Квантовая теория двойного и тройного деления атомных ядер. Кадменский С.Г - 13 стр.

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ɞɟɥɢɬɟɥɶɧɵɟ ɮɚɡɵ ɫ ɭɱɟɬɨɦ ɡɚɤɨɧɚ ɫɨɯɪɚɧɟɧɢɹ ɩɨɥɧɨɝɨ ɫɩɢɧɚ ɞɟɥɹɳɟɝɨɫɹ
ɹɞɪɚ.
2. Ʉɜɚɧɬɨɜɚɹ ɬɟɨɪɢɹ ɫɩɨɧɬɚɧɧɨɝɨ ɢ ɧɢɡɤɨɷɧɟɪɝɟɬɢɱɟɫɤɨɝɨ ɜɵɧɭɠɞɟɧɧɨɝɨ
ɞɜɨɣɧɨɝɨ ɞɟɥɟɧɢɹ ɹɞɟɪ
Ɉɛɳɢɟ ɩɪɟɞɫɬɚɜɥɟɧɢɹ ɤɜɚɧɬɨɜɨɣ ɬɟɨɪɢɢ ɞɜɨɣɧɨɝɨ ɞɟɥɟɧɢɹ ɹɞɟɪ
Ʉɜɚɧɬɨɜɚɹ ɬɟɨɪɢɹ ɫɩɨɧɬɚɧɧɨɝɨ ɢ ɧɢɡɤɨɷɧɟɪɝɟɬɢɱɟɫɤɨɝɨ ɜɵɧɭɠɞɟɧɧɨɝɨ
ɞɟɥɟɧɢɹ, ɛɚɡɢɪɭɸɳɚɹɫɹ ɧɚ ɫɬɚɰɢɨɧɚɪɧɨɦ ɮɨɪɦɚɥɢɡɦɟ ɦɧɨɝɨɱɚɫɬɢɱɧɨɣ
ɬɟɨɪɢɢ ɹɞɟɪɧɵɯ ɪɟɚɤɰɢɣ [15] ɢ ɬɟɨɪɢɢ ɨɬɤɪɵɬɵɯ ɮɟɪɦɢ-ɫɢɫɬɟɦ [16],
ɢɫɩɨɥɶɡɭɸɳɚɹ ɨɫɧɨɜɧɵɟ ɞɨɫɬɢɠɟɧɢɹ ɬɪɚɞɢɰɢɨɧɧɨɣ ɬɟɨɪɢɢ ɞɟɥɟɧɢɹ ɢ
ɤɜɚɧɬɨɜɨɦɟɯɚɧɢɱɟɫɤɢɯ ɩɨɞɯɨɞɨɜ ɪɚɛɨɬ [10–13] ɢ ɨɩɢɪɚɸɳɚɹɫɹ ɧɚ ɩɨɧɹɬɢɹ
ɜɨɥɧɨɜɵɯ ɮɭɧɤɰɢɣ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ ɢ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ, ɚɦɩɥɢɬɭɞ
ɩɚɪɰɢɚɥɶɧɵɯ ɞɟɥɢɬɟɥɶɧɵɯ ɲɢɪɢɧ ɢ ɞɟɥɢɬɟɥɶɧɵɯ ɮɚɡ, ɛɵɥɚ ɪɚɡɜɢɬɚ ɜ
ɪɚɛɨɬɚɯ [17–19].
ȼ ɪɚɦɤɚɯ ɤɜɚɧɬɨɜɨɣ ɬɟɨɪɢɢ ɞɜɨɣɧɨɝɨ ɞɟɥɟɧɢɹ [17–19] ɞɟɥɟɧɢɟ
ɪɚɫɫɦɚɬɪɢɜɚɟɬɫɹ ɤɚɤ ɪɚɫɩɚɞ ɤɜɚɡɢɫɬɚɰɢɨɧɚɪɧɨɝɨ ɫɨɫɬɨɹɧɢɹ ɞɟɥɹɳɟɝɨɫɹ
ɹɞɪɚ, ɨɩɢɫɵɜɚɟɦɨɝɨ ɜɨɥɧɨɜɨɣ ɮɭɧɤɰɢɟɣ
Ȍ
J
M
S
V
, ɤɨɬɨɪɚɹ ɭɞɨɜɥɟɬɜɨɪɹɟɬ
ɭɪɚɜɧɟɧɢɸ ɒɪɟɞɢɧɝɟɪɚ:

