Квантовая теория двойного и тройного деления атомных ядер. Кадменский С.Г - 10 стр.

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10

,0
2
JK
f
KK
J
g
G
*
*
, ɝɞɟ
J
* – ɩɨɥɧɚɹ ɲɢɪɢɧɚ ɪɚɫɩɚɞɚ ɫɨɫɬɨɹɧɢɹ
ɫɨɫɬɚɜɧɨɝɨ ɹɞɪɚ ɜ ɩɟɪɜɨɣ ɹɦɟ ɩɨɬɟɧɰɢɚɥɚ ɞɟɮɨɪɦɚɰɢɢ ɜɨ ɜɫɟ ɨɬɤɪɵɬɵɟ
ɤɚɧɚɥɵ, ɚ
J
K
f
*
– ɞɟɥɢɬɟɥɶɧɚɹ ɲɢɪɢɧɚ. ȼ ɫɥɭɱɚɟ ɞɢɚɝɨɧɚɥɶɧɨɫɬɢ ɫɩɢɧɨɜɨɣ
ɦɚɬɪɢɰɵ ɩɥɨɬɧɨɫɬɢ
'
J
MM
U
ɩɨ ɩɪɨɟɤɰɢɹɦ
M
, 'M :
''
J
J
M
MMMM
a
UG
, ɝɞɟ
J
M
a – ɩɚɪɚɦɟɬɪ ɨɬɧɨɫɢɬɟɥɶɧɨɣ ɡɚɫɟɥɟɧɧɨɫɬɢ ɩɨɞɭɪɨɜɧɟɣ JM
S
ɞɟɥɹɳɟɝɨɫɹ
ɹɞɪɚ, ɍɊɎ ɞɜɨɣɧɨɝɨ ɞɟɥɟɧɢɹ
(4) ɩɪɢɧɢɦɚɟɬ ɜɢɞ [2]:


00
,
JJJ
J
MK K
KM K
MK K
dP dP dP
ga g
ddd
SSS
tt
:::
:::
¦¦
(5)
ɝɞɟ

 
22
21
ȦȦ.
8
J
JJ
MK
MK M K
dP
J
DD
d
S
T
S
:
ªº
«»
:
¬¼
(6)
ȿɫɥɢ ɫɨɫɬɨɹɧɢɹ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ ɫ ɩɪɨɟɤɰɢɹɦɢ
M ɫɩɢɧɚ J ɧɚ ɨɫɶ
Z
ɥ. ɫ.
ɡɚɫɟɥɟɧɵ ɨɞɧɨɪɨɞɧɨ, ɬ. ɟ. ɦɚɬɪɢɰɚ ɩɥɨɬɧɨɫɬɢ
''
1
21
J
M
MMM
J
UG
,
ɮɨɪɦɭɥɚ
(4) ɩɪɢɜɨɞɢɬɫɹ ɤ ɜɵɪɚɠɟɧɢɸ
 
22
0
1
ȦȦ
8
JJ
KMK MK
MK
gD D
S
t
ªº
«»
¬¼
¦
, ɤɨɬɨɪɨɟ ɩɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ
ɮɨɪɦɭɥɵ
 
*
1
MK
JJ
MK MK
DD
ZZ
r
B
B
, ɬɟɨɪɟɦɵ ɭɦɧɨɠɟɧɢɹ
D -ɮɭɧɤɰɢɣ ȼɢɝɧɟɪɚ ɢ ɫɭɦɦɢɪɨɜɚɧɢɢ ɩɨ ɩɪɨɟɤɰɢɹɦ M ɨɤɚɡɵɜɚɟɬɫɹ ɧɟ
ɡɚɜɢɫɹɳɢɦ ɨɬ ɭɝɥɨɜ
T
ɢ
M
, ɬ. ɟ. ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɢɡɨɬɪɨɩɧɨɦɭ ɍɊɎ ɞɟɥɟɧɢɹ.
Ⱥɧɚɥɨɝɢɱɧɨ, ɟɫɥɢ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɜɟɪɨɹɬɧɨɫɬɟɣ
K
g ɹɜɥɹɟɬɫɹ ɨɞɧɨɪɨɞɧɵɦ,
ɬ. ɟ.

