Самарин В.В. Атомная и ядерная физика
Подождите немного. Документ загружается.
171
"
,
"
. & , -
"
%
,
"
" .
6 " -
"" 2 -
, ', -
$ 2" " (". 4.3, 4.4) -
$ . 1" $ " -
" ", $ " , -
"
, "" 2" (".
4.4).
& % " ,
− , " -
, , % , ""
". # " "" % 2" (". -
4.2). - "$. (
" " (". . 12.9),
" $ ". ) "$ , "
. & " -
$ ". # " %, %$
2$, $ % 2 " (". 4.6).
(% " $ 2
− ( " -
) (% , -
" ) , 2 ,
(". ).
& "$
" % -
" " .
172
2. +, &) !$,,2 $ &,&.
-
" """,
ρ
-
" 7="
r>R
(". 4.7), 2" "$ $ 2-
$ "
(
)
(
)
(
)
(
)
(
)
,
n p c
V r B r V r B r V r
= − ρ = − ρ +
, (11.1)
V
c
(r) – "
R
c
""" "
(
)
eZ 1
−
+
.
( )
( )
2
2
2
1
3
,
2
1
.
c
c c
c
c
Z e
r
r R
R R
V
Z e
r R
r
−
− ≤
=
−
>
(11.2)
( 5 (". 4.10) , 2-
"" 2 ,
" "" "
0
1 exp
c
r R
a
ρ
ρ =
−
+
, (11.3)
" ", ". " (7.8). '"
c
R
" " , "
-
% . 0 " (11.1), (11.3) -
2 $
&-0
( )
0
1 exp
n
n
n
n
V
V r
r R
a
= −
−
+
. (11.4)
'
2
%
2$
c
V
( ) ( )
0
1 exp
p
p c
n
n
V
V r V r
r R
a
= − +
−
+
. (11.5)
,
n p c
R R R
R
.
"
0 0
,
n p
V V
"
-
"
,
"
(11.2) - (11.5)
2""
"
.
#
"
173
,
"
"
.
(
,
"
0 0
,
n p
V V
40-50
2&
.
$
$%
2"
"
"
:
1 3
0 0 0 0 0
0
1 0.63 , 53
2&, , 1.28 ";
1 0.63 , , 0.65 ".
n n
p p c p n
N Z
V V V R R r A r
A
N Z
V V R R R a a a
A
−
= − = = = =
−
= + = = = = =
(11.6)
)
"
"
,
"
-
-
.
'2"
p
V
0
n
V
0
"
N Z
−
.
0
"
-
"
(11.4), (11.5)
2
,
-
"
-
"
""
,
"$%"
"
2""
-
"
"
-
"
(
"
.
4.3, 4.4).
(
"
"
"
2
"
.
&
"
2
"
"
(
2
"
,
-
)
-
"""
U(r).
0
-
"""
"
"
"
l (l=0,1,…)
"
"
"
n –
""
"
"
l (l=1,2,…),
2
(
)
lnEE
,
=
.
0
l=0,1,2,3,4,5,…
,
%
"
,
$
"
"
s, p, d, f, g, h,…
-
.
&
"
"
l
"
-
"
"
n
’
=n+l, n=1, 2,…
"
n
’
-
"
0
n
’
-1.
'"
"
:
"
"
n
’
=3: 3s, 3p, 3d;
"
"
l=0: 1s,
2s, 3s, …; c l=2: 3d, 4d, 5d,….
&
-
"
l
"
"
"
n=1, 2,…
"
n
-
"
$
-
1.
'"
"
"
...;
,
3
,
2
,
1
:
0
s
s
s
l
=
2: 3 , 4 , 5 , ...
l d d d
=
.
&"
"
−
-
"
"
−
"
, ,
x x y y z z
→ − → − → −
.
174
&
"
"
-
"
(+),
"
−
"
"
(−).
-
"
"
"
l
( 1)
l
π = −
,
.
.
-
s,d,g ….
,
p,f,h….
.
"
"
-
"$%
"
1 2
( 1)
l l
+ +
π = −
.
