd,

59

kd 1

e =

k2|1 S0|2 =

k2|1 e2ikd|2 = 4

k2sin2 kd 4d2.

2(E Er) = ctg,

1

k

12e

E Er i2=

1

k

e

sin ei.

e =4

k2

e

sin ei + sin kd eikd2

.

.

() (. . 2.6.).

. 2.6. E/Er

- . ( ) - , - Fv > 0. , x = x0 cost, F v = x0 sint = x0 cos (t /2), ..

60

/2 . - , .

, , . , .

5. . 1/v

Ea 40 A - , .. - :

rintern Rintern = CeiKr.

K2 = k2+2 (E = Ea+V ), K , =2mV /h.

f = iKd iX,

.. f0 = 0; h = X,

S0 = e2ixxXx+X

r =

k2

(1 (xX)

2

(x+X)2

)=

4

k2xX

(x+X)2=

4K

k(k +K)2,

k r 4

k 1

v 1

E.

1/v .

6.

A S0.

(r) =B

r(eikr S0eikr)

S-

= eikr +A

reikr =

l

l,

0 =i

2rk

[eikr (1 + 2ikA)eikr

].

61

S0 = 1 + 2ikA.

A A = +i, :

e =

k2|1 S0|2 = 4|A|2 = 4(2 + 2). (2.62)

r =

k2(1 |S0|2) = 4

k 4(2 + 2) = 4

k e. (2.63)

(2.62), (2.63) t = e + r,

t =2

k2(1 Re S0) = 4

k,

:

= Im A =k

4t. (2.64)

. (2.62) (2.64)

=

e4

2 = e4

(kt4

)2. (2.65)

, e t, , :

A = e4

(kt4

)2+ i

kt4

. (2.66)

7.

, , - R0. , - :

a = limk0

A.

,

= eikr + Aeikr

r.

k 0 R0 r = r + A, r = A .

62

2.5

-, , , . , , , -. , . , 1/2 , -, I.

, - I 1/2. (+ ) j:

j = I 12. (2.67)

, , -: A+ ( j+ = I + 12) A j = I 12 .

-

+ =I + 1 + 2(IS)

2I + 1; (2.68)

=

I 2(IS)2I + 1

. (2.69)

, :

+jm =

jm j = I +

12

0 j = I 12(2.70)

jm =

0 j = I + 12jm j = I 12

. (2.71)

, 2(IS)

2(IS) = j2 I2 S2 = j(j + 1) I(I + 1) 34.

63

j :

2(IS) =

I j+ = I +

12

(I + 1) j = I 12. (2.72)

, , - ( j) - A+ A, , :

=

eikr + Aeff

eikr

r

jm, (2.73)

Aeff = +A+ + A =1

2I + 1{(I + 1)A+ + IA + 2(IS)(A+ A)} .

(2.74) , (- + ),

Acoh =1

2I + 1{(I + 1)A+ + IA} , (2.75)

, ,

Ainc =1

2I + 12(IS)(A+ A) B(IS), (2.76)

. (Ainc = 0), A+ = A, .. , . , , - (I = 0). Ainc 9Be 40Zr. , , "" .

-, , ..

e = 4|Aeff |2 = 4|Acoh + B(IS)|2. (2.77)

64

, , -, , -, IS = 0, ( IS) .

(IS)2 = I2xS2x + I2yS2y + I2zS2z =I(I + 1)

4, (2.78)

(IS)2 = 3I2xS2x = 3I2xS2x

I2x =

1

3I2 = 1

3I(I + 1);

S2x =1

3S2 = 1

3 34=

1

4.

, :

e = coh+inc = 4(|Acoh|2+|B|2(IS)2) = 4|Acoh|2 + |B|2I(I + 1)

4

,

(2.79)

coh = 4|Acoh|2 = 4I + 1

2I + 1A+ +

I

2I + 1A

2

; (2.80)

inc = 4B2(IS)2 = 4I(I + 1)

(2I + 1)2|A+ A|2. (2.81)

:

e = coh + inc =4

2I + 1

[(I + 1)|A+|2 + I|A|2

]. (2.82)

2(I + 1) = 2j+ + 1 2I = 2j + 1, :

e =4

2(2I + 1)

[(2j+ + 1)|A+|2 + (2j + 1)|A|2

]. (2.83)

. (2.83), t = 4|A+|2 s = 4|A|2, , I = 1/2.

66

, - :

V (r r) = 2h2

ma(r r). (2.86)

a (a = A), m - , r - .

, - (2.86), :

A = m2h2

eiqrV (r)d3r = a .

, - , RN (.. 1012 , ., , , -, , . , - () , , , - . , .

, - N - (). , , - () ( ) () i- l- :

(d

d

)

li=

k

k0|Ali()|2,

Ali = 2h2

lk|V (r, r)|ik0 = (2.87)=

2h2l|

d3reiqr

V(r r)|i.

67

Ali :

m =mn Mmn +M

= (2.88)

= mnA

1 + A= mn

1

1 + 1A

- M A ,

= mn1

1 + 1A(2.89)

(), A =

A.

, V = 2h2

ma(r r) (2.87), -

Ali =

l|beiqr |i, (2.90)

b =am

=1 + 1A1 + 1

A

a (2.91)

, ,(d

d

)

li=

k

k0

bl|eiqr |i

2. (2.92)

2.5.2

- . J = I1+I2, I1 I2, , >> d, d . exp(iqr) 1, :

(d

d

)

ii= D2(a1eff + a2eff)2, (2.93)

D =1 + 1A1 + 12A

. (2.94)

68

- . ,

d

d= D2[2acoh + b(I1S + I2S)]2 = (2.95)= D2[4a2coh + b

2(JS)2+ 4acohb(JS)]. , - J = I1 + I2.

- , .., ,

(JS) = 0

(JS)2 = J(J + 1)4

,

d

d= D2[4a2coh +

J(J + 1)

4b2]. (2.96)

2.5.3 -

: 1, , 0, . J = 1 -, J = 0 . D = 4/3. - (2.75) (2.76) I = 1/2:

acoh =I + 1

2I + 1a+ +

I

2I + 1a =

3

4a+ +

1

4a, (2.97)

b =2(a+ a)2I + 1

= a+ a. (2.98) a+ a . - ,.. t s. - ,

69

, , , Ws.

,

d

d=

4

9[(3a+ + a)2 + J(J + 1)(a+ a)2]. (2.99)

4. ,

) (J = 0)

par =16

9(3a+ + a)2; (2.100)

) (J = 1)

ort =16

9[(3a+ + a)2 +2(a+ a)2] = par + 32

9(a+ a)2. (2.101)

, ort > par

ortpar

= 1 +2(a+ a)2(3a+ + a)2

= 1 + 2

(1 x3 + x

)2, (2.102)

x = a/a+. , ort/par - - . , x = 3 .

