Квантовая теория двойного и тройного деления атомных ядер. Кадменский С.Г - 41 стр.

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41
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ȼ ɮɨɪɦɭɥɭ ɞɥɹ
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F ɜɯɨɞɢɬ ɫɩɢɧɨɜɚɹ ɦɚɬɪɢɰɚ ɩɥɨɬɧɨɫɬɢ
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ɭɱɢɬɵɜɚɸɳɚɹ ɢɧɬɟɪɮɟɪɟɧɰɢɸ ɫɨɫɬɨɹɧɢɣ ɪɚɡɥɢɱɧɵɯ
s
-ɧɟɣɬɪɨɧɧɵɯ
ɪɟɡɨɧɚɧɫɨɜ, ɢɦɟɸɳɢɯ, ɜ ɩɪɢɧɰɢɩɟ, ɪɚɡɥɢɱɧɵɟ ɫɩɢɧɵ [24]. ɉɨɞɨɛɧɚɹ
ɢɧɬɟɪɮɟɪɟɧɰɢɹ ɹɜɥɹɟɬɫɹ ɭɧɢɤɚɥɶɧɵɦ ɫɜɨɣɫɬɜɨɦ ɹɜɥɟɧɢɹ ɞɟɥɟɧɢɹ ɹɞɟɪ. ɗɬɚ
ɦɚɬɪɢɰɚ ɩɥɨɬɧɨɫɬɢ ɞɥɹ ɫɥɭɱɚɹ ɡɚɯɜɚɬɚ ɩɨɥɹɪɢɡɨɜɚɧɧɨɝɨ ɧɟɣɬɪɨɧɚ
ɧɟɩɨɥɹɪɢɡɨɜɚɧɧɵɦ ɹɞɪɨɦ-ɦɢɲɟɧɶɸ ɫɨ ɫɩɢɧɨɦ
I
ɢɦɟɟɬ ɫɬɪɭɤɬɭɪɭ:
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, (65)
ɝɞɟ ɮɭɧɤɰɢɹ
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ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɪɨɢɡɜɟɞɟɧɢɟɦ ɫɩɢɧɨɜɨɣ ɦɚɬɪɢɰɵ
ɩɥɨɬɧɨɫɬɢ ɧɟɩɨɥɹɪɢɡɨɜɚɧɧɨɝɨ ɹɞɪɚ-ɦɢɲɟɧɢ ɧɚ ɫɩɢɧɨɜɭɸ ɦɚɬɪɢɰɭ
ɩɥɨɬɧɨɫɬɢ ɩɨɥɹɪɢɡɨɜɚɧɧɨɝɨ ɧɟɣɬɪɨɧɚ ɫ ɜɟɤɬɨɪɨɦ ɩɨɥɹɪɢɡɚɰɢɢ
n
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ɧɚɩɪɚɜɥɟɧɧɵɦ ɩɨ ɨɫɢ y :
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(66)
ɋɩɢɧɨɜɭɸ ɦɚɬɪɢɰɭ ɩɥɨɬɧɨɫɬɢ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ
(65) ɦɨɠɧɨ ɩɪɢɜɟɫɬɢ ɤ
ɜɢɞɭ:
 
