Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://nuclphys.sinp.msu.ru/mirrors/1999_11b.pdf Äàòà èçìåíåíèÿ: Tue Jan 13 15:51:52 2009 Äàòà èíäåêñèðîâàíèÿ: Tue Oct 2 00:14:30 2012 Êîäèðîâêà: Windows-1251

IONIZATION ENERGY LOSS OF CHARGED PARTICLES
S. P. DENISOV The kinematics of elastic scattering and the dynamics of the Coulomb interaction are considered. Obtained results are used to derive the Rutherford Formula and a relation for the density of ionization energy loss in small angle approximation. The dependence of ionization energy loss on particle energy is discussed. êÒÒÏÓÚ ÂÌœ ÂÎflÚË,ËÒÚÒÍfl ÍËÌÂÏÚËÍ ÛÔ Û,,Ó,,Ó ÒÒÂflÌËfl Ë ËÌÏËÍ ÍÛÎÓÌÓ,ÒÍÓ,,Ó ,ÁËÏÓÂÈÒÚ,Ëfl. èÓÎÛ~ÂÌ̜ ÂÁÛÎåÚÚœ ËÒÔÓÎåÁÓ,Ìœ Îfl ,œ,Ó ÙÓ ÏÛÎœ êÂÁ ÙÓ Ë ÒÓÓÚÌÓ?ÂÌËfl Îfl ÔÎÓÚÌÓÒÚË ËÓÌËÁ^ËÓÌÌœi ÔÓÚ å Ì ,,ËË ÁflÊÂÌÌœi ~ÒÚË^ , Ô ËžÎËÊÂÌËË ÏÎœi Û,,ÎÓ,. éžÒÛÊÂÌ Á,ËÒËÏÓÒÚå ËÓÌËÁ^ËÓÌÌœi ÔÓÚ å Ì ,,ËË ÓÚ Ì ,,ËË ~ÒÚË^œ.
¿ ÑÂÌËÒÓ, ë.è., 1999


ë. è. ÑÖçàëéÇ
åÓÒÍÓ,ÒÍËÈ ,,ÓÒÛ ÒÚ,ÂÌÌœÈ ÛÌË, ÒËÚÂÚ ËÏ. å.Ç. ãÓÏÓÌÓÒÓ,

1. ÇÇÖÑÖçàÖ

, , , . . . , , . . , . . , . , , .. , . , . , . , . . , . : . dE / dx, . . dE / dx .

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ëéêéëéÇëäàâ éÅêÄáéÇÄíÖãúçõâ ÜìêçÄã, <11, 1999


, .
2. äàçÖåÄíàäÄ ìèêìÉéÉé êÄëëÖüçàü

T m 0 : 2 ( pc ) mc cos 0 T = ----------------------------------------------------------- . 22 2 ( E + m c ) - ( pc ) cos 0
2 2 2

(2)

, , . , . , . M, , p E = ( pc ) + ( Mc ) ( - ) m. E ' p' , T, p0 , 0 .
2 22

, T 0 . , [1]. (1), : 0 p' p, 0 /2 T, p0 0, - ( ), (p0 p) , , , , ; , 0 = /2 m; - m, (2), 0 = 0, : T
max

p = p ' + p (. 1) E = E ' + T, p = p' cos + p0 cos 0 , 0 = p' sin - p0 sin 0 , E ' = ( p ' c ) + ( Mc ) ,
2 22

0

2 mc = ---------------------------------------- , m2 m 1 + 2 ---- + ---- M M
22 2

(3)

(1)

T = ( p 0 c ) + ( mc ) - mc .
2 2

22

(1) : E ', T, p', p0 , , 0 . (1), . , p'


p

= / c = E / M - - . (3) m). ( 1) (M Tmax = 2p2m / M 2 = 4E(m / M )2, . ( > 1), 2m / M 1, Tmax 2m22. (2m / M 1) Tmax M = E, . , : . , . , .
3. ÑàçÄåàäÄ äìãéçéÇëäéÉé êÄëëÖüçàü



0

p

0

. 1.

, , p, ze (e - ) b m Ze (. 2). - , , . p0 T, , b

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91


y 2b dS m, ze, p r d
c

x, y, z -

r (x, y, z) [2]: 1- z er = ------- --------------------------------------- . 3 3/2 r ( 1 - 2 sin 2 c )
2

(5)

b

c

M, Ze

x

. 2. p0

1. , m , . , . . , p0 , , pt , y (. 2). pt , , M F M = zZ e / b , F M p , 2b tM = 2b / ( ). pt = py = Fy ty = FM tM ,
2 2

(5) , ( 1) (c = 0 = ze /(2r 2)) (c = /2 = ze / r 2). . 2 (5) , dt = = ds / M ds = rdc / sin c p0 d p0 = Z e
y 2 zZ e ( 1 - ) sin c dt = ---------- --------------------------------------- d c . b ( 1 - 2 sin 2 c ) 3 / 2 2

b = r sin c y = sin c . dp0 0 , , (4). , , , Fm = zZe2 / b2, FM . tM : p0 2 b t m = ----- = ----- . F m (6)

2 zZ e p t = p 0 = ------------- . b


2

(4)

(6) , , M , . . (4) p0 b, T (b). m , , , T = p 2 / ( 2 m ) 0 2 zZ e T = --- ---------- . m b
22

, ,

(7)

-



F y ( t ) dt , -

( ). tM . (4), . p0 , , , . c, , - - -

, m . , y = 0 t m b , y - , 0 - m, 0 /2 = p0 /(2m). (4) (6), b bmin = = 2zZe2 /(m2). ( c) bmin = 2re / , re = = e2 /(mec2) = 2,818 10-13 - . pt

