Диссертация (Процессы ионизации при взаимодействии быстрых частиц с веществом), страница 10

-@& %% (% 7-? 95% F>4=G q = 2m T E %8 -?D% ? 5& %? 56 95% ')%'2e&  . H%6 &56:, 95% -%' -%, nl 7%5 5@ %<5 V (r) = −αZ/r &, %%:, (% %,---7, %: % l me k 1 2S(nl) (T, q ) =dΩk |ϕ−k |ρ(q)|ϕnlm | .3(2π) 2l + 1F>""G2m=−l`-6 ϕ P 5' (<' 9%, 7%5E ϕ P -'A'' 5'5 -5' 95%  56 kE k = |k| = 2m T − p E ?- p = αZm /nP 95%:, 56 n., 7, 7% 5%& :8'-5' %&: 95% - (5 F>""G -:E E 7% ]#>4^ <E  A6D 8 :5%6 %? %5 ?5 :5% &? 95% F>""G 5%& 1% )-@&E -E ):%' %& :5, -5' 756; )&, nH9% 8 ?&' 5&' n = 1, 2 %',E %: % @ -%%& -5' -%< % )5&? --E-%5? -)-5 >4#nlm−ke2nne!2!56)' )56%%: 7%: ]#>"^E 8 )%6 (<D F>""G n = 1, 2 q 2 fnl (q 2)28me p6n3[1 − exp(−2πη)] [(q 2 − k 2 + p2n )2 + 4p2nk 2 ]2n+12pnk,× exp −2η arctan 2q − k 2 + p2nS(nl) (T, q 2) =F>">G?- 5-% 7%6 % %?E %: %&D% )&'E )5D&@: %5 % - πE η = αZm /k P % `(56-Ef (q ) = 3q + k + p ,F>"/Ge1s22221f2s(q 2) = 8 3q 10 − (32p22 + 11k 2)q 8 + (82p42 + 72p22k 2 + 14k 2)q 6+(20p62 − 62p42k 2 − 20p22k 4 − 6k 6)q 4 + (p22 + k 2 )47 6 47 4 2p2 − p2 k − 7p22k 4 − k 6 q 2 + (4p22 + k 2 )(p22 + k 2 )4 ,×55F>"0Gf2p(q 2 ) = 2p22 36q 8 − 48(p22 + k 2 )q 6 + (152p42 − 48p22k 2 − 8k 4)q 4 + (p22 + k 2)1712 4 1568 2 244×p2 +p2k + 16k 4 q 2 +p22 + 4k 2 (p22 + k 2 )3 .15153F>"2G  >4 -%5: &5: )56%%: -5' ?%? -((@<56? &' )< F>4"GE ?- 95% -%' 1s 7@%5E (<' T /ε E ?- ε = α Z m /2 P 9?' ') 95% `&@' : ?% -((<56 & ?? '',% 7- 95% F>=G 8 -%6E &% &5: )56@%%: 5& E ε 75) 5& mM )56%% &%9% 8 7b'%6 5-DA 75D-' .:E 5%<5 %'8' %' 7& &5 '): %',E -@%:, % 9?, %: :%'  % )<bνbb22e!2# F= M$ > &1124 % %( $ 1s $&&& $& ! $$! $ T /εb 4 4 Eν $ & Eν = 50 εb Eν = 100 εb ( ? .%:E - )& 56 95% 1s %' %6p = p E - ) ? 56 5 :5% % Δp %E&% Δp = 2m T E % % 8E 5& 7-? 95%-' ) )56%%E -%5:  >4E 8 8-%6E &%56 ') 95% % -58 7:%6 )&%56,E 5 E ε -@ %: 7%: ]#"2^ ;5 %58 )5D&DE E&% ?% -((<56 & 56 )%% 75?-' 9((@% )<E ?- T ∼ ε H-58:, 7% ]#"2^ ) 5&'?%? 5- )<D 7)%' 5?  < (%@)< 7:5 %& :;E q → T 56 %56? (%%%' D %6 T −q = 0 9% -5 -5' &,e1e2eeνb22b!24%: -8-: -((<56? &' ?%? '' F>#/Gμ σ (T )dσ,=F>"=GdT dqπ T?- σ (T ) P & (%)< -5' 9? (% , T ]#>>^ H@-56:, 5&, F>"=G 56)5' 7% ]#"2^  %5 %@?' :- -((<56? -, 9? &'?%? '' , --E &-E 7E % -:@%?56' (<' 7:% 7:% ) 5&: q % T -(2E −T ) E 7 ?- q r E ?- r P %:, %:, - F @-5 PB r = Z αm ]!42^G - -:%?56,(< ):% 56 %5 % %&? 8E %@&DA? 5&D 56? (% H 9%, & 5& ?%?-((<56? &'E 5& 7% ]#"2^E '5'%' ;7&:% %6 %?5: F>">G F>4/G 78- 5& @)< --7-7? % ?% 7:%6 :&5: 5%& FH58 G 756; %5 )&, 9% %?5 % mM 5? F>" G F>"!G 75D-%' )< ? T = |E |56)' )56%%: H58' E -5' %%%DA %%56:5& 9% &% 5& ]! 0^22νl(μ)2γ⊥γ22ν−2a2−1a1/32aen(1s)I1(F E)I1(2s)I1(F E)I1(2p)I1(F E)I1(1s)=I2(F E)I2=1−1639 −8e = 0.96335,=1−152101 −8e = 0.98434,=1−457 −4e = 0.95726,3(2s)I2(F E)I2=1−871 −8e = 0.98052,15=1−103 −8e = 0.99770.15(2p)I2(F E)I2F>> G:;-: )56%%: ):D% &-D %-<DC & 756@; n lE % 758 )&' I I mM )&' 56 %@%56 %5 % mM 758' :;% 56 <%1% 75D-' 7:D% )5&, --E :, 8(nl)1(nl)2!2"& ! .+ -95% 758 ?56% % - H = p /2mV (r)E 5')<' (<' F>4!G 8% 7:%6 ) 2 −iq·r−1 iq·r F (T, q ) = 0 e[T − H(p, r) + E0 − i0] e 0 −1 = 0 [T − H(p + q, r) + E0 − i0] 00 −1 12qp·q=0 T −−− H(p, r) + E0 − i00 .2memee+2F>>!G&-E &% %56 - :8' 5-, %& (@5: F>>!G ')  %% % (p · q) &5%5E %8 %E &% %%  ?56% H 7)E 5%&@, &% ?, (< F>>!G -&? %%? (%@ ):%' )8: %56 56 &%: 5&' -)-@5 >4! %, &% 7:5 -%5 -5' )< --7-7? %E-'A?' 1sE 2s 2p %'' &%%E 7:5 )E &% %5@' %?5 F>4/G F>40G % mM )&, &6 5:C 756;%5 75D-%' %&% )< ?E ?-E E8-:, ) 1s %?5 %%%DA mM )&DE 8 9((<% (1 − 7 e /3) ≈ 0.957 F F>> GG ) F!G %8 5-%E &%7 %?5 -(<D%' -: 7)E % %; 5D7 )& T %%' % 8E 5& 7-? 95%CI (T )/I (T ) = 2m T - % - %?5 <(& %56-5' )< ) ? %'' 5 %<5 %'8'H75 :&5' %?5 F>4/G F>40G 8% 7:%6 ; )5& 758E % 7?% %%%6D% 95%? 56 p  ?56% %% @%: 9%? % 7:&: &5 9% 758E &%:'E &%(H − E ) |0 = 0E :5'' - :8' 5-, %& F>>!G 5' -? 56 qE 5& 5-DAD (5 -5'−4210e!2>-&? %%? (%C 22qmpqpqqe−θ T −,S(T, q 2) =+−θ T−2p q2me me2me meF>>#G?- θ P (<' I,- :8 F>>#G %5& % 5' %56 75@% )&, qE -5%'DA 5D −p q/m < T −q /2m < p q/m E % 8- F58%56:G ' 7 ?% (<, I,-Cq = 2m T + p −p q= 2m T + p +p 8 -%6E &% %&::; ; -? -56%.

