Квантовая теория двойного и тройного деления атомных ядер. Кадменский С.Г - 32 стр.

UptoLike

ВУЗ: 

ВГУ | Воронеж

Составители: 

Рубрика: 

32

33
arccos
m
E
E
H
, (47)
ɝɞɟ
3
m
E
– ɦɚɤɫɢɦɚɥɶɧɚɹ ɷɧɟɪɝɢɹ ɬɪɟɬɶɟɣ ɱɚɫɬɢɰɵ
12
3
123
m
c
AA
EQ
A
AA

.
Ɋɚɫɫɦɨɬɪɢɦ ɜɨɩɪɨɫ ɨ ɩɪɢɦɟɧɢɦɨɫɬɢ ɚɞɢɚɛɚɬɢɱɟɫɤɨɝɨ ɩɪɢɛɥɢɠɟɧɢɹ
(25)–(27), ɢɫɩɨɥɶɡɨɜɚɧɧɨɝɨ ɩɪɢ ɨɩɢɫɚɧɢɢ ɞɜɨɣɧɨɝɨ ɞɟɥɟɧɢɹ ɹɞɟɪ, ɤ
ɬɪɨɣɧɨɦɭ ɞɟɥɟɧɢɸ ɹɞɟɪ. Ʉɚɤ ɫɥɟɞɭɟɬ ɢɡ ɷɤɫɩɟɪɢɦɟɧɬɚ [22], ɩɨɹɜɥɟɧɢɟ
ɬɪɟɬɶɟɣ ɱɚɫɬɢɰɵ ɩɪɢɜɨɞɢɬ ɤ ɭɦɟɧɶɲɟɧɢɸ ɷɧɟɪɝɢɢ ɨɬɧɨɫɢɬɟɥɶɧɨɝɨ
ɞɜɢɠɟɧɢɹ ɮɪɚɝɦɟɧɬɨɜ ɬɪɨɣɧɨɝɨ ɞɟɥɟɧɢɹ, ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɚɧɚɥɨɝɢɱɧɨɣ
ɷɧɟɪɝɢɟɣ ɞɥɹ ɞɜɨɣɧɨɝɨ ɞɟɥɟɧɢɹ ɧɚ ɜɟɥɢɱɢɧɭ ɩɪɢɦɟɪɧɨ ɪɚɜɧɭɸ ɩɨɥɨɜɢɧɟ
ɚɫɢɦɩɬɨɬɢɱɟɫɤɨɣ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɬɪɟɬɶɟɣ ɱɚɫɬɢɰɵ
3
E
. ȼɟɥɢɱɢɧɚ
3
E
ɞɥɹ ɜɫɟɯ ɬɪɟɬɶɢɯ ɱɚɫɬɢɰ ɨɤɚɡɵɜɚɟɬɫɹ ɡɚɦɟɬɧɨ ɦɟɧɶɲɟ (
3
E
< 30 Ɇɷȼ)
ɨɬɧɨɫɢɬɟɥɶɧɨɣ ɷɧɟɪɝɢɢ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ (

