Елесин В.Ф., Кашурников В.А. Физика фазовых переходов
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70
1
1
SS N T
Zq
q
¦
1
1
/[exp(/)]!
Z
. Ɍɨɱɤɚ ɩɟɪɟɯɨɞɚ ɛɭɞɟɬ ɫɨ-
ɨɬɜɟɬɫɬɜɨɜɚɬɶ ɧɭɥɟɜɨɣ ɩɪɨɟɤɰɢɢ ɫɩɢɧɚ ɧɚ ɨɫɶ
z, ɨɬɫɸɞɚ ɭɫɥɨ-
ɜɢɟ:,ɫɨɜɩɚɞɚɸɳɟɟ ɫ ɭɫɥɨɜɢɟɦ
ɧɚ ɬɟɦɩɟɪɚɬɭɪɭ ɛɨɡɟ-ɤɨɧɞɟɧɫɚɰɢɢ ɫ ɩɟɪɟɨɛɨɡɧɚɱɟɧɢɟɦ
(
N/V)
SN T
q
q
¦
1
1
/[exp(/)]!
Z
2/3
=S
2/3
a
-2
, a - ɩɟɪɢɨɞ ɪɟɲɟɬɤɢ. ɍɱɬɟɦ, ɱɬɨ ɜ ɞɥɢɧɧɨɜɨɥ-
ɧɨɜɨɦ ɩɪɟɞɟɥɟ
!
!
Z
q
JSa q
m
JSa
22
2
2
2*
. Ɉɤɨɧɱɚɬɟɥɶɧɨ
. ɉɪɢ
S ~1 ɪɟɡɭɥɶɬɚɬ ɧɟ ɫɢɥɶɧɨ ɨɬɥɢɱɚɟɬɫɹ ɨɬ
ɩɨɥɭɱɟɧɧɨɝɨ ɜ ɩɪɢɛɥɢɠɟɧɢɢ ɫɪɟɞɧɟɝɨ ɩɨɥɹ (
Z~10).
TJS
C
662
52
.
/
T
ZJS
2
3/
4.4.
3. Ɉɰɟɧɢɬɶ ɷɮɮɟɤɬɢɜɧɭɸ ɦɚɫɫɭ ɦɚɝɧɨɧɨɜ ɜ ɠɟɥɟɡɟ,
4
= 1043Ʉ, ɧɚɦɚɝɧɢɱɟɧɧɨɫɬɶ ɧɚɫɵɳɟɧɢɹ M
0
=1752 Ƚɫ, ɪɟɲɟɬɤɚ
ɈɐɄ,
a=2.87 A. ɇɚɣɬɢ ɨɬɧɨɲɟɧɢɟ m*/m.
Ɋɟɲɟɧɢɟ
. ɍɞɟɥɶɧɵɣ ɦɚɝɧɢɬɧɵɣ ɦɨɦɟɧɬ ɧɚɫɵɳɟɧɢɹ ɜ
ɠɟɥɟɡɟ
M
0
=n
P
0
S. Ɂɞɟɫɶ ɩɥɨɬɧɨɫɬɶ n=2/a
3
ɞɥɹ ɈɐɄ ɪɟɲɟɬɤɢ.
Ɉɬɫɸɞɚ
P
0
S=2.1·10
-20
ɷɪɝ/Ƚɫ. Ⱦɥɹ ɫɪɚɜɧɟɧɢɹ
P
B
=9.3·10
-21
ɷɪɝ/Ƚɫ,
P
0
S/
P
B
=2.2. Ⱦɚɥɟɟ:
!
2
2
2m
JSa
*
'
, ɝɞɟ -
aa' 32 - ɪɚɫɫɬɨɹɧɢɟ ɦɟɠɞɭ ɛɥɢɠɚɣɲɢɦɢ ɫɨɫɟɞɹɦɢ ɜ ɈɐɄ
ɪɟɲɟɬɤɟ. ɍɱɢɬɵɜɚɹ (ɞɥɹ ɈɐɄ), ɨɬɫɸɞɚ ɧɚ-
ɯɨɞɢɦ:
T
SZJ Z
2
38/,
m
a
*. x
8
9
91 10
2
2
27
h
T
ɝ,
ɨɬɤɭɞɚ
m*/m
|
10.
4.4.
4. ɇɚɣɬɢ ɦɚɝɧɢɬɧɵɣ ɦɨɦɟɧɬ ɢɨɧɚ Ni ɜ ɮɟɪɪɨɦɚɝ-
ɧɢɬɧɨɦ ɫɨɫɬɨɹɧɢɢ. ɇɚɦɚɝɧɢɱɟɧɧɨɫɬɶ ɧɚɫɵɳɟɧɢɹ
M
0
=510Ƚɫ,
ɪɟɲɟɬɤɚ ȽɐɄ,
a=3.52A. ȼɵɪɚɡɢɬɶ ɦɚɝɧɢɬɧɵɣ ɦɨɦɟɧɬ ɜ ɦɚɝɧɟ-
ɬɪɨɧɚɯ Ȼɨɪɚ
P
B
.
Ɉɬɜɟɬ
:
P
0
S/
P
B
= 0.6.
4.4.5. ɉɨɥɭɱɢɬɶ ɹɜɧɵɣ ɜɢɞ ɫɩɟɤɬɪɚ ɫɩɢɧɨɜɵɯ ɜɨɥɧ ɞɥɹ
ɈɐɄ ɪɟɲɟɬɤɢ ɜ ɩɪɢɛɥɢɠɟɧɢɢ ɛɥɢɠɚɣɲɢɯ ɫɨɫɟɞɟɣ. ɉɨɤɚɡɚɬɶ,
ɱɬɨ ɜ ɞɥɢɧɧɨɜɨɥɧɨɜɨɦ ɩɪɟɞɟɥɟ ɫɩɟɤɬɪ ɜɨɡɛɭɠɞɟɧɢɣ ɤɜɚɞɪɚɬɢ-
ɱɟɧ ɩɨ ɢɦɩɭɥɶɫɭ.
