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Nuclear Physics
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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 ().
, - ()
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