Квантовая теория двойного и тройного деления атомных ядер. Кадменский С.Г - 17 стр.

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17
ɭɱɟɬɟ ɨɪɬɨɝɨɧɚɥɶɧɨɫɬɢ ɤɚɧɚɥɨɜɵɯ ɮɭɧɤɰɢɣ (14), ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ
ɪɚɡɥɢɱɧɵɦ ɞɟɥɢɬɟɥɶɧɵɦ ɦɨɞɚɦ
q ɢ ɡɧɚɱɟɧɢɹɦ ɩɪɨɟɤɰɢɣ
K
, ɜɵɪɚɠɟɧɢɟ
ɞɥɹ ɩɨɥɧɨɣ ɞɟɥɢɬɟɥɶɧɨɣ ɲɢɪɢɧɵ
J
S
V
* ɩɪɢɧɢɦɚɟɬ ɜɢɞ:
22 22
.
JJ JJJ JJJ
ɫ qKɫ KqK qKKqK
ɫɫqK qK
ab ab
SS S S S S
VV V DV
D
* * * *
¦¦ ¦
(24)
Ⱦɥɹ ɤɥɚɫɬɟɪɧɨɣ ɨɛɥɚɫɬɢ ɢɫɩɨɥɶɡɭɟɬɫɹ ɚɞɢɚɛɚɬɢɱɟɫɤɨɟ ɩɪɢɛɥɢɠɟɧɢɟ,
ɨɫɧɨɜɚɧɧɨɟ ɧɚ ɬɨɦ, ɱɬɨ ɪɚɞɢɚɥɶɧɨɟ ɨɬɧɨɫɢɬɟɥɶɧɨɟ ɞɜɢɠɟɧɢɟ ɮɪɚɝɦɟɧɬɨɜ
ɞɟɥɟɧɢɹ ɩɪɨɢɫɯɨɞɢɬ ɛɵɫɬɪɟɟ, ɱɟɦ ɢɯ ɭɝɥɨɜɨɟ ɨɬɧɨɫɢɬɟɥɶɧɨɟ ɢ
ɜɪɚɳɚɬɟɥɶɧɨɟ ɞɜɢɠɟɧɢɹ.
Ⱦɥɹ ɩɪɢɦɟɧɢɦɨɫɬɢ ɚɞɢɚɛɚɬɢɱɟɫɤɨɝɨ ɩɪɢɛɥɢɠɟɧɢɹ ɞɨɥɠɧɵ
ɜɵɩɨɥɧɹɬɶɫɹ ɫɥɟɞɭɸɳɢɟ ɭɫɥɨɜɢɹ. ȼɨ-ɩɟɪɜɵɯ, ɤɢɧɟɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ

kin
scc
E
R ɨɬɧɨɫɢɬɟɥɶɧɨɝɨ ɞɜɢɠɟɧɢɹ ɩɟɪɜɢɱɧɵɯ ɮɪɚɝɦɟɧɬɨɜ ɜ ɨɤɪɟɫɬɧɨɫɬɢ
ɬɨɱɤɢ ɪɚɡɪɵɜɚ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ
sc
R
ɞɥɹ ɜɫɟɯ ɨɬɤɪɵɬɵɯ ɤɚɧɚɥɨɜ c ɞɨɥɠɧɚ
ɛɵɬɶ ɝɨɪɚɡɞɨ ɛɨɥɶɲɟ ɰɟɧɬɪɨɛɟɠɧɨɝɨ ɩɨɬɟɧɰɢɚɥɚ, ɫɜɹɡɚɧɧɨɝɨ ɫɨ ɜɫɟɦɢ
ɜɨɡɦɨɠɧɵɦɢ ɡɧɚɱɟɧɢɹɦɢ ɨɬɧɨɫɢɬɟɥɶɧɵɯ ɨɪɛɢɬɚɥɶɧɵɯ ɦɨɦɟɧɬɨɜ
L
ɩɟɪɜɢɱɧɵɯ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ:


2
kin
sc
2
sc
1
.
