Квантовая теория двойного и тройного деления атомных ядер. Кадменский С.Г - 42 стр.

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42
ɫɩɢɧɨɜɨɣ ɦɚɬɪɢɰɵ ɩɥɨɬɧɨɫɬɢ ɹɞɪɚ, ɫɨɜɩɚɞɚɸɳɢɦ ɫɨ ɫɩɢɧɨɜɨɣ ɦɚɬɪɢɰɟɣ
ɩɥɨɬɧɨɫɬɢ ɹɞɪɚ ɞɥɹ ɧɟɩɨɥɹɪɢɡɨɜɚɧɧɵɯ ɧɟɣɬɪɨɧɨɜ, ɢ ɩɪɢɧɢɦɚɟɬ ɜɢɞ [14]:




'' ' '
'
3
0
2
'
'
'
2
'
4
,,
21
1
,,
22 1
sss s s ss
s
s
ss s s s
ss s
n
JJJ J J sJsJ
J
s
sqKc
s
K K sqK s qK qK
ss J J qK c
n
d
B
ddd
k
J
aab b h h f
I
k
SS
VS
H
H
TH
::{
::
{*
¦¦
Rr
Rr
rR
(69)
Ɇɟɬɨɞɵ ɤɜɚɧɬɨɜɨɣ ɬɟɨɪɢɢ ɞɟɥɟɧɢɹ ɞɚɥɢ ɜɨɡɦɨɠɧɨɫɬɶ ɨɛɴɹɫɧɢɬɶ
ɩɪɢɪɨɞɭ Ɍ-ɧɟɱɟɬɧɨɣ ɚɫɢɦɦɟɬɪɢɢ ɩɪɢ ɭɱɟɬɟ Ʉɨɪɢɨɥɢɫɨɜɚ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ
ɨɪɛɢɬɚɥɶɧɨɝɨ ɦɨɦɟɧɬɚ l ɬɪɟɬɶɟɣ ɱɚɫɬɢɰɵ ɫɨ ɫɩɢɧɨɦ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ.
Ƚɚɦɢɥɶɬɨɧɢɚɧ Ʉɨɪɢɨɥɢɫɨɜɚ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ
l
Cor
H ɞɥɹ ɫɥɭɱɚɹ
D
-
ɱɚɫɬɢɰɵ ɢɦɟɟɬ ɜɢɞ:

2
Cor
0
ˆ
2
H
Jl Jl
J
 
=
, (70)
ɝɞɟ ɨɩɟɪɚɬɨɪɵ J
r
ɢ l
r
ɨɩɪɟɞɟɥɹɸɬɫɹ ɤɚɤ
'' ''
, ,
x
yxy
JJiJ llil
rr
r r
(71)
ɩɪɢɱɟɦ
'
x
J ,
'y
J ɩɪɨɟɤɰɢɢ ɨɩɟɪɚɬɨɪɚ ɫɩɢɧɚ J ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ ɧɚ ɨɫɢ '
x
ɢ 'y ɜ. ɫ., ɚɢ
'
x
l ,
'y
l ɩɪɨɟɤɰɢɢ ɨɩɟɪɚɬɨɪɚ ɨɪɛɢɬɚɥɶɧɨɝɨ ɦɨɦɟɧɬɚ ɬɪɟɬɶɟɣ
ɱɚɫɬɢɰɵ ɨɫɢ '
x
ɢ 'y ɜ. ɫ. Ⱦɟɣɫɬɜɢɟ ɨɩɟɪɚɬɨɪɨɜ (71) ɧɚ ɮɭɧɤɰɢɸ

J
MK
D
Z
ɢ
ɲɚɪɨɜɭɸ ɮɭɧɤɰɢɸ
'
l
lK
Y :
r
ɨɩɢɫɵɜɚɟɬɫɹ ɮɨɪɦɭɥɚɦɢ
 
12
1
1;
JJ
MK MK
JD J K J K D
ZZ
r
r ªº
¬¼
B
B (72)




