Диссертация (Процессы ионизации при взаимодействии быстрых частиц с веществом), страница 7

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A: 95% ? :;D%:, 6E 758 %56? %55 -%5'%' @;, %, %&,E 7 -5 ), <%< 5&, 5&: %<5 V V `-6 5-% %%%6E &% 7A 5& -)56: 758' FE {ncE csc necG 7: &%6 %%%& (5%< & % 9((%:758? '-E % 55)<' %', ( ?%@: %E 755: )'-&% & m€nO F4! G 5& '-&? 5 5'&5 -% %&:, 95% F4!!G - : )5 ;%M(k , k ) =M (k , k ),F44=G?-M (k , k ) = k |V g (E )W + W g (E )V |k .F4" G56)' F440GE 5&M (k , k ) = ξ M (k , k ) + (1 − ξ )M (k , k ).F4"!GjBssjAs0js0jjjss00sjj +s 0jAss0+0j0jBjss00!4#H-% F44=G F4! G -%dσks ke (−)(−)=χke |Mj (ks , k0)A−()Mj+ (ks, k0)|χke .5dEsdEedΩs dΩe(2π) k0 F4"#Gjj`-6 - -95%' %56' (<'A− () =|ii|δ( − i ),F4"4G = Es + Ee − E0 .iocc:5'' (?< - F4"#GE 78  -@)56: -95%: 5'<: &5C'(χke |Mj (ks , k0)A−()Mj+ (ks, k0)|χke( − ' +((−) '= χke | Mj (ks , k0) A () Mj (ks , k0) |χk(−)e(−)(−)−++δjj x χke |MjA (ks , k0)A ()MjA (ks, k0)|χke (−)(−)−++(1 − x) χke |MjB (ks, k0)A ()MjB (ks, k0)|χke ('( (−)(−) '− χke | Mj (ks , k0) A−() Mj+ (ks , k0) |χke .F4""GH :- F4""G %8 7:5 -5 -58E &%('('Mj (ks, k0 ) = ks |Vsj g0+ (Es) W + W g0+ (E0) Vsj |k0 ,F4">G% 7:5 A: (5%< g (E ) − 'g (E )( Fr = s, 0G W − W 7)E -5' (?< -? &' m€nO -+0)dσdEsdEedΩs dΩe?- 5?:)dσcohdEs dEedΩs dΩe**=)=r+0dσcohdEsdEe dΩsdΩer*)+dσincohdEsdEedΩs dΩe*,F4"/Gks ke(2π)5k0 (−) '( − ' +( (−) ×χke | Mj (ks , k0) A () Mj (ks , k0) |χke jj F4"0G!44)dσincohdEsdEedΩs dΩe*=ks ke(2π)5k0(−)(−)−+×x χke |MjA (ks , k0)A ()MjA (ks, k0)|χke j+(1 − x)−(−)(−)+χke |MjB (ks , k0)A−()MjB(ks, k0)|χke ( − ' +( (−) (−) 'χke | Mj (ks, k0) A () Mj (ks, k0 ) |χke F4"2G%6 ?%:, ?%:, 5-: & m€nOE 755: @?%: ?%: 7%: ' -DA? 95@% %%% :8' F4"0G F4"2G ?5 F4"!G('F4"=GM (k , k ) = xM (k , k ) + (1 − x)M (k , k ).7- %8 %%%6E &% :- :8, F4"0G F4"2G -5@56 .57 -58, -5 (?<? -' @%56 &56 & %'' 95% ; @E 9% - 8% 7:%6 :5 758' {nc 5~~d nec 35 %?E ): 758' ?% 7:%6 56): -5' @&56? &? %', 95% ;_%7: ,% (?< - & m€nO F4!#GE %&@DA 5&D ?% %5 % %- 1E )%E &%%% & F!>G )% % %%, (?< %5-%56E )* ('dσkkdσ=F4> GA (k, ) .dE dE Ω dΩ(2π) k dΩ 7)E & F4> G % 'D (<D %56, (@< '-&? %5 A (k, ) E &% kE % )@'D%' 1 9%E E 5-%56E (<' A (k, ) 8%jss0ejAsse0jBs e3−0s0ee−−!4"7:%6 5- 75 -%56: 7) 1% ; 55D%% )@%:, (%E &% %- 1 75-% 7: %<5 -5' 5-''-&: %E 5& %: %%% %5'<, @% )%-'% -5 )% A (k, ) % 5? % k (%9: 9% F(% -% ; 9?DE 9% -:, 56 %& 5DG−' ( !&* (e, 2e)&$ )$ 9% )-5 5)D%' 9((%: )<? 