2
c
c
LL
ER
MR
!!
=
(25)
ȼɵɩɨɥɧɟɧɢɟ ɞɚɧɧɨɝɨ ɭɫɥɨɜɢɹ ɩɪɢɜɨɞɢɬ ɤ ɧɟɡɚɜɢɫɢɦɨɫɬɢ ɞɟɥɢɬɟɥɶɧɵɯ ɮɚɡ
J
S
D
G
ɨɬ ɜɟɥɢɱɢɧɵ
L
. ȼɨ-ɜɬɨɪɵɯ, ɤɢɧɟɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ

kin
scc
E
R ɞɨɥɠɧɚ
ɛɵɬɶ ɝɨɪɚɡɞɨ ɛɨɥɶɲɟ ɜɪɚɳɚɬɟɥɶɧɵɯ ɷɧɟɪɝɢɣ ɩɟɪɜɢɱɧɵɯ ɮɪɚɝɦɟɧɬɨɜ
ɞɟɥɟɧɢɹ ɞɥɹ ɜɫɟɯ ɜɨɡɦɨɠɧɵɯ ɡɧɚɱɟɧɢɣ ɫɩɢɧɨɜ
i
J ɮɪɚɝɦɟɧɬɨɜ


2
kin
sc
1
,
2
ii
c
i
JJ
ER
J
!!
=
(26)
ɝɞɟ
i
J – ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ i -ɝɨ ɮɪɚɝɦɟɧɬɚ. ɗɬɨ ɭɫɥɨɜɢɟ ɩɨɡɜɨɥɹɟɬ ɫɱɢɬɚɬɶ
ɩɨɬɟɧɰɢɚɥɶɧɵɟ ɞɟɥɢɬɟɥɶɧɵɟ ɮɚɡɵ
J
S
D
G
ɧɟ ɡɚɜɢɫɹɳɢɦɢ ɨɬ ɫɩɢɧɨɜ
i
J ɢ
ɫɭɦɦɚɪɧɨɝɨ ɫɩɢɧɚ
F
ɩɟɪɜɢɱɧɵɯ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ. ɇɚɤɨɧɟɰ, ɜɪɟɦɹ
ɮɨɪɦɢɪɨɜɚɧɢɹ ɭɝɥɨɜɵɯ ɪɚɫɩɪɟɞɟɥɟɧɢɣ ɩɟɪɜɢɱɧɵɯ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ
0
t
ɞɨɥɠɧɨ ɛɵɬɶ ɝɨɪɚɡɞɨ ɦɟɧɶɲɟ ɩɟɪɢɨɞɨɜ ɜɪɚɳɟɧɢɹ
rot
i
t [21] ɩɟɪɜɢɱɧɵɯ
ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ ɞɥɹ ɜɫɟɯ ɜɨɡɦɨɠɧɵɯ ɡɧɚɱɟɧɢɣ ɫɩɢɧɨɜ
i
J ɭɤɚɡɚɧɧɵɯ
ɮɪɚɝɦɟɧɬɨɜ
rot
0
2
,
ci
i
ci
R
J
tt
J
S
X
'
=
(27)
ɝɞɟ
c
R
' – ɨɛɥɚɫɬɶ ɮɨɪɦɢɪɨɜɚɧɢɹ ɭɝɥɨɜɵɯ ɪɚɫɩɪɟɞɟɥɟɧɢɣ ɩɟɪɜɢɱɧɵɯ
ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ, ɤɨɬɨɪɵɟ ɨɩɪɟɞɟɥɹɸɬ ɭɝɥɨɜɵɟ ɪɚɫɩɪɟɞɟɥɟɧɢɹ
ɤɨɧɟɱɧɵɯ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ. ɗɬɨ ɭɫɥɨɜɢɟ ɩɨɡɜɨɥɹɟɬ ɫɱɢɬɚɬɶ, ɱɬɨ ɜɨ ɜɫɟɣ
ɭɱɟɬɟ ɨɪɬɨɝɨɧɚɥɶɧɨɫɬɢ ɤɚɧɚɥɨɜɵɯ ɮɭɧɤɰɢɣ (14), ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ
ɪɚɡɥɢɱɧɵɦ ɞɟɥɢɬɟɥɶɧɵɦ ɦɨɞɚɦ q ɢ ɡɧɚɱɟɧɢɹɦ ɩɪɨɟɤɰɢɣ K , ɜɵɪɚɠɟɧɢɟ
ɞɥɹ ɩɨɥɧɨɣ ɞɟɥɢɬɟɥɶɧɨɣ ɲɢɪɢɧɵ *VJ S ɩɪɢɧɢɦɚɟɬ ɜɢɞ:
