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1
:
. .
2010
7/25/2019 Pyrinikes Antidraseis 7ou. Blackboard
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2
1.1.
( )
( ).
.
: ) (
), ) , )
.
. ) ,
)
) .
.
)
.
: )
, ddE
d 2.
d/dE. )
,
.
Pin Pout.
. , ,
.
: )
) ,
7/25/2019 Pyrinikes Antidraseis 7ou. Blackboard
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3
, ,
.
, )
, linc
.
.
1.2
.
, . .
, ,
( ) ().
.
()
- (
L.S). To .
. .
( ).
.
, ( ).
.
,
, . :
+ + (1.1)
C, :
+ C + (1.2)
( )
7/25/2019 Pyrinikes Antidraseis 7ou. Blackboard
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4
.
(, )
. .
, ,
, .
.
. ,
, .
1.1 . .
,
. , , .
, ,
1, 1.1.
1 .
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5
TPP MM = )( (!.3)
:
PTp
p
MM
M
+= (1.4)
, CMV ,
.
. :
LABTMPM
PMPP
TMPMPM
CMTPCM EMVMME ++ ==+= 2
212
21 )( (1.5)
LABE . cmE
(
) :
CMcmLAB EEE += (1.6)
:
2
21
cmLABTMPM
TMcm EE == + (1.7)
:
TMPMTMPM
+= (1.8)
, cm , P .
r, )(rV ,
:
)(rVEE cm= (1.9)
( ) b ,
,
( 1.2) .
:
bLcm
= prL = (1.10)
h .
b
. :
kbL ==h
l (1.11)
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6
( fmMeVc .327,197=h ). l
, , h , :
2
2
hh
cmEcm == (1.12)
.
1.2 .
1.3
.
.
inN 1.3.
dx, ndx,
n .
1.3 . .
:
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8
d
d
, .
1.4 .
.
-. :
)(nSxS
NxnNin = (1.19)
S . (S
inN
)
.
-, 1.2.
:
R2= (10)
2fm
2= 10
-28m
2= 10
-24cm
2
barn. H
barns/steradian (b/sr).
b. b Coulomb
. ( )
. ,
, , .
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9
b,
:
2
0
2 A
Ab
A bbdb == (1.19)
,
l. l,
b = l/ b =
(l+1)/. :
2
)12(22
2])1[(
kk
+=+ lll (1.20)
(1.19) :
2
20
2)1()12( +=+= A
k
A
kA ll
l (1.21)
l :
AAA kbkb = 1l (1.22)
1.4
.
( ).
dx .
dxEn )( n ( )
)(E . To )(E ,
. :
dxEInxdI )()( = (1.23)
:
xeoIxANeoI
xEneoIxI === /)()()( (1.24)
x=0 =Io, = /)(E , x
. :
== eIeIxI oxAN
o
/)()( (1.25)
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10
=x / (
gr/cm2).
2
:
)(1
=
n
(1.26)
:
/)(
xoeIxI
= (1.27)
()
, ,
. :
)()()()( EEEE rinel ++= (1.28)
, .
Coulomb .
()
, .
, (1.24) (1.25).
.
. .
2x xxddNNxxxx++ddxx..
:: ==
oN
oNoN
dN
oN
xdN
xdNx
0
1
0
0
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11
2.
2.1 :
.
.
Coulomb
.
.
. ,
8.7 MeV 60
, 2.1.
. , 4
4, .
=28.
.
= 20, 28, 50, 82, 126
.
2. 1 . 4.
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12
-
.
.
. Coulomb ( )
()
=. (
) , .
() , , .
-
.
(,) ( 2) ,
= ,
.
Coulomb,
.
2. 2 , .
.
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13
. - >206.
(,) Segre
,
.
2. 3.
2.3 . .
- , ,
2.4. ,
(2.4). , ,
, , (2.4). -
- -
. - - ,
, .
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14
Coulomb
.
.
,
( )
. .
2.4 =135 =102.
2. 2
,
MeV Coulomb
( ).
Coulomb
,
. 6-8 MeV
. ,
( 2.5).
- .
.
Coulomb
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15
2.5 . 1.
. 2. .
3. .
.
. , (n,).
1/.
2.6.
,
(n,). 1
.
-.
,
14
(n,p)14
C, 14
C.
,
( ).
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16
2. 6 (=69). 1/
.