12
200EE!
Ɇɷȼ). Ⱦɥɹ
ɜɵɩɨɥɧɢɦɨɫɬɢ ɚɞɢɚɛɚɬɢɱɟɫɤɨɝɨ ɩɪɢɛɥɢɠɟɧɢɹ
(25)–(27) ɞɥɹ ɬɪɨɣɧɨɝɨ
ɞɟɥɟɧɢɹ ɧɟɨɛɯɨɞɢɦɨ, ɱɬɨɛɵ, ɤɚɤ ɢ ɜ ɫɥɭɱɚɟ ɞɜɨɣɧɨɝɨ ɞɟɥɟɧɢɹ,
ɤɢɧɟɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɨɬɧɨɫɢɬɟɥɶɧɨɝɨ ɞɜɢɠɟɧɢɹ ɮɪɚɝɦɟɧɬɨɜ ɜ ɦɨɦɟɧɬ
ɪɚɡɪɵɜɚ (
3
sc
R
R ) ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ ɧɚ ɮɪɚɝɦɟɧɬɵ ɞɟɥɟɧɢɹ ɞɨɥɠɧɚ ɛɵɬɶ
ɞɨɫɬɚɬɨɱɧɨ ɛɨɥɶɲɨɣ:
3
sc
10
kin
c
ER! Ɇɷȼ. ɉɨɫɤɨɥɶɤɭ, ɤɚɤ ɨɬɦɟɱɚɥɨɫɶ
ɜɵɲɟ, ɷɧɟɪɝɢɹ ɨɬɧɨɫɢɬɟɥɶɧɨɝɨ ɞɜɢɠɟɧɢɹ ɞɜɭɯ ɮɪɚɝɦɟɧɬɨɜ ɜ ɬɪɨɣɧɨɦ
ɞɟɥɟɧɢɢ ɦɟɧɶɲɟ ɷɧɟɪɝɢɢ ɨɬɧɨɫɢɬɟɥɶɧɨɝɨ ɞɜɢɠɟɧɢɹ ɞɜɭɯ ɮɪɚɝɦɟɧɬɨɜ ɜ
ɞɜɨɣɧɨɦ ɞɟɥɟɧɢɢ, ɬɨ ɷɬɨ ɭɫɥɨɜɢɟ ɫɜɢɞɟɬɟɥɶɫɬɜɭɟɬ, ɱɬɨ
3
sc
R
ɞɥɹ ɬɪɨɣɧɨɝɨ
ɞɟɥɟɧɢɹ ɛɨɥɶɲɟ
2
sc
R
ɞɥɹ ɞɜɨɣɧɨɝɨ ɞɟɥɟɧɢɹ. ɉɪɢ ɜɵɩɨɥɧɟɧɢɢ ɭɫɥɨɜɢɹ
ɚɞɢɚɛɚɬɢɱɧɨɫɬɢ
(25) ɬɚɤ ɠɟ, ɤɚɤ ɢ ɜ ɫɥɭɱɚɟ ɞɜɨɣɧɨɝɨ ɞɟɥɟɧɢɹ, ɦɨɠɧɨ
ɢɫɩɨɥɶɡɨɜɚɬɶ ɞɨɩɭɳɟɧɢɟ, ɱɬɨ ɭɝɥɵ ɗɣɥɟɪɚ, ɨɩɪɟɞɟɥɹɸɳɢɟ ɨɪɢɟɧɬɚɰɢɸ
ɨɫɟɣ ɫɢɦɦɟɬɪɢɢ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ ɢ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ, ɫɨɜɩɚɞɚɸɬ ɜ
ɨɛɥɚɫɬɢ ɮɨɪɦɢɪɨɜɚɧɢɹ ɭɝɥɨɜɵɯ ɪɚɫɩɪɟɞɟɥɟɧɢɣ ɩɪɨɞɭɤɬɨɜ ɞɟɥɟɧɢɹ.
ɉɨɫɤɨɥɶɤɭ ɚɬɨɦɧɵɣ ɜɟɫ
3
A
ɢɡɚɪɹɞ
3
ɬɪɟɬɶɟɣ ɱɚɫɬɢɰɵ ɝɨɪɚɡɞɨ ɦɟɧɶɲɟ
ɚɬɨɦɧɵɯ ɜɟɫɨɜ
i
A
ɢ ɡɚɪɹɞɨɜ
i
Z
(1,2i ) ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ, ɬɨ ɜɟɥɢɱɢɧɵ
ɹɞɟɪɧɵɯ ɢ ɤɭɥɨɧɨɜɫɤɢɯ ɩɨɬɟɧɰɢɚɥɨɜ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɬɪɟɬɶɟɣ ɱɚɫɬɢɰɵ ɫ
ɮɪɚɝɦɟɧɬɚɦɢ ɞɟɥɟɧɢɹ ɛɭɞɭɬ ɝɨɪɚɡɞɨ ɦɟɧɶɲɟ ɜɟɥɢɱɢɧ ɹɞɟɪɧɨɝɨ ɢ
ɤɭɥɨɧɨɜɫɤɨɝɨ ɩɨɬɟɧɰɢɚɥɨɜ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɭɤɚɡɚɧɧɵɯ ɮɪɚɝɦɟɧɬɨɜ.
ɉɨɷɬɨɦɭ ɜ ɬɪɨɣɧɨɦ ɞɟɥɟɧɢɢ ɩɪɚɤɬɢɱɟɫɤɢ ɛɟɡ ɢɡɦɟɧɟɧɢɹ ɛɭɞɟɬ