-& %% (% @-'%' )5& 758 5 K6-%5L 8- q q :&5 %?5 F>4/G F>40G  A6D :8' F>>#G 95@% )56%% -E &% %?5: 78- 758%<5'PP355D9 F~‚ P QWTQR$~UfXQUZ$‚UkRRVYkWG -D%@' mM :8' F>" G F>"!GCe2mine2max22ee2e2min2max(W KB)I1=1,T(W KB)I2F>>4G= 2me.H'5 )-6 mM :8, '5'%' 8-:E 56 (@5 F>>#G %8 %&% 5&D '' ,% 7- 95% 56 p )< D  5& 7-? 95% )5D@&%' -) )&, -, 9? T ,%%56E :8@' F>>4G : %56 :; ? )<E % T ≥ |E | 8? )< 95% %%' K%:LH5- 75D- 7b''% % ): %&% -)56%% &5: &% ]#""^ E &% & dσ/dT-5' )< %, 7%5 % mM )%6 % -, 9@? T 5%6 - )<? ? -5' -, 7%5 %%56%5 % 9%, )% :;% 56 <% 1% @75D-' )55 % 7%: ]#""^ (5%6 %&% @758 -5' %;' &, '' ,% 95% % 0!2/ 7-: 95% F &% - 95%GCdσ/dT1 f (T ) ≡=ni θ(T − |Ei |),(dσ/dT )F EZ iF>>"G?-  -%'  %: 7%5'  9?' ') E &5 )5' n &-E &% (% f (T ) %%56&5 %: 95% % 9? T E % % 95%E-5' %: < )< )8 %& H 9%, &(<D f (T ) &% ):D% H--' %? - )-5E 8 -5%6 :-E &% -((<56@: -, 9? &' 758 7-: 95% F>2G F>=G '-  %&%: - %? (% F>>"G 7&@D% -%  ,%, -, )< 58? % %?' 5%6 - -%%& ) -: 9?, %&%6 %@? -- 75) )<? ? %5'% >ˆ F% :%:%6G -5' K 95%E 5 -%6 ) 5%& %5?-' -((<56? &' 5& ? %'' -@--7? % 8 %5E &% %: 9((%: )'D%:8' -5' -((<56: &,E 5&: 758 @7-: 95%E 56) )5&? 758' @-5 ): 95% 1% 5%& )56%%: -%8-D%78 -% &5: &% -5 -? 5'- 57? ?%? 5- )<D )5&: %: @;, ,%: - ]#"#$#">^ % 8 'E - &5: &@%: -5' < ν̄ .-, )< ?5' ]!! ^ ?' ]#>/^ ):D% -5 57? ?%? -((<56: &, %%56%&%? 758' 8 -, 9? 1% -5@ 8% 7:%6 7b' 9((% 95%: 5'<,E -@95%: 5'<'E %: '):  %(<, 5?: % ρ(q) F>##GE %&DA ): 95% ): 9((%:iie!2078-D%' 5-DA )-5' ! & *"$ H % )< 56? ?95%? % 56%@5'%% ,%E %7%' :&5%6 )%6 &5 %:95% % T E 7A 5&E %8 <%6 9((%: 95%.95@%: 5'<, 5' 5) 5- 75 --'A, ;6D'5'%' % ?5'E 5'< 95% %E ; )%E?D% &6 756;D 56&" , %: -, 7%: ]#>!^ 785 -% &5: &@%E &% ?%:, 5- )<D ?5, %, ; %: %%: %,% 56 %5'%' % %&%? 758@'E A% 5&'6 D  758 7-: 95@% ?5 ]#>!