Квантовая теория двойного и тройного деления атомных ядер. Кадменский С.Г - 16 стр.

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16
 
,
JM J JM J
UfR UgR
FG
R
R
SS SS
DD DD
DD
. (17)
ȼ ɮɨɪɦɭɥɟ
(17) ɪɚɞɢɚɥɶɧɵɟ ɮɨɪɦɮɚɤɬɨɪɵ

J
f
R
S
D
ɢ
J
gR
S
D
ɹɜɥɹɸɬɫɹ
ɪɟɲɟɧɢɹɦɢ ɪɚɞɢɚɥɶɧɨɝɨ ɭɪɚɜɧɟɧɢɹ ɒɪɟɞɢɧɝɟɪɚ, ɨɩɢɫɵɜɚɸɳɟɝɨ
ɨɬɧɨɫɢɬɟɥɶɧɨɟ ɞɜɢɠɟɧɢɟ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ ɫ ɷɧɟɪɝɢɟɣ
12
12
J
J
J
c
QE E E
V
V
V
:

  
2
2
22 2
1
2
0,
JJ
ɫ
c
LL
M
d
kf R V Rf R
dR R
SS
DDDD
§·

¨¸
¨¸
©¹
=
(18)
ɝɞɟ

''' '' '
2
2
, ,
JM JM
cc c
cc
c
M
Qk
VRUVU k
M
SS
DD D D
X
=
=
, (19)
ɩɪɢɱɟɦ
ɫ
X
– ɫɤɨɪɨɫɬɶ ɨɬɧɨɫɢɬɟɥɶɧɨɝɨ ɞɜɢɠɟɧɢɹ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ;
ɫ
M – ɩɪɢɜɟɞɟɧɧɚɹ ɦɚɫɫɚ ɮɪɚɝɦɟɧɬɨɜ. Ɏɨɪɦɮɚɤɬɨɪɵ

J
f
R
S
D
ɢ

J
gR
S
D
ɢɦɟɸɬ ɫɥɟɞɭɸɳɢɟ ɚɫɢɦɩɬɨɬɢɤɢ ɩɪɢ
R
of:

sin ,
2
JJ
c
L
fR kR
SS
DD
S
G
§·
o
¨¸
©¹
(20)

cos
2
JJ
c
L
gR kR
SS
DD
S
G
§·
o
¨¸
©¹
, (21)
ɝɞɟ
S
D
G
– ɩɨɬɟɧɰɢɚɥɶɧɵɟ ɞɟɥɢɬɟɥɶɧɵɟ ɮɚɡɵ.
Ɉɛɨɥɨɱɟɱɧɚɹ ɜɨɥɧɨɜɚɹ ɮɭɧɤɰɢɹ
ˆ
PȌ
J
M
qK
S
ɦɨɞɵ ɞɟɥɟɧɢɹ q ,
ɨɩɢɫɵɜɚɸɳɟɣ ɩɪɟɞɪɚɡɪɵɜɧɭɸ ɤɨɧɮɢɝɭɪɚɰɢɸ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ, ɜ
ɤɥɚɫɬɟɪɧɨɣ ɨɛɥɚɫɬɢ, ɝɞɟ ɮɨɪɦɢɪɭɸɬɫɹ ɩɟɪɜɢɱɧɵɟ ɮɪɚɝɦɟɧɬɵ ɞɟɥɟɧɢɹ,
ɩɟɪɟɯɨɞɢɬ ɜ ɮɭɧɤɰɢɸ
ˆ
J
M
qK
Q
S
< , ɚɫɢɦɩɬɨɬɢɤɚ ɤɨɬɨɪɨɣ ɩɪɢ ɛɨɥɶɲɢɯ
R
ɩɪɟɞɫɬɚɜɥɹɟɬɫɹ ɜ ɜɢɞɟ [10]:
2
ˆ
,
J
c
L
ikR
J
qK
JM JM
qK
c
e
QU
R
S
D
S
G
S
D
SS
D
X
§·

¨¸
©¹
*
<o
=
(22)
ɝɞɟ
J
qK
S
D
* – ɚɦɩɥɢɬɭɞɚ ɩɚɪɰɢɚɥɶɧɨɣ ɞɟɥɢɬɟɥɶɧɨɣ ɲɢɪɢɧɵ, ɨɩɪɟɞɟɥɹɟɦɚɹ
ɤɚɤ


ˆ
2.
J
JJM
qK A qK
fR
UHP
R
S
SS
D
DD
S
* < (23)
ɋɨɝɥɚɫɧɨ ɡɚɤɨɧɭ ɫɨɯɪɚɧɟɧɢɹ ɱɟɬɧɨɫɬɢ ɜ ɩɪɨɰɟɫɫɟ ɞɟɥɟɧɢɹ ɜɟɥɢɱɢɧɚ
J
qK
S
D
* ɨɬɥɢɱɧɚ ɨɬ ɧɭɥɹ ɩɪɢ ɜɵɩɨɥɧɟɧɢɢ ɭɫɥɨɜɢɹ:

