1611143555-22ae02dc410aecb2fd3cbdc2740b0b9d (825017), страница 9
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9PF8 44 8@4ω=1 + (V /c)ω = ω0 · p= ω0 ·21 − (V /c)ϕ0 = π1 − (V /c)ω = ω0 · p= ω0 ·21 − (V /c)V1−cssω0 .S0ϕ0 = 01 + (V /c),1 − (V /c)V cVω = 1+ω0 .c1 − (V /c)1 + (V /c).V1 + cos ϕ0ω = ω0 · p c.1 − (V /c)2(17.5)S(17.6a)ω > ω0(17.6b)(17.7a)ω < ω0V c(17.7b)957872252)4:28:942 3 85 81 > :2 53 8:53 553 ; 52 42 ;2 92 :5 8:7 92 28897 2 4: 8; 9527 ;:57 47 45 4: 4:9 9 ;57 42 452 557 2 857 857 8572 455 7 4882 66582 892 15 927 4822 88 15 4 6:52 895 17 ;:2 :2184 12 9 5 3 27 2 7 5 4: 489 ;: ;2 8 1482 8 ;:55 8 17 8 6 85:7 12 62 87 ;57 5 1 8:74;4 5 2 45 48 ;5 82 9 :5 5 482 :2 4557 : 2 ; 5 7514;592 2 657 72 2 92 4 89 55 6:2 872482 5 42 ;8 ;; 9 9 42 8 2 447825455 :3 ;:7 8 7 8 142 445 6:28 5 82554428952 27 ;2 92 97 5 4299 8; 55 ;8 : 1 6;2 9 48(17.4)+ " - & .
!'( " * ( (/ " " , " * * ## / . # "(# "" # ( * ( # & % ,%, ( (%"" " .( #.(*(" *# (/ / / "%( J"F+)9: 8 %% + ( (F ( ( /5(F' ($$ " $"17554PF:49F7+6512:5V= γε · 1 + cos ϕ0c082 6: ;; 68: 2 2 2:/ 657 5% 87 6:5 45 (2-19;$2 6:5 4 5 ; "4 575:5 !845 4 *2 8;8 84 8( 2 38 32 457 89(7 "- + 142 8 622 65 2 8 :7 56285* 4 7 8O ; 4 4 69;2 :9 9 4- 8;8O:5 482 892 3 :73;:57 5 485-1757 82 :5 2 58( 45 692( 27 3 8:" 5 ; &'+$ 48$5 8772 5 2 14768: 8573 2785 2 8877 15;4 48;3( 8+ 12 42 8+97 :787 6522 *524468:&"9%) ' * ε = γ (ε + Vp0x)17 95 + :9( !72 ;5 4 5%3 :5 "9 48: 5%5: 4 ;)2 " +9 :# ) 1 :;5 ;:25*/ 7445 5 4 ;2 :55 :57 657 84 7 (235 22 48 5%65 45 95 6 44 / 45 :5 "4 :2 : /88 19 6:7 ,7 ;8#895 :57 457 892 :27 ;523583 84 87 "9 65 952 8 8 ;452 72 9557847 8( : 145 5 272 8 ,5 92 : 5$ 5557 *42 @: 245 8 54,4822 8157 B: 48; 8( 844 ;5%)142 @4 28 : ;84 9223 81528 482 ,8# 17 7 ;557 :57 "5 4+ # 6:5 68: "9(572 8$3 27027543+268:& 7) 85*2857 1485;' 85 1(482Sω0 − ω H= r,ωcω0V cV = H r.(17.8)ωrHV = HrH(17.8)S 486:54̄53";:5":92;!88p=j(∆λ/λ)max = 1, 2 · 10−4τ = 30M 2 c2 =X εjXε2 −−p=pj .c2cjj2εjXpj2p + p → p + p + p + p̄2jX8867λ = 0, 55ε=17 4278! 