Квантовая теория двойного и тройного деления атомных ядер. Кадменский С.Г - 18 стр.

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18
ɨɛɥɚɫɬɢ ɮɨɪɦɢɪɨɜɚɧɢɹ ɭɝɥɨɜɵɯ ɪɚɫɩɪɟɞɟɥɟɧɢɣ ɩɟɪɜɢɱɧɵɯ ɮɪɚɝɦɟɧɬɨɜ
ɞɟɥɟɧɢɹ ɨɫɢ ɫɢɦɦɟɬɪɢɢ ɩɟɪɜɢɱɧɵɯ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ ɫɨɜɩɚɞɚɸɬ ɩɨ
ɧɚɩɪɚɜɥɟɧɢɸ ɫ ɨɫɶɸ ɫɢɦɦɟɬɪɢɢ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ, ɤɨɝɞɚ
12
ZZ Z
.
ɍɫɥɨɜɢɹ
(25)–(27) ɪɟɚɥɢɡɭɸɬɫɹ ɞɥɹ ɞɟɥɟɧɢɹ ɚɤɬɢɧɢɞɧɵɯ ɹɞɟɪ ɩɪɢ
kin
10
c
E ! Ɇɷȼ, 60
cn
Mm| ,
sc
15R | ɮɦ, 5
c
R' ɮɦ ɢ ɦɚɤɫɢɦɚɥɶɧɵɯ
ɡɧɚɱɟɧɢɹɯ
L
ɢ
i
J
ɪɚɜɧɵɯ 30 ɢ 15 ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ. ɇɟɡɚɜɢɫɢɦɨɫɬɶ
ɞɟɥɢɬɟɥɶɧɵɯ ɮɚɡ
J
S
D
G
ɨɬ
L
,
1
J ,
2
J , F ɩɪɢɜɨɞɢɬ ɤ ɢɧɬɟɪɮɟɪɟɧɰɢɢ
ɫɨɫɬɨɹɧɢɣ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ ɫ ɪɚɡɥɢɱɧɵɦɢ ɤɜɚɧɬɨɜɵɦɢ ɱɢɫɥɚɦɢ
L
,
1
J ,
2
J , F ɜ ɚɦɩɥɢɬɭɞɚɯ ɍɊɎ ɞɟɥɟɧɢɹ ɫ ɮɢɤɫɢɪɨɜɚɧɧɵɦɢ ɤɜɚɧɬɨɜɵɦɢ
ɱɢɫɥɚɦɢ
112 2
K
K
VV
. ɗɬɨɬ ɪɟɡɭɥɶɬɚɬ ɨɬɥɢɱɚɟɬɫɹ ɨɬ ɩɪɟɞɫɬɚɜɥɟɧɢɣ ɪɚɛɨɬɵ
ȼ.Ɇ. ɋɬɪɭɬɢɧɫɤɨɝɨ, ɝɞɟ ɩɪɟɧɟɛɪɟɝɚɟɬɫɹ ɢɧɬɟɪɮɟɪɟɧɰɢɟɣ ɪɚɡɥɢɱɧɵɯ
ɡɧɚɱɟɧɢɣ
L
.
Ʉɚɤ ɨɬɦɟɱɚɥɨɫɶ ɜɵɲɟ, ɧɨɪɦɢɪɨɜɚɧɧɨɟ ɧɚ ɟɞɢɧɢɰɭ ɍɊɎ ɞɜɨɣɧɨɝɨ
ɞɟɥɟɧɢɹ

J
MK
dP
d
S
:
:
ɢɡ ɫɨɫɬɨɹɧɢɹ JMK
S
ɬɪɚɞɢɰɢɨɧɧɨ ɪɚɫɫɱɢɬɵɜɚɟɬɫɹ ɩɪɢ
ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɮɨɪɦɭɥɵ (6), ɤɨɬɨɪɚɹ ɢɦɟɟɬ ɭɧɢɜɟɪɫɚɥɶɧɵɣ ɯɚɪɚɤɬɟɪ ɞɥɹ
ɜɫɟɯ ɤɚɧɚɥɨɜ ɞɟɥɟɧɢɹ
12
cJ J FL . ȼ ɨɫɧɨɜɟ ɷɬɨɣ ɮɨɪɦɭɥɵ ɥɟɠɢɬ
ɤɚɱɟɫɬɜɟɧɧɨɟ ɮɢɡɢɱɟɫɤɨɟ ɞɨɩɭɳɟɧɢɟ, ɫɨɝɥɚɫɧɨ ɤɨɬɨɪɨɦɭ ɮɪɚɝɦɟɧɬɵ
ɞɟɥɟɧɢɹ ɜɵɥɟɬɚɸɬ ɬɨɥɶɤɨ ɩɨ ɧɚɩɪɚɜɥɟɧɢɸ ɢɥɢ ɩɪɨɬɢɜ ɧɚɩɪɚɜɥɟɧɢɹ ɨɫɢ
ɫɢɦɦɟɬɪɢɢ
'
Z
ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ. ɗɬɨ ɨɡɧɚɱɚɟɬ, ɱɬɨ ɍɊɎ ɞɟɥɟɧɢɹ ɜɨ ɜ. ɫ.