4.5. Ɍɟɪɦɨɞɢɧɚɦɢɤɚ ɦɚɝɧɨɧɨɜ
ɉɨɤɚɠɟɦ, ɤɚɤ, ɜɨɫɩɨɥɶɡɨɜɚɜɲɢɫɶ ɜɢɞɨɦ ɮɭɧɤɰɢɢ ɪɚɫ-
ɩɪɟɞɟɥɟɧɢɹ ɦɚɝɧɨɧɨɜ
n
q
(T) (4.20), ɨɩɪɟɞɟɥɢɬɶ ɜɤɥɚɞ ɦɚɝɧɨɧ-
ɧɵɯ ɜɨɡɛɭɠɞɟɧɢɣ ɜ ɫɪɟɞɧɢɣ ɦɚɝɧɢɬɧɵɣ ɦɨɦɟɧɬ
P
(T) ɢ ɬɟɩɥɨ-
ɟɦɤɨɫɬɶ
C(T). Ɋɚɫɫɦɨɬɪɢɦ ɞɥɢɧɧɨɜɨɥɧɨɜɵɣ ɩɪɟɞɟɥ qa << 1,
ɬɚɤ ɤɚɤ ɢɫɯɨɞɹ ɢɡ ɜɢɞɚ (4.20) ɢɦɟɧɧɨ ɜ ɷɬɨɦ ɫɥɭɱɚɟ ɜɤɥɚɞ ɦɚɤ-
ɫɢɦɚɥɟɧ. ɂɫɩɨɥɶɡɭɟɦ ɡɚɤɨɧ ɞɢɫɩɟɪɫɢɢ
.
!
Z
q
SJa q
22
71
!
Ɋɚɫɫɦɨɬɪɢɦ ɦɚɝɧɢɬɧɵɣ ɦɨɦɟɧɬ. ȿɫɥɢ ɬɟɦɩɟɪɚɬɭɪɚ ɪɚɜ-
ɧɚ ɧɭɥɸ, ɜɨɡɛɭɠɞɟɧɢɣ ɧɟɬ, ɢ
<M> = SN. ɉɪɢ ɭɜɟɥɢɱɟɧɢɢ ɬɟɦ-
ɩɟɪɚɬɭɪɵ ɧɟɨɛɯɨɞɢɦɨ ɭɱɟɫɬɶ ɜɨɡɛɭɠɞɟɧɢɹ:
!
¦
MSN aa
ll
l
. (4.21)
Ɋɚɫɫɱɢɬɚɟɦ:
! !
{
o
¦¦
¦
³
aa aa n T
Na q
ll
l
qq
q
q
q
q
()
( ) exp( )
,.
3
3
3
21
1
SEZ
d
h
(4.22)
ɍɱɢɬɵɜɚɹ, ɱɬɨ ɨɫɧɨɜɧɨɣ ɜɤɥɚɞ ɜ ɢɧɬɟɝɪɚɥɟ (4.22) ɧɚɛɢɪɚɟɬɫɹ
ɩɪɢ ɦɚɥɵɯ
q, ɚ ɬɚɤɠɟ ɱɬɨ J ~
4
, ɢɦɟɟɦ
!
f
³
MSN T
xx
x
[(/) ],
exp[ ]
(5/ )
~,
/
/
1
1
21
32
16
1
32
2
2
2
0
32
TK
K
S
9
S
d
(4.23)
ɝɞɟ
9
(x) - ɞɡɟɬɚ-ɮɭɧɤɰɢɹ Ɋɢɦɚɧɚ (
9
(5/2)=1.341). Ɂɞɟɫɶ ɭɱɬɟɧɨ,
ɱɬɨ
xx
x
ZZ
Z
f
³
1
0
1
d
exp[ ]
()(),*
9
Ƚ(Z)- ɝɚɦɦɚ-ɮɭɧɤɰɢɹ
(Ƚ(5/2)=3/4Ƚ(1/2)=3
S
4). ɂɡ (4.23) ɜɢɞɧɨ, ɱɬɨ ɬɟɦɩɟɪɚɬɭɪ-
ɧɵɣ ɫɩɚɞ ɦɚɝɧɢɬɧɨɝɨ ɦɨɦɟɧɬɚ (~
T
3/2
) ɫɬɟɩɟɧɧɨɣ, ɜ ɨɬɥɢɱɢɟ ɨɬ
ɷɤɫɩɨɧɟɧɰɢɚɥɶɧɨɝɨ (
~ exp(-2
4
/T), ɫɦ. ɝɥɚɜɭ 2), ɤɨɬɨɪɵɣ ɩɪɟɞ-
ɫɤɚɡɵɜɚɟɬ ɩɪɢɛɥɢɠɟɧɢɟ ɫɪɟɞɧɟɝɨ ɩɨɥɹ ɜ ɦɨɞɟɥɢ ɂɡɢɧɝɚ.
ɋɬɟɩɟɧɧɨɣ ɡɚɤɨɧ (4.23) - ɬɚɤ ɧɚɡɵɜɚɟɦɵɣ
ɡɚɤɨɧ Ȼɥɨ-
ɯɚ
. ɋɥɟɞɭɟɬ ɬɚɤɠɟ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɨɩɢɫɚɧɢɟ ɜɨɡɛɭɠɞɟɧɧɨɝɨ ɫɨ-
ɫɬɨɹɧɢɹ ɮɟɪɪɨɦɚɝɧɟɬɢɤɚ ɫ ɩɨɦɨɳɶɸ ɦɚɝɧɨɧɨɜ ɫɩɪɚɜɟɞɥɢɜɨ
ɩɪɢ ɭɫɥɨɜɢɢ ɢɯ ɦɚɥɨɝɨ ɱɢɫɥɚ ɜ ɫɪɟɞɧɟɦ ɧɚ ɭɡɥɟ (
n
i
<<1), ɱɬɨ ɫ
ɭɱɟɬɨɦ (4.22)-(4.23) ɩɪɢɜɨɞɢɬ ɤ ɭɫɥɨɜɢɸ
T<<
4
. Ɍɚɤɢɦ ɨɛɪɚ-
ɡɨɦ ɬɨɥɶɤɨ ɜ ɧɢɡɤɨɬɟɦɩɟɪɚɬɭɪɧɨɦ ɩɪɟɞɟɥɟ ɤɨɪɪɟɤɬɧɨ ɜɜɟɞɟɧɢɟ
ɤɜɚɡɢɱɚɫɬɢɰ - ɦɚɝɧɨɧɨɜ.