Ȍ 0,
JJM
A
HE
S
VV
(7)
ɝɞɟ
A
H
– ɝɚɦɢɥɶɬɨɧɢɚɧ ɹɞɪɚ
A
ɜɫ. ɰ. ɦ.,

2
JJJ
EEi
S
VVV
* ,
J
E
V
ɫɨɜɩɚɞɚɟɬ ɫ ɬɨɱɧɨɫɬɶɸ ɞɨ ɡɧɚɤɚ ɫ ɷɧɟɪɝɢɟɣ ɫɜɹɡɢ ɹɞɪɚ,
J
S
V
* – ɩɨɥɧɚɹ
ɲɢɪɢɧɚ ɪɚɫɩɚɞɚ ɹɞɪɚ ɜɨ ɜɫɟ ɨɬɤɪɵɬɵɟ ɤɚɧɚɥɵ.
ɋ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɬɟɯɧɢɤɢ ɩɪɨɟɤɰɢɨɧɧɵɯ ɨɩɟɪɚɬɨɪɨɜ ɦɧɨɝɨɱɚɫɬɢɱɧɨɣ
ɬɟɨɪɢɢ ɹɞɟɪɧɵɯ ɪɟɚɤɰɢɣ ɢ ɬɟɨɪɢɢ ɨɬɤɪɵɬɵɯ Ɏɟɪɦɢ-ɫɢɫɬɟɦ ɜɨɥɧɨɜɚɹ
ɮɭɧɤɰɢɹ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ
Ȍ
J
M
S
V
ɩɪɟɞɫɬɚɜɥɹɟɬɫɹ ɜ ɜɢɞɟ:
  
ˆ
ˆ
,
JM JM JM
PQ
SSS
VVV
WWW
< << (8)
ɝɞɟ ɨɩɟɪɚɬɨɪ
ˆ
P ɩɪɨɟɤɬɢɪɭɟɬ ɫɨɫɬɨɹɧɢɹ ɹɞɪɚ
A
ɧɚ ɜɧɭɬɪɟɧɧɸɸ
(ɨɛɨɥɨɱɟɱɧɭɸ) ɨɛɥɚɫɬɶ ɤɨɧɮɢɝɭɪɚɰɢɨɧɧɨɝɨ ɩɪɨɫɬɪɚɧɫɬɜɚ, ɫɜɹɡɚɧɧɭɸ ɫ
ɩɨɥɧɵɦ ɧɚɛɨɪɨɦ ɤɨɨɪɞɢɧɚɬ
W
ɹɞɪɚ ɜ ɫ. ɰ. ɦ. ȼ ɷɬɨɣ ɨɛɥɚɫɬɢ ɹɞɪɨ
A
ɢɦɟɟɬ
ɨɞɧɨɫɜɹɡɧɭɸ ɮɨɪɦɭ ɢ ɦɨɠɟɬ ɛɵɬɶ ɨɩɢɫɚɧɨ ɩɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ
ɨɪɬɨɧɨɪɦɢɪɨɜɚɧɧɨɝɨ, ɧɨ ɨɝɪɚɧɢɱɟɧɧɨɝɨ ɛɚɡɢɫɚ

Ȍ
JM
n
S
W
ɦɧɨɝɨɱɚɫɬɢɱɧɵɯ
ɨɛɨɥɨɱɟɱɧɵɯ ɮɭɧɤɰɢɣ, ɫɬɪɨɹɳɢɯɫɹ ɜ ɪɚɦɤɚɯ ɨɛɨɛɳɟɧɧɨɣ ɦɨɞɟɥɢ ɹɞɪɚ [20]
ɫ ɭɱɟɬɨɦ ɧɨɪɦɚɥɶɧɵɯ ɢ ɫɜɟɪɯɬɟɤɭɱɢɯ ɧɭɤɥɨɧ-ɧɭɤɥɨɧɧɵɯ ɤɨɪɪɟɥɹɰɢɣ ɢ
ɤɨɥɥɟɤɬɢɜɧɵɯ ɦɨɞ ɞɜɢɠɟɧɢɹ, ɝɞɟ ɢɧɞɟɤɫ n ɩɪɢɧɢɦɚɟɬ ɞɢɫɤɪɟɬɧɵɣ ɢ
ɤɨɧɟɱɧɵɣ ɪɹɞ ɡɧɚɱɟɧɢɣ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɨɩɟɪɚɬɨɪ
ˆ
P ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɤɚɤ
ˆ
.
J
MJM
nn
n
Pop
SS
< <
¦
(9) 
ɞɟɥɢɬɟɥɶɧɵɟ ɮɚɡɵ ɫ ɭɱɟɬɨɦ ɡɚɤɨɧɚ ɫɨɯɪɚɧɟɧɢɹ ɩɨɥɧɨɝɨ ɫɩɢɧɚ ɞɟɥɹɳɟɝɨɫɹ
ɹɞɪɚ.