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º
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(67)
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(68)
ɝɞɟ 1/2JI
!
, 1/ 2JI
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ɉɪɢ ɩɨɞɫɬɚɧɨɜɤɟ ɮɨɪɦɭɥɵ
(61) ɜ ɮɨɪɦɭɥɭ (59) ɢ ɩɪɨɜɟɞɟɧɢɢ
ɢɧɬɟɝɪɢɪɨɜɚɧɢɹ ɩɨ d
Z
ɫ ɭɱɟɬɨɦ ɫɜɨɣɫɬɜ ɮɭɧɤɰɢɣ ȼɢɝɧɟɪɚ [2] ɱɥɟɧ,
ɫɬɨɹɳɢɣ ɜ ɮɢɝɭɪɧɵɯ ɫɤɨɛɤɚɯ ɮɨɪɦɭɥɵ
(62), ɩɪɢɜɨɞɢɬɫɹ ɤ ɞɢɚɝɨɧɚɥɶɧɨɦɭ
ɩɨ ɢɧɞɟɤɫɚɦ
M , 'M ɜɢɞɭ. ɇɨ ɬɨɝɞɚ ɡɚɜɢɫɹɳɚɹ ɨɬ ɩɨɥɹɪɢɡɚɰɢɢ ɧɟɣɬɪɨɧɚ
ɫɩɢɧɨɜɚɹ ɱɚɫɬɶ ɦɚɬɪɢɰɵ ɩɥɨɬɧɨɫɬɢ ɹɞɪɚ
'
'
s
J
J
M
M
U
(67), ɤɨɬɨɪɚɹ ɢɦɟɟɬ ɬɨɥɶɤɨ
ɧɟɞɢɚɝɨɧɚɥɶɧɵɟ ɩɨ ɢɧɞɟɤɫɚɦ
M , 'M ɤɨɦɩɨɧɟɧɬɵ, ɧɟ ɞɚɫɬ ɜɤɥɚɞɚ ɜ
ɜɟɥɢɱɢɧɭ
(62) ɢ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɜ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɟ ɫɟɱɟɧɢɟ ɪɟɚɤɰɢɢ
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,nf . ɍɤɚɡɚɧɧɨɟ ɫɟɱɟɧɢɟ ɜ ɷɬɨɦ ɫɥɭɱɚɟ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɟɪɜɵɦ ɱɥɟɧɨɦ
                                       * J                 J     G sJ s s ' J s '
                               hsJ s    hs 's '    hsJ s hs 's ' e                  .         (64)
                                       J Js'                                                 J J
     ȼ ɮɨɪɦɭɥɭ ɞɥɹ FK s                           ɜɯɨɞɢɬ ɫɩɢɧɨɜɚɹ ɦɚɬɪɢɰɚ ɩɥɨɬɧɨɫɬɢ U MM
                                                                                       s s' ,
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                                          s
ɭɱɢɬɵɜɚɸɳɚɹ ɢɧɬɟɪɮɟɪɟɧɰɢɸ ɫɨɫɬɨɹɧɢɣ ɪɚɡɥɢɱɧɵɯ s -ɧɟɣɬɪɨɧɧɵɯ
ɪɟɡɨɧɚɧɫɨɜ, ɢɦɟɸɳɢɯ, ɜ ɩɪɢɧɰɢɩɟ, ɪɚɡɥɢɱɧɵɟ ɫɩɢɧɵ [24]. ɉɨɞɨɛɧɚɹ
ɢɧɬɟɪɮɟɪɟɧɰɢɹ ɹɜɥɹɟɬɫɹ ɭɧɢɤɚɥɶɧɵɦ ɫɜɨɣɫɬɜɨɦ ɹɜɥɟɧɢɹ ɞɟɥɟɧɢɹ ɹɞɟɪ. ɗɬɚ
ɦɚɬɪɢɰɚ ɩɥɨɬɧɨɫɬɢ ɞɥɹ ɫɥɭɱɚɹ ɡɚɯɜɚɬɚ ɩɨɥɹɪɢɡɨɜɚɧɧɨɝɨ ɧɟɣɬɪɨɧɚ
ɧɟɩɨɥɹɪɢɡɨɜɚɧɧɵɦ ɹɞɪɨɦ-ɦɢɲɟɧɶɸ ɫɨ ɫɩɢɧɨɦ I ɢɦɟɟɬ ɫɬɪɭɤɬɭɪɭ:
                                                                              1
                                Js Js '                     JsM     JsM     I
                              U MM   '            ¦ '
                                                           C 1     C 1     U 2 '
                                                            I M I m I M I m M I M I mm '
                                                                                         ,    (65)
                                              M I M I mm '   2       2
                           1
                          I
 ɝɞɟ ɮɭɧɤɰɢɹ U             2                  ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɪɨɢɡɜɟɞɟɧɢɟɦ ɫɩɢɧɨɜɨɣ ɦɚɬɪɢɰɵ
                          M I M I' mm '
 ɩɥɨɬɧɨɫɬɢ ɧɟɩɨɥɹɪɢɡɨɜɚɧɧɨɝɨ ɹɞɪɚ-ɦɢɲɟɧɢ ɧɚ ɫɩɢɧɨɜɭɸ ɦɚɬɪɢɰɭ
 ɩɥɨɬɧɨɫɬɢ ɩɨɥɹɪɢɡɨɜɚɧɧɨɝɨ ɧɟɣɬɪɨɧɚ ɫ ɜɟɤɬɨɪɨɦ ɩɨɥɹɪɢɡɚɰɢɢ p n ,
 ɧɚɩɪɚɜɥɟɧɧɵɦ ɩɨ ɨɫɢ y :
                       1
                      I  1
                  U    2      G           ª                        º.
                                       ' G m, m '  pn V y            (66)
                     2 2 I  1 M I , M I «¬
                      M I M I' mm '                        m, m ' »¼