12
''
1
1
l
l
lK l l
lK
lY l K l K Y
r
r
ªº
: r :
¬¼
rr
B . (73)
ɉɨɷɬɨɦɭ ɞɟɣɫɬɜɢɟ ɨɩɟɪɚɬɨɪɚ
Cor
ˆ
H ɧɚ
(70) ɧɚ ɜɨɥɧɨɜɭɸ ɮɭɧɤɰɢɸ
s
s
J
M
qK
S
<
ɦɨɞɵ ɞɟɥɟɧɢɹ q ɫɭɳɟɫɬɜɟɧɧɨ ɢɡɦɟɧɹɟɬ ɫɬɪɭɤɬɭɪɭ ɷɬɨɣ ɜɨɥɧɨɜɨɣ ɮɭɧɤɰɢɢ.
ȼ ɧɟɣ ɢɫɱɟɡɚɟɬ ɜɟɞɭɳɢɣ ɱɥɟɧ ɫ 0l
, ɚ ɨɫɧɨɜɧɭɸ ɪɨɥɶ ɧɚɱɢɧɚɸɬ ɢɝɪɚɬɶ
ɱɥɟɧɵ ɫ 0l
z . Ⱦɥɹ ɩɨɥɭɱɟɧɢɹ ɚɦɩɥɢɬɭɞɵ ɩɚɪɰɢɚɥɶɧɨɣ ɞɟɥɢɬɟɥɶɧɨɣ
ɲɢɪɢɧɵ
Cor
s
s
J
qK
S
D
§·
*
¨¸
©¹
ɩɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ Ʉɨɪɢɨɥɢɫɨɜɚ ɝɚɦɢɥɶɬɨɧɢɚɧɚ (70)
ɜɦɟɫɬɨ ɝɚɦɢɥɶɬɨɧɢɚɧɚ
A
ɜ ɮɨɪɦɭɥɟ (50) ɤɚɧɚɥɨɜɵɟ ɮɭɧɤɰɢɢ
s
J
M
U
S
D
(48)
ɧɟɨɛɯɨɞɢɦɨ ɡɚɦɟɧɢɬɶ ɧɚ ɧɨɜɵɟ ɤɚɧɚɥɨɜɵɟ ɮɭɧɤɰɢɢ
s
J
M
U
S
D
(
, 1mm
DD
{ r
), ɭɱɢɬɵɜɚɸɳɢɟ ɯɚɪɚɤɬɟɪ ɞɟɣɫɬɜɢɹ ɝɚɦɢɥɶɬɨɧɢɚɧɚ
Cor
ˆ
H ɧɚ
ɜɨɥɧɨɜɭɸ ɮɭɧɤɰɢɸ
s
s
J
M
qK
S
<
. ɗɬɨ ɩɪɢɜɟɞɟɬ ɤ ɡɚɦɟɧɟ ɮɭɧɤɰɢɣ
ɫɩɢɧɨɜɨɣ ɦɚɬɪɢɰɵ ɩɥɨɬɧɨɫɬɢ ɹɞɪɚ, ɫɨɜɩɚɞɚɸɳɢɦ ɫɨ ɫɩɢɧɨɜɨɣ ɦɚɬɪɢɰɟɣ
ɩɥɨɬɧɨɫɬɢ ɹɞɪɚ ɞɥɹ ɧɟɩɨɥɹɪɢɡɨɜɚɧɧɵɯ ɧɟɣɬɪɨɧɨɜ, ɢ ɩɪɢɧɢɦɚɟɬ ɜɢɞ [14]:
    d 3V       4S 0
                   B : R , :r , H {
d : R d :r d H kn2
     1                        J       J       J S    Js  J S                J    2J s  1                       sJ s ' J s '
{              ¦
    kn2 ss ' J s J s 'qK s
                             aKs aKs ' bsqK
                                  s
                                          s b s'
                                          s  s ' qK hs hs '
                                                    s
                                                           s'
                                                               s                2 2I  1
                                                                                              ¦       * qK s c f qKs
                                                                                                                   s
                                                                                                                               TrR , H ,
                                                                                               c
                                                                             (69)
     Ɇɟɬɨɞɵ ɤɜɚɧɬɨɜɨɣ ɬɟɨɪɢɢ ɞɟɥɟɧɢɹ ɞɚɥɢ ɜɨɡɦɨɠɧɨɫɬɶ ɨɛɴɹɫɧɢɬɶ
ɩɪɢɪɨɞɭ Ɍ-ɧɟɱɟɬɧɨɣ ɚɫɢɦɦɟɬɪɢɢ ɩɪɢ ɭɱɟɬɟ Ʉɨɪɢɨɥɢɫɨɜɚ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ
ɨɪɛɢɬɚɥɶɧɨɝɨ ɦɨɦɟɧɬɚ l ɬɪɟɬɶɟɣ ɱɚɫɬɢɰɵ ɫɨ ɫɩɢɧɨɦ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ.
      Ƚɚɦɢɥɶɬɨɧɢɚɧ Ʉɨɪɢɨɥɢɫɨɜɚ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ H              l Cor ɞɥɹ ɫɥɭɱɚɹ D -
ɱɚɫɬɢɰɵ ɢɦɟɟɬ ɜɢɞ:
                                          =2