2. Ʉɜɚɧɬɨɜɚɹ ɬɟɨɪɢɹ ɫɩɨɧɬɚɧɧɨɝɨ ɢ ɧɢɡɤɨɷɧɟɪɝɟɬɢɱɟɫɤɨɝɨ ɜɵɧɭɠɞɟɧɧɨɝɨ
ɞɜɨɣɧɨɝɨ ɞɟɥɟɧɢɹ ɹɞɟɪ

Ɉɛɳɢɟ ɩɪɟɞɫɬɚɜɥɟɧɢɹ ɤɜɚɧɬɨɜɨɣ ɬɟɨɪɢɢ ɞɜɨɣɧɨɝɨ ɞɟɥɟɧɢɹ ɹɞɟɪ
    Ʉɜɚɧɬɨɜɚɹ ɬɟɨɪɢɹ ɫɩɨɧɬɚɧɧɨɝɨ ɢ ɧɢɡɤɨɷɧɟɪɝɟɬɢɱɟɫɤɨɝɨ ɜɵɧɭɠɞɟɧɧɨɝɨ
ɞɟɥɟɧɢɹ, ɛɚɡɢɪɭɸɳɚɹɫɹ ɧɚ ɫɬɚɰɢɨɧɚɪɧɨɦ ɮɨɪɦɚɥɢɡɦɟ ɦɧɨɝɨɱɚɫɬɢɱɧɨɣ
ɬɟɨɪɢɢ ɹɞɟɪɧɵɯ ɪɟɚɤɰɢɣ [15] ɢ ɬɟɨɪɢɢ ɨɬɤɪɵɬɵɯ ɮɟɪɦɢ-ɫɢɫɬɟɦ [16],
ɢɫɩɨɥɶɡɭɸɳɚɹ ɨɫɧɨɜɧɵɟ ɞɨɫɬɢɠɟɧɢɹ ɬɪɚɞɢɰɢɨɧɧɨɣ ɬɟɨɪɢɢ ɞɟɥɟɧɢɹ ɢ
ɤɜɚɧɬɨɜɨɦɟɯɚɧɢɱɟɫɤɢɯ ɩɨɞɯɨɞɨɜ ɪɚɛɨɬ [10–13] ɢ ɨɩɢɪɚɸɳɚɹɫɹ ɧɚ ɩɨɧɹɬɢɹ
ɜɨɥɧɨɜɵɯ ɮɭɧɤɰɢɣ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ ɢ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ, ɚɦɩɥɢɬɭɞ
ɩɚɪɰɢɚɥɶɧɵɯ ɞɟɥɢɬɟɥɶɧɵɯ ɲɢɪɢɧ ɢ ɞɟɥɢɬɟɥɶɧɵɯ ɮɚɡ, ɛɵɥɚ ɪɚɡɜɢɬɚ ɜ
ɪɚɛɨɬɚɯ [17–19].
    ȼ ɪɚɦɤɚɯ ɤɜɚɧɬɨɜɨɣ ɬɟɨɪɢɢ ɞɜɨɣɧɨɝɨ ɞɟɥɟɧɢɹ [17–19] ɞɟɥɟɧɢɟ
ɪɚɫɫɦɚɬɪɢɜɚɟɬɫɹ ɤɚɤ ɪɚɫɩɚɞ ɤɜɚɡɢɫɬɚɰɢɨɧɚɪɧɨɝɨ ɫɨɫɬɨɹɧɢɹ ɞɟɥɹɳɟɝɨɫɹ
ɹɞɪɚ, ɨɩɢɫɵɜɚɟɦɨɝɨ ɜɨɥɧɨɜɨɣ ɮɭɧɤɰɢɟɣ ȌVJ S M , ɤɨɬɨɪɚɹ ɭɞɨɜɥɟɬɜɨɪɹɟɬ
ɭɪɚɜɧɟɧɢɸ ɒɪɟɞɢɧɝɟɪɚ:
                                 H A  EVJ ȌVJ S M       0,                    (7)