83" 6:52 45%21 2 7 8!7 "8( 89( 5727 2)45 557 555 745 ,482 427N& 3> 82' 45%0`n445 95573 4448 ") ;5 (8 ;2 ! :8 455 1) 5;:2 4952 8(45 5( 148286 *45 828:5( 5( 86545 *45 522 .8 84:2 45 52;!8 5 45 5$ m95 *5583 455 6:2 82;:57578*9482445575/887(562956;45 4 8 :2 7 M ``5:7 7 4:5 422 455 82 "7 n442 427 8 52 72 45 8 3 7 4 95 8# 8 84 3 52 48 427 6 5 55 3 6: 83 7 17 7 4 8 ;5 "4 4 6:5 8 :5 65 48 6:5 95 1# 58 ; 65 8 2 4 22 8# 7 5 8 ;; :5 853 42 6:7 8! 94:2 : :2 5 67 2 6 65 8 67 442 2 4 15 52 :22 3 4 :5 ; +67 8 5 ;2 67 67 46 75 6 6: :5 557 8: 922 4 53 4 :2 :289 $( ( " #2 2 ("$*% (" ! (# " ( ) * + "" ") # $( $ $λ = 0, 727 85 6:2 ;8 27 9 :9 8 4 827 65 9 ;65 8 84 42 ;87 ;95 95 5 6 ;5 57 97 1 ;8 ;: 8 8:52 2 2 53 ;5452 4 8 15 81 57 ; 4 ;: ;7:7 8: 42 87 ;827 492 44 665 47 :55768: 62 7 : 1485 7 55 12 :2 971 42 45 7 ;5 495 4 :5 65 27 5545 8627 82 9 7 :2 95 ; 952 495 ;2 2 18 95 62 42 8 :5 348; : 4 7 4 ;: 82 872 4 88 7 92 8 4 87 52 931:2 8 8 5 92 81 2 65 9 82 48 8 823 52 8 5 ;; : :9 5 488 95 77 9 4 2 4 6:2 95945 225 (+/ .#(,("/ ( ! ( *% "( " /% "%/% #&!" "%.
( + * / "( * ( , ' +"( * % &" #""(#""((("# . ' % #+ %* ( */.( "" $ $$$ $ "e+ + e− → γ4"5 "3 4:5& 47:( 5 12 ;:5845 4572 :223 2287 45 4 95; 9223 :22 ;8:2842 ;57 8 &812 6:% 4';5% 82 6 ;57'8) 84:2 ":588 5) 487 4%(;:57 QO "982 ) 7;7:23 5) 6:5$ 5 5$4:)2 ,:2 88$ 482 5)8 ;5 6 6 5 : 7 ":# : 57 2 "514 : 5( 7 !;45 8:5 957 4 !:4#5 ;527 482 ;5 ! ( $9 ;52 1 : π0π0 → γ + γZZ → e+ + e−(εj /c, pj ), j = 1, .
. . , NM(18.1)p(18.2)Kmax = 6, 3 r) " L- D & B - ?r & %L D- @ @? IAr%L & # & CB, 1 C ? C r r L & G *) r 1= Lr E! -L1 <r )1 &Lr ) -L * -r G? - CLr -r 1 BL- Lr* + -1G& 3 & )r $ r <w r , D% ,L(p0)2µpµ = (ε1 + mpc2)/c, p161022= ε /c − p0 = 16m2pc2 .0210me c = 0, 51.9mp c = 0, 942p0µε0 = 4mpc2(18.3)(18.4)·10−1949F`5 2 ;842 "4 ;83812 22 ;;2 ;7 2 47;5 52 4) 445 924":2 ,42 8:2 615 876:5 4)2 : 2 4:954 88: 49 84"548:;57 925:47452 ) ) + 84:9 8848 45;55:5%4 5 (" 72 26 187512 ;97:1 925 ;5557 :45 9,482 53: :54 5%7872272' 8$" & $/ 4 3 5 8 85 6:5 242445 53 5 18 45 848 78:2 :95 6;5 1:2 6: 4 :5;8 ;5 9 895 2 8;5 88 47 87 2 8 :5 84 75 :5 1 57 5 12 47245 42 7 6: 7 65687 48 83 455 ;952 4895 6:55 899;2 2 57 : 97 95 499 5 5 95 42 5 8682 : 12 27 8: 5 42 :54:2 9 88 45 8: 4588 : 8 6 :2 4 88 85 922 7 ; 2 6 8 4 8 6:27 18 2 < 2 2 "+( .
