Квантовая теория двойного и тройного деления атомных ядер. Кадменский С.Г - 30 стр.

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30
ɜɨɥɧɨɜɭɸ ɮɭɧɤɰɢɸ
J
M
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V
< ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɜ ɜɢɞɟ (8) ɩɨ ɚɧɚɥɨɝɢɢ ɫ
ɞɜɨɣɧɵɦ ɞɟɥɟɧɢɟɦ.
Ⱦɥɹ ɨɩɢɫɚɧɢɹ ɨɬɧɨɫɢɬɟɥɶɧɨɝɨ ɞɜɢɠɟɧɢɹ ɩɪɨɞɭɤɬɨɜ ɞɟɥɟɧɢɹ
i
A
,
i
Z
,
ɝɞɟ 1, 2, 3i , ɜɜɨɞɹɬɫɹ ɨɬɧɨɫɢɬɟɥɶɧɵɟ ɪɚɞɢɭɫɵ-ɜɟɤɬɨɪɵ
12
RR Rɢ


11 2 2
3
12
AA
AA
RR
rR
, ɝɞɟ
1
R ,
2
R ,
3
R – ɤɨɨɪɞɢɧɚɬɵ ɰɟɧɬɪɨɜ ɬɹɠɟɫɬɢ
ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɮɪɚɝɦɟɧɬɨɜ, ɬɟɥɟɫɧɵɟ ɭɝɥɵ
:
R
ɢ
:
r
ɨɩɪɟɞɟɥɹɸɬ
ɧɚɩɪɚɜɥɟɧɢɹ ɪɚɞɢɭɫɨɜ-ɜɟɤɬɨɪɨɜ
R
ɢ
r
ɜɥ. ɫ.. ɗɧɟɪɝɢɹ ɨɬɧɨɫɢɬɟɥɶɧɨɝɨ
ɞɜɢɠɟɧɢɹ
c
Q ɩɪɨɞɭɤɬɨɜ ɬɪɨɣɧɨɝɨ ɞɟɥɟɧɢɹ ɜ ɤɚɧɚɥɟ c ɨɩɪɟɞɟɥɹɟɬɫɹ
ɫɨɨɬɧɨɲɟɧɢɟɦ
3
11 2 2
3
J
cK K K
QE E E E
VV V
V
, ɝɞɟ
K
E
V
,
11
K
E
V
,
22
K
E
V
ɢ
3
3
J
E
V
– ɷɧɟɪɝɢɢ ɫɨɫɬɨɹɧɢɣ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ, ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ ɢ ɬɪɟɬɶɟɣ
ɱɚɫɬɢɰɵ.
Ɋɚɞɢɚɥɶɧɚɹ ɪɟɝɭɥɹɪɧɚɹ ɜɨɥɧɨɜɚɹ ɮɭɧɤɰɢɹ
,
Ll
R
r
\
, ɨɩɢɫɵɜɚɸɳɚɹ
ɞɜɢɠɟɧɢɟ ɩɪɨɞɭɤɬɨɜ ɞɟɥɟɧɢɹ ɜ ɚɫɢɦɩɬɨɬɢɱɟɫɤɨɣ ɨɛɥɚɫɬɢ, ɝɞɟ ɦɨɠɧɨ
ɩɪɟɧɟɛɪɟɱɶ ɩɨɬɟɧɰɢɚɥɨɦ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɩɪɨɞɭɤɬɨɜ ɞɟɥɟɧɢɹ,
ɭɞɨɜɥɟɬɜɨɪɹɟɬ ɭɪɚɜɧɟɧɢɸ ɒɪɟɞɢɧɝɟɪɚ:
 
@

22
22
22
2222
11
11
22
22
,0,
ab
ab
cLl
LL ll
dd dd
Rr
MdRdRMdrdr
RrMRMr
QRr
\
ª

§· §·

«
¨¸ ¨¸
©¹ ©¹
«
¬
==
==
(39)
ɝɞɟ
12
12
aa
A
A
MmAm
A
A
,
3
3
a
b
a
A
A
Mm
A
A
– ɩɪɢɜɟɞɟɧɧɵɟ ɦɚɫɫɵ
ɩɪɨɞɭɤɬɨɜ; m – ɦɚɫɫɚ ɧɭɤɥɨɧɚ,
L
– ɨɬɧɨɫɢɬɟɥɶɧɵɣ ɨɪɛɢɬɚɥɶɧɵɣ ɦɨɦɟɧɬ
ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ, l – ɨɬɧɨɫɢɬɟɥɶɧɵɣ ɨɪɛɢɬɚɥɶɧɵɣ ɦɨɦɟɧɬ ɬɪɟɬɶɟɣ
ɱɚɫɬɢɰɵ.
Ɉɬ ɤɨɨɪɞɢɧɚɬ
R
ɢ
r
ɦɨɠɧɨ ɩɟɪɟɣɬɢ ɤ ɧɨɜɵɦ ɝɢɩɟɪɫɮɟɪɢɱɟɫɤɢɦ
ɤɨɨɪɞɢɧɚɬɚɦ
U
ɢ
H
:
sin ; cos
ɫɫ
ab
MM
Rr
MM
U
HUH
, (40)
ɝɞɟ ɭɝɨɥ
H
ɦɟɧɹɟɬɫɹ ɜ ɢɧɬɟɪɜɚɥɟ 0
2
S
H
dd ,
ɫ ab
MMM . ɉɪɢ ɷɬɨɦ
ɮɚɡɨɜɵɣ ɨɛɴɟɦ ɩɪɟɨɛɪɚɡɭɟɬɫɹ ɤɚɤ
22 52 2
=sincos .
R
dR r dr d d
U
HHUH
(41)
ȼ ɧɨɜɵɯ ɤɨɨɪɞɢɧɚɬɚɯ ɭɪɚɜɧɟɧɢɟ
(39) ɩɪɢɧɢɦɚɟɬ ɜɢɞ
ɜɨɥɧɨɜɭɸ ɮɭɧɤɰɢɸ

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