ɢɦɟɟɬ
G
-ɨɛɪɚɡɧɵɣ ɯɚɪɚɤɬɟɪ ɜɢɞɚ
'
(1)
G[
B , ɝɞɟ
'
T
– ɭɝɨɥ ɦɟɠɞɭ ɜɟɤɬɨɪɨɦ
R ɢ ɨɫɶɸ ɫɢɦɦɟɬɪɢɢ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ
'
Z
, ɚ
''
cos
[
T
. ɍɤɚɡɚɧɧɵɟ
G
-
ɮɭɧɤɰɢɢ ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɤɚɤ

'' '
00 0
00
(1) 2 ()(1) 21 (1) (),
mm
lL
L
lL L
lL
YY L Y
G[ S [ S [
r
¦¦
B (28)
ɝɞɟ ɜɟɥɢɱɢɧɚ
m
L
ɪɚɫɫɦɚɬɪɢɜɚɟɬɫɹ ɜ ɩɪɟɞɟɥɟ
m
L o f
. Ɏɨɪɦɭɥɚ (28)
ɨɬɪɚɠɚɟɬ ɤɜɚɧɬɨɜɨɦɟɯɚɧɢɱɟɫɤɨɟ ɫɨɨɬɧɨɲɟɧɢɟ ɧɟɨɩɪɟɞɟɥɟɧɧɨɫɬɢ ɦɟɠɞɭ
ɨɪɛɢɬɚɥɶɧɵɦ ɦɨɦɟɧɬɨɦ
L
ɢ ɭɝɥɨɦ ɜɵɥɟɬɚ ɱɚɫɬɢɰɵ
'
T
, ɢɡ ɤɨɬɨɪɨɝɨ
ɫɥɟɞɭɟɬ, ɱɬɨ ɡɚɞɚɧɢɟ ɬɨɱɧɨɝɨ ɧɚɩɪɚɜɥɟɧɢɹ ɜɵɥɟɬɚ ɱɚɫɬɢɰɵ ɜɨɡɦɨɠɧɨ
ɥɢɲɶ ɩɪɢ ɩɨɥɧɨɣ ɧɟɨɩɪɟɞɟɥɟɧɧɨɫɬɢ ɜ ɡɧɚɱɟɧɢɹɯ ɨɪɛɢɬɚɥɶɧɨɝɨ ɦɨɦɟɧɬɚ
L
ɱɚɫɬɢɰɵ (0
L
ddf). ɉɨɫɤɨɥɶɤɭ ɜ ɩɪɨɰɟɫɫɟ ɞɟɥɟɧɢɹ ɹɞɟɪ ɦɨɝɭɬ
ɩɨɹɜɢɬɶɫɹ ɬɨɥɶɤɨ ɤɨɧɟɱɧɵɟ ɡɧɚɱɟɧɢɹ ɫɩɢɧɨɜ
i
J ɢ ɨɬɧɨɫɢɬɟɥɶɧɵɯ
ɨɪɛɢɬɚɥɶɧɵɯ ɦɨɦɟɧɬɨɜ
L
ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ, ɬɨ ɮɨɪɦɭɥɚ (6) ɦɨɠɟɬ
ɢɦɟɬɶ ɥɢɲɶ ɩɪɢɛɥɢɠɟɧɧɵɣ ɯɚɪɚɤɬɟɪ. ȼ ɬɨ ɠɟ ɜɪɟɦɹ ɮɨɪɦɭɥɚ
(6) ɭɫɩɟɲɧɨ
ɨɩɢɫɵɜɚɟɬ ɲɢɪɨɤɢɣ ɤɥɚɫɫ ɹɜɥɟɧɢɣ, ɫɜɹɡɚɧɧɵɯ ɫ ɞɟɥɟɧɢɟɦ ɹɞɟɪ, ɱɬɨ
ɫɜɢɞɟɬɟɥɶɫɬɜɭɟɬ ɨ ɟɟ ɞɨɫɬɚɬɨɱɧɨ ɜɵɫɨɤɨɣ ɬɨɱɧɨɫɬɢ. ɉɨɧɹɬɶ ɷɬɨɬ
ɨɛɥɚɫɬɢ ɮɨɪɦɢɪɨɜɚɧɢɹ ɭɝɥɨɜɵɯ ɪɚɫɩɪɟɞɟɥɟɧɢɣ ɩɟɪɜɢɱɧɵɯ ɮɪɚɝɦɟɧɬɨɜ
ɞɟɥɟɧɢɹ ɨɫɢ ɫɢɦɦɟɬɪɢɢ ɩɟɪɜɢɱɧɵɯ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ ɫɨɜɩɚɞɚɸɬ ɩɨ
ɧɚɩɪɚɜɥɟɧɢɸ ɫ ɨɫɶɸ ɫɢɦɦɟɬɪɢɢ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ, ɤɨɝɞɚ Z Z1 Z2 .