7'- '-&: 7: 5 %55 -((<56: &'(e, 2e) < 9%, <56D 7:5 -: &5: &%: -5' 5&'5 5D'  )5&: sp.%55 F ?% %8GE %8 5&' 5 -  5 F ?% %8E % ?% %5G 5' :&5' (?<? -? 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A? 95% FH58 G 5-% )%%6E &% 758 %56? %55%8 -5 -5' 95%: %', ): -% 55D'  sp.%55 5 5% 9((% '' 95% @-% 9% %5 -E 5 -  5E %: %'%@' -: %55E 95%: -% :%:D% -%%&56 ' %<5 ;% `-6 75 -%: ):@%' 758 ?%? %<5 _%7: )%6 -@5%6E ')D  &: 8) )&%&: %',E%%' 9' %&? 95%  ' B &%56): %55& Ns.%<5:E 5&: ) ?5@: :&5, 758 556, 5%% Fl€c P RVSfR iQWZkT\!4>f[[UV…kXfTkVWGE 5): %- ~~d& / ) spD  4!! ) 5 -5 9?' -&: 95% -5' (e, 2e) < % *F !G )5&:5 cR  sp.%55 ?% %8 5& &%? 5D@' Fx = 1G 75D-D%' %-56' %% 75% 0.5 > |(E − E )/E | - :8: %%: -) 1 ≥ |(E − E )/E | > 0.5 %@&D% -(< 95%, : % 7%, ;% g = (00) g = ±(11) ]"#E !20^ %%% 5  4!! % 9?%@&D ;5 ;5 5: %E % ; %, %%@:E <%, 5 E = E E ):%' , 2k (<'% '%' 5& 5E 5 7&6 ?%, &@%6D &' F4"2GE % 9% 5& 7 95% -8%' (%56, '-&, ;%E :, 758 %56@? %55 1((% )%? 7'- ?%D &%6 &@' F4"0G -%' 5;6 &6 5 )D (? 56 5& 5 cR Ng cR lk E % %& )% 5@& 5 cR ex 5 &6 56, <%< ex 87:5 8-%6E &% ?%? 5- F4"2G & F4"/G 5'% )56%%: -5' 5 cR Ng & 5, )<: 8- -)56@: Ns.%<5 % F F440GG - 5&' cR lk 7 cR ex 756;' )< 8- Ns.%<5 %-% 56 ?% 7% 'D -DA? 95%@E &% &% '% : 5? -5' 9@?' ,%%56E  %%%DA : 8 -5%6E7A ?'E )5D& % -(< 95%, :E%: %6 D% 5&, -(< % 7%, ;%g = (00) g = ±(10) &%%E -(<' %%E %&DA'sseetottots0.850.9850.15e0.9F0.10.0150.850.150.90.9850.0150.1!4/110AlxMg1-x010-110x=1x=0.85 (coherent)x=0.85-210-3cross section (a.u.)10110AlxPb1-x010-110x=1x=0.985 (coherent)x=0.985-210-310110AlxLi1-x010-110x=1x=0.9 (coherent)x=0.9-210-310-1-0.500.51(Es-Ee)/Etot = & )$+ * )$+$ 4 1$% % Etot $ & % E0 = 200 @ $4 JV)EE+ $ $4 $ 4& $ Q! Etot = E0 − Φ )Φ ' $4&+ W $ $ θs = θe = 45◦ ) =+ K ϕs = 0◦ ϕe = 180◦ 1% EE#! $% x!40g = (00)E ? :8 %5& % 5&'E ?- : 7?5' )<? 7'- 7% ' -DA? 95@% 1% %8% ; ) ' ? 5? @% 95%, :E 5556? % 7)E %' %E &% 5, % ')? 95%E 5556:, %E'5'%' %: &5 758 %56? %55E 5&5 cR lk cR ex 75D-%' &%' %-<' % ',(< ).) 9((% )<? 7'- -(e, 2e) < %; )56%%E -%5:  4!!E 5-% %%%6E&% 75%6 % -&, -5E )58, )-5 4!E 7A 5& -5?% %&D % |(E − E )/E | ∼ 15' %? ' %, %%: 75% E = E E 7A?'E 7- &%:%6 5'< 8- -' 95%E %::-'% ) -&, -5 F %? &% 8 ,% 7% ]#2^G -E %'A' -&' -56 ):%' 5 -@%, -8 5& : %, - &: 95%E 569((%: 95%: 5'<, %, ?% 56 -@5: ).) 756;? ?5 8- 95% &, ]#2^0.90.10.9850.015sestote&  4!# -%5: &5: )56%%: -5' (e, 2e) < % *F !G 5 -  5 %, 8 %E &%  4!! 