ɂɫɫɥɟɞɭɟɦ ɩɨɜɟɞɟɧɢɟ ɬɟɩɥɨɟɦɤɨɫɬɢ
C(T). Ɍɚɤ ɤɚɤ
C=
w
E
w
T, ɪɚɫɫɦɨɬɪɢɦ ɬɟɦɩɟɪɚɬɭɪɧɭɸ ɡɚɜɢɫɢɦɨɫɬɶ ɷɧɟɪɝɢɢ:
E
Na
q
N
T
a
xx
x
N
T
a
T
q
q
o
³³
3
3
3
52
2522
4
2
52
32 52 2
52
212
15
32
72
()exp[ ] exp[]
(/)~ .
/
/
/
//
/
S
Z
EZ S T
ST
9
d
d
1
(4.24)
Ɉɬɫɸɞɚ
C ~ T
3/2
, ɬ.ɟ. ɜɤɥɚɞ ɦɚɝɧɨɧɨɜ ɩɪɢɜɨɞɢɬ ɤ ɫɬɟɩɟɧɧɨɣ
ɡɚɜɢɫɢɦɨɫɬɢ ɬɟɩɥɨɟɦɤɨɫɬɢ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ. Ɍɚɤ ɤɚɤ ɷɬɚ ɡɚɜɢ-
ɫɢɦɨɫɬɶ ɪɟɡɤɨ ɨɬɥɢɱɚɟɬɫɹ ɨɬ ɷɤɫɩɨɧɟɧɰɢɚɥɶɧɨɝɨ ɫɩɚɞɚ, ɩɪɟɞ-
ɫɤɚɡɵɜɚɟɦɨɝɨ ɫɪɟɞɧɢɦ ɩɨɥɟɦ ɩɪɢ ɦɚɥɵɯ ɬɟɦɩɟɪɚɬɭɪɚɯ
(ɫɦ.ɝɥɚɜɭ 2), ɬɨ ɷɬɨɬ ɜɤɥɚɞ ɦɨɠɧɨ
ɧɚɛɥɸɞɚɬɶ ɧɚ ɷɤɫɩɟɪɢɦɟɧɬɟ (ɪɢɫ.9).
Ɋɢɫ.9. ȼɤɥɚɞ ɦɚɝɧɨɧɨɜ ɜ ɬɟɩ-
ɥɨɟɦɤɨɫɬɶ: I -ɪɟɡɭɥɶɬɚɬ ɫɪɟɞ-
ɧɟɝɨ ɩɨɥɹ (aexp[-2T/T]);
II - ɞɨɛɚɜɤɚ ɡɚ ɫɱɟɬ ɫɩɢɧɨɜɵɯ
ɜɨɡɛɭɠɞɟɧɢɣ - ɦɚɝɧɨɧɨɜ
(
~
/
T
32
)
72
4.6. ɉɥɨɫɤɢɣ ɮɟɪɪɨɦɚɝɧɟɬɢɤ.
Ⱥɧɢɡɨɬɪɨɩɧɚɹ ɦɨɞɟɥɶ Ƚɟɣɡɟɧɛɟɪɝɚ
ȼ ɷɬɨɦ ɩɚɪɚɝɪɚɮɟ ɦɵ ɨɛɫɭɞɢɦ ɝɚɦɢɥɶɬɨɧɢɚɧ Ƚɟɣɡɟɧ-
ɛɟɪɝɚ ɫ ɚɧɢɡɨɬɪɨɩɧɵɦ ɜɡɚɢɦɨɞɟɣɫɬɜɢɟɦ, ɚ ɢɦɟɧɧɨ: ɫɢɥɶɧɨɟ
ɜɡɚɢɦɨɞɟɣɫɬɜɢɟ ɫɩɢɧɨɜ ɦɟɠɞɭ ɫɨɛɨɣ ɜ ɩɥɨɫɤɨɫɬɢ
xy ɢ ɫɥɚɛɨɟ
ɩɨ ɨɫɢ
z. Ȼɭɞɟɦ ɬɚɤɠɟ ɩɨɥɚɝɚɬɶ, ɱɬɨ ɜɧɟɲɧɟɟ ɩɨɥɟ ɜɡɚɢɦɨɞɟɣ-
ɫɬɜɭɟɬ ɬɨɥɶɤɨ ɫ
z-ɩɪɨɟɤɰɢɟɣ. ɗɬɨ ɢɧɬɟɪɟɫɧɚɹ ɫɢɬɭɚɰɢɹ, ɤɨɝɞɚ
ɞɥɹ ɪɟɚɥɢɡɚɰɢɢ ɮɟɪɪɨɦɚɝɧɢɬɧɨɝɨ ɭɩɨɪɹɞɨɱɟɧɢɹ ɜ ɩɥɨɫɤɨɫɬɢ
xy ɧɟɨɛɯɨɞɢɦɨ ɫɢɥɶɧɨɟ ɫɬɚɛɢɥɢɡɢɪɭɸɳɟɟ ɩɨɥɟ ɩɨ ɨɫɢ
z, ɩɪɢ-
ɜɟɞɟɬ ɧɚɫ ɤ ɫɚɦɨɫɨɝɥɚɫɨɜɚɧɧɨɦɭ ɭɪɚɜɧɟɧɢɸ ɧɚ ɩɚɪɚɦɟɬɪ ɩɨ-
ɪɹɞɤɚ, ɫɨɜɩɚɞɚɸɳɟɦɭ ɫ ɚɧɚɥɨɝɢɱɧɵɦ ɭɪɚɜɧɟɧɢɟɦ ɜ ɬɟɨɪɢɢ
Ȼɚɪɞɢɧɚ, Ʉɭɩɟɪɚ ɢ ɒɪɢɮɮɟɪɚ (ȻɄɒ) ɞɥɹ ɫɜɟɪɯɩɪɨɜɨɞɧɢɤɨɜ.