                              Hˆ Cor             J l  J l ,            (70)
                                         2 J0
ɝɞɟ ɨɩɟɪɚɬɨɪɵ J r ɢ lr ɨɩɪɟɞɟɥɹɸɬɫɹ ɤɚɤ
                              J r J x ' r iJ y ' , lr l x ' r il y ' ,       (71)
ɩɪɢɱɟɦ J x ' , J y ' – ɩɪɨɟɤɰɢɢ ɨɩɟɪɚɬɨɪɚ ɫɩɢɧɚ J ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ ɧɚ ɨɫɢ x '
ɢ y ' ɜ. ɫ., ɚ ɢ l x ' , l y ' – ɩɪɨɟɤɰɢɢ ɨɩɟɪɚɬɨɪɚ ɨɪɛɢɬɚɥɶɧɨɝɨ ɦɨɦɟɧɬɚ ɬɪɟɬɶɟɣ
                                                                 J
ɱɚɫɬɢɰɵ ɨɫɢ x ' ɢ y ' ɜ. ɫ. Ⱦɟɣɫɬɜɢɟ ɨɩɟɪɚɬɨɪɨɜ (71) ɧɚ ɮɭɧɤɰɢɸ DMK Z ɢ
ɲɚɪɨɜɭɸ ɮɭɧɤɰɢɸ YlKl :r' ɨɩɢɫɵɜɚɟɬɫɹ ɮɨɪɦɭɥɚɦɢ
                             J                                                       12    J
                        J r DMK Z                       ª¬ J r K         J B K  1 º¼     DMK B1 Z ;                               (72)
                                                                                    12
                       lrYlKl :r'                   ª¬ l B Kl l r Kl  1 º¼              Yl   Kl r1     :r' .                      (73)
                                                                                                                                 J SM
ɉɨɷɬɨɦɭ ɞɟɣɫɬɜɢɟ ɨɩɟɪɚɬɨɪɚ Ĥ Cor ɧɚ (70) ɧɚ ɜɨɥɧɨɜɭɸ ɮɭɧɤɰɢɸ < qKs
                                                                                                                                       s
ɦɨɞɵ ɞɟɥɟɧɢɹ q ɫɭɳɟɫɬɜɟɧɧɨ ɢɡɦɟɧɹɟɬ ɫɬɪɭɤɬɭɪɭ ɷɬɨɣ ɜɨɥɧɨɜɨɣ ɮɭɧɤɰɢɢ.
ȼ ɧɟɣ ɢɫɱɟɡɚɟɬ ɜɟɞɭɳɢɣ ɱɥɟɧ ɫ l 0 , ɚ ɨɫɧɨɜɧɭɸ ɪɨɥɶ ɧɚɱɢɧɚɸɬ ɢɝɪɚɬɶ
ɱɥɟɧɵ ɫ l z 0 . Ⱦɥɹ ɩɨɥɭɱɟɧɢɹ ɚɦɩɥɢɬɭɞɵ ɩɚɪɰɢɚɥɶɧɨɣ ɞɟɥɢɬɟɥɶɧɨɣ
                                      Cor
ɲɢɪɢɧɵ §¨ * qKs D ·¸
            J S
                     ɩɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ Ʉɨɪɢɨɥɢɫɨɜɚ ɝɚɦɢɥɶɬɨɧɢɚɧɚ (70)
         ©      s ¹

ɜɦɟɫɬɨ ɝɚɦɢɥɶɬɨɧɢɚɧɚ H A ɜ ɮɨɪɦɭɥɟ (50) ɤɚɧɚɥɨɜɵɟ ɮɭɧɤɰɢɢ UDJ sS M (48)
                                                                                                                                 J SM
ɧɟɨɛɯɨɞɢɦɨ                    ɡɚɦɟɧɢɬɶ                   ɧɚ            ɧɨɜɵɟ     ɤɚɧɚɥɨɜɵɟ              ɮɭɧɤɰɢɢ                UD s
( D { D m, m r1 ), ɭɱɢɬɵɜɚɸɳɢɟ ɯɚɪɚɤɬɟɪ ɞɟɣɫɬɜɢɹ ɝɚɦɢɥɶɬɨɧɢɚɧɚ Ĥ Cor ɧɚ
                                                        J SM
ɜɨɥɧɨɜɭɸ               ɮɭɧɤɰɢɸ                  < qKs              .    ɗɬɨ     ɩɪɢɜɟɞɟɬ           ɤ      ɡɚɦɟɧɟ          ɮɭɧɤɰɢɣ
                                                           s


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