,

ts

=WsWt

0, 03,

.. |a+|/|a| 0, 2 |x| 5. a+ a (x = 5), (2.102)

ortpar

1, 5;, (ort/par)max = 3 x .

70

a+ a (x = 5), (2.102) -

ortpar

19.

- , ort/par 30. , - , .

a+ a

a+ = 5, 38 , a = 23, 69 , |a|/|a+| = 4, 40. (2.102)

ortpar

1, 42 x = 4, 4

ortpar

30, 8 x = 4, 4.

, J(J + 1) , .. ( I = 1/2)

J(J + 1)4

=1

4

[3

41(1 + 1) +

1

40(0 + 1)

]=

3

8,

= 416

9[4a2coh +

3

8b2],

- :

(1, 2) = 416

9[4a2coh + 2inc],

(IS)2 = I(I + 1)

4=

3

16;

inc(1, 2) = 2inc = 23

16b2.

71

, , - - , ( - 0 1 ). , - ( E = 0, 0147 ), . ( , 20K, ) - . - . - .

1. .. . .: , 1963.

2. ., . . .: , 1958.

3. .., .. . .: ,1989.

4. .., . . .: , 1969.

3

3.1 -

, . , , - . rn - , , a1,a2,a3 :

rn =3

i=1niai, (3.1)

ni , . . 3.1.

. 3.1.

, rn, :

V (r) =nVn(r rn) = 2h

2

nan(r rn). (3.2)

72

73

A = 2h2

n

eiqrVn(r rn)d3r rrn=r

=

= 2h2

nVn(q)e

iqrn =nAn(q)e

iqrn, (3.3)

An n- . , - ( ) a, ( )

d

d=

a2

N

neiqrn

2=

a2

N

n1n2n3ein1qa1+in2qa2+in3qa3

2 a

2

NF (q),

F (q)=|n1n2n3 |2. N . C, , , ( ) q

qrn = (n1a1 + n2a2 + n3a3)q = 2n, (3.4)

n . n = N ; d/d Na2. ( q) , , N , , 1 3 N 1023 -. , , (3.4)1. (3.4) , - q

a1q = 2h; a2q = 2k; a3q = 2l. (3.5)

. - o q, , b1, b2, b3, q ( - ).

1 , N , F (q) = (2)3(N/V )(q g), g , - (3.4).

74

q = hb1 + kb2 + lb3,

h, k l , . ,

1) a1b1 = 2; a1b2 = 0; a1b3 = 0.

2) a2b1 = 0; 2a2b2 = 2; a2b3 = 0.3) a3b1 = 0; a3b2 = 0; a3b3 = 2.

1- : b1 a2 a3. 2-, : b2 a1 a3. 3-: b3 a1 a2.

b1 = 2a2 a3

(a1[a2 a3]); b2 = 2[a3 a1]

(a1[a2 a3]); b3 = 2[a1 a2]

(a1[a2 a3]).

() . . - :

q = k k = g, g = hb1 + kb2 + lb3. (hkl) . . - , g , g = |g| d = 2/g. -, , 2/|b1| -, a1,a2,a3, , a2,a3, , , .. - , .

- .

75

, , ( ) . - ,

k = k0 + g. (3.6)

, ,

k2 = |k0 + g|2 = k20. (3.7) , . (3.7) :

2k0g + g2 = 0. (3.8)

- k0: = /2, k0 g, g = 2/d k = 2/, (3.8) = B, ,

2d sin B = , (3.9)

.

3.2

(3.2),

V (r) = V (r + ai), (3.10)

, - (. . 3.2). - g, - g = 2/d, d . - .

76

- g.

. 3.2. ) - . - , . ) - ( ) , g.

, , , - g. x g, . - x:

V (x+ d) = V (x),

:

Vg(r) =nVn exp(

2i

dnx) =

gn

Vgneignx, (3.11)

gn = 2 n/d, g1 = g. , , , , gn , - , ,

77

dn = d/n ( - n- , dn = d/n). - {g} , , , ..

V (r) =nVn(r rn) =

gVge

igr = V0 +g2vg cos(gr + g). (3.12)

, , ,

Vg = Vg, (3.13)

Vg = vg e

ig . (3.14)

. , ,

V (r + ai) =gVge

igr+iaig = V (r),

, gai = 2 n. , . (3.12):

A = m2h2

gVg

V=1

ei(qg)rd3r = (3.15)

= m2h2

gVgqg = N

gA(g)qg,

A(g) , -

Vg =

V=1

V (r)eigrd3r =neigrn

Vn(r)eigrd3r =

= N

Vn(r)eigrd3r =

2h2

mNA(g). (3.16)

78

, grn = 2n, , - : An(g) A(g), , N , N = 1/. , , q = g, .., , , - N2.

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

3.3 .

- , , -, .

,

V (r) =aVa(r ra). (3.17)

, - . , - , . i , -

79

, n - , ra

ra = rn + ri, (3.18)

rn (3.1). ,

. V(r) == 2mV (r)/h2k2e , - hke.

2mV (r)

h2k2e= V(r) =

geigrVg, (3.19)

Vg = 2mh2k2e

V=1

eigrV (r)d3r =2m

h2k2e

a

eigrVa(r ra)d3r =

=2m

h2k2e

aeigra

Va(r)e

igrd3r =

n ()

i ()

=

=2m

h2k2e

neigrn

i

eigriVi(r)e

igrd3r

=

=2mNch2k2e

i

eigriVi(r)e

igrd3r

. (3.20)

Nc , , grn = 2n, , V(n+i)(r) = Vi(r), . , fi(q),

Vi(r)e

igrd3r = Vi(g) = 2h2

mfi(g).

Vg = 2mh2k2e

2h2

mNe

i

eigrifi(g) = 4Nck2e

Fg.

80

Fg .

Fg =i

eigri

. , , , - . - g, Fg = 0 ( ). , ( ), , , , -.

, . -, .. , .

ua a- ra, ra = ra + ua, -

V (r, ua) =aV (r ua ra).

:2m

h2k2eV (r, ua) =

geigrVg(ua),

Vg(ua) = 2m

h2k2e

aeiguaeigra

eigrVa(r)d

3r.

. - (.. - ),

81

ua =q>

(U qe

iqra +U qeiqra) .

eigua = eig(

q) =

qeig(U qe

igr+Uqeigr).

exp :

eig(U qeiqr+Uqe

iqr) = 1 + ig(U qe

iqr +U qeiqr) |gUq|2 + . . .

, ,

eigua

= q

{1 |gU q|2

}= 1

q|gU q|2 eWg ,

Wg =

q|gU q|2 = |gua|2.

eWg -. ,

Vg = 4Nck2e

Fg,

:

Fg =i

eWigfi(g)eigri.