ɍɫɥɨɜɢɹ (25)–(27) ɪɟɚɥɢɡɭɸɬɫɹ ɞɥɹ ɞɟɥɟɧɢɹ ɚɤɬɢɧɢɞɧɵɯ ɹɞɟɪ ɩɪɢ
Eckin ! 10 Ɇɷȼ, M c | 60mn , Rsc | 15 ɮɦ, 'Rc 5 ɮɦ ɢ ɦɚɤɫɢɦɚɥɶɧɵɯ
ɡɧɚɱɟɧɢɹɯ L ɢ J i ɪɚɜɧɵɯ 30 ɢ 15 ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ. ɇɟɡɚɜɢɫɢɦɨɫɬɶ
ɞɟɥɢɬɟɥɶɧɵɯ ɮɚɡ GDJ S ɨɬ L , J1 , J 2 , F ɩɪɢɜɨɞɢɬ ɤ ɢɧɬɟɪɮɟɪɟɧɰɢɢ
ɫɨɫɬɨɹɧɢɣ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ ɫ ɪɚɡɥɢɱɧɵɦɢ ɤɜɚɧɬɨɜɵɦɢ ɱɢɫɥɚɦɢ L , J1 ,
J 2 , F ɜ ɚɦɩɥɢɬɭɞɚɯ ɍɊɎ ɞɟɥɟɧɢɹ ɫ ɮɢɤɫɢɪɨɜɚɧɧɵɦɢ ɤɜɚɧɬɨɜɵɦɢ
ɱɢɫɥɚɦɢ V1K1V 2 K 2 . ɗɬɨɬ ɪɟɡɭɥɶɬɚɬ ɨɬɥɢɱɚɟɬɫɹ ɨɬ ɩɪɟɞɫɬɚɜɥɟɧɢɣ ɪɚɛɨɬɵ
ȼ.Ɇ. ɋɬɪɭɬɢɧɫɤɨɝɨ, ɝɞɟ ɩɪɟɧɟɛɪɟɝɚɟɬɫɹ ɢɧɬɟɪɮɟɪɟɧɰɢɟɣ ɪɚɡɥɢɱɧɵɯ
ɡɧɚɱɟɧɢɣ L .
      Ʉɚɤ ɨɬɦɟɱɚɥɨɫɶ ɜɵɲɟ, ɧɨɪɦɢɪɨɜɚɧɧɨɟ ɧɚ ɟɞɢɧɢɰɭ ɍɊɎ ɞɜɨɣɧɨɝɨ
            JS
          dPMK  :
ɞɟɥɟɧɢɹ             ɢɡ ɫɨɫɬɨɹɧɢɹ J S MK ɬɪɚɞɢɰɢɨɧɧɨ ɪɚɫɫɱɢɬɵɜɚɟɬɫɹ ɩɪɢ
             d:
ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɮɨɪɦɭɥɵ (6), ɤɨɬɨɪɚɹ ɢɦɟɟɬ ɭɧɢɜɟɪɫɚɥɶɧɵɣ ɯɚɪɚɤɬɟɪ ɞɥɹ
ɜɫɟɯ ɤɚɧɚɥɨɜ ɞɟɥɟɧɢɹ cJ1J 2 FL . ȼ ɨɫɧɨɜɟ ɷɬɨɣ ɮɨɪɦɭɥɵ ɥɟɠɢɬ
ɤɚɱɟɫɬɜɟɧɧɨɟ ɮɢɡɢɱɟɫɤɨɟ ɞɨɩɭɳɟɧɢɟ, ɫɨɝɥɚɫɧɨ ɤɨɬɨɪɨɦɭ ɮɪɚɝɦɟɧɬɵ
ɞɟɥɟɧɢɹ ɜɵɥɟɬɚɸɬ ɬɨɥɶɤɨ ɩɨ ɧɚɩɪɚɜɥɟɧɢɸ ɢɥɢ ɩɪɨɬɢɜ ɧɚɩɪɚɜɥɟɧɢɹ ɨɫɢ
ɫɢɦɦɟɬɪɢɢ Z ' ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ. ɗɬɨ ɨɡɧɚɱɚɟɬ, ɱɬɨ ɍɊɎ ɞɟɥɟɧɢɹ ɜɨ ɜ. ɫ.
