Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://physelec.phys.msu.ru/study/comp/vozb.pdf Äàòà èçìåíåíèÿ: Mon Dec 3 09:09:24 2012 Äàòà èíäåêñèðîâàíèÿ: Mon Feb 25 12:01:51 2013 Êîäèðîâêà:

2. .. 1 , , , , , , . , , , ( , ,) , , . , , . , , , , : ; , , ; ; .. , . , © .., 2012 © , 2012
1


m n (Imn) (Nm) [1]: (1 ) Imn = NmhmnAmn , mn Amn m­n. , .. , (1) . , . , ( ) ( ) , () ( ) , ( ), , , , . . , , , . . , , . , , [2]. . 1. , . 2. . 3. . 2


: 0 k 0m N 0 ne N m Amj , (2) j m kom ­ , m­ , Amj ­ m j­ , . :
N
m



k 0 m N 0 ne , Amj
j m

(3 )

kom :


k

0m

Const
U



dE

0m

E f , ,

(4 )

MI NP

N0 ne ­ , , om ­ m­ , f(E) ­ (E), Umin ­ m ­ . , , , , :
0 k 0 m N 0 ne Nm d

(5)

(6) , , N0=3.5410 p , d=0.910­3pR2 ( , R ­ ) [3], :
d

N m k 0 m N 0 ne
16 ­3

N

p



k

0p

3.54 1016 pn


j p

e

Apj

(7)

: (8) , .
0m

Nm k

3.19 1013 ne p

2

3


, , , , . . 1 ( ) , (7) (8). (7) (8), , , , .

. 1. : 1 ­ , 2 ­ . , , , , . : N m Amp N m ne vE mp E , (9)
p
­­­ , v ­ . 4


() , , , . , . , . , , , . , , m­ :
Nm = N
0

gm U exp m , g0 kT

(10)

go gm ­ , , Um ­ m­ . , . , , (9): N m n e vE mp E N m Amp , (11)
p m p< m

.. . , (9) (11) ne<1011­1012 ­3, , , ne>1017­1018 ­3. , 12 10

, , - [2]. , . , , , . , , , . . 1. n = 1, 2, 3, 4 5. n = 1 , n = 2, 3, 4 5 ­ . 2. n = 4, 5 S, P, D . F , . . , P . 3. S, P, D , n = 3, 4 5, , n (. . 2). , , , , . 1 , ; , , (fm) (Amn) [4,5]. 6


. 2. , , . 1. , , , , 0 3 þ . . fmn10 Amn10­6, c­1 33 P012 23 S1 3888,65 1000 64 9,45 3964,73 4026,19 4120,82 4387,93 4437,55 4471,48 4713,16 4921,93 5015,68 5047,74 5875,62
41 P1 21 S
3 3
0

20 50 12 10 3 250 30 20 100 10 1700

140 47 3,8 43 3,2 120 11 120 150 8,7 610

19,89 11,6 4,5 8,97 0,68 24,1 9,95 19,9 13,3 6,86 71 7

53 D123 23 P012 5 S1 2 P012
51 D2 21 P1

51 S0 21 P1
43 D123 23 P012 43 S1 23 P012 41 D2 21 P1 31 P1 21 S
0

41 S0 21 P1

33 D123 23 P012


6678,15 7065,19 7281,35

31 D2 21 P1 33 S1 23 P012 31 S0 21 P1

200 500 100

710 70 49

64 28,2 18,58

2. 1­ 2­ , , , . , , . . , , , . 3. , n =3, 4 5. , . . n3 , U jk E, Ujk ­ j k, E ­ ; , 1­ 2­ , . 2. 6 ­1 A jk 10 j k , 3 2 S1 N1 19,82 0
21 S
0

N2 N3 N4 N5 N6 N7 N8 N9

20,61 20,96 21,22 22,78 22,92 23,09 23,07 23.01

0 18,5 1800 28,2 18,6 580 64 32 8

2 3 P012
21 P1 33 S1 31 S
0

31 P1 31 D2 33 P012


33 D123 43 S1 41 S
0

N10 N11 N12 N13 N14 N15 N16 N17 N18 N19 N20 N21 N22 N23 N24

23,07 23,59 23,67 23,74 23,74 23,71 23,74 23,74 23,74 23,97 24,01 24,04 24,04 24,03 24,04