- g. . - ( -) "" ua, , hg h/ua. -. , , -, , - ( ), .. ()

82

. , . , - ( h2g2/2M) , , , . - .

- - . - - ( -), hg - hk. -.

3.4

, (. 3.3), n , -.

. 3.3.

, nr = 0.

, , :

i = eiker. (3.21)

-

83

:

1

k2e2+

1 2mV (r)

h2k2e

= 0, (3.22)

2mV (r)

h2k2e= V(r) =

geigrVg. (3.23)

, - ( - ). g, -

k0 =g,s

ugsei(k0+g)r|s, (3.24)

k0 . (3.24) (3.22)

gs

1 (k0 + g

)2

k2e

ugse(k0+g

)r|s ggs

Vgugse(k0+g+g)r|s = 0. (3.25)

g = g + g (,, g = g g) - ugs:

1 (k0 + g

)2

k2e

ugs

gVgugg,s = 0. (3.26)

. - k0, - .

, - |kg |k0 + g - Eg = h2k2g/2m.

84

, - -. , . , - ugs , , . -, |k0 |k0 + g k0 k0 + g,

k2e k20 |k0 + g|2, , . , - .

, - , - (nr) = 0. , , - , . , -.

k0 = ke + n. . .

ket . , - - . , - .

-.

85

. - , , (3.26), . (3.26), (-) :

1 k

20

k2e V0

u0 = 0. (3.27)

- s. - , .., -, n ( . [1, 2]):

n2 k20

k2e= 1 V0 = 1 + 4Nc

k2eF0. (3.28)

-, -, - V0. ,

V0 =h2k2e2m

V0 = Nc[i

Vi(r)]d3r =

1

c

[i

Vi(r)]d3r V . (3.29)

, - , - , -. ., (3.26)

[k2e (k0 + g)2

]ug

gk2eVgugg = 0,

, g = 0,[k2e (k0 + g)2

]ug k2eV0ug

g =0

k2eVgugg = 0.

86

[k20 (k0 + g)2

]ug =

g =0

Ugugg,

k20 = k2e(1 V0), Ug = k2eVg. ug = 0g, , - , - ug = Ug/[k20 (k0 + g)2]. , , - , , :

= eik0r +g

Ugk20 k2g

eikgr eik0r1

g

Ug2g

eigr ,

kg=k0+g,g = (k2gk20)/2 g.

||2 = 1 g

|Ug|g

cos(gr + g).

, g , .. , - , - , (. (3.12)). , , - (.. ) .

, (g 0) g - "" , g |Ug|. (g = 0) - , Ek

87

, - hk0 h(k0 + g). , , .

. - , -, G, k0 kG = k0 + G, (3.26)

1 k

20

k2e V0

u0 VGuG = 0, (3.30)

1 (k0 + G)

2

k2e V0

uG VGu0 = 0.

(- det = 0)

n2 k

20

k2e

n2 (k0 + G)

2

k2e

|VG|2 = 0. (3.31)

k0 - (.. ) (-) . ( ) , - . - .

3.4.1

, , -, . . -

88

V0. - , :

n2 =k20k2e

= 1 V0 = 1 + 4k2e

i

Nifi(0), (3.32)

Ni . - - , , u0.

, hke. , ( - ), - k0

k0 = ke + n. (3.33) (3.32),

k2e + 2(ken) + 2 = k2e k2eV0.

:

2 + 2(ken) + k2eV0 = 0

2

k2e+ 2

kee + V0 = 0, (3.34)

e =ken

ke= cos ,

(.. - ).

ke

= e 2e V0 = e e

1 V02e

e(1 ),

89

=

1 V02e

.

= kee(1 ) = ken ken, , k0 (3.33) n, -

k0n = ken+ = ken = kee,.. , . - , . , , .

,

= c1eik0+r + c2e

ik0r.

c1 c2 .

3.4.2

- , :

eiker +reik

er,

r , ke , , |ke| = |ke|. - (- ), - , , .. ket = ket; ken = ken.

90

, k0n > 0, k0+.

= ceik0r.

- nr = 0. k0 k0 = k0t +k0n, -

eiketr +reik

etr = ceik0tr.

r , - - ( ). : 1 +

r = c. -

( - ):

ken+r(ken) = ck0n = cken.

, , ken = ken, :

1 +r = c,

1r = c. r |c|2

r =

1 1 +

2

(3.35)

|c|2 =

2

1 +

2. (3.36)

- , - . . D - , ,

91

D cos = D(ken)/ke, , .. D cos 0 = D(k0n)/k0. , ,

Je =hkem

D(ken)ke

=h(ken)

mD.

, :

J0 = |c|2 hk0m

Dk0nk0

= |c2|hk0nm

D.

, - , - . ,

hkenm

= rhkenm

+ |c|2 hk0nm

=hkenm

(r + |c|2), (3.37), ,

r + bc2 = 1. (3.38)

- , - , - .

=1 V0/2e = 0 -

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

92

. .

, , (r = 1). ==

1 V0/2ec = 0, c, -

:2e cos2 = V0.

. , - , "" - ( - ) h2k2en/2m = h

2k2e cos2 /2m V0. -

.

, e < ec = V0

(k0n) = k0n = kee

1 V02e

=i

L,

:

= eketrnr/L.

( ) L:

L =1

kee|| . -

, n = k0/ke = /2 .

r =

(n2 cos2 )1/2 sin (n2 cos2 )1/2 + sin

(3.39)

L =

2n2 cos2

. (3.40)

93

, , - -

cos c = n. (3.41)

,

n2 = 1 V0 = 1 + 4Nck2e

F0 = 1 +4Nck2e

i

fi(0),

, ke = 2 , , , , , :

n2 = 1 2

i

Niai.

sin2 c = 1 cos2 c = 1 n2 = V0

, - .

, -, .. a 1012 , ()

V0 = 2

Na

2 1023 1012 3

2 1011 2

.

0, 1 A, .. 109 V0 1018 1011 107,

c sin c =

V0 0, 3 103,.. .

, , .. c = 2 . n = 0,.. V0 = 1. , -, , .

94

Ec = V0 = V0 h2k2e2m

=4N

k2ea h

2k2e2m

=2h2

mNa,

-

h242

2m2c=

2h2

mNa,

..c =

Na.

N 1023 3, a 1012 , 2 1011 2,

c 0, 6 105 = 600 A., N = NA/A, , A , NA , NA 6, 02 1023 3.

, , - (), , . , , , , ( ). c 1 A v 4 105 /==4000 /, c 600 A v 6, 7 /. Ec 2, 3 107 . (), , , (. 3.4). , 3.1.

3.5

.. - 1959 . [3], - . 1974 .

95

E < 104 . 1974 . 2- .. . [4] :

: E < 104 , : E < 107 . .