Ʉɪɨɦɟ ɬɨɝɨ, ɦɵ ɩɨɤɚɠɟɦ ɬɚɤ ɧɚɡɵɜɚɟɦɭɸ ɫɩɢɧɨɜɭɸ ɚɧɚɥɨɝɢɸ
ɞɥɹ ɫɜɟɪɯɩɪɨɜɨɞɧɢɤɨɜ (ɫɦ. ɡɚɞɚɱɢ ɜ ɤɨɧɰɟ ɩɚɪɚɝɪɚɮɚ), ɤɨɝɞɚ ɢɡ
ɝɚɦɢɥɶɬɨɧɢɚɧɚ ȻɄɒ ɞɥɹ ɫɩɚɪɟɧɧɵɯ ɫɜɟɪɯɩɪɨɜɨɞɹɳɢɯ ɷɥɟɤ-
ɬɪɨɧɨɜ ɦɨɠɧɨ, ɜ ɫɜɨɸ ɨɱɟɪɟɞɶ, ɩɨɥɭɱɢɬɶ ɝɟɣɡɟɧɛɟɪɝɨɜɫɤɭɸ
ɚɧɢɡɨɬɪɨɩɧɭɸ ɦɨɞɟɥɶ. ɗɬɢ ɚɧɚɥɨɝɢɢ ɢɡ ɞɨɫɬɚɬɨɱɧɨ ɞɚɥɟɤɢɯ
ɨɛɥɚɫɬɟɣ ɮɢɡɢɤɢ ɤɨɧɞɟɧɫɢɪɨɜɚɧɧɨɝɨ ɫɨɫɬɨɹɧɢɹ ɫɜɹɡɚɧɵ ɟɞɢ-
ɧɨɣ ɤɨɧɰɟɩɰɢɟɣ ɩɪɢɛɥɢɠɟɧɢɹ ɫɪɟɞɧɟɝɨ ɩɨɥɹ, ɜ ɪɚɦɤɚɯ ɤɨɬɨɪɨ-
ɝɨ ɪɚɛɨɬɚɸɬ ɢ ɬɟɨɪɢɹ ȻɄɒ, ɢ ɬɟɨɪɢɹ ɮɟɪɪɨɦɚɝɧɟɬɢɡɦɚ.
Ɋɚɫɫɦɨɬɪɢɦ ɝɚɦɢɥɶɬɨɧɢɚɧ Ƚɟɣɡɟɧɛɟɪɝɚ, ɭɱɢɬɵɜɚɸɳɢɣ
ɜɡɚɢɦɨɞɟɣɫɬɜɢɟ ɦɟɠɞɭ ɫɩɢɧɚɦɢ ɜ ɩɥɨɫɤɨɫɬɢ
xy ɢ ɜɡɚɢɦɨɞɟɣɫɬ-
ɜɢɟ ɫ ɜɧɟɲɧɢɦ ɩɨɥɟ ɩɨ ɨɫɢ
z:
HHV
k
Z
kk
kkk
kk
¦¦
A
o
A
o
PV P VV
00
2
1
2
'
'
'
. (4.25)
Ɂɞɟɫɶ
VVV
kk
X
k
XA
o
{,,0},
VVV
k
X
k
Y
k
Z
,, - ɦɚɬɪɢɰɵ ɉɚɭɥɢ (4.3).
73
Ɋɚɡɪɟɠɟɦ ɜɡɚɢɦɨɞɟɣɫɬɜɢɟ ɜ ɩɥɨɫɤɨɫɬɢ ɜ ɩɪɢɛɥɢɠɟɧɢɢ
ɫɪɟɞɧɟɝɨ ɩɨɥɹ ɩɨ ɩɪɚɜɢɥɭ
V
V
V
V
V
V
V
V
kk kkkk k k'''
| ! ! ! !
'
. (4.26)
ɉɨɫɥɟɞɧɢɣ ɱɥɟɧ ɜ (4.26) ɨɛɵɱɧɨ ɨɩɭɫɤɚɸɬ, ɬɚɤ ɤɚɤ ɷɬɨ ɚɞɞɢ-
ɬɢɜɧɚɹ ɤɨɧɫɬɚɧɬɚ, ɨɞɧɚɤɨ ɞɥɹ ɫɨɯɪɚɧɟɧɢɹ ɬɨɱɧɨɫɬɢ ɫɪɟɞɧɟɩɨ-
ɥɟɜɨɝɨ ɪɚɡɥɨɠɟɧɢɹ ɟɝɨ ɩɨɥɟɡɧɨ ɨɫɬɚɜɢɬɶ.
Ʌɟɝɤɨ ɨɰɟɧɢɬɶ, ɱɬɨ ɜɵɪɚɠɟɧɢɟ (4.26) ɫɩɪɚɜɟɞɥɢɜɨ ɫ
ɬɨɱɧɨɫɬɶɸ ɞɨ ɤɜɚɞɪɚɬɢɱɧɵɯ ɩɨɩɪɚɜɨɤ ɤ ɨɬɤɥɨɧɟɧɢɸ ɫɩɢɧɚ ɨɬ
ɫɪɟɞɧɟɝɨ:
{}{ }
''
V
V
V
V
kkk k
! ! 1).
ȼɜɟɞɟɦ ɫɪɟɞɧɟɟ ɩɨɥɟ ɜ ɜɢɞɟ
'
kkk
kk
k
V
o
A
o
¦
PV
0'
'
'
! . (4.27)
ȼɟɥɢɱɢɧɚ (4.27) ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚ ɫɬɟɩɟɧɢ ɭɩɨɪɹɞɨɱɟɧɢɹ ɜ
ɩɥɨɫɤɨɫɬɢ
xy ɢ ɟɟ ɭɞɨɛɧɨ ɛɭɞɟɬ ɜɡɹɬɶ ɜ ɤɚɱɟɫɬɜɟ ɩɚɪɚɦɟɬɪɚ
ɩɨɪɹɞɤɚ ɜ ɧɚɲɟɦ ɩɨɞɯɨɞɟ. Ɍɨɝɞɚ ɝɚɦɢɥɶɬɨɧɢɚɧ (4.25) ɫɭɱɟɬɨɦ
(4.26)-(4.27) ɩɪɟɞɫɬɚɜɥɹɟɬɫɹ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ:
HH
k
Z
kk
k
kk
k
!