( % ( (! + ,, # % * $ - (! * $ "")+'( ) ) * $ , + %+ . $ # ! &+ . $ $ ' $ $p2µp2µ(pγ + pe)µ = (p0γ + p0e)µ65$p = p0 = 0L: :8F - pµ = (p1 + p2)µ , p0µ = (p01 + p02 + p03 + p04)µ .18 849 ;4584: :#57452 4482557 8$45 6,4822 7pµ = p0µ , (( 2j = 1, 2 , 3 , 47:85:724 6:8 8255 574 :24 48) ;:2 44522 68::227 192 877 1 78:9 !9 2 2 4 ; 742 6;5 7 82 "#&+89 55 +1 8 8;5 .8 4:22 45:3 4142 6#7 8259( 4) "1#' :55 4553495 44 4278; 12 8: 8! ;9 18 7 :9 55 " 5:3 :#/ ; 42 :5% 974859(5 84 + + 7 872;9 ;95 .8#7 4: !2": 6# 6: "8% 4:25 5 6 $9 2; 72 4955 ) 7 84:2:5 1$ 5$ 5% 4$ !88p0jµ;872 89 4957 81 89( 5) 7 88;2 "4# 87 5 88( 8 7 818 4 4 57 :9 9277 18 <D 1 8 442 4 542 #5 177 L: "4# 52 8 "4)2,4452 82 55%8F: 57 *455 88:1%7 8::7 8 89% "92 4% 88655 95 84 84) 7%87 95% < ;5 8:2 "48 :7 45 ) *2 +; 192 2 " 8# ) 452 4 4812 "4 65 5 145 "#445 :2 " 5 172 :# 9 5 8!%4 845 452 :7 42 :# 45 85$ $2 $2$( 9 (% 9mπ c2 = 1403:5 872:455 57% 1/492% 9795 (:5% 446:5 +754 ;576;5 8:857 2265) 235 4 ("9p1µpµp2µ = 2m2pc2 + 2ε1 mp .ε21 − p21 c2 = m2pc4ωω0(18.5)ε1 = 7mpc2(p0)2µKmin = ε1 − mpc2 = 6 mpc2 = 5, 6,(18.6)Kmax = 6, 3γ + e → γ + e.(18.7)(p0e)2µ = (pγ + pe − p0γ )2µ(p0γ )µ(pγ + pe)µ = (pγ )µ(pe)µ .λ = 2πc/ω(18.8) 4822 4:5 615 4:)2 ;892 ;95 ::H E: 7/ 727 15 :#5541 72 482 8; 7 ":#5 8: PFI 6: 892 42 ,554 268775<F 8 8 6, 9* 25@545 27 55 ":# 2 1;5 47 54 62 5 482 "95) 9 495 .8 )2 5 6 ;55 15 4)2 .+2; 4557 "97 4 ;: .2 PPF4 ,89 17 8: 2):45 495 ;55 97 455 :92 5 2 8: ;672:9) 7 :72 %@491B2885 4( 4:)2 ) 7 "57 : @@ )2 8: 42 42 ; 53 ; 8 43 ! 88: 8 8 ;7 5%) 2 9::H 4:5 41 55 2 62 ; 7 5 4:2 !2 5 5 "42 45 8 1;4841 8 ; ;95 :(2 "%9P: 455 45 44: 8F -2 "2 9 ;485 "745 5 4142 # 7 @5 455 727 5) 46 "%* 55 7 45 FJ4 6 92 2;$2 :9$ 5$ 495 $ ;95 8GP: :$22 4452 80~ω 0 mec2 + ~ω − ~ω cos θ = ~ω mec2 ,θ2π~θλ − λ = 2λe sin , λe =≈ 2, 4 · 10−122me c2εγ ∼ 1,εe m e c(18.9)2597 52 8:9 4:5 55 85) 123 4958 45 7 6:# 495 "65 ,5 "5 5 ;; 81/ ;55 9 2365 42 65 6 ": ;5 "44 ,2 18 57 827 952 5 326 6:7:)29"8 4:44521+ : 53 8/7"2 992 82 8 4 + 4:2 4 "2& 44 : ;957 48 88);!8 2 4)2 "# 7 82 (24 7 422++ : 7>&.