. 3.4. ,

3.1. ,

acog c Ec vc/3 1012 A 107 /

1,80 0,78 580 2, 4 6,8BeO 2,90 558 2, 62 7,1 2,0 0,66 687 1, 73 5,75D2O 1,105 702 1, 66 5,6 2,70 0,35 1230 0,54 3,2 7,86 0,96 620 2,1 6,3 8,92 0,79 698 1,72 5,7 7,14 0,59 900 1,02 4,4 11,34 0,96 969 0,82 4,1

1968 . .. - [5]. -1 (. , ), , , - . -

96

. 103 2c1 ( 106 /3). , - . . ( ) - , -. kT . vc ( mv2c/2 kT ) (. [6])

18

mv

2c

kT

2

.

kT 0, 025 (T = 300 K) vc 6 / 1011.

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

1968 . - . ( , . -). -, ( 1014 /2) . -

97

. 3.5. , - , 2, 5 105 / ( 0, 6 104 /2 .

70- , - [7, 8], - (, . , -) HFR ( 1015 /2) - . - , .

, , , - - . - 5 , 15 , . 1, 8109 /2 (PF1).

: , - , - FRM-2, , - , - . , - (SINQ) -, ( , 1,8 , .. 1016/) 590 . - , - , -

98

- - ( ). 1,3 570 ( 0, 74 ) , 10 , . - 1014 /2, , -. - . , - [9, 10] , - - () .

, , , - Ec, - . , , - , 1, 94107 (650 A). Ec1 > Ec0 ( ) Ec0 < E < Ec1. , , - . , - , :

Be 580 A 650 A (6,1 6,8 /), Fe 620 A 650 A (6,3 6,8 /). -

, - , . , 1 2 107 - 4,4 /.

99

. 3.5. - - [7, 8] (. .. .) ( - ). ( ) -

100

3.2 . ()

N n[s] /1 885,4 0,9 0,4 . ., 2000 [11](1a) 885,4 1,2 . ., 1997 [12]2 889,2 4,8 J. Byrne et al., 1995 [13]3 882,6 2,7 W. Mampe et al., 1993 [14]4 888,4 3,1 1,1 . ., 1992 [15](4a) 888,4 2,9 . ., 1990 [16]5 878 27 14 R. Kosakowski et al., 1989 [17]6 887,6 3,0 W. Mampe et al., 1989 [18]7 877 10 W. Paul et al., 1989 [19, 20]

( )8 876 10 19 J. Last et al., 1988 [21]9 891 9 . , 1988 [22]10 870 17 M. Arnold et al., 1987 [23]11 903 13 . ., 1986 [24](11a) 875 95 . ., 1980 [25](2a) 937 18 J. Byrne et al., 1980 [26](9a) 881 8 . ., 1978 [27]12 918 14 C.J. Christensen et al., 1972 [28]13 885,7 0,8 Abele, 2000 [29]

Particle Data Group, 2002 [30]

- (), .

3.5.1

3.2 , .

, - , (, )

101

- (,) -2 [24, 25]. - . - 900 , , 10 -. . , , - ( ). , , , , , , -. , , 105 [31]. [32].

- , - , . ( 700 10 ) - -. . , - , (. . 3.6). , .

" " - ( ) - - (, ) - [15, 16, 33]. , ,

102

- , - ,.. , .

( - ) - - ( -).

. 3.6 . -, , - , ( , ,.. ) - . - , "" , - . , . - . ( , , 15 ), - . - - , - . - [23], 3,3 ( - 0,4%).

2000 . , , - n == 885, 4 0, 9stat 0, 4syst [11, 12], 0, 9stat , -, 0, 4syst , -

103

. 3.6. - (. .. ): 1 ,2 , 3 , 4, 9 , 5 , 6 , 7 , 8 , 10 -, 11 , 12

104

. - , - ( 2004 .) n = 885, 7 0, 8 c.

, . , - . , , - ( ), - ( ). . , , 3 .

2004 . , - (. 3.6), - [34]. (lowtemperature fomblin LTF) C, O F. 2354, - 1,83 /3, 1, 03 107 . 160 , , , , ( - 2, 2 106 ). - 5 , - 5 . 100 . , - - - (, ).

105

. 3.7 ( ).

. 3.7. - ( 0) . ,

: n = 878, 5 0, 7stat 0, 3syst. 7,2 6,9 [11]. - 6,5 5,6 , .

, .-, ( 3- ) ( .

106

). - [35], 0,15% - , -, . -, , - - 15%. , - .

- . . - - . , - .

3.5.2

. [36] 1951 . .. [37] 1960 . - ( ), ( -) ( , ). : , - B . - , - . ( ) (.. 3.8)

U = B(r),..

107

, -, - , . - r

n2 = 1 nB(r)Ee

,

,

sin c =

nB(r)

Ec

1/2

, Ec = nB(r0).

, B - (1 = 104 ) - nB 107 , . 1 3,4 / ( 0, 6 107 ), , . , . - . , - , , , 0 = 2B/h.

. 3.8.

|+ |, 0. - T ,

108

, T r/v, r - , , v/r.

109

. 3.11. -

. 3.12. Z

. 3.13. [19, 20], - ( ). - RS, . - ((B)/r)

110

, , - |B(r)| r(. . 3.11). , , Z . 3.12. , - .

( - , .. ) B(r) = B0r2/r20, .. ( 2n- rn1 [38]). , . .[19, 20] , . . 3.13. B0 3, 5 . - 5 20 /. , , 2(R+r0) =113 , 2(R r0) =104 . - ( |B|) . 3.14.

20012004 . (-) - (, ) - - 15,6 ( 18 , - 55 ), [39, 40]. - , , .. - . 20- - - , . . 3.15 3.16. , 1 - B 1, 2 . - 2 /.

111

. 3.14. (- |B|)

. -

. . 3.17. , . . 3.6. - , , - , ( ) . ( ), . - , ( , ), - . , .

-

112

. 3.15.

113

. 3.16. , -

878 6 c. , ( ) . , .. -. 2005 .

3.6 .

-, , , - .

, , - . -

114

. 3.17. - - . 1 , 2 , 3 - , 4 , 5 , 6 , 7 , 8

115

c

Een =h2k2en2

=h2k2e sin

2 c2

= V0 Ec,

Ec , .

sin2 c = V0 = EcEe

,

c 1c =

V0 =

Na =

c=

vcv,

c , vc .,

c =

V (2)0 V(1)0 =

N (2)a2 N (1)a1.

- , , . - .

3.6.1 .

() - .

U = B, B , , = , .

116

- , , :

n2 = 1 VEe

= 1 2

Na 2m

h2k2eB = 1

2

[Na m

2h2B

],

(1,2)c =

[Na m

2h2B

].

, , , - , .

, , -

m

2h2B > Na.

, , (Co) - B 0, 65B, B -. , . P 0, 98 0, 99. -, () -, .. .

