Мартыненко Т.П. и др. Практический курс физики. Квантовая физика. Элементы физики твёрдого тела и ядерной физики
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161
, :
[
]
np
2
mm·)ZA(m·Z·E --+= . (5.6)
,
, , :
[
]
[
]
mm·)ZA(m·Z·5,931E
nH
--
+
=
(5.6 )
( . . .).
,
. :
A
c·m
A
E
E
2
.
∆
==
. (5.7)
.
. 5.1
.
,
50 60.
8,75 / .
7,5
/ .
:
1)
( ).
2) -
( ).
,
,
10
-15
, ,
.
.
0 50
100
150 200 250
A
[ ]
.
8
6
4
2
. 5.1
162
.
1. – .
:
- , -n, n-n .
2. .
.
3. – .
4. . ,
( )
1
D
2
, .
5. .
– .
1935
. 1947
. - :
+
(+ , m
+
= 273m ,
+
= 10
–8
, S = 0),
-
(- , m
-
= 273m ,
-
= 2,55·10
–8
, S = 0),
0
(0, m
0
= 264m ,
0
= 2,1·10
–16
, S = 0).
,
–
. ,
– ,
E
t
∆
≥∆
. ,
m
π
, ,
, R,
∆t ( ):
.
·cm
·cm
c·
E
c
t·cR
2
π
π
π
==
∆
⋅
=∆=
(5.8)
,
R ≅ 1,5⋅10
–15
.
.
.
.
, , γ - .
163
,eNN
t
0
λ−
⋅=
(5.9)
N - t, N
0
–
, –
,
.
N(t) . 5.2.
– ,
.
: .
T
2ln
=λ
τ, :
.
1
λ
=τ (5.10a)
, ∆t,
:
).e1(NNN
t
00
λ−
= --
(5.11)
∆t
,
:
t··NNNN
00
∆
λ
=
∆
=
-
, (5.12)
∆N – , ∆t. N,
t, m:
,N
M
m
=N
A
N
A
– , – .
A. N – ,
, :
.
dt
dN
A −=
(5.13)
, A
, ,
dt
dN
N
N
0
2
N
0
2/1
T
. 5.2
t
164
. " " ( ):
1 = 1 = 3,7·10
10
/ , " ” ( ):
1 = 3,7·10
7
.
a :
.
m
A
=a
(5.14)
: - , -
γ - .
, , , .
- - ,
(
2
H
4
)
2
4
.
- ,
> 200. , 200 ,
,
. - ,
. -
,YX
4
2
4A
2Z
A
Z
α+→
−
−
α
(5.15)
A
Z
X
– ,
4A
2Z
Y
−
−
– . -
( ).
- –
.
- :
(
–1
0
), (
+1
0
)
- ,
- .
-
0
0
ν
,
~
0
0
ν
, , /2.
:
.enp
,
~
epn
0
0
0
1
1
0
1
1
0
0
0
1
1
1
1
0
ν++→
ν++→
+
−
(5.16)
:
165
.eYX
,
~
eYX
0
0
0
1
A
1Z
e
A
Z
0
0
0
1
A
1Z
e
A
Z
ν++→
ν++→
+−
+
−+
−
(5.16a)
- .
,
. -
. -
( . 5.3).
. 5.3
-
,
:
,nep
0
0
1
0
0
1
1
1
ν+→+
−
.YeX
0
0
A
1Z
0
1
A
Z
ν+→+
−+
(5.17)
A
1Z
Y
−
, - ,
.
, γ - ,
. ,
, γ - .
γ-
ν 10
19
,
. , ,
. γ - ,
, ( . . ).
,eJJ
x
0
⋅−
⋅=
(5.18)
dN
dE
E
E
max
166
J
0
– , J –
, – ,
– .
.
.
r 10
–13
,
.
, a
Y b:
X + a → Y + b. (5.19)
:
X(a,b)Y. (5.19a)
,
b.
b :
0
n
1
,
1
1
,
1
d
2
, -
2
4
,
0
γ
0
.
:
1. : Z
1
+ Z
2
= Z
3
+ Z
4
.
2. :
1
+ A
2
= A
3
+
4
.
3.
1
+
2
= E
3
+
4
,
,cmTcmcp
2
0
42
0
22
+=+=
– , T – , m
0
c
2
–
, .