# 87 895 842 182 27 48' 89; 5 9( # 7 492 "355 5 8) 5 5 4 452 8:5% 495' ;2 4: :53 53 24 4:55 :7 "#) 17 472 53" 9 8 9 $ ;$2 8! 482 ,2+;45 51452 975 55 8)42 4(14289:944282&'4#854:)28(pe)µ =ε0γ ≈εe = 46::288977;55);:245~ω~ω 0(1, 1, 0, 0) , (pγ )0µ =(1, cos θ, sin θ, 0) ,cc(pe)µ = (mec, 0, 0, 0) .65)5895822#8)(414829:944282&'651255745$4822 579,(pγ )µ =65 8(;55 :55:42 52245 ;459;7 8%8# 8(12% 44222 8284"954":7442";6)7 4:58:22 4(4 182$ 84 6 +7" +517 528! 4:)282 88+ 89 8:;5%657495;8θ7) + :7 49 = ;45 187 "4 7 "44:2 5 5 49 8 12 % (2 7 5 8:82% "6 45 482 :7 4: 455 8 :(2 "4: ;8:5 "6 92/4# "47) 15 ;: 5( 55 657 44 8 2 # 975 :2 953" 45 4 ( 52 55 ! #;) 8: 8%2 "1 : " :9 5 85 4 $ 8 ;:7 22 972 "4# 8) ;8# 4 : 95 87) M7 4:2 #5 :;89 = 42 22 4)2 =& ;72 4:2 4)2 ;:2 "#: ' 2' 82 8: & 68:4 2 & 8=487 ) ;= 957 4: 4% 15 % 2% 955 27 45 ) ;8# "# 523 ) 5) 873 :(24: : 7 187 8#5 2 7 ) ) 8;:7495 ! " 9 8 1 & 7 Q" QQ N'8 ) ;# ; 82 15 2 84 Q>'55 ;2 65 *2 87 18 4)2 ;52 : ;89 )24 4:5 1 2 7 8: : ;: 8 ;:8 " $ 5$ 9 $7 $7 7 5$ λ0 = 2πc/ω 0εεγ, |pe|, 0, 0 , (pγ )µ = (1, −1, 0, 0) ,cce(pγ )0µε0γ =ε0γ= (1, 1, 0, 0) .cεγ (εe + c | pe |).2εγ + εe − c | pe |εe + c | pe |≈ 2εe , εe − c | pe |≈ε0γ= 0, 42m2e c4,2εex4εγ εeεe, x = 2 4 .x+1me cεe = 5εγ = 1, 2x = 0, 092(18.10) ε2 + (m22 − m21)c4ε =, ε = ε1 + m2c2, ε = ε1 + ε2 .2m2c2(18.12)8)99":*4824#85p = p1 + p2 = 0p18!7 93 ;:57 8977 52 47 4( 2 ;65 8:2 455 4:9 4:5 66:52 84 ;895 .862 46:" 5 8 7;;( 2 43 8: 92812517:184789/:221(5479 5 2 2 ( 8 8; :2 42 5 2 2 72 " 7 7 2 48 4: %7 !42 9& 4 2 457 45 5 44 ;2 ; 9% ; 89 4:5 8#7 5%7 957 : ;55 " # 8; 5 84% :53"8 :5 4 8:2 7 :72 85 )257 872 :2 842 :5%*2 ;: 82 :5 4' 6: :2 8) ; 65 18 4; ;: : 2( "14 !88: :3 57 ( 1 !8 8:53 ( 77 "4% 6:22 465 9552 "445+ 5 5%3 5 5 8 48 ; : 14 8 18 8%&89.