.

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

117

, ( ) , - .

3.6.2

c - (. . 3.18) - , , . , , - .

. 3.18. - Ir . a c, - . b , -

< c - ( - D, , . . 3.19).

. 3.19. . < c , , (D) sin

- (-).

118

, - :

= 2d sin B.

.

, , - , , (-, ), , (.. -), , > D = 2dmax, dmax , .. . - < 2dmax -, , , E < ED. . 3.3 , .

3.3. ,

D (A) ED ()Be 3,95 0,0052BeO 4,4 0,004Pb 5,7 0,0025C () 6,69 0,00183Bi 8,0 0,00128

, : , . (, ),

N (2)a(2) = N (1)a(1).

119

, .

3.6.3 , -

c, , , - . , , , , - E0 ( 0) , c . c,, () , .

sin2 c =2

Nacog =

V0Ee

,

Ee = h2k2en/2m "" , . - ( ) "" (), , "-" "" (. . 3.20).

. 3.20. , -

-

V0,

Ee =

= h2k2en/2m. "-

"

V0: E0 = h2k2en/2mV0. "-

"

( z) -

Eemin = V0

120

0. 0 , , - :

< (0) =

Nacog

sin 0 = c sin 0.

, ,

Emin =Ec

sin2 .

1, Ec 107 , Emin 103 . . , "-" , . : , - . 3.21.

. 3.21. ,

,

, .

-

Emin < E < ED

0 = 30, - (, ) 5 104 - 5 103 , .

3.7

1964 . .. .. - [41, 1]. . -, "", , .

121

. -

= NgI,

N , I . H , z (..

H ez), Em = H = NgHIz.

EmkT

= Iz m,

=NgH

kT.

En T - :

P =em

mem

,

m, . , ( )

Iz =mmem

mem

=1

z

z

,

z =I

m=Iem =

m(1 +

2m2

2+ . . .).

I

122

Iz = 1

z

z

=

I(I + 1)(2I + 1)

3(2I + 1)=

=I(I + 1)

3=

NgIH(I + 1)

kT=

H(I + 1)

3kT.

V0 ( ) -

V0 = 4k20

N(acog + bIhS), h = ez , - ,

bI = bIz = 2(a+ a)(I + 1)H(2I + 1)3kT

.

,

a = acog + b(IS) ia,

acog =1

2I + 1[(I + 1)a+ + Ia],

b =2(a+ a)2I + 1

.

bIS = bIzhS bIhS,

bI = bIz = 2(a+ a)(I + 1)H(2I + 1)3kT

.

, Sz = 12 - . , - (nB). ,

123

n2 = 1 V0 == 1 4N

k2e(acog + bIhS) n(BS) 2m

hk2e=

= 1 (VN0 + V), V = n(BN + B)) , ,

BN =2h2NbIh

m2n.

, , , - . - . .

, - . ( y) - . x. 1

2, -

Sz ( - z)?

, 1/2 : S = /2,

x =

0 11 0

; y =

0 i

i 0

; z =

1 00 1

.

12

,

0 = c11212+ c21

2 12 ,

, :

0|Sx|0 = 12, Sy = Sz = 0.

124

0 =

c1c2

= c1

10

+ c2

01

.

:

1

2x0 =

1

20

0 11 0

c1c2

=

c2c1

,

c2c1

=

c1c2

.

c21 + c22 = 1,

c1 = c2 =12,

0 =

12

11

.

.

y0 =1

2

i

i

,

0|y|0 = i+ i = 0.

z0 =

11

0|z|0 = 0.

,

0 =1

2

11

= 1

2

10

+ 1

2

01

125

, x. 1/2 z - . 1/2 , - x . , (x, y) , .

-

k0 = ke1 V0 ke(1 1

2V0) = ke[1 1

2(VN0 V0 )] = k0

1

2k.

,

12+e

ikey +12eikey,

y

(y) =12eik0y

(+e

ik2 y + eik2 y

)=

= eik0y12

e

ik2 y

eik2 y

.

? , , ..(y)|x|(y), (y)|y|(y), (y)|z|(y). , .

1) (y)|x|(y):

x(y) = x

e

ik2 y

eik2 y

=

e

ik2 y

eik2 y

,

(y)|x|(y) = 1

2

(eiky + eiky

)= cosky.

2) (y)|z|(y) = 0.

126

3) (y)|y|(y):

y(y) = y

e

ik2 y

eik2 y

=

iei

k2 y

ieik2 y

,

(y)|y|(y) = 1

2i

(eiky eiky) = sinky.

, (1,0,0), - y (cosky,sinky, 0). (xy), - . , ,

= ky = keVy = 4Nke

< bI >

2y =

4N

ke (a+ a)(I + 1)N

(2I + 1)3kTy.

. , ( ). h, -, , .

-. y = vt, = kvt = t,

= vk =hkk

m=

h

2m(k2+ k2) =

E

h=

2(B +BN)

h,

E = 2(B + BN) 1/2. , (.. ), ( ) (B +BN), - , (B +BN). = 2(B + BN)/h.

127

I

n=In2.

In=I

n2 = (I).

(0) = 0,

(I + 1) = (I) + (I 1)2 + (I + 1)2 = (I) + 2I2 + 4I + 2,,

(I) = I3 + I2 + I + .

(0) = 0, = 0.

(I+1)(I) = (I3+3I2+3I+1I3)+(I2+2I+1I2)+ = 2I2+4I+2. I,

I2 : 3 = 2 = 2/3;I : 3+ 2 = 4 = 1;

I0 : + + = 2 = 13.

,

(I) =2

3I3 + I2 +

1

3I =

1

3I(I + 1)(2I + 1).

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[2] .. . .: ,1986.

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4

4.1

( ), H. - : :

ih

t= H. (4.1)

( ) - U , U :

U = U (4.2)

-, , , (1) U :

ihU

t= UH U1U

1

,

..

ihU

t= HUU , (4.3)

HU = UHU1. (4.4)

134

(U+U = 1) U

U = eiT ,

, ,U+ = U1 = eiT ,

T (.. T = T+), , , -, (4.4) :

HU = eiTHeiT . (4.5)

( )

HU = (1 + iT )H(1 iT ) = H + i [T,H]. (4.6) , , T (.., - , , , ), T -:

[T,H] = 0. (4.7), HU = H.

, -:

dT

dt=

1

ih[TH]. (4.8)

, T , , T .

, , - , -.

, .

, :

t=

(t+ )(t)

=1

ihH, (4.9)

135

..U = ( + t) =

(1 +

ihH

)(t), (4.10)

T = Hh, (4.11)

.. - . (- ) , H .

, . ,

U = (r + a) = (1 + a)(r), (4.12)

T =i= p

h, (4.13)

p= ih .

, - - .

. 4.1. - - , - -

r (, ) (. . 4.1)

r = [ r], (4.14) , |r| = r sin , r .