12
1
L
SS S
. ɉɪɢ
                     UDJ S M fDJ S R        UDJ S M gDJ S R
                    FD               , GD                   .      (17)
                             R                      R
ȼ ɮɨɪɦɭɥɟ (17) ɪɚɞɢɚɥɶɧɵɟ ɮɨɪɦɮɚɤɬɨɪɵ fDJ S R ɢ gDJ S R ɹɜɥɹɸɬɫɹ
ɪɟɲɟɧɢɹɦɢ ɪɚɞɢɚɥɶɧɨɝɨ ɭɪɚɜɧɟɧɢɹ ɒɪɟɞɢɧɝɟɪɚ, ɨɩɢɫɵɜɚɸɳɟɝɨ
ɨɬɧɨɫɢɬɟɥɶɧɨɟ   ɞɜɢɠɟɧɢɟ         ɮɪɚɝɦɟɧɬɨɜ   ɞɟɥɟɧɢɹ       ɫ ɷɧɟɪɝɢɟɣ
Qc    EVJ  EVJ1  EVJ 2 :
               1      2

                § d 2 L L 1         ·          2M
               ¨¨ 2            kc2 ¸ fDJ S R  2 ɫ VDD R fDJ S R                      0,   (18)
                             2       ¸           =
                © dR       R         ¹
ɝɞɟ
                                                     =k c    2 M cQc
             VD 'D '' R    UDJ S'' M V UDJ S' M , kc      , (19)    2
                                                                         , Xc
                                           =         Mc
ɩɪɢɱɟɦ Xɫ – ɫɤɨɪɨɫɬɶ ɨɬɧɨɫɢɬɟɥɶɧɨɝɨ ɞɜɢɠɟɧɢɹ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ;
M ɫ – ɩɪɢɜɟɞɟɧɧɚɹ ɦɚɫɫɚ ɮɪɚɝɦɟɧɬɨɜ. Ɏɨɪɦɮɚɤɬɨɪɵ fDJ S R ɢ gDJ S R
ɢɦɟɸɬ ɫɥɟɞɭɸɳɢɟ ɚɫɢɦɩɬɨɬɢɤɢ ɩɪɢ R o f :
                                      §        LS         ·
                        fDJ S R o sin ¨ kc R      GDJ S ¸ ,  (20)
                                      ©         2         ¹
                                      §        LS         ·
                        gDJ S R o cos ¨ kc R      GDJ S ¸ ,  (21)
                                      ©         2         ¹
ɝɞɟ GDJ S – ɩɨɬɟɧɰɢɚɥɶɧɵɟ ɞɟɥɢɬɟɥɶɧɵɟ ɮɚɡɵ.
                                                          JS M
      Ɉɛɨɥɨɱɟɱɧɚɹ     ɜɨɥɧɨɜɚɹ       ɮɭɧɤɰɢɹ          P̂Ȍ qK            ɦɨɞɵ       ɞɟɥɟɧɢɹ    q,
ɨɩɢɫɵɜɚɸɳɟɣ ɩɪɟɞɪɚɡɪɵɜɧɭɸ ɤɨɧɮɢɝɭɪɚɰɢɸ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ, ɜ
ɤɥɚɫɬɟɪɧɨɣ ɨɛɥɚɫɬɢ, ɝɞɟ ɮɨɪɦɢɪɭɸɬɫɹ ɩɟɪɜɢɱɧɵɟ ɮɪɚɝɦɟɧɬɵ ɞɟɥɟɧɢɹ,
                         JS M
ɩɟɪɟɯɨɞɢɬ ɜ ɮɭɧɤɰɢɸ Qˆ < qK   , ɚɫɢɦɩɬɨɬɢɤɚ ɤɨɬɨɪɨɣ ɩɪɢ ɛɨɥɶɲɢɯ R
ɩɪɟɞɫɬɚɜɥɹɟɬɫɹ ɜ ɜɢɞɟ [10]:
                                       §       LS      ·
                                     i ¨ kc R  GDJ S ¸     JS
                                       ©        2      ¹   * qK
                  JS M             e                            D
             Qˆ < qK   o UDJ S M                                    ,                        (22)
                                            R               =Xc
         JS
ɝɞɟ    * qK D – ɚɦɩɥɢɬɭɞɚ ɩɚɪɰɢɚɥɶɧɨɣ ɞɟɥɢɬɟɥɶɧɨɣ ɲɢɪɢɧɵ, ɨɩɪɟɞɟɥɹɟɦɚɹ
ɤɚɤ
                        JS             f JS R                          JS M
                      * qK D     2S UD D      HA                  Pˆ < qK           .        (23)
                                          R
ɋɨɝɥɚɫɧɨ ɡɚɤɨɧɭ ɫɨɯɪɚɧɟɧɢɹ ɱɟɬɧɨɫɬɢ ɜ ɩɪɨɰɟɫɫɟ ɞɟɥɟɧɢɹ ɜɟɥɢɱɢɧɚ
   JS                                                                          L
 * qK D ɨɬɥɢɱɧɚ ɨɬ ɧɭɥɹ ɩɪɢ ɜɵɩɨɥɧɟɧɢɢ ɭɫɥɨɜɢɹ:                           1        SS1S 2 . ɉɪɢ
                                           16

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