^E 78:, 9((% 5E ?- 5& T%%' )< ? -5' ?5' T = 24.5874 9E %%565& ?%? -((<56? &' %5'% &% 10  9% )56%% 7:5 -5 :-E &% 78:, 9((% 5&@' ?%? 5- 8% -%5'%6 8%6 -5'  ?%?% ,% μ E 5 ? 5& 58% -) 10 − 10 μ - -)-5 )E &% )56%% 7%: ]#>!^ '5'%' ;7&:E %&% 758 F>>"G %8 5& ?5'E ) 5D&@ 75% 9?, T ∼ T E %, -((<56 & ''A% 6;%' %%56 mM )&'% < '' 95%? %,%  9?, E % qQ -: 9? 56 T q %%% ?@&' )<: 5 9%? < %& 8I8−13ν−12BIν!22T E E % -5' %: FE ∼ 1 9G %%: FE ∼ 10 9G%,%E ?- T → T 3- &%%6E &% % qQ -%' @ %' |Φ  9?, E H56 -5' ?5' αZ 1E ?- )''- Z = 2E %' |Φ 8 :%6 5'%% @758  %% 75%6 9?, T ∼ T E 9% & ?5%' |Φ F - 95% %G 8 %8 :%6 5'%% 758H (5: :; 5' -&, %%:, (@% F>#0G :&5'%' ?5νννIiiiIfΦf (E1 , E2)|eiq·r1 + eiq·r2 |Φi (E1, E2 )2 δ(T − Ef + Ei),S(T, q ) =2F>>>Gf?-  -%'  &: ?5: %''  - 95@% %E E P 9? 9% %',5' :&5 -&? %%? (% F>>>G 56)% 8 -5 &56? &? %', % qQE &% 7% ]#>!^&56 %' -%5'% 7, )- - ---7:1s 5: (<,  9((%: )'- '- Z CfiΦi(E1 , E2 ) = ϕ1s(Zi , E1 )ϕ1s(Zi, E2 ),?- a0= 1/(αme)ϕ1s (Zi, E) =Zi3 −Zir/a0e,πa30F>>/GP 7, - & %' % -1−Φf (r1, r2 ) = √ [ϕ−k (Zf , r1 )ϕ1s (Z, r2) + ϕk (Zf , r2 )ϕ1s (Z, r1 )],2F>>0G?- ϕ (Z , r) P -'A'' 5' 5 -5' 98%? 95% 56 k Z P 9((%:, )'-E %:, K-%L 98%:,95% 5 &? qQ 5- )78-: %', qQ -&, %%:, (% 78 5E 5 5% :%'  5, (<, K 95% % qQ )78 ()& 9((%E '):  %?56%6D−kff++!2=%', F>>/G F>>0GE 56) %?5)<D Pv-%|Φf → |Φf − Φi |Φf |Φi .H-% F>>/G F>>0G F>>>G -%2dkk|F (k, q)|2δ T −+ 2α2 me − Zi2α2 me ,3(2π)2meS(T, q 2) =?- k = 2m (T + 2α m2eF (k, q) =√e− Zi2α2 me )F>>2GEiq·r12ϕ−+ eiq·r2 − 2ρ1s (q)|ϕ1s(Zi, r1 )ϕ1s(Zi , r2)k (Zf , E1 )ϕ1s (Z, E2 )|eF>>=GP ?, ((%E %F>/ G56,;, &% -&? %%? (% 8% 7:%6 :5@ 5%& FE E ]!42^G )56%% 5&2 αmZ ZS(T, q ) =A (k, q) + B(k, q)A (k, q) + B (k, q) , F>/!G(1 − e )(2 + Z )?