15
,
. .
27Al(p,)
28Si.
( ).
1. (n,)
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17
2. 3
,
.
, .
. .
.
2.7
206
Pb .
(
).
Coulomb
3 ( ).
.
2.7. (p,xn) 206
Pb .
3 ,
.
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19
2.4
. , ,
. .
.
.
.
.
,
2.8.
. ,
( )
.
32S(n,p)
32P
7Li(p,n)
7Be
. 32
,
, ..
in vivo
.
, 7Li(p,n)
7Be,
.
9Be
9Be(d,n)
10B. (stripping)
( )
.
2.9
12C(p,pn)
11C.
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21
2. 10 2/.
.
, 2.11, 1
MeV.
.
.
, 0,025 eV
.
. .
( 2.1)
1 MeV/ 190 MeV
. 170 MeV .
.
(80% 20% ).
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22
2.11 . ) ) .
( 2.2)
-.
.
, ,
.
.
.
(
).
,
92
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23
2.6 .
.
50 MeV
.
.
, (> 150 MeV)
, .
, ,
.
70 MeV 38
Cl.
. , ,
(8Li) .
, 500 MeV (),
, .
. 2.11
. 1 GeV
. .
.
.
.
.
, 12
C
16
O . Coulomb
Rytherford. Coulomb.
.
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25
2.12
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26
3.
3.1
. Coulomb - - .
Coulomb .
,
,
. , ,
.
,
, .
.
2.2.
,
.
,
.
MeV,
.
3.2
,
.
,
:
112211 mmm +=
211
222
211 mmm +=
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27
3.1 , .
:
( )21A1A
+=
. ,
,
.
.
, ( )
:
( )21A
12A
2
EE EE+
++ ==
.
(dE/dx).
, ( ).
(
)
,
.
1-2 MeV. :
( )kTE
2kT
E econst)E(N
=
.
.
. 10 MeV
7/25/2019 Pyrinikes Antidraseis 7ou. Blackboard
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28
10 s,
100 s.
.
3.3
,
.
- .
. 14
(n,)15
10.8 MeV, (n,)D 2.3 MeV .
( 2.2)
.
, 10
(n,)7Li,
11
7Li.
, 1 mbarn 103-10
4barn Cd
(2550 barn Cd) (46000 barn).
1-10 barns.
1/, Breit-
Wigner.
:
( ) 4/22 +
. Breit-Wigner,
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29
.
, -=/2.
R2, R .
D ( D== 2ph ).
:
( )2R+= D R>>D 2D=
,
:
24 D=
22D . :
( )4
22
22
+
= D
/
, :
( )4
22
o
2+
= D
Breit-Wigner
.
(>>)
2
. :
h~
: 2D ( )
2
mh
1
1/ (n,)
.
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30
3.4
, .
,
. , .
,
,
( ).
3.5 ,
,
2/ ( ) ( 2.5).
,
.
, ,
. .
Coulomb,
.
200 MeV.
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32
4.
4.1 Fermi
, .
6
Fermi.
( ) Pauli.
, Pauli,
( Fermi).
.
.
, Fermi,
.
,
.
,
, 4.1
c Coulomb:
Re
C ZZE2
)1(5
3=
Ec.
,
. .. ,
. ,
.
, .
,
Pauli.
6 , , (..
). ,
, Fermi-Dirac.
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4.1 .
, ,
,
. ,
Fermi, EF, EF,n EF,p.
:
2md8
2h2nnE = ......3,2,1n= (4.1)
m d .
d3 :
)nnn(E 2322
212
md8
2h3n2n1n
++= (4.2)
: ......3,2,1n1=
......3,2,1n2=
......3,2,1n3=
, .
(n1, n2, n3) = (1,1,1)
, :
(2,1,1) (1,2,1) (1,1,2)
. :
(1,2,6), (1,6,2), (2,6,1) (2,1,6) (6,1,2) (6,2,1) (3,4,4) (4,3,4) (4,4,3)
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.
EF EF
F. (n1, n2, n3)
:
2h
2dFmE823
22
21 nnn ++ (4.3)
:
2h
2dFmE82R = (4.4)
(4.3) :
223
22
21 Rnnn ++ ((44..55))
n1, n2, n3 , R
. (n1, n2, n3)
. ,
, .