'
"
π
""
L
$
.
0
"
$
"
"
j
,
"$%"
1
1 2
j l
= +
2
1 2
j l
= −
.
&
$
2$
-
"
$
2
1
( )( 1) 2,
1 2,
( )
( ) 2,
1 2.
sl
j
sl
U r l j j l
V r
U r l j j l
+ = = −
=
− = = +
(11.7)
1
( ) 0
sl
dV
U r b
r dr
= ≥
,
0
b
>
. (11.8)
2
2 2
0 0
2 2 2
0
0,022
2
b x K x K
m x c
= =
, (11.9)
b
−
-
"
,
0
x
=
1
"
,
m
−
"
,
c
−
,
K
−
"
.
# "
6
2
( ) ( )
2
j
V r V r E
m
− ∆ψ + + ψ = ψ
. (11.10)
"
$
6
(
-
$%"
"
""
"
6
)
2
2
( ) ( ) ( ) 0
ef
m
y r E V r y r
′′
+ − =
, (11.11)
2"
"
,
$$%"
2
2
( 1)
( ) ( ) ( )
2
ef j
l l
V r V r V r
mr
+
= + +
. (11.12)
(11.11)
∗
,
"
2
( , , )
E n l j
,
%
, ,
n l j
-
( ) ( )
f r y r r
=
(
(0) 0
y
=
).
!
2
( , , )
E l n j
-
$
,
"
$
"
2
.
)
-
∗
" "
6 , ". ", [36] [41]
175
"
"
l
j=l+1/2
-
-
"
%
.
4
(
)
$
'
,
2
"
(
"
.
4.2-4.4).
0
$
"
"
j
m
j
z
,
"$%
2j+1
m
j
=j,j
−
1,…,
−
j+1,
−
j.
'2"
j
"
"
2j+1
-
.
'$
$%"
2"
$
"
,
"
4
3 2
1
p
,
2
1 2
1
p
.
)
"
-
$
2
"
.
0
""
j
j-j
,
-
"
"
(
"
.
4.3).
'
""
J
-
$
"
"
j
$
.
'
,
.
"
(
)
"
-
.
>
##% –
2
"
"
"""
-
$
"
,
"
2-3
2&
.
'2"
""
-
$
"
-
""
$
.
0
,
$%
$
"
"
"
“
”-
7
"""
$
,
"
2
.
4"
:
-
3
3 2
1
p
:
1
3 2
1
p
.
'
ρ
$
-
""
.
&
2"
"
7
$"
,
-
"
"
,
$%
$
"
"
2, 8, 20, 28, 50, 82, 126 (
).
>
,
"$%
(
)
,
""
,
$
$
$
"
.
>
-
"
,
"
""
,
"$
$
"
$
"$
(
. 11.1).
&
. 11.2
2
-
2"
(
[36]).
"
"
$
%
"
.
>
"
,
"
"
,
"$
-
.
-
-
"
"
2""
"
(
. 11.1, 11.2).
176
#
11.1
> Z N
# -
-
" -
)"-
-
#
-
" -
0
17
O 8 9
d
5/2
(5/2)
+
43
Se
21 22
f
7/2
(7/2)
−
209
Pb 82 127
g
9/2
(9/2)
+
209
Bi 83 126
h
9/2
(9/2)
−
4
23
Mg 12 11 (5/2)
+
(3/2)
+
(3/2)
+
#
11.2,
[36]
, (,
8
Z
=
, 0,
Z
=
20
, Ni,
Z
=
28
, Zr,
Z
=
40
A
E
, 2&
A
E
, 2&
A
E
, 2&
A
E
, 2&
13
−
17.008
35
−
16.782
51
−
15.721
82
−
13.401
14
−
23.175
36
−
18.949
52
−
19.285
83
−
10.341
15
−
13.