A
o
A
oo
A
o
¦¦
PV V P V
00
1
2
{}
''. (4.28)
ȼ ɩɟɪɜɨɦ ɨɩɟɪɚɬɨɪɧɨɦ ɱɥɟɧɟ (4.28) ɩɨɞ ɡɧɚɤɨɦ ɫɭɦɦɵ ɧɚɯɨ-
ɞɢɬɫɹ ɦɚɬɪɢɰɚ 2ʉ2 ɜ ɩɪɨɫɬɪɚɧɫɬɜɟ ɦɚɬɪɢɰ ɉɚɭɥɢ. ɍɱɬɹ ɢɯ ɨɩ-
ɪɟɞɟɥɟɧɢɟ (4.3), ɡɚɩɢɲɟɦ ɜ ɹɜɧɨɦ ɜɢɞɟ
''
''
''
A
o
A
o
§
©
¨
·
¹
¸
VV
k
Z
kk
k
X
k
Y
k
X
k
Y
H
H
iH
i
. (4.29)
ȼɢɞɧɨ, ɱɬɨ ɟɫɥɢ ɛɵ ɜɡɚɢɦɨɞɟɣɫɬɜɢɟ
V
kk’
ɨɬɫɭɬɫɬɜɨɜɚɥɨ, ɬɨ
(4.29) ɛɵɥɨ ɛɵ ɨɛɵɱɧɵɦ ɢɡɢɧɝɨɜɫɤɢɦ ɱɥɟɧɨɦ
V
Z
H, ɢɭɪɚɜɧɟ-
ɧɢɟ ȼɟɣɫɫɚ ɦɨɠɧɨ ɛɵɥɨ ɛɵ ɡɚɩɢɫɚɬɶ ɫɪɚɡɭ. ȼ ɨɛɳɟɦ ɫɥɭɱɚɟ
ɜɵɪɚɠɟɧɢɟ (4.29) ɧɟɨɛɯɨɞɢɦɨ ɞɢɚɝɨɧɚɥɢɡɨɜɚɬɶ, ɬ.ɟ. ɪɟɲɢɬɶ
74
ɫɟɤɭɥɹɪɧɨɟ ɭɪɚɜɧɟɧɢɟ ɜɢɞɚ . ɇɟɫɥɨɠɧɨ ɧɚɣɬɢ ɫɨɛ-
ɫɬɜɟɧɧɵɟ ɱɢɫɥɚ
'
O
I 0
O
12
222 2
,
||,|| ( ) ( ) r H
XY
'' ' '
2
.
Ɉɬɫɸɞɚ (4.29) ɜ ɞɢɚɝɨɧɚɥɶɧɨɦ ɜɢɞɟ ɩɪɟɞɫɬɚɜɥɹɟɬɫɹ ɫɥɟɞɭɸ-
ɳɢɦ:
''
§
©
¨
·
¹
¸
10
01
2
HHHH
kk
Z
kk k
V
,||
2
. (4.30)
ɋɨɨɬɜɟɬɫɬɜɟɧɧɨ, ɞɢɚɝɨɧɚɥɢɡɨɜɚɧɧɵɣ ɝɚɦɢɥɶɬɨɧɢɚɧ (4.28) ɢɦɟ-
ɟɬ ɜɢɞ ɨɛɵɱɧɨɝɨ ɝɚɦɢɥɶɬɨɧɢɚɧɚ ɂɡɢɧɝɚ (ɩɪɨɰɟɞɭɪɚ ɞɢɚɝɨɧɚɥɢ-
ɡɚɰɢɢ ɜ ɝɟɨɦɟɬɪɢɱɟɫɤɨɦ ɫɦɵɫɥɟ ɷɤɜɢɜɚɥɟɧɬɧɚ “ɨɬɤɥɨɧɟɧɢɸ”
ɩɪɨɟɤɰɢɢ
z ɩɨɞ ɧɟɤɨɬɨɪɵɦ ɭɝɥɨɦ ɨɬɧɨɫɢɬɟɥɶɧɨ ɫɬɚɪɨɝɨ ɩɨɥɨ-
ɠɟɧɢɹ, ɬɚɤ ɱɬɨ ɩɨɞ ɧɨɜɵɦ ɭɝɥɨɦ ɜɡɚɢɦɨɞɟɣɫɬɜɢɟ ɫ ɷɮɮɟɤɬɢɜ-
ɧɵɦ ɩɨɥɟɦ
H
k
ɞɢɚɝɨɧɚɥɶɧɨ)
HH
k
Z
k
kk
kk
!
¦¦
o
A
o
PV P V
00
1
2
' (4.31)
ɛɟɡ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ
.
ɍɱɬɟɦ
,
ɱɬɨ
V
Z
=r1,
ɬ
.
ɟ
.
ɫɭɦɦɢɪɨɜɚɧɢɟ ɜ
ɫɬɚɬɢɫɬɢɱɟɫɤɨɣ ɫɭɦɦɟ ɫ ɝɚɦɢɥɶɬɨɧɢɚɧɨɦ (4.31) ɛɭɞɟɬ ɢɦɟɬɶ
ɜɢɞ exp(
-V)+exp(+V) = 2ch(V), ɧɟɫɥɨɠɧɨ ɡɚɩɢɫɚɬɶ ɫɬɚɬɢɫɬɢɱɟ-
ɫɤɭɸ ɫɭɦɦɭ:
QH
kk
k
k
k
!
o
A
o
¦
exp{ } { ( )}
E
PV EP
2
2
00
' ch
. (4.32)
ɋɜɨɛɨɞɧɚɹ ɷɧɟɪɝɢɹ F ɩɨɥɭɱɚɟɬɫɹ ɢɡ (4.32):
FTQ T H
kk
k
k
k
!
o
A
o
¦¦
ln { ( )}
1
2
2
00
PV EP
' ch . (4.33)
ȼɚɪɶɢɪɭɹ F ɩɨ ɩɪɨɟɤɰɢɢ <
V
A
l
> ɫ ɮɢɤɫɢɪɨɜɚɧɧɵɦ ɭɡɥɨɦ l:
w
F
w
<
V
A
l
> = 0 , ɩɨɥɭɱɚɟɦ ɫɚɦɨɫɨɝɥɚɫɨɜɚɧɧɨɟ ɢɧɬɟɝɪɚɥɶɧɨɟ
ɭɪɚɜɧɟɧɢɟ:
75
''
'
'
kkk k
k
k
k
VH
H
¦
PEP
00
22
22
''
'
'
'
{}th . (4.34)
ɍɪɚɜɧɟɧɢɟ (4.34) ɫɨɜɩɚɞɚɟɬ ɩɨ ɜɢɞɭ ɫ ɭɪɚɜɧɟɧɢɟɦ ȻɄɒ (Ȼɚɪ-
ɞɢɧɚ, Ʉɭɩɟɪɚ ɢ ɒɪɢɮɮɟɪɚ) ɜ ɬɟɨɪɢɢ ɫɜɟɪɯɩɪɨɜɨɞɢɦɨɫɬɢ, ɩɪɢ-
ɱɟɦ ɪɨɥɶ ɜɧɟɲɧɟɝɨ ɩɨɥɹ H ɬɚɦ ɢɝɪɚɟɬ ɷɧɟɪɝɢɹ ɷɥɟɤɬɪɨɧɚ, ɨɬ-
ɫɱɢɬɚɧɧɚɹ ɨɬ ɭɪɨɜɧɹ Ɏɟɪɦɢ. ȼ ɡɚɞɚɱɚɯ 4.6.3-4.6.5 ɩɨɫɥɟ ɷɬɨɝɨ
ɩɚɪɚɝɪɚɮɚ ɦɵ ɩɨɤɚɠɟɦ, ɤɚɤ ɢɡ ɝɚɦɢɥɶɬɨɧɢɚɧɚ ȻɄɒ ɩɨɥɭɱɢɬɶ
ɫɩɢɧɨɜɵɣ ɝɚɦɢɥɶɬɨɧɢɚɧ (4.25).