7:5 %& :;E 758 %56? %55E-5?DA 5%6 9((% '' 95% %<5 ;%@E  --% -5' ' 95%, %%: 5 -@: %55 H9% -5' 9% <5, &% 56) 75 -@%E - % 5& ]=0E==E! ^E 758 ~~d nec ]"0^I%: %%:E 75D-:  4!#E %&D%E 5&!42cross section (a.u.)1041010210101010CuCu75Ni25Ni75Cu25Ni310-1-2-1 -0.8 -0.6 -0.4 -0.200.2 0.4 0.6 0.81(Es-Ee)/Etot = L 3! =! $ $$ &  4!!E , -(< ]"#E!20^ % 7%, ;% g = (00) g = ±(11) H56 )< 8- Ns.%<5 -: 5@: )5 ;% &6 5E ?%:, 5- F4"2G & ?%%%D 56 7)E 5, % ')? 95%E5556:, %E '5'%' ; %: &5 &%:'5- 7%'%56% -' ) ' ? 5? %@ 95%, : 5% F !GE 5: -5@' 9?'E ):  4!#E %&D% &D %B k.%% ) 58, 5&%  )@ <%< x 5' %8% %%%DA ) %B 5 nY ok  4!4 -%5: )56%%: &% -5' %56, (@< A (k, ) (5 F4> G = E %: ):D% &%@: 7) '%' %6 B 5% F !G )% %<%< 5' % x 75D-%' 95D<' % %, 95%@, % - - ?5%,  -:&: KL 5(1−x)−xF!4= == K$4 Q $ $ /X(1−x) YZx $ )EE+ $4 & <<O /58 ;9! 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E2 +! )σ1! σ2+ $ )θ1! θ2 + &$4 1$&5'D%' ?5F"#G?- |k k ≡ |k ⊗ |k P -95%: %'' 55 @ 7) Fk ≡ kμG (5 F"#G %Mk1 ,k2 = Ψp(−)|D12 |k1 k2,1 p21 212D12 = −i"1 ! iq·r1e · ∇1 + eiq·r2 · ∇2cF"4G:% )-,% (%E DA? 56 q 5')<D E 95%, , 5, 57 ∇ · A = 0E ?- A P %:, @%<5 `-6 5-% %6 -E &% 75) % 5& A 8%) '%6'E ;' 5 ∇ · A = 0 _%7: )78%6 %, %<E5-% :7%6 (%D &%% -5 % 5): ) ]!="^& %' (%95%, : |Ψ ')  5@: : -95%: %' |p p ≡ |p ⊗ |p 5-DA7)C+,(−)p1 p21 212(−)|Ψp(−) = 1 + G12 (E1 + E2)V12 |p1 p2.1 p2`-6 G (E + E ) %6 8DA, -95%:, ?% 9((@% %<5 V = V + V + U E ?- 7A 5& %<5: )@-,%' 95%  ;6D FV V ) 8- 7, FU G '5'D%'%&E )'A % 9? 556:(−)12121212121212!"4,% 7:&: -E &%%E %'A' H@-' ]!=>E!=/^E ; :D%' %-%, %, 3v ]!=0E!=2^ ?5 9%, %E 8 %&, %%: T E %&DA, @- %5 -'AD ()E 95%.( )-,%-% 9((% %'8D 8- -' 95%  %@58: 56  75) ' B ε 1% 95%:7)D% D Fne P nVV[QU [fkUG ]!==^E %' -%5'% @7, ') -95% %'  5: : 56  )56%% %? ' % (%' 7).-@%  E &% -% 8D 5, 9? '5DA5 Δ(T ) '- 56 9 5%% 95%: %', 5ε 1%E D &-6E -% -5D %5,E 755@DA 7:& 95%& %5E E 5-%56E )&'%%: T E ?- %5' 9?' ):%' 6; 5&: A5 5%% %',E %5 -%% 5 %5 95@%& % ]>2^ %5& % 5&' 7:&: 3v.-E) -% H.-' %%' -  :'@: FE E ]/#E/4^G %  % A%% <5:, '- ), %E &% <, ' 95% 5)%' 9% %5 ]# ^7%' :8D -5' €eM % F"!G B?DA' -&@%&' %56' (<' A -5'% 5%%6 '%% 8-@' % - -: )56%% &%8' - 95%  @, 9?, E 9% (<' % 'D (<D :95%: 5'<' ; 56 -%5 8-5%6 5-DA 7)CcFF(−)1212A12 (k1k2 k1 k2 ; E12) =∞(−)−∞`-6 c+k (t)Fdt −iE12 t +eck1 (t)c+k2 (t)ck2 ck1 .2π−iHt= eiHtc+ck (t) = eiHt ck e−iHtkeF""GGE ?- H P ?56% %:E!""-%5'D% 7, %: 8-' F&%8'G 95%  %@: &5 k ≡ kμ Fk P 5, %E μ P G 5& 7:&?-'A? 7)<E -'A?' %% T < T E %-@& - .