71 10,1 9,1 2220 27 6,9 2,6 12 12 7 0,68 3,9 9 3,9 15

41 P1

41 D2 43 P012 43 D123 41 F3
43 F234

53 S1
51 S
0

51 P1 51 D2 5 P012 53 D123
3

4. 31 D2 33 D123 43F234 41F3 , . . , 31 D2 33 D123 . 43F234 41F3. 5. , , . 6. , , .. . 2. , , , , , [4]. : 9


dN1 (k 01N 0 k10 N1 )ne dt

N
24 j= 2

j

v j1(E) N1 v1 j(E) ne N j A j1
j= 2



24

N1 , D1

(12)

dN 2 (k 02 N 0 k 20 N 2 )ne dt

N
24 j=3

j

v j 2(E) N 2 v 2 j(E) ne N j A j1
j= 2



24

N N 1 v12(E) N 2 v 2 j(E) ne 2 D2
dN 3 (k 03 N 0 k 30 N 3 )ne dt





(13)

N
24 j= 4

j

v j 3(E) N 3 v 3 j(E) ne N j A j 3
j= 4



24

N
2 j=1

j

v j 3(E) N 3 v 3 j(E) ne N j A3
j=1



2

(14)

j 24

dN 4 (k 04 N 0 k 40 N 4 )ne dt

N
24 j=5

j

v j 4(E) N 4 v 4 j(E) ne N j A j 4
j=5



N
3 j=1

j

v j 4(E) N 3 v 4 j(E) ne N j A4
j=1



3

(15)

j

p = 5 ­ 10:
dN dt
p

(k 0 p N 0 k p 0 N p )ne

N
24 j=11

j

v jp(E) N p v pj(E) ne N j A jp
j=11



24

N
4 j=1

j

v jp(E) N p v pj(E) ne N j Apj
j=1



4

(16)

p = 11 ­ 18:
dN dt
p

(k 0 p N 0 k p 0 N p )ne

N
24 j=19

j

v jp(E) N p v pj(E) ne N j A jp
j=19



24

N
10 j=1

j

v jp(E) N p v pj(E) ne N j Apj
j=1



10

(17)

p = 19 ­ 24:
dN dt
p

(k 0 p N 0 k p 0 N p )ne

N
18 j=19

j

v jp(E) N p v pj(E) ne N j Apj
j=1



18

(18)

N0 ­ ; k0p kp0 ­ 1­ 2­ ; jp pj ­ ; ­­­ ; ne v ­ , . (23S1 21S0), ­ (23P012 21P1); 4 10


n = 2. 6 , n = 3, , . (17) , n = 4, , (43F234 41F3). 6 n = 5. 1­ 2­ , . , Ajp, . , , . (12) (13) , D1 D2 . k0p kp0 f(U) [6]:


k

0p

Const
U




dE

0p

E f , ,

(19)

MI NP

:


k jp Const
U

dE

jp

E f , ,

(20)

MI NjP

Uminp Uminjp ­ p j­ , , v=5.93107 E ­ (U E ­ ). 0P ( E) , .. [7]:
0p ( E) = 2.72
max

E-U min E-U min exp U -U U max -U min max min



(21)

Umax ­ , (max) p. jp Uminjp , Umaxjp maxjp : 11


0p ( E) = 2.72

E-U
max jp

min jp min jp

U

max

-U

E-U min exp U max jp -U

jp min jp



(22)

( ) [6]: (23) pj(E)E =jp(E+Ujp)( E+Ujp), , U0p = Up0 = Umin :
p 0(E)=2.72
max

E+U min exp U U max -U min

E max -U
minpj

min

,

(24)

, Ujp = Upj = U :
pj ( E) = 2.72
E+U
max jp min jp min jp


E -U ,

U

max jp

-U

exp U

(25)

max jp

min jp

max Umax, (21 ­ 25), [4,8], , .. [5]. [6]: (26) 1/D1=D1/2, (27) 1/D2=D2/2, D1 D2 ­ , ­ , : (28) 1/2 = (2,4/ R)2, R­ . D1 D2 [3,9], , , , : (29) 1/ D1 = 1/ D2 = 2,451031/pR2 , , . , [6]:
f(E)dE = 2 E (kTe )1
,5

E exp kT dE , e

(30) 12


Te ­ . (12­18) , , ne, :
0 (k 01N 0 k10 N1 )

N
24 j= 2
24

j

v j1(E) N1 v1 j(E)



24

N n

j

j= 2

A j1
N n
j

e
24

N ne

1 D1

,

(31)

0 (k 02 N 0 k 20 N 2 )

N
j=3

j

v j 2(E) N 2 v 2 j(E)



j= 2

A j1

e

N N 1 v12(E) N 2 v 2 j(E) ne
0 (k 03 N 0 k 30 N 3 )