ɫɨɯɪɚɧɹɬɶɫɹ ɦɟɯɚɧɢɡɦ ɧɚɤɚɱɤɢ ɛɨɥɶɲɢɯ ɡɧɚɱɟɧɢɣ ɨɬɧɨɫɢɬɟɥɶɧɵɯ
ɨɪɛɢɬɚɥɶɧɵɯ ɦɨɦɟɧɬɨɜ
L
ɢ ɫɩɢɧɨɜ
i
J ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ, ɩɨɫɬɪɨɟɧɧɵɣ
ɞɥɹ ɞɜɨɣɧɨɝɨ ɞɟɥɟɧɢɹ ɹɞɟɪ. ɗɬɨɬ ɜɵɜɨɞ ɩɨɞɬɜɟɪɠɞɚɟɬɫɹ
ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɦɢ ɪɟɡɭɥɶɬɚɬɚɦɢ, ɞɟɦɨɧɫɬɪɢɪɭɸɳɢɦɢ ɨɬɫɭɬɫɬɜɢɟ
ɢɡɦɟɧɟɧɢɣ ɜ ɭɝɥɨɜɵɯ ɪɚɫɩɪɟɞɟɥɟɧɢɹɯ ɢɫɩɭɫɤɚɟɦɵɯ ɮɪɚɝɦɟɧɬɚɦɢ ɞɟɥɟɧɢɹ
ɦɝɧɨɜɟɧɧɵɯ
J
-ɤɜɚɧɬɨɜ ɩɪɢ ɩɟɪɟɯɨɞɟ ɨɬ ɞɜɨɣɧɨɝɨ ɤ ɬɪɨɣɧɨɦɭ ɞɟɥɟɧɢɸ ɢ
                            H       arccos   E3 E3m ,                (47)
                                                          A1  A2
ɝɞɟ E3m – ɦɚɤɫɢɦɚɥɶɧɚɹ ɷɧɟɪɝɢɹ ɬɪɟɬɶɟɣ ɱɚɫɬɢɰɵ E3m      Qc          .
                                                       A1  A2  A3
      Ɋɚɫɫɦɨɬɪɢɦ ɜɨɩɪɨɫ ɨ ɩɪɢɦɟɧɢɦɨɫɬɢ ɚɞɢɚɛɚɬɢɱɟɫɤɨɝɨ ɩɪɢɛɥɢɠɟɧɢɹ
 (25)–(27), ɢɫɩɨɥɶɡɨɜɚɧɧɨɝɨ ɩɪɢ ɨɩɢɫɚɧɢɢ ɞɜɨɣɧɨɝɨ ɞɟɥɟɧɢɹ ɹɞɟɪ, ɤ
 ɬɪɨɣɧɨɦɭ ɞɟɥɟɧɢɸ ɹɞɟɪ. Ʉɚɤ ɫɥɟɞɭɟɬ ɢɡ ɷɤɫɩɟɪɢɦɟɧɬɚ [22], ɩɨɹɜɥɟɧɢɟ
 ɬɪɟɬɶɟɣ ɱɚɫɬɢɰɵ ɩɪɢɜɨɞɢɬ ɤ ɭɦɟɧɶɲɟɧɢɸ ɷɧɟɪɝɢɢ ɨɬɧɨɫɢɬɟɥɶɧɨɝɨ
 ɞɜɢɠɟɧɢɹ ɮɪɚɝɦɟɧɬɨɜ ɬɪɨɣɧɨɝɨ ɞɟɥɟɧɢɹ, ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɚɧɚɥɨɝɢɱɧɨɣ
 ɷɧɟɪɝɢɟɣ ɞɥɹ ɞɜɨɣɧɨɝɨ ɞɟɥɟɧɢɹ ɧɚ ɜɟɥɢɱɢɧɭ ɩɪɢɦɟɪɧɨ ɪɚɜɧɭɸ ɩɨɥɨɜɢɧɟ
 ɚɫɢɦɩɬɨɬɢɱɟɫɤɨɣ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɬɪɟɬɶɟɣ ɱɚɫɬɢɰɵ E3 . ȼɟɥɢɱɢɧɚ
 E3 ɞɥɹ ɜɫɟɯ ɬɪɟɬɶɢɯ ɱɚɫɬɢɰ ɨɤɚɡɵɜɚɟɬɫɹ ɡɚɦɟɬɧɨ ɦɟɧɶɲɟ ( E3 < 30 Ɇɷȼ)
 ɨɬɧɨɫɢɬɟɥɶɧɨɣ ɷɧɟɪɝɢɢ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ ( E1  E2 ! 200 Ɇɷȼ). Ⱦɥɹ
                                                     