 ɋɩɢɧɨɜɭɸ ɦɚɬɪɢɰɭ ɩɥɨɬɧɨɫɬɢ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ (65) ɦɨɠɧɨ ɩɪɢɜɟɫɬɢ ɤ
 ɜɢɞɭ:

   Js Js'        1                         ipn                     J M'          J M'
 U MM   '             G J , J G M ,M '           A J s , J s ' ªC J s1' M 1  C J s1' M 1 º , (67)
              2 2I  1 s s '             2 2I  1               ¬ s               s         ¼
                                          §    Js                J 1         ·
            A Js, Js'         G Js ,Js' ¨           G J s , J  s G J s , J! ¸ 
                                          ¨ 2 Js 1               2Js         ¸
                                          ©                                   ¹               (68)
          2Js  1                    2J s  1
                G J s , J s ' 1            G J , J 1,
           2J s                     2 Js 1 s s'
ɝɞɟ J ! I  1/ 2 , J  I  1/ 2 .
     ɉɪɢ ɩɨɞɫɬɚɧɨɜɤɟ ɮɨɪɦɭɥɵ (61) ɜ ɮɨɪɦɭɥɭ (59) ɢ ɩɪɨɜɟɞɟɧɢɢ
ɢɧɬɟɝɪɢɪɨɜɚɧɢɹ ɩɨ dZ ɫ ɭɱɟɬɨɦ ɫɜɨɣɫɬɜ ɮɭɧɤɰɢɣ ȼɢɝɧɟɪɚ [2] ɱɥɟɧ,
ɫɬɨɹɳɢɣ ɜ ɮɢɝɭɪɧɵɯ ɫɤɨɛɤɚɯ ɮɨɪɦɭɥɵ (62), ɩɪɢɜɨɞɢɬɫɹ ɤ ɞɢɚɝɨɧɚɥɶɧɨɦɭ
ɩɨ ɢɧɞɟɤɫɚɦ M , M ' ɜɢɞɭ. ɇɨ ɬɨɝɞɚ ɡɚɜɢɫɹɳɚɹ ɨɬ ɩɨɥɹɪɢɡɚɰɢɢ ɧɟɣɬɪɨɧɚ
                                                                       J J
ɫɩɢɧɨɜɚɹ ɱɚɫɬɶ ɦɚɬɪɢɰɵ ɩɥɨɬɧɨɫɬɢ ɹɞɪɚ U MM
                                         s s ' (67), ɤɨɬɨɪɚɹ ɢɦɟɟɬ ɬɨɥɶɤɨ
                                            '
ɧɟɞɢɚɝɨɧɚɥɶɧɵɟ ɩɨ ɢɧɞɟɤɫɚɦ M , M ' ɤɨɦɩɨɧɟɧɬɵ, ɧɟ ɞɚɫɬ ɜɤɥɚɞɚ ɜ
ɜɟɥɢɱɢɧɭ (62) ɢ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɜ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɟ ɫɟɱɟɧɢɟ ɪɟɚɤɰɢɢ
 n, f . ɍɤɚɡɚɧɧɨɟ ɫɟɱɟɧɢɟ ɜ ɷɬɨɦ ɫɥɭɱɚɟ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɟɪɜɵɦ ɱɥɟɧɨɦ

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