,0
2
~
21
K
K
g
J
G
, ɬɨ ɜ ɮɨɪɦɭɥɟ (4) ɞɥɹ ɍɊɎ ɞɟɥɟɧɢɹ ɩɨɹɜɥɹɟɬɫɹ
ɜɵɪɚɠɟɧɢɟ:
   
**
'' '
'
1
ȦȦ Ȧ Ȧ
8
JJ J J J
MM MK M K M K M K
MM K
DD D D
U
S

ªº
¬¼
¦
,
ɤɨɬɨɪɨɟ ɩɪɢ ɫɭɦɦɢɪɨɜɚɧɢɢ ɩɨ ɩɪɨɟɤɰɢɹɦ
K
ɬɚɤɠɟ ɨɤɚɡɵɜɚɟɬɫɹ
ɧɟɡɚɜɢɫɹɳɢɦ ɨɬ ɭɝɥɨɜ
T
ɢ
M
, ɱɬɨ ɨɡɧɚɱɚɟɬ ɢɡɨɬɪɨɩɢɸ ɍɊɎ ɞɟɥɟɧɢɹ.
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɩɨɹɜɥɟɧɢɟ ɚɧɢɡɨɬɪɨɩɢɣ ɜ ɍɊɎ ɞɜɨɣɧɨɝɨ ɞɟɥɟɧɢɹ
ɜɨɡɦɨɠɧɨ ɬɨɥɶɤɨ ɜ ɫɥɭɱɚɟ, ɤɨɝɞɚ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɩɪɨɟɤɰɢɣ M ɢ
K
ɫɩɢɧɚ
ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ J ɜɛɥɢɡɢ ɬɨɱɤɢ ɪɚɡɪɵɜɚ ɹɞɪɚ ɧɟɨɞɧɨɪɨɞɧɵ.
ɇɟɨɞɧɨɪɨɞɧɨɫɬɶ
M -ɪɚɫɩɪɟɞɟɥɟɧɢɹ, ɨɩɪɟɞɟɥɹɟɦɚɹ ɫɩɢɧɨɜɨɣ ɦɚɬɪɢɰɟɣ
ɩɥɨɬɧɨɫɬɢ
'
J
MM
U
, ɞɨɫɬɢɝɚɟɬɫɹ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ ɩɭɬɟɦ ɨɪɢɟɧɬɚɰɢɢ ɫɩɢɧɚ
J ɫɩɨɧɬɚɧɧɨ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ ɜ ɥ. ɫ., ɧɚɩɪɢɦɟɪ, ɜ ɫɢɥɶɧɵɯ ɦɚɝɧɢɬɧɵɯ
      * JK
        f
gK        2  G K ,0 , ɝɞɟ * J – ɩɨɥɧɚɹ ɲɢɪɢɧɚ ɪɚɫɩɚɞɚ ɫɨɫɬɨɹɧɢɹ
      *J
ɫɨɫɬɚɜɧɨɝɨ ɹɞɪɚ ɜ ɩɟɪɜɨɣ ɹɦɟ ɩɨɬɟɧɰɢɚɥɚ ɞɟɮɨɪɦɚɰɢɢ ɜɨ ɜɫɟ ɨɬɤɪɵɬɵɟ
ɤɚɧɚɥɵ, ɚ * JK
            f – ɞɟɥɢɬɟɥɶɧɚɹ ɲɢɪɢɧɚ. ȼ ɫɥɭɱɚɟ ɞɢɚɝɨɧɚɥɶɧɨɫɬɢ ɫɩɢɧɨɜɨɣ
                    J                             J           J
ɦɚɬɪɢɰɵ ɩɥɨɬɧɨɫɬɢ U MM ' ɩɨ ɩɪɨɟɤɰɢɹɦ M , M ' : U MM ' G MM 'aM , ɝɞɟ
 J
aM  – ɩɚɪɚɦɟɬɪ ɨɬɧɨɫɢɬɟɥɶɧɨɣ ɡɚɫɟɥɟɧɧɨɫɬɢ ɩɨɞɭɪɨɜɧɟɣ J S M ɞɟɥɹɳɟɝɨɫɹ
ɹɞɪɚ, ɍɊɎ ɞɜɨɣɧɨɝɨ ɞɟɥɟɧɢɹ (4) ɩɪɢɧɢɦɚɟɬ ɜɢɞ [2]:
            dP J S :                   JS
                                   J dPMK :         dP J S :
                        ¦     g K aM          ¦   gK K       ,    (5)
               d:      MK t 0           d:   K t0      d:
ɝɞɟ
                   JS
                 dPMK  :         2J  1 ª J      2      J        2º
                                         DMK Ȧ        DM
                                                       .  K Ȧ     (6)
                    d:            8S «¬           »
                                                  ¼E T
ȿɫɥɢ ɫɨɫɬɨɹɧɢɹ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ ɫ ɩɪɨɟɤɰɢɹɦɢ M ɫɩɢɧɚ J ɧɚ ɨɫɶ Z ɥ. ɫ.
                                                  J        1
ɡɚɫɟɥɟɧɵ ɨɞɧɨɪɨɞɧɨ, ɬ. ɟ. ɦɚɬɪɢɰɚ ɩɥɨɬɧɨɫɬɢ U MM     '          G MM ' ,
                                                         2J  1
ɮɨɪɦɭɥɚ (4)           ɩɪɢɜɨɞɢɬɫɹ             ɤ           ɜɵɪɚɠɟɧɢɸ
 1          ª J     2    J       2 º
     ¦ g K «¬ DMK
8S MK t0
                  Ȧ  DM   K Ȧ » ,
                                   ¼
                                       ɤɨɬɨɪɨɟ ɩɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ

              J*                    M BK
ɮɨɪɦɭɥɵ     DM  rK Z    1         DJM B K Z ,   ɬɟɨɪɟɦɵ    ɭɦɧɨɠɟɧɢɹ
D -ɮɭɧɤɰɢɣ ȼɢɝɧɟɪɚ ɢ ɫɭɦɦɢɪɨɜɚɧɢɢ ɩɨ ɩɪɨɟɤɰɢɹɦ M ɨɤɚɡɵɜɚɟɬɫɹ ɧɟ
ɡɚɜɢɫɹɳɢɦ ɨɬ ɭɝɥɨɜ T ɢ M , ɬ. ɟ. ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɢɡɨɬɪɨɩɧɨɦɭ ɍɊɎ ɞɟɥɟɧɢɹ.
Ⱥɧɚɥɨɝɢɱɧɨ, ɟɫɥɢ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɜɟɪɨɹɬɧɨɫɬɟɣ g K ɹɜɥɹɟɬɫɹ ɨɞɧɨɪɨɞɧɵɦ,
              2  G K ,0
ɬ. ɟ. g K ~                , ɬɨ ɜ ɮɨɪɦɭɥɟ (4) ɞɥɹ ɍɊɎ ɞɟɥɟɧɢɹ ɩɨɹɜɥɹɟɬɫɹ
               2J  1
ɜɵɪɚɠɟɧɢɟ:
         1               J   ª J     J*         J        J*      º
        8S
                ¦      U MM ' DMK Ȧ DM ' K Ȧ  DM  K Ȧ DM ' K Ȧ ,
                             ¬                                        ¼
              MM ' K
ɤɨɬɨɪɨɟ ɩɪɢ ɫɭɦɦɢɪɨɜɚɧɢɢ ɩɨ ɩɪɨɟɤɰɢɹɦ K ɬɚɤɠɟ ɨɤɚɡɵɜɚɟɬɫɹ
ɧɟɡɚɜɢɫɹɳɢɦ ɨɬ ɭɝɥɨɜ T ɢ M , ɱɬɨ ɨɡɧɚɱɚɟɬ ɢɡɨɬɪɨɩɢɸ ɍɊɎ ɞɟɥɟɧɢɹ.
    Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɩɨɹɜɥɟɧɢɟ ɚɧɢɡɨɬɪɨɩɢɣ ɜ ɍɊɎ ɞɜɨɣɧɨɝɨ ɞɟɥɟɧɢɹ
ɜɨɡɦɨɠɧɨ ɬɨɥɶɤɨ ɜ ɫɥɭɱɚɟ, ɤɨɝɞɚ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɩɪɨɟɤɰɢɣ M ɢ K ɫɩɢɧɚ
ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ J ɜɛɥɢɡɢ ɬɨɱɤɢ ɪɚɡɪɵɜɚ ɹɞɪɚ ɧɟɨɞɧɨɪɨɞɧɵ.
    ɇɟɨɞɧɨɪɨɞɧɨɫɬɶ M -ɪɚɫɩɪɟɞɟɥɟɧɢɹ, ɨɩɪɟɞɟɥɹɟɦɚɹ ɫɩɢɧɨɜɨɣ ɦɚɬɪɢɰɟɣ
            J
ɩɥɨɬɧɨɫɬɢ U MM ' , ɞɨɫɬɢɝɚɟɬɫɹ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ ɩɭɬɟɦ ɨɪɢɟɧɬɚɰɢɢ ɫɩɢɧɚ
J ɫɩɨɧɬɚɧɧɨ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ ɜ ɥ. ɫ., ɧɚɩɪɢɦɟɪ, ɜ ɫɢɥɶɧɵɯ ɦɚɝɧɢɬɧɵɯ

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