 ɜɵɩɨɥɧɢɦɨɫɬɢ ɚɞɢɚɛɚɬɢɱɟɫɤɨɝɨ ɩɪɢɛɥɢɠɟɧɢɹ (25)–(27) ɞɥɹ ɬɪɨɣɧɨɝɨ
 ɞɟɥɟɧɢɹ ɧɟɨɛɯɨɞɢɦɨ, ɱɬɨɛɵ, ɤɚɤ ɢ ɜ ɫɥɭɱɚɟ ɞɜɨɣɧɨɝɨ ɞɟɥɟɧɢɹ,
 ɤɢɧɟɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɨɬɧɨɫɢɬɟɥɶɧɨɝɨ ɞɜɢɠɟɧɢɹ ɮɪɚɝɦɟɧɬɨɜ ɜ ɦɨɦɟɧɬ
                3
 ɪɚɡɪɵɜɚ ( R   Rsc ) ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ ɧɚ ɮɪɚɝɦɟɧɬɵ ɞɟɥɟɧɢɹ ɞɨɥɠɧɚ ɛɵɬɶ
                                3
 ɞɨɫɬɚɬɨɱɧɨ ɛɨɥɶɲɨɣ: Eckin Rsc       ! 10 Ɇɷȼ. ɉɨɫɤɨɥɶɤɭ, ɤɚɤ ɨɬɦɟɱɚɥɨɫɶ
 ɜɵɲɟ, ɷɧɟɪɝɢɹ ɨɬɧɨɫɢɬɟɥɶɧɨɝɨ ɞɜɢɠɟɧɢɹ ɞɜɭɯ ɮɪɚɝɦɟɧɬɨɜ ɜ ɬɪɨɣɧɨɦ
 ɞɟɥɟɧɢɢ ɦɟɧɶɲɟ ɷɧɟɪɝɢɢ ɨɬɧɨɫɢɬɟɥɶɧɨɝɨ ɞɜɢɠɟɧɢɹ ɞɜɭɯ ɮɪɚɝɦɟɧɬɨɜ ɜ
                                                             3
 ɞɜɨɣɧɨɦ ɞɟɥɟɧɢɢ, ɬɨ ɷɬɨ ɭɫɥɨɜɢɟ ɫɜɢɞɟɬɟɥɶɫɬɜɭɟɬ, ɱɬɨ Rsc ɞɥɹ ɬɪɨɣɧɨɝɨ
                    2
 ɞɟɥɟɧɢɹ ɛɨɥɶɲɟ Rsc ɞɥɹ ɞɜɨɣɧɨɝɨ ɞɟɥɟɧɢɹ. ɉɪɢ ɜɵɩɨɥɧɟɧɢɢ ɭɫɥɨɜɢɹ
 ɚɞɢɚɛɚɬɢɱɧɨɫɬɢ (25) ɬɚɤ ɠɟ, ɤɚɤ ɢ ɜ ɫɥɭɱɚɟ ɞɜɨɣɧɨɝɨ ɞɟɥɟɧɢɹ, ɦɨɠɧɨ
 ɢɫɩɨɥɶɡɨɜɚɬɶ ɞɨɩɭɳɟɧɢɟ, ɱɬɨ ɭɝɥɵ ɗɣɥɟɪɚ, ɨɩɪɟɞɟɥɹɸɳɢɟ ɨɪɢɟɧɬɚɰɢɸ
 ɨɫɟɣ ɫɢɦɦɟɬɪɢɢ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ ɢ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ, ɫɨɜɩɚɞɚɸɬ ɜ