                                2             2                     2         2
 *VJ S   ¦ *VJ Sɫ ¦ * qKɫ
                      JS
                          aKJ       bVJ SqK               JS
                                                       ¦ *qK    J
                                                             D aK       bVJ SqK .   (24)
         ɫ       ɫqK                               D qK
     Ⱦɥɹ ɤɥɚɫɬɟɪɧɨɣ ɨɛɥɚɫɬɢ ɢɫɩɨɥɶɡɭɟɬɫɹ ɚɞɢɚɛɚɬɢɱɟɫɤɨɟ ɩɪɢɛɥɢɠɟɧɢɟ,
ɨɫɧɨɜɚɧɧɨɟ ɧɚ ɬɨɦ, ɱɬɨ ɪɚɞɢɚɥɶɧɨɟ ɨɬɧɨɫɢɬɟɥɶɧɨɟ ɞɜɢɠɟɧɢɟ ɮɪɚɝɦɟɧɬɨɜ
ɞɟɥɟɧɢɹ ɩɪɨɢɫɯɨɞɢɬ ɛɵɫɬɪɟɟ, ɱɟɦ ɢɯ ɭɝɥɨɜɨɟ ɨɬɧɨɫɢɬɟɥɶɧɨɟ ɢ
ɜɪɚɳɚɬɟɥɶɧɨɟ ɞɜɢɠɟɧɢɹ.
     Ⱦɥɹ   ɩɪɢɦɟɧɢɦɨɫɬɢ     ɚɞɢɚɛɚɬɢɱɟɫɤɨɝɨ    ɩɪɢɛɥɢɠɟɧɢɹ    ɞɨɥɠɧɵ
ɜɵɩɨɥɧɹɬɶɫɹ ɫɥɟɞɭɸɳɢɟ ɭɫɥɨɜɢɹ. ȼɨ-ɩɟɪɜɵɯ, ɤɢɧɟɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ
Eckin Rsc ɨɬɧɨɫɢɬɟɥɶɧɨɝɨ ɞɜɢɠɟɧɢɹ ɩɟɪɜɢɱɧɵɯ ɮɪɚɝɦɟɧɬɨɜ ɜ ɨɤɪɟɫɬɧɨɫɬɢ
ɬɨɱɤɢ ɪɚɡɪɵɜɚ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ Rsc ɞɥɹ ɜɫɟɯ ɨɬɤɪɵɬɵɯ ɤɚɧɚɥɨɜ c ɞɨɥɠɧɚ
ɛɵɬɶ ɝɨɪɚɡɞɨ ɛɨɥɶɲɟ ɰɟɧɬɪɨɛɟɠɧɨɝɨ ɩɨɬɟɧɰɢɚɥɚ, ɫɜɹɡɚɧɧɨɝɨ ɫɨ ɜɫɟɦɢ
ɜɨɡɦɨɠɧɵɦɢ ɡɧɚɱɟɧɢɹɦɢ ɨɬɧɨɫɢɬɟɥɶɧɵɯ ɨɪɛɢɬɚɥɶɧɵɯ ɦɨɦɟɧɬɨɜ L
ɩɟɪɜɢɱɧɵɯ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ:

                                                           =2 L L  1
                                     Eckin Rsc !!2
                                                    .              (25)
                                          2 M c Rsc
ȼɵɩɨɥɧɟɧɢɟ ɞɚɧɧɨɝɨ ɭɫɥɨɜɢɹ ɩɪɢɜɨɞɢɬ ɤ ɧɟɡɚɜɢɫɢɦɨɫɬɢ ɞɟɥɢɬɟɥɶɧɵɯ ɮɚɡ