U = (r+ r) = (1+ [r])(r) = (1+[r])(r), (4.15)

136

T = L

h, (4.16)

L = ih[r ] . -

- , .

, p, - S L, - , , p2/2M , , p, S L.

(- ) - . :

(pL), (pS), (LS), (p[S L]), (S[pL]), (L[p S]). - , - , . , -, (.. ), (LS), .

, , ,

H = (LS). (4.17)

- , , .

- . , - (.. - ).

137

-, , - , .

. - . - , - (., -, [1]).

4.2 ( )

, - (.. - , ) 180

. - - .

(P -) : - , ., , , .

- - , - , (. 4.2).

138

. 4.2. - -, , - .

-, , ,

, ,-, , , - . , P -. , , - - , , - .

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

- [2] 1956 . ()-, , + + -, . . , + + ( K+-),

139

, , (.. , . ). - . - 1957 [3], - 60Co (60Co 60 Ni+ e + ). -, (. . 4.3).

. 4.3. - - 60Co

, - (.. , . 4.3, ). :

W = W0[1 + aSP (SNpe)]. (4.18)

P - (Sp) - . - , . - (P ) - ( C). , - ( -), , -, CP . - (. 4.4).

140

. 4.4. CP - - 60Co

, , , - , , -, . , - , , - . - ( ) , [4] [5] 1957 .

P -

P - . - , . :

P = p. (4.19)

, - :

ihp

t= Hpp, (4.20)

Hp = PHP1. (4.21)

, p (4.21), , PHP1 = H

PH HP = [PH] = 0, (4.22) p . ,

141

, P . P :

P |u = p|u. (4.23) , , |u - ,

P 2|u = p2|u = |u (4.24), ,

p = 1. |u+,

P |u+ = |u+, .

|u:P |u = |u,

.

P -

H, - E, - P , - .

, H|u = E|u,

PHP1 P |u = EP |u

HP |u = EP |u.

E P |u - |u:

P |u = p|u,

142

, |u P ., . , .

Ylm(, ) sinm()(coslm + a coslm2 + . . .)eim. r r - r, , r, , + .

PYlm(, ) = (1)lYlm(, ). (4.25) -

, , - , :

PA(+)P1 = A(+); PA()P1 = A(). - (P -) ., ,

A = u|A|u, , ,

A = uP1P |A|P1Pu = A, A = 0.

P - , - ,

u+ + u|A()|u+ + u = u+|A|u+ u|A|u+ == 2Re u+|A|u. (4.26)

, , - , , .

143

, Q , .. P -, , , - , .. P -, , , - . , P - -. P - . - - P - cos p (.. cos ), aSP (4.18).

, - , - , .

4.3

1996 - . 1896 . , . , , , - , . - , , ( 1903 . : -, , - ). , , 82, , , - .

1898 . , - -, 1900 . , -

144

-, . - -

. - - , 1933 . , - , 1931 . - - (, , ), , - . - -, : , , . , - - - : GF = 1, 436 1049 3. h = 1, c = 1 GF 105/m2p. , -, G2F . , - - , GF . , (, 2 106 , 900 ) , -: 1 G2F5. ( , B-, -) - . , , - .

1958 - - . - (SnP e), (SnP ), Sn , P e, P , , - -.

, , ,

145

-

n p+ e + e, - ,

e + e + . -

, . [6]. (w) - ( = 1/w) ( )

w =1

=

2

h|H|2(E), (4.27)

H , (E) - ( 2 ). ., , :

A+ B C +D, :

A B c , , C D, .. .

H =C(C)

D(D)V (A,B,C,D)A(A)B(B)dAdBdCdD. (4.28)

146

V (A,B,C,D) -. , - - . , , - , c. , , , , , , P . - :

H = GC(P )

D(P )A(P )B(P )d. (4.29)

G -. , ( -) , A + B C +D,

A C +D + B,.. A C,D -B.

, B ( ) P (tB < tP ), (tB > tP ), . , -. , , , , ( B ).

147

, -. H , . - . , , - . , , - . - , - , -: . 1/2 4- . , - , , , . -.

4.3.1

( ) 1/2 - - x , 4- A(x) (,A), , , , -: ,

Vem = ej(x)A(x),

j = (, j) 4- , j(x) = p(x)p(x), p(x) (, ), p(x) == p+(x)0 , -, .

148

, .

ih

t= H, (4.30)

H = cp+ mc2, (4.31)

p = ih ,

=

0 0

=

1 00 1

,

2 = I, 2i = 1. i - : i + i = 0 ik + ki = 2ik, .. .

, ( - h = 1, c = 1), - :

i( + im) = 0, (4.32)

(p m) = 0. (4.33) p0 = i/t = i0, p = i,

= =

0 0

, 0 = =

1 00 1

,

20 = 1, 2i = 1 + = 0 = (, 0, 1, 2, 3, 1, 2, 3).

5 = i0123 = 0 II 0

,

149

25 = 1, 5 + 5 = 0,

5 = 0

0 , 1 + 5 =

I II I

.

. - x . , , - , , , :

, :

, , - . -

Vem =j(x)j(x

)D(x x)d4xd4x, D(x x) , (.. -) 1/|rr|, .. -. ,

150

, -, , .. h/mc, , , , :

, , - , , - , :

, - . - . - - :

H =GF h

3

c2

[p(x)n(x)] [e(x)e(x)] (x x) + ..

( ):

151

- (, - ) :

k|H|i = GF2

lk (r1)

Nk (r2)(r1 r2)li(r1)Ni (r2)d3r1d3r2 =

GF2,

, ,

a =me2h2

k|H |i me2

GF2 me 10

6

m2p me 10

20

mp.

, 1046 2.

, , - , - -.

jN = p(x)n(x)

( , , , - ), ,

je = e(x)(x).

H (V ) . , - , - , - (S), [pn][e], (P ) [p5n][e5], - (A) [p5n][e5] (T ), - , [pn][ee], = 12( ). - 1 ,

1C , - -

152

( ), , V - A-, S- T - ( , ).

4.3.2

- P - , .. . [2] ( - ) , [pn][e5], - [pn][e5], .. -

H =i

(pOin) (eOi(Gi +Gi5)) , (4.34)

Oi = 1, , , 5, 5. 10 Gi, G

i, .

-, , [5], [4] , - . -, (-, ), - . . [7] 1958 . . , L. . ( ) ( -), , s-. I = 0, 1, . - , l = 0 I > 1, , - - , , ( ., , [8, 9]).

153

-

= L + R, (4.35)

L =

1

2(1 + 5); R =

1

2(1 5) (4.36)

-.