ɢɦɟɟɬ G -ɨɛɪɚɡɧɵɣ ɯɚɪɚɤɬɟɪ ɜɢɞɚ G ([ ' B 1) , ɝɞɟ T ' – ɭɝɨɥ ɦɟɠɞɭ ɜɟɤɬɨɪɨɦ
R ɢ ɨɫɶɸ ɫɢɦɦɟɬɪɢɢ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ Z ' , ɚ [ '                cosT ' . ɍɤɚɡɚɧɧɵɟ G -
ɮɭɧɤɰɢɢ ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɤɚɤ
                    lm                        Lm
      G ([ ' B 1)   ¦ 2S Yl 0 ([ ' )YL0 ( r 1) ¦    2 L  1 S (  1) LYL 0 ([ ' ),   (28)
                    l 0                       L 0
 ɝɞɟ ɜɟɥɢɱɢɧɚ Lm ɪɚɫɫɦɚɬɪɢɜɚɟɬɫɹ ɜ ɩɪɟɞɟɥɟ Lm o f . Ɏɨɪɦɭɥɚ (28)
 ɨɬɪɚɠɚɟɬ ɤɜɚɧɬɨɜɨɦɟɯɚɧɢɱɟɫɤɨɟ ɫɨɨɬɧɨɲɟɧɢɟ ɧɟɨɩɪɟɞɟɥɟɧɧɨɫɬɢ ɦɟɠɞɭ
 ɨɪɛɢɬɚɥɶɧɵɦ ɦɨɦɟɧɬɨɦ L ɢ ɭɝɥɨɦ ɜɵɥɟɬɚ ɱɚɫɬɢɰɵ T ' , ɢɡ ɤɨɬɨɪɨɝɨ
 ɫɥɟɞɭɟɬ, ɱɬɨ ɡɚɞɚɧɢɟ ɬɨɱɧɨɝɨ ɧɚɩɪɚɜɥɟɧɢɹ ɜɵɥɟɬɚ ɱɚɫɬɢɰɵ ɜɨɡɦɨɠɧɨ
 ɥɢɲɶ ɩɪɢ ɩɨɥɧɨɣ ɧɟɨɩɪɟɞɟɥɟɧɧɨɫɬɢ ɜ ɡɧɚɱɟɧɢɹɯ ɨɪɛɢɬɚɥɶɧɨɝɨ ɦɨɦɟɧɬɚ
 L ɱɚɫɬɢɰɵ ( 0 d L d f ). ɉɨɫɤɨɥɶɤɭ ɜ ɩɪɨɰɟɫɫɟ ɞɟɥɟɧɢɹ ɹɞɟɪ ɦɨɝɭɬ
 ɩɨɹɜɢɬɶɫɹ ɬɨɥɶɤɨ ɤɨɧɟɱɧɵɟ ɡɧɚɱɟɧɢɹ ɫɩɢɧɨɜ J i ɢ ɨɬɧɨɫɢɬɟɥɶɧɵɯ
 ɨɪɛɢɬɚɥɶɧɵɯ ɦɨɦɟɧɬɨɜ L ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ, ɬɨ ɮɨɪɦɭɥɚ (6) ɦɨɠɟɬ
 ɢɦɟɬɶ ɥɢɲɶ ɩɪɢɛɥɢɠɟɧɧɵɣ ɯɚɪɚɤɬɟɪ. ȼ ɬɨ ɠɟ ɜɪɟɦɹ ɮɨɪɦɭɥɚ (6) ɭɫɩɟɲɧɨ
 ɨɩɢɫɵɜɚɟɬ ɲɢɪɨɤɢɣ ɤɥɚɫɫ ɹɜɥɟɧɢɣ, ɫɜɹɡɚɧɧɵɯ ɫ ɞɟɥɟɧɢɟɦ ɹɞɟɪ, ɱɬɨ
 ɫɜɢɞɟɬɟɥɶɫɬɜɭɟɬ ɨ ɟɟ ɞɨɫɬɚɬɨɱɧɨ ɜɵɫɨɤɨɣ ɬɨɱɧɨɫɬɢ. ɉɨɧɹɬɶ ɷɬɨɬ



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