GDJ S ɨɬ ɜɟɥɢɱɢɧɵ L . ȼɨ-ɜɬɨɪɵɯ, ɤɢɧɟɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ Eckin Rsc ɞɨɥɠɧɚ
ɛɵɬɶ ɝɨɪɚɡɞɨ ɛɨɥɶɲɟ ɜɪɚɳɚɬɟɥɶɧɵɯ ɷɧɟɪɝɢɣ ɩɟɪɜɢɱɧɵɯ ɮɪɚɝɦɟɧɬɨɜ
ɞɟɥɟɧɢɹ ɞɥɹ ɜɫɟɯ ɜɨɡɦɨɠɧɵɯ ɡɧɚɱɟɧɢɣ ɫɩɢɧɨɜ J i ɮɪɚɝɦɟɧɬɨɜ
                                    =2 Ji Ji  1
                          Eckin Rsc !!           ,                 (26)
                                         2 Ji
ɝɞɟ J i – ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ i -ɝɨ ɮɪɚɝɦɟɧɬɚ. ɗɬɨ ɭɫɥɨɜɢɟ ɩɨɡɜɨɥɹɟɬ ɫɱɢɬɚɬɶ
ɩɨɬɟɧɰɢɚɥɶɧɵɟ ɞɟɥɢɬɟɥɶɧɵɟ ɮɚɡɵ GDJ S ɧɟ ɡɚɜɢɫɹɳɢɦɢ ɨɬ ɫɩɢɧɨɜ J i ɢ
ɫɭɦɦɚɪɧɨɝɨ ɫɩɢɧɚ F ɩɟɪɜɢɱɧɵɯ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ. ɇɚɤɨɧɟɰ, ɜɪɟɦɹ
ɮɨɪɦɢɪɨɜɚɧɢɹ ɭɝɥɨɜɵɯ ɪɚɫɩɪɟɞɟɥɟɧɢɣ ɩɟɪɜɢɱɧɵɯ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ t0
ɞɨɥɠɧɨ ɛɵɬɶ ɝɨɪɚɡɞɨ ɦɟɧɶɲɟ ɩɟɪɢɨɞɨɜ ɜɪɚɳɟɧɢɹ tirot [21] ɩɟɪɜɢɱɧɵɯ
ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ ɞɥɹ ɜɫɟɯ ɜɨɡɦɨɠɧɵɯ ɡɧɚɱɟɧɢɣ ɫɩɢɧɨɜ J i ɭɤɚɡɚɧɧɵɯ
ɮɪɚɝɦɟɧɬɨɜ
                    'Rc          2S J i
                t0       tirot        ,                          (27)
                     Xc           =J i
ɝɞɟ 'Rc – ɨɛɥɚɫɬɶ ɮɨɪɦɢɪɨɜɚɧɢɹ ɭɝɥɨɜɵɯ ɪɚɫɩɪɟɞɟɥɟɧɢɣ ɩɟɪɜɢɱɧɵɯ
ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ, ɤɨɬɨɪɵɟ ɨɩɪɟɞɟɥɹɸɬ ɭɝɥɨɜɵɟ ɪɚɫɩɪɟɞɟɥɟɧɢɹ
ɤɨɧɟɱɧɵɯ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ. ɗɬɨ ɭɫɥɨɜɢɟ ɩɨɡɜɨɥɹɟɬ ɫɱɢɬɚɬɶ, ɱɬɨ ɜɨ ɜɫɟɣ
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