(pm) = (E0 p m) = 0. (4.37), , a a = a00 a 4- a. ,

=

,

-, :

=p

E +m. (4.38)

, 1 + 5, - L:

L =1

2(1 + 5) =

1

2

I II I

= 1

2

. (4.39)

, L + . ,

=(1 p

E +m

). (4.40)

E m v = p/E 1 (1 n), (4.41)

n = p/p . z ,

(1 z) = 0 00 1

. (4.42)

154

, = 10

,

z, = 01

z.

, L = 0, = 10

, L = 0, =

01

, ..

L , ( ). R - ( ). , -. , , . , -. .

- :

H =i

Gi (pOin) (eOiL) + .. (4.43)

4.3.3

1958 . , - [10] , [11]. , , L = (1 + 5)/2, eLOiL, Oi = 1, , , 5, 5:

eLOiL = e1 5

2Oi

1 + 52

.

, 1 5

2

1 + 52

=1 5

2

1 + 52

=1 5

251 + 5

2= 0.

, , - ,

155

. ,

1 52

51 + 5

2=

1 52

1 + 5

2=

1 + 52

,

H =GF h

3

c2[p(x)(1 + 5)n(x)][e(x)(1 + 5)(x)] + ..

. , - , , . - , e(x)(x), -, e(x)5(x), , (VA)-. -, 5c = ic, , v+c, - v pS, - -. - - . , , - , , , -. , - , , , .

( , - ) d- 1/3 u- 2/3 :

156

H =GF h

3

c2[u(x)(1 + 5)d(x)][e(x)(1 + 5)(x)] + ..]

GF2[jqj

l + ..] =

GF2[(V A)(v a) + ..],

jq = V A jl = v a , (V A)-. - d- u- :

, , ( - , ). -

H =GV2[(V + A)(v a) + ..],

= GA/GV - - GA GV . - , -

157

. - [12], 2003 . -,

= GA/GV = 1, 2695 0, 029. ( -

dEe de, d) , pe, p , - -:

WdEeded peEe(E0 Ee)2dEeded

[1 + a

pepEeE

+ bm

Ee+ n

(ApeEe

+ BpE

+Dpe pEeE

)].

b , - a, A, B D :

a =1 ||21 + 3||2 , A = 2

||2 + Re 1 + 3||2 ,

B = 2||2 Re 1 + 3||2 , D = 2

Im

1 + 3||2 . - ( ) Im = 0, D : D = 0.

A. [12] :

A = 0, 1173 0, 0013,B = 0, 983 0, 004,a = 0, 103 0, 004,D = (0, 6 1, 0) 103.

158

A [13], 2002 . Perkeo II, - , -: A = 0, 1189 0, 0007, = 1, 2739 0, 019.

4.3.4

- , . - -, - - .

. - G4, . , , - ?

. , 107 -. ? , ,

159

-2 (, , - ), P - , . . 4.5.

. 4.5. -, - - - , .. -

-? ( -), , .. -, (P - PHHP = 0). - , . , - P - d = er, P - - , (dE) (H) ( ) :

, , ,

(+)HW

().2 - (N+N)/(N++N+),

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

160

( HW P -, - .) , , , (+)1

()2 ,

1 =

(+)1 +

()2 ,

=+1 |HW |2

E1 E2 .

, , E1E2. 1 , - :

WEM ((+)1 +

()2

) HEM(+)0

2=

=(+)1

HEM(+)0 + ()2

HEM(+)0

2

|B(M1) + B(E1)|2 = (4.44)= |B(M1)|2 + [B(E1)B(M1) +B(E1)B(M1)] + 2|B(E1)|2.

- , 2|B(E1)|/|B(M1)|. , (- ) M1 - E1, .

- , (n, )- - , - . - - .. [14] (- 482 Ta181 396 Lu175). - - - P = (6, 01,0)106 181Ta P=+(4,01,0)105 175Lu.

161

- 1964 .. (- (), )[15], - ( ) 113Cd, ( 1965 ) . . - [16], - 181Ta. - P - - - .

- 181Ta - [17] , , -, : [14] - - 181Ta 30 , .

, . [14] - - ( , 8 , ). 1974 .., .. (), .., .. () - - . 3

-, - , , - . - P - -, -

3 . .. [18].

162

, - - . - A P - -

n+ p d+ . , , -, - . , A 6 108, , 10% 108. - -.

- - P - , P 5 107 ( CL = 90%). ( - 108), - .

4.3.5

, - - :

, () - , ,

163

. : -

, (.. d-) ( ) -, GV < GF .

, ( - . ) - S = 1 5 , S = Q. , s- Q = 1/3 - S = 1 u- Q = 2/3 S = 0.

, s- d- u-, . . 1963 [19]. , GF , - d- s-:

d = d cos C + s sin C, (4.45)

-

H =GF2[(ud)(ee)]+ .. GF

2[cos C(ud)(ee)+sin C(us)(ee)]+ ..

(V A)- . - , -. , , sin C 0, 23.

164

, - - ( ,, + p + n):

H =GF2[(ud)()] + ..,

(, ):

Hee =GF2[(ee)()] + ..

, , d, , ,

s = d sin C + s cos C. (4.46) Q = 2/3, s- Q = 1/3, , u- (Q = 2/3) d- Q = 1/3. 1964 . . - . , c- ( charm). 1970 . , - [20] cs,

jGIM = c(1 + 5)s.

, , c-. - 1974 . [21, 22], - [23] ( 12, 13 18 , ) J/- - (m = 3096, 87 0, 04 ) ( = 875 ). 3,7 . ,

165

- ( ) ( -, C = 0). 1976 . - () () - , . [24]. (cc-), - (C = 0) (., , [12]). , 1975 . : (e, e, u, d) - (, , c, s). , .. .

j = ee + + du + sc, (4.47) d s (4.45), (4.46):

d = d cos C + s sin C, s = d sin C + s cos C. , , :

Hc =GF2jj

+ , (4.48)

j , , - . (4.47), , -, ( ), j+ - , - .

4.3.6

(4.47) - : , . -, e - 1 2 ()

166

m1 m2:

e = 1 cos + 2 sin , = 1 sin + 2 cos , (4.49)

. 1 2 - , , . : . e ( ), t = 0 -, , e, t :

(t) = 1 cos eiE1t + 2 sin eiE2t, (4.50)

E1 =p2 +m21 p + m21/2p, E2 p + m22/2p. ,

E = E2 E1 = (m22 m21)/2p m212/2E, m212 = m22 m21. (4.49) :

1 = e cos sin , 2 = e sin + cos . (4.51)

(4.51) (4.50),

(t) = (e cos sin ) cos eiE1t + (e sin + cos ) sin eiE2t =

= e(cos2 eiE1t + sin2 eiE2t

)+ cos

sin (eiE2t eiE1t) .

t . W ()

W () =cos sin

(eiE2t eiE1t)

2 =sin 2

eiEti sin(Et

2

)2

=

=1

2sin2 2 [1 cos(Et)] = 1

2sin2 2

[1 cos

(El

v

)],

E = (E1+E2)/2, l , , v 1 .