(32)

2 D2

N
24 j= 4

j

v j 3(E) N 3 v 3 j(E)



24

N n

j

j= 4

Aj3

e

N
2 j=1

j

v j 3(E) N 3 v 3 j(E)



2

N n

(33)

j

j=1

A3

j

e

0 (k 04 N 0 k 40 N 4 )

N
24 j=5

j

v j 4(E) N 4 v 4 j(E) ne



24

N n

j

j=5

Aj 4

e

N
3 j=1

j

v j 4(E) N 3 v 4 j(E) ne



3

N n

(34)

j

j=1

A4

j

e

p = 5 ­ 10:
0 (k 0 p N 0 k p 0 N p )

N
24 j=11

j

v jp(E) N p v pj(E)



24

N n

j

j=11

A jp

e

N
4 j=1

j

v jp(E) N p v pj(E)



4

N n

(35)

j

j=1

Apj

e

p = 11 ­ 18:
0 (k 0 p N 0 k p 0 N p )

N
24 j=19

j

v jp(E) N p v pj(E)



24

N n

j

j=19

A jp

e

N
10 j=1

j

v jp(E) N p v pj(E)



10

N n

(36)

j

j=1

Apj

e

p = 19 ­ 24:
0 (k 0 p N 0 k p 0 N p )

N
18 j=19

j

v jp(E) N p v pj(E)



18

N n

j

j=1

Apj

(37)

e

, (31­37) : B1.1X1+B1.2X2+B1.3X3+..............+B1.24X24=B1.0 , (38) B2.1X1+B2.2X2+B2.3X3+.............+B2.24X24=B2.0 , (39) 13


B3.1X1+ B3.2X2+ B3.3X3+.............+ B3.24X24=B3.0 , (40) ... B24.1X1+ B24.2X2+ B24.3X3+..........+ B24.24X24=B24.0. (41) : B p 0 k0 P N 0 ­ ;
B jp k jp N n
j

A

jp

p (p­ )

e

j (jp) (jP) j p. Bjj (j=p) p , , :
B pj


j p

k pj


j p

N n

p

Apj ,

(42)

e

kjp kpj ­ (19, 20). (38­41) . , Bpj , (19, 20). b, :
b 1 U



E jP ( E) f(E) dE
U


MI N jP

b

E jP ( E) f(E) dE 0.00001 .

(43)

MI N jP

­ b=200, (43) . , , . (19, 20) . , Borland C++. Bjp (38 ­ 41) , . , 14


, . , , , , , ( ) . , ( , , 31 ­ 37), . , (31 ­ 37) 1010 ­3. " ". 1. , , . , , ne=108 ­3 ne=1019 ­3. . . 2. 1 , ne=109 ­3 ne=1012 ­3. , (7), (8), . 3. 1 2 . . . 4. , , (36­41), 15


. , . . 5. , , , ne=1014 ­3 ne=1018 ­3 ( , 100%). . , (10). . . : , , , . 1. .. . . . 1963 . 2. . . . . . . . . . . 1967. 3. .. , .. . " ". . . . 1. . 51. . 1976 . 4. .. , .. . . . . . 1973 . 5. .. . . .. . 1960 . 6. .. . . . . 1992 . 7. .. . . . 1952 . 8. R. Mewe. Positive column in helium. Physics. volume 47. N 3. C. 370. 1970 . 9. .. , .. , .. , .. . He­Xe. . . . 3. 1982 . 16


" " "HeI". . 1.

.1. 1. "Edit" "Parameters". 2. " " . 3. " " . , , . 4. 1 24 , , . 2 ­ 4 "View", , . 5. 17


: , .. "File", "Exit". . , "Edit" "Parameters". . 2.

. 2. 5 . 6. (Ne) . Nemin , Nemax NeStep, , Nemin=0.0, Nemax=100 NeStep=0.1. "Quantity of points" (Show) . 9990 . . 10000 . 10 10 ­3. Nemin . 7. (Condition) (Temperature) (Pressure) . 8. (Type of step) . (Add) (Multiply) 18


. (Add.) 6. , , 2­3 . (Multiply) . (Show). (Multiply) , , Nemin=10­4, Nemax=1010. , Nemin=106 ­3 Nemax=1020 ­3. . (Multiply) Nemin , , , Nemin=10­4 .. 9. , ( Levels) , , , (31­37). 4­ . . 1, 2, 3 5 24. 10. () . , , ( ) 1 24 (. 1). 11. , , , , ( ) 2,3 , , 1­ 24 (. 4 ), . , 1010 ­3. 19