ȿɫɥɢ ɜɡɚɢɦɨɞɟɣɫɬɜɢɟ V
kk’
=V
0
=const ɢ ɨɝɪɚɧɢɱɟɧɨ ɱɢɫ-
ɥɨɦ ɛɥɢɠɚɣɲɢɯ ɫɨɫɟɞɟɣ Z, ɬɨ ' ɬɚɤɠɟ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɢɧɞɟɤɫɚ k,
ɢ ɭɪɚɜɧɟɧɢɟ (4.34) ɭɩɪɨɳɚɟɬɫɹ:
''
'
'
ZV H
H
PEP
00 0
22
22
th{ } . (4.35)
ȼɢɞɧɨ, ɱɬɨ ɩɪɢ ɧɭɥɟɜɨɦ ɩɨɥɟ ɭɪɚɜɧɟɧɢɟ (4.35) ɟɫɬɶ ɨɛɵɱɧɨɟ
ɭɪɚɜɧɟɧɢɟ ȼɟɣɫɫɚ ɫ ɤɪɢɬɢɱɟɫɤɨɣ ɬɟɦɩɟɪɚɬɭɪɨɣ T
c
=
P
0
2
ZV
0
.
Ɂɚɞɚɱɢ
4.6.1. ɉɪɨɜɚɪɶɢɪɨɜɚɜ ɫɜɨɛɨɞɧɭɸ ɷɧɟɪɝɢɸ ɩɥɨɫɤɨɝɨ
ɮɟɪɪɨɦɚɝɧɟɬɢɤɚ (4.33) ɩɨ ɜɵɞɟɥɟɧɧɨɦɭ ɩɨɩɟɪɟɱɧɨɦɭ ɫɩɢɧɭ
<
V
>, ɩɨɥɭɱɢɬɶ ɫɚɦɨɫɨɝɥɚɫɨɜɚɧɧɨɟ ɭɪɚɜɧɟɧɢɟ ɞɥɹ ɩɚɪɚɦɟɬɪɚ
ɩɨɪɹɞɤɚ.
l
A
4.6.
2. Ɋɚɫɫɱɢɬɚɬɶ ɜ ɩɪɢɛɥɢɠɟɧɢɢ ɛɥɢɠɚɣɲɢɯ ɫɨɫɟɞɟɣ
ɩɪɢ ɤɨɧɟɱɧɨɦ ɩɨɥɟ H ɢ ɧɭɥɟɜɨɣ ɬɟɦɩɟɪɚɬɭɪɟ ɩɚɪɚɦɟɬɪ ɩɨɪɹɞɤɚ
ɞɥɹ ɩɥɨɫɤɨɝɨ ɮɟɪɪɨɦɚɝɧɟɬɢɤɚ ɢɫɯɨɞɹ ɢɡ ɫɚɦɨɫɨɝɥɚɫɨɜɚɧɧɨɝɨ
ɭɪɚɜɧɟɧɢɹ (4.35). ɉɨɥɭɱɢɬɶ ɤɪɢɬɢɱɟɫɤɨɟ ɩɨɥɟ, ɩɪɢ ɤɨɬɨɪɨɦ
ɢɫɱɟɡɚɟɬ xy ɭɩɨɪɹɞɨɱɟɧɢɟ.
Ɉɬɜɟɬ
:.'
0
2
0
2
0
22
0
2
0
()
PP
ZV H H ZV
c
76
ȼɜɟɞɟɧɢɟ ɤ ɡɚɞɚɱɚɦ 4.6.3 - 4.6.5 (ɫɩɢɧɨɜɚɹ ɚɧɚɥɨɝɢɹ
ɞɥɹ ɫɜɟɪɯɩɪɨɜɨɞɧɢɤɚ).
ɉɨɥɟɡɧɨ ɩɨɤɚɡɚɬɶ ɫɜɹɡɶ ɝɚɦɢɥɶɬɨɧɢɚ-
ɧɚ ɬɟɨɪɢɢ ɫɜɟɪɯɩɪɨɜɨɞɢɦɨɫɬɢ ɜ ɪɚɦɤɚɯ ɩɪɢɛɥɢɠɟɧɢɹ ȻɄɒ ɢ
ɫɩɢɧɨɜɨɝɨ ɝɚɦɢɥɶɬɨɧɢɚɧɚ (4.25).
Ʉɚɤ ɢɡɜɟɫɬɧɨ, ɜɨ ɜɬɨɪɢɱɧɨɦ ɤɜɚɧɬɨɜɚɧɢɢ ɝɚɦɢɥɶɬɨɧɢɚɧ
ȻɄɒ ɢɦɟɟɬ ɜɢɞ:
HaaVaaaa
kk k
k
kk
k
kk
k
kk
n
p
p
n
¦¦
[
VV
V
'
'
'
'
, (4.36)
ɝɞɟ
a
+
k
V
- ɨɩɟɪɚɬɨɪ ɪɨɠɞɟɧɢɹ ɷɥɟɤɬɪɨɧɚ ɫ ɢɦɩɭɥɶɫɨɦ k ɢɫɩɢ-
ɧɨɦ
V
;
[
k
k
m
E
!