W () 12sin2 2

1 cos m

212l

2E

= 1

2sin2 2

[1 cos 2 l

L

],

167

L 2E

=4E

|m22 m21| 4E

m212.

W (e) = 1 sin2 2 sin2 m212l

4E= 1 sin2 2 sin2

L.

. - 1957 ., . [25, 26], 19982002 . ( - -), , ( ) , , . [27, 28].

. - - K-, - . , , e . . , - N/Ne = 2. - , ( ), N/Ne > 2.

, . -, (N/Ne)DATA - (N/Ne)MC . , SuperKamiokande (SK, ) , - R = (N/Ne)DATA/(N/Ne)MC = 0, 63 0, 03stat 0, 04syst.

-, - , . -

168

20 . - 1000 . , - -, 13000 . , e-, e, , -, , - , , , .

, SK -, . - - -.

2005 . K2K (, ), 200 -, , , ( ), , , , , - .

, 12 , - SK, 250 .

107 , 151 . - - SK .

-, . , - sin2 223 = 1 ( 2 3) m223 = 2, 8 103 2. - , , .

, , - e .

169

(SNO), . SNO, - D2O, , -. , , e, e . SNO , - e. , - e () . - e :

m212 = 7, 1+1,20,6 105 2,

12 = 32, 5

+2,42,3 , sin2 212 = 0, 90 0, 04.

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

4.3.7

1975 . . (. [29]) , , - 1777, 00, 3 = (2911) 1015 . :

l + l + , h + ., l e , h K. - ,

j() = = (1 + 5) ,

170

, . -, , - .

, -- , 2/3 1/3, . top bottom t- b-. :true beauty .

1977 . . (. [30]) - - () (m 9, 4 , m 10 , m 10, 4 ) ( 60 ). , bb, .. . , 1995 ., - 20 b-, (- . . , ) - t- [31, 32],. [33]. , - , -, 174, 3 5, 1 [12], .

, , , - :

j = ee + + + du+ sc+ bt, (4.52)

d, s, b , - . d, s, b, () :

d

s

b

=

Vud Vus VubVcd Vcs VcbVtd Vts Vtb

d

sb

. (4.53)

171

Vik - (-), (, , 1973 . [34]) ( -) , , , ( ).

, d-, , :

d = Vudd+ Vuss+ Vubb.

: 0, 9739 Vud 0, 9751; 0, 221 Vus 0, 227; 0, 0029 Vub 0, 0045(CL=90%) [12]. , d- s, b, - |Vub|2 105. ( -):

|Vud|2 + |Vus|2 + |Vub|2 = 1. 2 |Vud|2 -

, ., , [13]:

1n = C|Vud|2(1 + 32)fR(1 + R), (4.54) ( . h = 1, c = 1) C = G2Fm5e/(23) = 1, 1613 104 1,fR = 1, 71482(15) , - , R = 0, 0240(8) , . , 32, - , - 1n G2V + 3G2A == GFV

2ud(1 + 3

2), GV = VudGF , , - , , - GA , - . 3.

172

. 4.6. Vud - , - .. 2004 . (, . ). - ( ) - . , PERKEOII ( )

173

. 4.6, , 23 . - - ( ), - |Vud| ( ), ( GF ). , |Vud|, - |Vud| =

1 |Vus|2 |Vub|2

( |Vub|2 , |Vud| ). |Vud|, - 0 0 ( , , ).

Particle Data Group (PDG) 2002[35] 2004 . [12] ( , -, , , -) , - . . 4.6 ( CL=90%) , - PDG 2004 . [12]. |Vud|, - , , , - , , .. 2002 , - - .

, , . , PERKEO-II . [13], , , . . 4.6 , - .

174

. , - , ( . 4.6). |Vud|, - - , -. . : , - -, , ( -, ). , , - CKM-. - , 7 .

, .. 2004 ., 6,5 . , - . . , n, |Vud|, (- ). , .

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

175

, , -.

4.3.8 ( )

- , . 1964 . [36], . [37].

- , , - P - , (sp) ( s p , ), , - ( ). ( ) , ,

fW =GFmnW

22

1 + (p)

mn

(h = c = 1),

W = (cpZ+cnN+ceZ) , Z , cp, cn ce - , , . - , , cn = 0 ce = 0. , f - ( )

f = fN + fW ,

fN . ,

f n:

n =

1 + 4k2

Nf 1 + 2k2

Nf.

176

, (p), , |+ | : n = n0 n/2, ,

n =2

k2N(f+ f) =

2GFWN

k

( p = k). , . z . |+ | - z,

z =

1 00 1

,

z| = |, ,

|+ = 10

; | =

01

.

ke ( z = 0)

|i = 12(|++ |) = 1

2

11

,

x =

0 11 0

,

.. x|i = |i. x. , x -

? |+ | - k = nke, , L -

|f = 12

(|+eiken+L + |eikenL) =

178

Bi209 N = 0, 3 1023 3. , , cp = 1, cn = 0, ce = 0, W 80 1, 4 106 /.

P - , , - - .

4.3.9

- - | |+. , , , , , - , - - , - .

= 4(a+

GFW

22

(mn k))2

4(a2 GFWk

2a

).

-, . ( ) GF :

+

=

2GFWk

a.

Pz , L,

Pz =N+ NN+ +N

12

(1 N

N+

), (4.57)

179

N k, - L.

N = N0eNL.

, - N0+ = N0, - L :

NN+

= eN(+)L eL 1 + L

,

- = 1/N, = (++)/2 = +. :

Pz =1

2 L

=NL

2=

12 L GFWk

a. (4.58)

A - L , - :

A =N+ NN+ +N

NL2

=2

kNL Im(f+ f). (4.59)

10 105 ( W 102, 4a2 1 ).

P - - 1980 . ( . [38]). , , :

(124Sn) = (0, 48 1, 49) 104 /,(117Sn) = (36, 7 2, 7) 104 /.

, , , (4.56), P - - (

180

). 1976 . [39], - p- - P - 124Sn. 5 104 / [39]. , - , , 117Sn [38], . . , ( p- -) .. .. [40], .. .. (. [41, 42].

, - , - -. -30 ( 30) p- 0,74 139La P - , 10% [43].

p- - : , , -, - . - [44], , P - 139La. [45]. , [44], . 4.7.

[40, 41] , p- - (n, ) - - - , P - .

, -

181

. 4.7. () p- 139La - () [44]: , . , -

. 1977 . .. (,) 233U, 235U 239Pu , . [46]., - , 104. -, , - .. [47] , .. - [48] .. [49] (, ), - . ,, (n, )-, - ( , - ), - -,

182

100 , , , -. , , ( 1010), , , - , .

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