222
37
−
14.793
53
−
14.797
84
−
13.101
16
−
15.663
38
−
16.969
54
−
17.897
85
−
9.731
17
−
4.143
39
−
13.288
55
−
14.195
86
−
12.726
18
−
8.044
40
−
15.641
56
−
16.641
87
−
9.614
19
−
3.955
41
−
8.362
57
−
10.246
88
−
12.347
20
−
7.608
42
−
11.48
58
−
12.218
89
−
9.316
21
−
3.806
43
−
7.932
59
−
8.999
90
−
11.969
22
−
6.849
44
−
11.131
60
−
11.388
91
−
7.194
23
−
2.735
45
−
7.414
61
−
7.82
92
−
8.634
24
−
3.721
46
−
10.393
62
−
10.597
93
−
6.734
47
−
7.276
63
−
6.837
94
−
8.22
48
−
9.946
64
−
9.658
49
−
5.146
65
−
6.098
50
−
6.
352
66
−
8.977
51
−
4.386
67
−
5.784
52
−
4.694
68
−
7.815
53
−
3.461
69
−
4.965
54
−
3.761
70
−
7.181
55
−
2.601
71
−
4.471
56
−
3.191
72
−
6.861
177
4
%
(
"
"
"
,
"
.
4.6)
$
$
"
.
#
"$
"
.
.
1.
-
2"
. 11.2 (
$
-
)
"
2
( )
E f A
=
.
!
"
2
.
3. &,* +)2 /( +$) ) &,&. . ) -
$&,&. $. '6$%2 /(
-
6
""
Shell_model
∗
,
$%
−
"
Z, A, r
0
, a, V
0
,
K,
input.txt (
. 11.1).
. 11.1. '"
16
(,
40
0
208
Pb,
: " "
Z
, "
,
, "
0
r
, $%
, "
a
(")
0
V
(2&) &-0,
"
K
- ",
$
: elev.txt
result.txt (
"
.
. 11.2)
$
"
2
"
(
"
.
. 11.3).
&
elev.txt
(
,
"
2
"
)
-
, ,
n l j
2
2 (
. 11.2).
&
result.txt
,
"
,
2
E
"
"
n
(
. 11.2).
∗
# "" 0++ [13]. 4 " ,- *-
> (7 , > , (. - -
.) http://nrv.jinr.ru/nrv/webnrv/map/ Shell model "
2 " .
178
4
2
"
"
(
"
,
"
,
"
,
"
)
"
"
(11.4)
(
"
.
. 11.3)
(11.5)
.
1
"
"
-
"
,
−
-
"
.
&
2
( )
f r
(
"
.
. 11.3).
1
-
-
$
"
"%$
"
"$
-
""
(
"
.
. 11.3
):
Edit-Select all (
-
&
),
"
Edit-Copy.
,
"
"
(
"
, Paint)
(Word, OpenOffice.org
Writer).
0
"%$
2
""
$%
:
1.
-
,
. 11.1
/
11.2
$
,
"
(
.
11.1,
"
– 0).
0
"
shell_model.exe
.
1
$
2
(
"
.
. 11.3),
$
(
"
, Paint).
0
"
-
. 11.2. '"
elev.txt (
) result.txt (
)
16
(.
& elev.txt
, ,
n l j
2
2
,
result.txt
2
E
" "
n
179
"
elev.txt (
"
.
. 11.2)
-
.
. 11.3. '"
2 " "
" (11.4)
(
)
" 2 "
( )
f r
(
)
16
(.
1 "
" ",
− ".
180
2.
&
"
'
"
"
result.txt (
"
.
. 11.2)
"
"
"
-
"
.
0
"
-
"
.
3.
(
2
"
-
.
(
,
-
"
. 11.1.
4.
,"
(
"
10%)
"
0
r
,
$%
-
"
.
'
""
"
"
.
&
"
-
"
"
(
"
. 2.9,
. 38)
"
""
.
0
–
"
-
"
.
1
2
""
-
"
"
.
. 11.4
0
2
(
"
)
5.
,"
(
"
20%)
"
0
V
,
$%
-
"
.
'
""
"
"
.
&
"
-
"
"
"
""
.
0
–
"
"
.
1
2
""
"
"
.
6.
,"
(
"
50%)
"
K
,
$%
-
-
"
"
.
'
-
""
(
"
"
)
$
"
.
&
"