22
2
f
ɷɧɟɪɝɢɹ ɷɥɟɤɬɪɨɧɚ, ɨɬɫɱɢɬɵɜɚɟɦɚɹ ɨɬ
ɭɪɨɜɧɹ Ɏɟɪɦɢ. ɉɟɪɜɵɣ ɱɥɟɧ ɜ (4.36) - ɤɢɧɟɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ
ɫɜɨɛɨɞɧɨɝɨ ɮɟɪɦɢ-ɝɚɡɚ, ɜɬɨɪɨɣ - ɩɪɢɬɹɝɢɜɚɸɳɟɟ ɜɡɚɢɦɨɞɟɣɫɬ-
ɜɢɟ [-
V
kk '
], ɩɪɢɜɨɞɹɳɟɟ ɤ ɨɛɪɚɡɨɜɚɧɢɸ ɤɭɩɟɪɨɜɫɤɢɯ ɩɚɪ. Ɍɚɤ,
ɨɩɟɪɚɬɨɪɵ ɪɨɠɞɟɧɢɹ ɩɚɪɵ ɷɥɟɤɬɪɨɧɨɜ
b
+
k
ɫ ɩɪɨɬɢɜɨɩɨɥɨɠɧɵ-
ɦɢ ɢɦɩɭɥɶɫɚɦɢ ɢ ɫɩɢɧɚɦɢ
(k
n,-kp) ɢ ɭɧɢɱɬɨɠɟɧɢɹ b
k
ɢɦɟɸɬ ɜɢɞ:
. (4.37)
baa baa
k
k
k
k
k
k
n
p
p
n
;
ɂɦɟɧɧɨ ɜɬɨɪɨɣ ɱɥɟɧ ɜ ɝɚɦɢɥɶɬɨɧɢɚɧɟ ȻɄɒ (4.36), ɨɩɢɫɵɜɚɸ-
ɳɢɣ ɩɪɢɬɹɠɟɧɢɟ ɩɚɪ ɢ ɩɟɪɟɦɟɳɟɧɢɟ ɢɯ ɢɡ ɫɨɫɬɨɹɧɢɣ ɫ ɢɦ-
ɩɭɥɶɫɨɦ
k’ ɜ ɫɨɫɬɨɹɧɢɹ ɫ ɢɦɩɭɥɶɫɨɦ k , ɩɪɢɜɨɞɢɬ ɤ ɤɨɧɞɟɧɫɚ-
ɰɢɢ ɤɭɩɟɪɨɜɫɤɢɯ ɩɚɪ ɢ ɫɜɟɪɯɩɪɨɜɨɞɢɦɨɫɬɢ.
ȼɵɛɟɪɟɦ ɞɥɹ ɤɚɠɞɨɝɨ ɢɦɩɭɥɶɫɚ
k ɩɚɪɧɵɣ ɛɚɡɢɫ
|0, 0>, |
kn,-kp>, ɨɩɢɫɵɜɚɸɳɢɣ ɫɨɫɬɨɹɧɢɹ ɷɥɟɤɬɪɨɧɨɜ ɜ ɤɭɩɟ-
ɪɨɜɫɤɨɣ ɩɚɪɟ. ɉɟɪɜɵɣ ɜɟɤɬɨɪ ɨɡɧɚɱɚɟɬ ɨɬɫɭɬɫɬɜɢɟ ɷɥɟɤɬɪɨɧɨɜ ɜ
ɷɬɢɯ ɫɨɫɬɨɹɧɢɹɯ, ɚ ɜɨ ɜɬɨɪɨɦ ɛɚɡɢɫɧɨɦ ɜɟɤɬɨɪɟ ɷɬɢ ɫɨɫɬɨɹɧɢɹ
ɡɚɩɨɥɧɟɧɵ. Ʌɟɝɤɨ ɜɢɞɟɬɶ, ɱɬɨ ɞɥɹ ɞɚɧɧɨɝɨ ɝɚɦɢɥɶɬɨɧɢɚɧɚ ɷɬɨɬ
ɛɚɡɢɫ ɹɜɥɹɟɬɫɹ ɩɨɥɧɵɦ, ɫ ɟɝɨ ɩɨɦɨɳɶɸ ɦɵ ɦɨɠɟɦ ɩɟɪɟɛɪɚɬɶ
ɜɫɟ ɫɨɫɬɨɹɧɢɹ ɫɢɫɬɟɦɵ.
Ɂɚɞɚɱɢ
77
4.6.3. Ɋɚɡɥɨɠɢɬɶ ɨɩɟɪɚɬɨɪ ɱɢɫɥɚ ɱɚɫɬɢɰ ɢ ɨɩɟɪɚɬɨɪɵ
ɪɨɠɞɟɧɢɹ ɢ ɭɧɢɱɬɨɠɟɧɢɹ ɤɭɩɟɪɨɜɤɢɯ ɩɚɪ ɩɨ ɛɚɡɢɫɭ
|00>, |
kn,-kp> ɜ ɩɪɨɫɬɪɚɧɫɬɜɟ 2ʉ2 ɞɥɹ ɤɨɧɤɪɟɬɧɨɝɨ k.
Ɋɟɲɟɧɢɟ
. Ɋɚɫɫɦɨɬɪɢɦ, ɱɟɦɭ ɪɚɜɧɵ ɦɚɬɪɢɱɧɵɟ ɷɥɟɦɟɧɬɵ
ɢɧɬɟɪɟɫɭɸɳɢɯ ɧɚɫ ɨɩɟɪɚɬɨɪɨɜ ɜ ɷɬɨɦ ɛɚɡɢɫɟ. Ɍɚɤ,
! np
np ! np!
n
nn
n
n
p
n
p
00 0 00 0
100
| |00 ; | | ;
| |00 ; | | .
aa aa k k
kkaa aakk
kk kk
k
k
k
k
!
0
(4.38)
Ɍɨɝɞɚ ɦɨɠɧɨ ɨɩɟɪɚɬɨɪɚɦ ɪɨɠɞɟɧɢɹ ɢ ɭɧɢɱɬɨɠɟɧɢɹ ɩɚɪɵ ɢ
ɨɩɟɪɚɬɨɪɭ ɱɢɫɥɚ ɱɚɫɬɢɰ ɜ ɷɬɨɦ ɛɚɡɢɫɟ ɫɨɩɨɫɬɚɜɢɬɶ ɦɚɬɪɢɰɵ
2ʉ2:
naa n
bb
kkk
k
kk
nn
n
p
§
©
¨
·
¹
¸
§
©
¨
·
¹
¸
§
©
¨
·
¹
¸
§
©
¨
·
¹
¸
00
01
00
01
00
10
01
00
,,
,.