ɝɞɟ H A – ɝɚɦɢɥɶɬɨɧɢɚɧ ɹɞɪɚ A ɜ ɫ. ɰ. ɦ., EVJ                 EVJ  i*VJ S 2 , EVJ

ɫɨɜɩɚɞɚɟɬ ɫ ɬɨɱɧɨɫɬɶɸ ɞɨ ɡɧɚɤɚ ɫ ɷɧɟɪɝɢɟɣ ɫɜɹɡɢ ɹɞɪɚ, *VJ S – ɩɨɥɧɚɹ
ɲɢɪɢɧɚ ɪɚɫɩɚɞɚ ɹɞɪɚ ɜɨ ɜɫɟ ɨɬɤɪɵɬɵɟ ɤɚɧɚɥɵ.
    ɋ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɬɟɯɧɢɤɢ ɩɪɨɟɤɰɢɨɧɧɵɯ ɨɩɟɪɚɬɨɪɨɜ ɦɧɨɝɨɱɚɫɬɢɱɧɨɣ
ɬɟɨɪɢɢ ɹɞɟɪɧɵɯ ɪɟɚɤɰɢɣ ɢ ɬɟɨɪɢɢ ɨɬɤɪɵɬɵɯ Ɏɟɪɦɢ-ɫɢɫɬɟɦ ɜɨɥɧɨɜɚɹ
ɮɭɧɤɰɢɹ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ ȌVJ S M ɩɪɟɞɫɬɚɜɥɹɟɬɫɹ ɜ ɜɢɞɟ:
                  < JS M W
                    V          Pˆ < J S M W  Qˆ < J S M W ,
                                   V                 V            (8)
ɝɞɟ ɨɩɟɪɚɬɨɪ P̂ ɩɪɨɟɤɬɢɪɭɟɬ ɫɨɫɬɨɹɧɢɹ ɹɞɪɚ A ɧɚ ɜɧɭɬɪɟɧɧɸɸ
(ɨɛɨɥɨɱɟɱɧɭɸ) ɨɛɥɚɫɬɶ ɤɨɧɮɢɝɭɪɚɰɢɨɧɧɨɝɨ ɩɪɨɫɬɪɚɧɫɬɜɚ, ɫɜɹɡɚɧɧɭɸ ɫ
ɩɨɥɧɵɦ ɧɚɛɨɪɨɦ ɤɨɨɪɞɢɧɚɬ W ɹɞɪɚ ɜ ɫ. ɰ. ɦ. ȼ ɷɬɨɣ ɨɛɥɚɫɬɢ ɹɞɪɨ A ɢɦɟɟɬ
ɨɞɧɨɫɜɹɡɧɭɸ ɮɨɪɦɭ ɢ ɦɨɠɟɬ ɛɵɬɶ ɨɩɢɫɚɧɨ ɩɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ
ɨɪɬɨɧɨɪɦɢɪɨɜɚɧɧɨɝɨ, ɧɨ ɨɝɪɚɧɢɱɟɧɧɨɝɨ ɛɚɡɢɫɚ Ȍ nJ S M W ɦɧɨɝɨɱɚɫɬɢɱɧɵɯ
ɨɛɨɥɨɱɟɱɧɵɯ ɮɭɧɤɰɢɣ, ɫɬɪɨɹɳɢɯɫɹ ɜ ɪɚɦɤɚɯ ɨɛɨɛɳɟɧɧɨɣ ɦɨɞɟɥɢ ɹɞɪɚ [20]
ɫ ɭɱɟɬɨɦ ɧɨɪɦɚɥɶɧɵɯ ɢ ɫɜɟɪɯɬɟɤɭɱɢɯ ɧɭɤɥɨɧ-ɧɭɤɥɨɧɧɵɯ ɤɨɪɪɟɥɹɰɢɣ ɢ
ɤɨɥɥɟɤɬɢɜɧɵɯ ɦɨɞ ɞɜɢɠɟɧɢɹ, ɝɞɟ ɢɧɞɟɤɫ n ɩɪɢɧɢɦɚɟɬ ɞɢɫɤɪɟɬɧɵɣ ɢ
ɤɨɧɟɱɧɵɣ ɪɹɞ ɡɧɚɱɟɧɢɣ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɨɩɟɪɚɬɨɪ P̂ ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɤɚɤ
                  Pˆ op ¦ < J S M < J S M .
                             n              n                       (9)
                         n

                                       13

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