4. :
.pppp
4321
+=+
5. .
,
.
. :
),mm(cE
ki
2
Σ−Σ=∆
(5.20)
167
Σm
i
– , ; Σm
k
–
, , = 3⋅10
8
/ –
.
Q:
2
c·mEQ
∆
=
∆
=
,· (5.20 )
∆m =Σm
i
– Σm
k
. ∆m > 0,
, ∆m < 0,
.
,
, ,
, .
:
,Q
m
mm
E
X
Xa
+
=
(5.21)
m – , m
X
– X, |Q| –
.
:
)TT()TT(Q
YbXa
+
−
+
=
, (5.22)
T
X
– , ; T
b
T
Y
– , .
,
:
,
, ,
.
b Y. :
b
+
Y
*
a
+
X
(5.23)
,
:
b
+
Y
a
+
X
,
.
5.1.
42
90
?
42
90
42
95
?
42
95
.
42
95
.
42
95
94,9769 . . .
42
90
– Z = 42,
48
=
Z
A
=
N
-
168
42
90
42
95
Z = 42 : 48 53 .
(5.4):
∆m = [42·1,0072765+53·1,0086650-94,9769] = 0,7879 . . .=1,30846⋅10
–27
.
(5.5):
E = ∆m·c
2
= 1,30846 ·10
–27
·9 ·10
16
= 11,7761 ·10
–11
= 733,93 .
(5.7):
./726,7
95
93,733
.
===
5.2.
7
N
15
m = 0,12396 . . .
.
(5.4):
np
mm·)ZA(m·Zm
−
−
+
=
∆
(1)
,
Z ,
, :
],mm)ZA(mZ[m
n
H
1
1
−
⋅
−
+
⋅
=
∆
(2)
1
1
– , m – .
(2) :
],mm)ZA(mZ[m
n
H
1
1
−⋅−+⋅=∆
, .,..00783,1m
1
1
=
m
n
= 1,00867 . . .,
: m
= 7⋅1,00783 +8⋅1,00867 – 0,12396 = 15,000 . . .
5.3. R = 1,3·A
1/3
, –
, ,
.
:
V
m
=ρ , m – , m = ⋅1,66⋅10
–27
;
V – ,
3
R
3
4
V π= .
./102
][)10(A)3,1(14,34
][31066,1A
R3/4
m
317
33153
27
3
⋅≅
⋅⋅
⋅⋅⋅
=
π
=ρ
−
−
169
,
.
3
R
3
4
π
.102,1
][)10(A)3,1(14,34
A3
R3/4
A
n
344
331533
−
−
⋅≅
⋅⋅
=
π
=
5.4. π - ,
R = 1,5 . π-
?
,
(5.8) π- :
.10233,0
/103105,1
1005,1
Rc
m
27
815
34
−
−
−
π
⋅=
⋅⋅⋅
⋅⋅
==
m
e
= 9,1⋅10
–31
.
.260
101,9
10233,0
m
m
31
27
e
≅
⋅
⋅
=
−
−
π
m
π
= 260m
e
.
5.5.
92
U
238
?
.
= 238.
,
Z = 92 .
m
= 238·1,66·10
–27
.
m = 92·9,11⋅10
–31
.
%.02,0%100
1066,1238
1011,992
m
m
27
31
=⋅
⋅⋅
⋅⋅
=
−
−
,
0,02 % .
170
5.6. σ
1
/σ
2
83
i
209
13
l
27
.
r,
( ) :
σ = π·r
2
. (1)
,
( ) (5.1), (1)
:
.Ar
3/22
0
π=σ (2)
3/2
1
2
01
Arπ=σ , –
3/2
2
2
02
Arπ=σ . , :
.
3/2
2
1
2
1
=
σ
σ
1
= 209
2
= 27, :
.91,3
27
209
3/2
2
1
≅=
σ
σ
5.7.
N
0
1
,
N
2
( )
2
. ,
, N
2
= 0.
(5.9)
.eNN
t
01
1
⋅λ−
⋅=
dt
dt
N
dN
⋅
⋅
λ
−
=
,
N
dt
dN
λ−=
– .
:
,NN
dt
dN
2211
2
⋅λ−⋅λ−=
.NeN
dt
dN
22
t
01
2
1
⋅λ−⋅⋅λ=
⋅λ−