- η = −αZ m /k F-' 7)& p = αZ m Gρ1s(q) = ϕ1s (Zi, r)eiq·r ϕ1s(Zi, r) dr.16 425ef6i2πηfei16iexp 2η arccos √A1(k, q) =[(p2i+4kq 2+q2+p2i +q 2 −k 2(p2i +q 2 +k 2 )2 −4k 2 q 2k 2 )222−ie(pi + ηk)2(p2i + q 2 + k 2 )24k 2q 2 ]31 2 2 2 2kpi − η kpi − η 2 k 3 − ηpi (p2i + q 2 + k 2 ) ,332 exp η arccos √p2i +q 2 −k 2F>/#Gη (k + q)2 + p2iplnA2 (k, q) =cosi(p2i + q 2 + k 2 )2 − 4k 2q 22 (k − q)2 + p2iη (k + q)2 + p2ip2i − q 2 + k 2,sinln+2q2 (k − q)2 + p2i(p2i +q 2 +k 2 )2 −4k 2 q 2F>/4G(Zi − Zf )αmei(k 2 + p2i )22η arctg pkB(k, q) = e(2 + Zi )4α4 m4e32p4i−[(2 + Zi)2 α2m2e + q 2 ]2 (4p2i + q 2 )2.F>/"G!=<E 5 :7D%' 5-DA )&' 9((%: )@'-C Z = 27/16 ≈ 1.69 Z = 1 FE E ]#>0^ <%D %5%%G `& Z = 27/16 5-% ) <, <-:E %@' )% 9?D ? %', E E % ' )&Z = 1 7&% 56D %% &? %'' -%: 7%: ]#>!^ 56)5  &% %: Z = 1.79 Z = 1.1E %: 5&5 ) -? -: &' (%)@< ?5'E :5,  A6D %'A -5, ?5: %',%5' -((<56: &, F>4"G F>4>G % 758'7-: 95% %)D%' %%%DA %: (%@Cdσ /dTdσ /dTf ==F>/>G,f,dσ /dTdσ /dTifiififSMSMFESMNMM(μ)FE(μ)?- dσ /dT dσ /dT %&D% 57 ?% 5- -((@<56 & '' 95%: %,% 7-: 95%@ `-6 5-% %%%6E &% ?5 7% ]#>!^ 5-% 8-%6 )&@' f 5 10 T → T _5: )56%%: -5' %: (% F>/>G ):  >" %&D% %& 8 T αm 2E E %:, T <200 9 5)%' -5' %:E % %%: %,% 5-%%%%6E &% % 5& 8 7) A7 -5' %&% 58%6 @, -5 %?' F>4"G F>4>G : 7&%E 56-&, %%:, (% S(T, q ) 7:% 7:%E ?- q αm E %& 5D 75% q αm )  >" 8 -%6E &% @- %: (% 8 -5' 7 7 )&, 9((%:)'- Z Z E 78-;' :; E 56: )&' %@: (% F∼ 0.5G 75D-D%' )< ? T = T E (%: %'%' -<  % T H5- ')  758 mM -5 8 8 -%6E &% 75 5 6) %5FESMFE(μ)8NMMIeν2eeifI!=! FB f 1 )F"F+ 12 &% E#!=#F> 10 %G %'A )56%% % %&%? 758' 75D-%' 75% ) 9?, T < 100 9 1% %5 8 7b'%6 9((@% 95%.95%: 5'<, % qQ ,%%56E 5 95@%: )-,%D% -?  -?E % -'%' ---7@: 1s %'' F %58: G 9% 5& %5)&, %: (% % -<:E ?5 )56%% )-5 >4!E6; >ˆ 7)E )56%%: &%E -%5:  >"E -@%8-D% 56 5& ?%? 5- -((<56 &@ %%56 758' 7-: 95% 35 %?E %%@%  )5&: &% -5' -? %: ;, ]! >$! 0E#"#$#">E#"0^E 9((%: ') 95% % qQ -'% )% 6;D-((<56? &' %%56 mM )&' ;7& -)@E -5 7% ]#>!^E 7') 56)D -&, -5E%' 7)%' %, 5?  (%)<,  -@5E 78-56 -)-5 >##E %56:, (% )<<E 755 F9((%:G ?