898#7 87 61 ;5 + 4) 23 4 92 4 88 " 87 ( "% 4 57 65 ; 5 :2 4 2 2 + ( :2 5 +17 5) 8 :5% : 8 84 4:2 7 2 687 ;8# ;8 8:( 45 17 8:(8! 4:2 ' :3 8!85 89 :5 "3 99 4 "9 97 +9 = 45 +; 8! "445:7&& 884 4:9 +5 "442 :53 !8 6:2 5 88 +7 1::2 97 : "4 8 %74 722 8 8&988%4 '7%561'7382 4 5 ;5 4:5 65 41 ;27 ;8 57 7 27 :2 :( + ;82 :42:5 5 2 87+ 5528%2,98436.:71:2% 847 82 877 42 45 :2 :3 :2 + : 8 15 7 :21$ 95 8' $2 45% 5$7 *8$ 5$ 9$ 7 182 8$ ;2 $7 *$ε1978722!4:2842!88:5*849284::942= 218::9489x = 0, 85$ %(p1 + p2)2µ = m21c2 + m22c2 + 2ε1 m2 ,(p1 + p2)2µ = (ε1 + ε2 )2 /c2 .x45 )2 7) ?5) ;: 4:2;:2 485 82%45 2)615 4286 +8: )55 ) 849 5 25 ) 17 4:)2 2 88 52 8:3 8 : 741 42 4 "ε0γ;5 7:5 5 8:53 8: +7" : :54 ;2 8:5% +!8 28( 53 8)6:2 :( 9 5 :5" 98#7 48: "592 5$2( 7244 45 +4 .8;:57 68:82 :522 45% 8 68: 53 :2 "42 9 9 : 97 97 495 :9 ; :7 8 65 ;; :7 89 )2 "4 85 `22 5 9 5 1:2 1 42 8 ; #5 ! 6 " 6: #5 *4 ; # 2 5 a 2) 97126 4:3 ;2 / ;57 "2 1; 48 1 "4 4 ;9 8# 2 5 7 #' 9 2 5% :5 ;57 %7 , 2 4:5 6 8: ; 8 2 53 8 4 + 55 42 7 45( : 45 85 7 8 4 8: 89 847 ;:57 65$( :2 2 "7 8: 82 "4 457 ;:2 61 4)2 ":# 57 12 495 84 86 42 ,42 84 2 6#5 957 82 8: : 3 5 57 4 18 49 9 ; 8: 7 ;5 65 1 57 6: :2 5 + "8 6# 1 92 ;45 : 55 7 83 9 ( 5 8 7 ;5 : 65 15 42 482 5" 24:4 92 42 :9 : " 8 4: ,8 " 5 4 9 4 8) ; 85 % " 3 5 845 8 5) 48% 88 22 65 45 & 87 9/ "8% "42 2 ;5 4:5 8;2 2 :53 5 8 :( 5( 5)361 48 1 7 5( 6 7 1 45 57 5( 4) 7 * "6 2+%63.