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ëéêéëéÇëäàâ éÅêÄáéÇÄíÖãúçõâ ÜìêçÄã, <11, 1999


= pt / p (pt p) p = = M, m : max = 2zZe2 / bminp = m / M.
4. ÑàîîÖêÖçñàÄãúçõÖ ëÖóÖçàü äìãéçéÇëäéÉé êÄëëÖüçàü

n0dx = 1, d / dT : 2 zZ e d d N ----- = ------ ( n 0 d x = 1 ) = ----- ---------- . m T dT dT
22

(10)

M, E ze dx , dE , dE E. dN T T + dT. , , b b + db , b | db |, (. 3): dN = 2b | db | n0dx,
3

. (10) , , T. (10) , ÷- (z = Z = 1) : d 2 ----- = ----dT m e
2 e T T ------ 1 - 2 --------- + -------- , T T max 2 E 2 2 2

(11)

(8)

n0 - 1 . b (7): 2 b = 2 zZ e / mT . , | db | , b | db | (8), 2 d N = ----m zZ e- dTn d x . ---------0 T
22

me - . , T Tmax (11) (10), . = p0 / p T = p 2 / ( 2 m ) , T = p22 /(2m). 0 dT dT T (10), d 2 zZ e 1 ----- = 2 ------------- ---- . - p 3 d
22

(9)

(12)

. T 1 2,

db

b

p

. 3. b b + db

. (9)-(12) , . 3 . , (11), . ( ). 1913 , - , . , , . , : , . . . 40 .

dx

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93


. . . . 70- -- 40 (1 = 1,6 10-19 - , 1 ). --. 10-13 . , , ÷- : . - .
5. èãéíçéëíú àéçàáÄñàéççõï èéíÖêú ùçÖêÉàà

. (9) , dx T T + dT 2 zZ e dT T d N = ----- ---------- ----- n 0 d x . m T
22

T0 , , Tmin Tmax :
2 T max 2 zZ e T 0 = ----- ---------- n 0 d x ln --------- . m T min 2

Tmin . , : , . I. , Tmin I. . , , , T, T / t, - t - . t tm (6) Tmin = / tm = /(2bmax) = I, bmax - , , . , , py y p0 /(2bmax) I /(). p0min = I /() = p0min . Tmin T min = p 2 min / ( 2 m e ) = I 2 / ( 2 m e 2 2 ) . 0 . , , , . Tmin (14) = / c,
2 2 m e c T max dE 2 2z - ----- = 2 r e m e c ---- Z n ln ----------------------------------- , 2 2 dx I 2 22

T0 = - dE, dE - dx, T max dE 2 zZ e - ----- = ----- ---------- n 0 ln --------- . m T min dx
22

(15)

(13)

, . . Z = 1 n0 = Zn, n - 1 3, m Amn , A - mn - Amn /(Zme). , dEe / dEn A / Z 2 mn / me 2 103, 4 103. 4000 , . , (13) dE 2 - ----- = ----dx me
2 T max ze ------ Z n ln --------- . T min 2

re = e2 /(mec2) - . , (/2). , (15) . n = NA / A (NA - ), (16)
2 z Z 2 m e c T max dE -- -------- = K ---- ------ ln ----------------------------------- , 2 2 dx 2A I 2 22

(16)

K = 4 r e m e c N A = 0,307 M/(/2).
2 2

(14)

Tmax (3) . (14) , -

I . (10 + 1) Z . Z / A = 1/2, (16) . /2.

94

ëéêéëéÇëäàâ éÅêÄáéÇÄíÖãúçõâ ÜìêçÄã, <11, 1999


, , -: z dE - -------- = K ---2 dx
2

Z --A

1 -- ln 2 m e c T max - 2 - -- . - ----------------------------------2 2 2 I
2 22

(17)

- dE --------- , ------------- dx / 2 10 9 8 7 6 5 4 3

H2

(16) 2 /2. 2 (. (11)). , (17) 30. , 2, 10-15%. /2 . 1 bmax = c /(2I ) ( / I []) 10- 5 (. ) . - bmax bmax . . /2. 1 = 2 ln ( × × p / I ) - 1, p = 28 ,8 Z / A - ( /3). . , . , , 3, > a , a Zc, = e2 /( c) 1/137 - . A Z. : (- dE / dx) = w j ( - dE / d x ) j , wj = j / - =



2 C Al Fe Sn Pb

1 0,1

1,0

10

100

1000

10 000 pc = -----M

. 4. = pc / M, p - M - . [3]


j

tm (6) . c ln 2 (bmax ) Tmax 2 (. 2). , ( 1) bmax Tmax E. . 4, 3 4. (- dE / dx) 1 2 /(/2), 1 = 10 6 . , (- dE / dx)min 4 /(/2). , Z / A = 1, 1/2, . (- dE / dx)min [3].
7. áÄäãûóÖçàÖ

j- j- , (- dE / dx)j - , j- .
6. áÄÇàëàåéëíú èãéíçéëíà àéçàáÄñàéççõï èéíÖêú éí ùçÖêÉàà óÄëíàñõ

(17) . 4. < 1 p0

, . . (- dE / dx), (. 3), , -. , , ,

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95


, . . . , . , , , . (. 2). . ( < a ) . . . . ,

, [4].
ãàíÖêÄíìêÄ
1. .., .., .. . .: , 1987. . 85-92. 2. .., .. . .: , 1960. . 116. 3. Barnett R.M. et al. Review of Particle Physics // Phys. Rev. D. 1966. Vol. 54, 1. P. 72, 132. 4. .., .., ., .. . .: , 1988.

*** , , , - . , , -3 t-. . 200 .

96

ëéêéëéÇëäàâ éÅêÄáéÇÄíÖãúçõâ ÜìêçÄã, <11, 1999