%: % ,%E 8@ %%6 56:, %56 q → T -E %? F>4"G -%' %5 )&, q % T - 2E − T H56 E T E758 56? (% ):%' : %56 75) 8@? -5 %?' -5 % 9%, 75% )&, -?56 75D-%' 56 %5 % 758' 56? (%E %? -:%?56' (<' %' %%,  %5 %?'E , )&D 9%, (< %& q = T E% ν11S(T, q 2) = 2 S(T, T 2).2qTν:, --E &-E ;7& E % 7)E -% ;7&:- % ?%? 5- -((<56 &!=4 )5D& -%5? %%&? 5) < )@< % ?5' 95%: %,% ]!! ^ 8 -5%6 :-E &% @56) ?5, ; -% 56.7-6 )% % &@%%56% 9%  ?%: % ,% %@&% 758 ):%' :  %&%6D - 56<% 5%6 - )&, -, 9? '- ! 9 8 9%,9? 75D-%' )% 6; 5& 57? ?%? -(@(<56: &, %%56 758' 7-: 95%E @% 56 75) )<? ? 75D-:, 9((% @8' 5&: &, 755 56: 5'<' 95% ?@5&" 3 A B C -5 PB FE E ]!42^G 95%' % %@ :%' :8-:, ?) 95%E -'A' %<5φ(r) )5'DA 56 %% %'' 5%6 - 9?BE % 5%6 - 56 p (r)E %?E &% p /2m − eφ = 0 5E 95@%' 5%%6 n(r) = p /(3π ) -5'% %<5 φ(r) %%% H )<' )& -, 9? T @ 78-, -5 )8 %56 -5' 9?, 95% :; −T E% 5& 95%  56 756; p (r)E %:, -5%'%5D p /2m − eφ = −T 15%:  75 ) 9?' %::&5'' 5%%6 %: 95% p /(3π ) :&%' &5) Z E 5& (5 -5' %: (%E % -5' %%56? &5%: 95% Z /Z (<, T C20030e2T2Te3T2effZeff (T )=1−f (T ) =Zx0(T )0χ(x)T−xT03/2x2 dx ,F>//G!="?- χ(x) P (<' PB F)&' %, ; )%: )%75:G 7)), , x = 2(4/3π) m αZ E x (T ) P%&E %, -:%?56' (<' 7A%' 56E % %&D@A' - (: ) -5 %,  95%: '5'D%' %: - )& T 1?' T -5'%' 2/3e1/300 2/34T0 = 2me α2 Z 4/3 ≈ 30.8 Z 4/3 ,πF>/0G5' ?' FŒ4#G )& 9? T 758 T ≈ 3.1 9%:, (% -5 PB -5' ?'E :&@5:, 7) F>//GE ) ;%, ,  ## )%E78-' -56 :% 7b: ,% 95% %  %@%56, %&%6D O(Z ) %'' rE -5%'DA 5DZ m αr 1E %E 56)' 7))D D xE 9@5% Z x Z _% %' (5: F>//G -5' &5 %:95%E %6 (56 ;%' T ∼ Z T E % )&' -, 9?E :  9?, ') 95% %@ 75& - 9((% K-%<L 95%  % 7@5& )&%5C ? 5& '- Z D 7A &595% Z -?, %:E ) T E 5D&' 75 %D75%6 T ∼ T E %?5 F>//G -5'%' -) )&, x '--<:E -5' %? 78- -56  ; 71? ') 95% % K, L M 7%5' %?' ; )%: FE E ]2!^G %:, (% %&@% 758 F>>"GE ):, 5;, 5,  >>E :&5 56) 9% -: -5' )&, -, 9? T 5%6 -9?, ') M 95%E % -5' T > |E | ≈ 0.18 9 8 -%6E &%- %? (% %&% 758 9?%&%5 8- 95%: 75& ? -% )56@%% -5 PB 7)E ? 8 %@00−2/3−1e−2/31/32/3−10M0!