 ɨɛɥɚɫɬɢ ɮɨɪɦɢɪɨɜɚɧɢɹ ɭɝɥɨɜɵɯ ɪɚɫɩɪɟɞɟɥɟɧɢɣ ɩɪɨɞɭɤɬɨɜ ɞɟɥɟɧɢɹ.
 ɉɨɫɤɨɥɶɤɭ ɚɬɨɦɧɵɣ ɜɟɫ A3 ɢ ɡɚɪɹɞ Z3 ɬɪɟɬɶɟɣ ɱɚɫɬɢɰɵ ɝɨɪɚɡɞɨ ɦɟɧɶɲɟ
 ɚɬɨɦɧɵɯ ɜɟɫɨɜ Ai ɢ ɡɚɪɹɞɨɜ Z i ( i 1,2 ) ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ, ɬɨ ɜɟɥɢɱɢɧɵ
 ɹɞɟɪɧɵɯ ɢ ɤɭɥɨɧɨɜɫɤɢɯ ɩɨɬɟɧɰɢɚɥɨɜ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɬɪɟɬɶɟɣ ɱɚɫɬɢɰɵ ɫ
 ɮɪɚɝɦɟɧɬɚɦɢ ɞɟɥɟɧɢɹ ɛɭɞɭɬ ɝɨɪɚɡɞɨ ɦɟɧɶɲɟ ɜɟɥɢɱɢɧ ɹɞɟɪɧɨɝɨ ɢ
 ɤɭɥɨɧɨɜɫɤɨɝɨ ɩɨɬɟɧɰɢɚɥɨɜ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɭɤɚɡɚɧɧɵɯ ɮɪɚɝɦɟɧɬɨɜ.
 ɉɨɷɬɨɦɭ ɜ ɬɪɨɣɧɨɦ ɞɟɥɟɧɢɢ ɩɪɚɤɬɢɱɟɫɤɢ ɛɟɡ ɢɡɦɟɧɟɧɢɹ ɛɭɞɟɬ
 ɫɨɯɪɚɧɹɬɶɫɹ ɦɟɯɚɧɢɡɦ ɧɚɤɚɱɤɢ ɛɨɥɶɲɢɯ ɡɧɚɱɟɧɢɣ ɨɬɧɨɫɢɬɟɥɶɧɵɯ
 ɨɪɛɢɬɚɥɶɧɵɯ ɦɨɦɟɧɬɨɜ L ɢ ɫɩɢɧɨɜ J i ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ, ɩɨɫɬɪɨɟɧɧɵɣ
 ɞɥɹ   ɞɜɨɣɧɨɝɨ    ɞɟɥɟɧɢɹ      ɹɞɟɪ.     ɗɬɨɬ   ɜɵɜɨɞ    ɩɨɞɬɜɟɪɠɞɚɟɬɫɹ
 ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɦɢ ɪɟɡɭɥɶɬɚɬɚɦɢ, ɞɟɦɨɧɫɬɪɢɪɭɸɳɢɦɢ ɨɬɫɭɬɫɬɜɢɟ
 ɢɡɦɟɧɟɧɢɣ ɜ ɭɝɥɨɜɵɯ ɪɚɫɩɪɟɞɟɥɟɧɢɹɯ ɢɫɩɭɫɤɚɟɦɵɯ ɮɪɚɝɦɟɧɬɚɦɢ ɞɟɥɟɧɢɹ
 ɦɝɧɨɜɟɧɧɵɯ J -ɤɜɚɧɬɨɜ ɩɪɢ ɩɟɪɟɯɨɞɟ ɨɬ ɞɜɨɣɧɨɝɨ ɤ ɬɪɨɣɧɨɦɭ ɞɟɥɟɧɢɸ ɢ

                                       32

Страницы