(n1, n2, n3) 4.3;
R; n1, n2,
n3 1/8 . :
23
2h
2dFmE8
6
3
3
4
8
1 )(R = (4.6)
.
. Pauli d3 :
23
2h
2dn,FEnm8
3)(N = (4.7)
:
ArR3
4d 3o3
43o
3 =
= (4.8)
ro , ro= 1,2 fm.
, Fermi, EF,n,
:
32
AN3
2
A4N9
2ornm2
2
n,F ).()(E == h (4.9)
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35
:
32
AZ3
2
A4Z9
2orpm2
2
p,F ).()(E == h (4.10)
EF, PF,n,p :
m2
2F
P
FE = (4.11)
= = /2 :
EF= 32 MeV
8 MeV ,
4.2 :
Vo= EF+ EB= 40 MeV
:
)(Em2
2F
p
53
Fp0
p3d
Fp0
p3Ed=
= (4.12)
20 MeV.
4.2 Fermi. , Vo, .
:
==+=+= + )()()ZpNp(m10
3EZENN,Z(E
32
A
35
Z35
N32
49
2or
2
1032
Z2nZN
h
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37
ER,
:
iMimim
R EE += (4.17)
.
7.
* :
LMimM
i*
E)(EE +=+
(4.18)
L i .
.
Fermi.
Bethe Weisskopf.
, .
EF *
:
TTE 2
FE4N2* = (4.19)
. - :
TaTE
2*
= (4.20) :
)())((aFEA
4
2
p,FEZ
n,FEZA
4
2 =+= (4.21)
F .
:
2*aTE = (4.22)
:
a
*ET= (4.23)
:
7 115In
235, 238U.
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4.4. .
.
4.2
.
: 20, 28, 50, 82 126. 2 ( ) 8 (
16) l=
0 l= 1.
,
.
.
Schrodinger
,
V(r) r .
:
0)rR(Mr2
)1()r(VE
2
2
2M2
2dr
)rR(2d =
++
hll
h
(4.28)
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40
lh , R ,
.
:
2
2
r2
)1()r(VV hll ++=
(4.29)
nl
V.
n
l(n-1). To l
(-1)l. s, p, d, f. O (2l+1)
l .
V(r) Coulomb
, . Coulomb
.
.
22rm2
1U)r(V += (4.30)
m .
,
:
+= h)n(E21
n ((44..3311))
:
+++= h)nnn(E23
3213n2n1n (4.32)
= n1 + n2 + n3 ( 0) .
. ,
n l.
:
= 2n l 2 (4.33)
l = 2
l= 0 n = 2 ( s) l= 2 n = 3 ( d) .
, .. ,
(+1) (+2)
n, l, m
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41
Pauli.
, :
2, 8, 20, 40, 70, 112
,
Woods-Saxon.
, :
[ ]a
)Rr(o
exp1
V)r(V
+= ((44..3344))
Fermi.
,
4.5 -.
( 4.6).
,
J .
r r2
4.5. fm3 .
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42
4.6 - . Woods-Saxon.
l.s .
.
:
MeVA40 31
h (4.35)
1949 Mayer Haxel, Jensen
Suess. ,
- .
, . Vso
. :
Vso(r) = Vls( r).l.s (4.36)
l s
h. l s s=1/2
( 6) :
21J = l (4.37)
:
32
)21()
21(
A)12(10EE
+ += l
ll (4.38)
J
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43
l.
4.6.
. 4.7
, Woods-Saxon.
-. J, RJ +1
, Pauli, mj J
+J. ,
4.7,
2, 8, 20, 28, 50, 82, 126.
4.7. Woods-Saxon
ls.
.
Pb20882 ,
, (
)
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44
. Pb20882
Pb20882 .
J = 0.
J. .
:
)
.
.
) .
, J =
0. J . (.
) J = 0.
J (
).
, . 17
1d5/2, J=5/2 (-1)l= (-1)
2= + .
, .
(. p-p n-n)
Jl, ml.
0+.
)
-
. - ( )
(
0) ( ).
,
. L ,
, 2.7927 -1.9155 .
L -
:
J = L + S
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45
: J = L 1/2
S :
= gsS
gs= -3.826 + 5.586 .
=== 18pm2eN T.eV10.1525.3h
124 gauss.ergs10.05.5
:
= gLL
gL= 0 .
H J ( S L )
J.
Z.
J Z
. S L
J S L J .
4.8.
4.8 .
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