=> FF f% 1 f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m NV 5: (@< 9? '): %: %', :&5'56 5'%%@? %- I%PB ]#>2E#>=^ 556 758 -5' 7@5'<? %<5 ]#/ ^ 5: (< A: 95%:&5'56 -% &5? ;' ' % 8 @?5 %<5E 5& 5: (<, -%:%', :5: 7% ]#""^  A6D %? -- &5:&%: -5' )< % ,- %: %,% )55 @% -58%6 -D %&%? 758' F>>"G%: -, %%&, 7%: ]#>/^ -%5 56%(@?< 5'%% 758 5&,: () FNnddec P XYRTk.!=0SVW„gYUfTkVW UQRfTkhkZTkS UfWiVX.[jfZQ f[[UV…kXfTkVWG ]#/!E#/#^ -5' &% %@: (% 5& ?' :, %-  %<758 I%PB ]#/4^ -E 75?-' 56 8: %@5&%56: &%E 5&; 7:&? %(? 758' -@-% -5' ' - %  )5: 75& 756@; )&' Z .:E 5& %  )5: 75&A%%E 5E 75 -, (?<E DA, %7: ,@% ? %'' H9% 56  %( @%' -58 7:%6 7) 5,, 7<, );: (?@<,E % -58 -%5'%6 7, 56%(?< %' .%:E 5& %  756; )&' Z 56)' ?@%6 5'%% 56) -? '% ' v-? )5'% &%6 5'%% 5?: ?56% % %7%: 7)  ? &5 .%%6E-&%&: 5'< -5 %( 758D 7A 5& 8: -5' )78-: %', -: %&:95% H758 5&,: () &%:% ): -5%56:-&%&: 5'< F&%<: ?% -%6' 5%: %'@'E % %'' G %56 -5' )78-?E -5' ?%''E -' ? 5&' ; ?5  9% ]#/"^35 %?E 7:5 ) ]#/>^E ' 758' 5&,: ()'D% 57&D %%6E &% 7&% %, %756@% ;,%- Nnddec ; '5' (%)78-D (%@)< -5%: %E % ‚QE NgE ŒW - F%: )56@%%: 7: ]#//^G 5-' 8 --E %: 7%: ]#>/^ )'595%D (?<D ?' E  )5: %''5%6 - 4p 7%5, H56 : %' % pQ '5'%'P %'E -%5'% 7, 5,D 7<D - (?@30!=2<,C ]ŒW^4p ]ŒW^4p %%%DA' 5' (<' :&5'56 A6D % 6D%: ? 56%(?<?-.(? 758' ]#/0^ )78-: %'' %E )-,@%: 57 ?% ' ,%E :56E 56@)' E E % 7)E -56 -: %&: 95%: 9% &%  %: % 5-:56 (& 56@%5'E &: %'' '' ):56 7) (&?  ?&: 5 -'A,' 5:5-% %%%6E &% D  -:-A 7% ]#"#$#">E#"0^E %: %8 56)5' --E :, 5'%%758 I%PBE -- Nnddec %5&%' 56 %@;' .:E 5 &% :8-% , N (4p ) N (4p )E56) 56%(?<? ? %'' ):%' 7@-: .%:E 556:, (, &5 &%:%' %&E % 7)' 556? 758' -5' 7: %<5 .%%6E)78-: %'' :&5'D%'  &% -&%&: 5'<,E%: NnddecE % -% ;' 5? 5@? ' %%& K--:&L - 5  >/ -%5: &5: Nnddec )56%%: ) 7%: ]#>/^-5' )< ?' 95%: %,% 8 -%6E &% -@) 9?, T 1 9 ; 7b''D%' %&%: 758@ F>>"G % 8 'E 79 -)E % ?- 95%:  K L 75& ?' %D%' K%:LE 57:,E % ?%:,5-: ):D%' 56 -5: %%56 %&%? 75@8' :, )?5'-E % - ?5%'  )5&--E 78-;' -)-5 >4#E %%%  %: 8@-%'E &% )<' 5& '): 95%: %',E %@ -58A M N 75&E -58: 5&; -5%'%6 @758D 7-: 95% 9%, ') 5-% )%%6E &% 821/223/2II3/2III1/2!