(4.39)
Ɉɩɟɪɚɬɨɪɵ (4.39) ɦɨɠɧɨ ɜɵɪɚɡɢɬɶ ɱɟɪɟɡ ɦɚɬɪɢɰɵ ɉɚɭɥɢ (4.3) :
In n
bib
k
k
Z
XY XY
n
p
§
©
¨
·
¹
¸
10
01
1
2
1
2
V
VV VV
,
(),(i ).
(4.40)
4.6.
4. ɂɫɯɨɞɹ ɢɡ ɮɟɪɦɢɨɧɧɵɯ ɫɨɨɬɧɨɲɟɧɢɣ ɤɨɦɦɭɬɚ-
ɰɢɢ, ɩɨɤɚɡɚɬɶ, ɱɬɨ ɜɜɟɞɟɧɧɵɟ ɫ ɩɨɦɨɳɶɸ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ
(4.40) ɫɩɢɧɨɜɵɟ ɨɩɟɪɚɬɨɪɵ ɩɨɞɱɢɧɹɸɬɫɹ ɤɨɦɦɭɬɚɰɢɨɧɧɵɦ
ɫɨɨɬɧɨɲɟɧɢɹɦ ɞɥɹ ɦɚɬɪɢɰ ɉɚɭɥɢ.
78
4.6.5. ɂɫɯɨɞɹ ɢɡ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɮɟɪɦɢɨɧɧɵɯ ɨɩɟɪɚɬɨ-
ɪɨɜ ɜ ɫɩɢɧɨɜɵɟ (4.40), ɩɨɤɚɡɚɬɶ, ɱɬɨ ɝɚɦɢɥɶɬɨɧɢɚɧ ȻɄɒ ɩɪɟ-
ɨɛɪɚɡɭɟɬɫɹ ɜ ɫɩɢɧɨɜɵɣ, ɚ ɭɪɚɜɧɟɧɢɟ ɞɥɹ ɩɚɪɚɦɟɬɪɚ ɩɨɪɹɞɤɚ
ɫɨɜɩɚɞɚɟɬ ɫ ɪɚɧɟɟ ɩɨɥɭɱɟɧɧɵɦ (4.34).
Ɋɟɲɟɧɢɟ
. ɉɨɞɫɬɚɜɢɜ (4.40) ɜ ɝɚɦɢɥɶɬɨɧɢɚɧ (4.36), ɩɨɥɭ-
ɱɚɟɦ:
HV
kk
Z
k
kk k
X
k
X
k
Y
k
Y
kk
¦¦
[V VVVV
() {
''
'
1
1
4
}
'
. (4.41)
ȿɫɥɢ ɩɟɪɟɨɛɨɡɧɚɱɢɬɶ ɜ (4.41)
HVV V
H
k
kk
kk k
kk
k
k
kk
kk
k
oo
A
¦
[
P
P
P
V
P
[P
0
0
2
0
2
0
2
2
2
0
2
1
2
1
,,
[], ,
'
'
'
'
'
'
'' '
!,
(4.42)
ɬɨ, ɜɨ-ɩɟɪɜɵɯ, ɫ ɬɨɱɧɨɫɬɶɸ ɞɨ ɧɟɫɭɳɟɫɬɜɟɧɧɨɣ ɩɨɫɬɨɹɧɧɨɣ
ɩɨɥɭɱɚɟɦ ɫɩɢɧɨɜɵɣ ɝɚɦɢɥɶɬɨɧɢɚɧ (4.25) ɢ ɭɪɚɜɧɟɧɢɟ ɧɚ ɩɚɪɚ-
ɦɟɬɪ ɩɨɪɹɞɤɚ '
k
(4.34) ɢ, ɜɨ-ɜɬɨɪɵɯ, ɞɥɹ ɩɟɪɟɧɨɪɦɢɪɨɜɚɧɧɨɝɨ
ɩɚɪɚɦɟɬɪɚ
'
k
ɢɦɟɟɦ ɫɥɟɞɭɸɳɟɟ ɫɚɦɨɫɨɝɥɚɫɨɜɚɧɧɨɟ ɭɪɚɜɧɟ-
ɧɢɟ:
''
'
'
k
kk k
k
k
k
k
k
V
¦
1
2
2
2
2
2
'
'
'
'
'
[]th
E[
[
. (4.43)
ɍɪɚɜɧɟɧɢɟ (4.43) ɹɜɥɹɟɬɫɹ ɨɫɧɨɜɧɵɦ ɭɪɚɜɧɟɧɢɟɦ ȻɄɒ ɜ ɬɟɨ-
ɪɢɢ ɫɜɟɪɯɩɪɨɜɨɞɢɦɨɫɬɢ.
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ
, ɜ ɡɚɞɚɱɚɯ 4.6.3 - 4.6.5 ɦɵ ɩɨɤɚɡɚɥɢ ɩɨɥ-
ɧɭɸ ɚɧɚɥɨɝɢɸ ɦɟɠɞɭ ɫɩɢɧɨɜɨɣ ɚɧɢɡɨɬɪɨɩɧɨɣ ɦɨɞɟɥɶɸ Ƚɟɣ-
ɡɟɧɛɟɪɝɚ (4.25) ɢ ɦɨɞɟɥɶɸ ȻɄɒ ɞɥɹ ɫɜɟɪɯɩɪɨɜɨɞɧɢɤɨɜ. Ɂɚɦɟ-
ɬɢɦ, ɱɬɨ ɪɨɥɶ ɜɧɟɲɧɟɝɨ ɫɬɚɛɢɥɢɡɢɪɭɸɳɟɝɨ ɩɨɥɹ, ɧɚ ɮɨɧɟ ɤɨ-
ɬɨɪɨɝɨ ɪɚɡɵɝɪɵɜɚɟɬɫɹ ɫɜɟɪɯɩɪɨɜɨɞɹɳɟɟ (ɢ ɮɟɪɪɨɦɚɝɧɢɬɧɨɟ)
ɭɩɨɪɹɞɨɱɟɧɢɟ, ɜ ɫɜɟɪɯɩɪɨɜɨɞɧɢɤɟ ɢɝɪɚɟɬ ɷɧɟɪɝɢɹ ɷɥɟɤɬɪɨɧɚ
[
k
,
ɨɬɫɱɢɬɚɧɧɚɹ ɨɬ ɭɪɨɜɧɹ Ɏɟɪɦɢ.
_____________
79