== F" % )gGHh+ % )YTT+ $& $ &112 ν̄e DiG2 Eν = 1 e@ F"# $ $ $$,* $ ( 3 )Rb8+ M 11$ $ *$4 , μν̄ = 2.9 × 10−11μB 9 #e#- %: (% 75D-%' -5' ?5' 75) )<?? F  >"G 7b''%' 9((% 95%.95%: @5'<, 7)E 8 -58%6E &% 5'<: 9((%:) -5 ): 95% -'% -5D %:(% 75% ) -: 9?, 1% 7%'%56% 8% ?@%6 8D 56 9%  ?: -%% 5-DA?5'E 7  %E &6 9?%& ? 58% 79-) ]00$0=^ `-6E -E 7- &%:%6E &% 8T - )&' T = 2E /(E + M )E ?- M %6  '-E '5'%' -@5%56:, 5 '' P ?% ? ' ,% '- ]#/2^E % -  A 75D-56 9%56 % - 5 '' ')  %E &% 5D7 %5 %%%DA@? 9%56 )? &' % %& )%? %@-%, -5 )&' ]#/=^ 58% ) () ) -5%-%, -5 F ]#0 $#04^G H: :% %%&? 5)%: 9((% ?% ? ' ,% '- @ %-%, -5 8 ,% 7% ]#"!E#0"E#0>^ - %@%E %: &%: ?%? 5- & %? < %8-%5'D% 8%6 H<: ?%? ?? '' ,%E755: ,%: ?%: %E %-56: % %55 %%& %56 %56 7% ]#0/^ -E 7@-: -56,; 5-' -5' %, %%< 7-A )@, 5: )&' T ]#00^ _% %' %: 9% pQ -%%E % 5- ?%? '' 9% 9% 8@-%'E  &% 9((% &? ]#02E#0=^E 9?' 8 400 − 500 9H&E ?5 %-%, -5E ? 5& -58 ? '-:;%6 5- % ?? '' ,% 95% FE @E ]#2 ^G2ννNN#!'' 5 ) 3 5E 9((%:E '):  %-&, .%%E &%:D%' -58E &% % '-E 7-& ? %'85 -DA, &%<:E%' - %5' -E 5& < )< %%: %,% %&' 9?' %-& .%% 8%7:%6 ,  9?, ') 95% % 8E 5-' 7% ]!!"^E -5 ): 95% )5&? 758'5)%' 56 %-& %? '- 78-: < )< &%%E 5-%' 5' 9((% %-& .%% @%6 %&%? 758' F>>"GH E &% &%6 9? T E -, < )@< % ,%E -% %&D 9?D %-& .%%E %@' 5'%% 758 %6 T = q /(2M )E ?- M P %' ?-E :, ?% (< S(T, q ) (5 F>4"G F>4>G-58 7:%6 ) 2Raa2Tq = T − TR = T −q2.2Ma`'' -5 T → T F>>#GE 5&qmeθ(qa − q) θ(q+ − q) θ(q − q− ),2pqqa = 2Ma (T − TI ) q± = p2 + 2me T ± pS(Tq , q 2 ) =F>/2G?-E ) F>/2G 5-%E &% 9((%:%-& ?D% 5E 5 q > q ,%%56E % 5& )56@%% F>>4G %%' ): E %%%E %D%' ): :@8' -5' &, F>4"G F>4>GE %: %&D% 758D 7-:95% %E ?- q < q F>/2GE &' %'%' -5:@ D  758 7-: 95% -8 7AD%' 56 q ≥ q aaa½++−-" + +&" & # # Ma − me − TI ≈ Ma ##&-E &% -&, %%:, (% 56? % @% 75 58D )%6 % T q D  )5&758 F>/2G %' 9%E ) 758 )-%?5: &%: 7%E A %&, (< S(T , q )E @E % %&: )-5 >4 ; -? -56%.