242N 122 95 42292 ;;87 4 51;5:95;49554N 4:54497 8 8# 5" 77 8 6 6 " 45% 82 8 ;95 "# 4 :86 8 792:29 7 94;55:55)55728892 ! 8: % #7 5% 145 :2 ( 83 QN :9 5 ;8 57 45 47 17 842 ;452 41 857 17 ;57 "4#2 85 ;45 6 *89 48 8:7 "2 7 9 97 1 1 8! :27 "14 4 8! 8: 17+$ 95 M2 57 8 : !42 45 8( ;8' 65 ;7 1 .+8 1:2 4 4 7 9 1# 15% :2 : 2 8!97 99 97 +7 ;2 : "2 4 ; : 8:5 92 #7 "4 5%) "# ;5 7 7 7 5( # 8#8+14:2 ; 14:2 !: 8:5 !888 :972 8:53 1 8# ;955 82 672 17 86 4:2 17 4:5 :55 !1&"8! 4672 444 "53 8#9(8 $ 4$ 1$ 2 7 $2 $ 57 :$ 8! 1$ 88 8! 5 5 5$ "# 1$ $"$ 8 # $ "εγ = 1, 21, 5 · 1011(p1 + p2)2µε1(18.11a)(18.11b)e+ + e− → ρ787 !" "8 :2( 87 ;:5 2757 58 ;458 4892 :5(3 1#995 877 !817 +28! .8#m1m2X0v1v2Nπ0π0π0π0mm = 140ε+ = 3, 1Xε0ε0 = mc2 .θ = 60oγε1 = ε2 = 0, 7X0γθ1 = θ2 = 45oX0.m2ρc2ε222= ε − me c =− me c =− mec2 ≈ 59022mec2meρ:( "4 "3 65) !45 )2 $2( 5 $<65( ;4:5 4553 4:)2 8: 5 :( 8 9745 53& 95 14:25) : 7 "#4:2 :5 97 688 4 5 1;#615 877 4:2 $89 2 886 52(4= 4' 85( =:* :5 ) *:5( 435 557 447 272567,2%2 45 95 5 6958 1$ ;52<&*'$ 5= 0, 776`s̀Y= 8: 2 4 8 2 2 1557 5 78 4 ;:56:5 827;5 8:2 4$<2% 17) :4:2 5382% 65( 6:8: 82 )45 4:5 Q ) ! # ( !ε1= mρ c 44( 147 573"462 4:)2 "46 55 6:52 189 5 53 685( ;95 2 ;9$ 4:)2 ,99 7 57 *9 8 482 :53 88 55) 689 23 72 :23 :95( "4:5 :55 $$ 47) ;4 +8 $ 27% " N ( 2 ) & 5 *2 42 $ 1) $4- 629727%827 ;5 9 ") 5 ; 42 4) 45 2) ,2 5 ; 42 4) 8: :9 52( 45( 8! % 9( 47 % ) : 7 5 2 487 42 : 9 8 :2 5 42 7% 2 : "584+:5:4642:4:)2 4:# 7 82 (2 *"4 ( 88 8: 88 :92 8: ": 2 2&M+8 27 67 ;:55 88 482 4 ;81 "2 685 ; *; 4:52 9 ! ( 8 5( 81: 8 ) *89 817/ 27 7 6;5 :2 52 53 ;7 2 "2 4 8:2 +4 "4 5 M7 482 1 4 8; 2 192 7 8 445 = < 7 :2 7 89 48: 8; 842 45 17 89 27 8 2 5 2 :2 ;2 ) 5 :7 $ $ :7 2 81 8! 877 "42 9 ;:5 4: !5 82 !88 4)2 142 52( 452( 655 4 ;27 4 *2 9 + " ; ( %:5% ; 457 ;55 849 92' 67 45( 45 " :' 872 4)2 45 95% 6: "# 7 "5 1 : 8 8 8 53 :(2 "44 ;9$ 4:)2 /:"7 2 87 6% 4 8 7 :28 874/575 888 88( !86 145 : 481 9 17 61 7 M) 8:: 5 +53 8 8 4 2 592 ) ;% ; 95 5 % :(2 ;5 ; 8 7 488 ;5:;;1!585$ S2 8$ 9 5 $ 9 $2 5$ 2 8$$ 8" 8mρ6;5 5 74 7572 9 49) 525 52 7 12 7(";45 :5:#7 67442 278 8:2 (7 5889 577$ 48%J%;3KC?#%1218 ;4 8:7& 68 : N' 92 9 ;248 "2 + 198 .+ 8!7) *482 88#7 % 17 2 6:786 "8! 814: 25) 655 78 57 4244 84; 8 4" 5 99"7 8) ;9$1$ 4:$2 4ε2§Mγc2e+e−ε− = 9e+ + e− → Xm(19.1);2 44 42 65 8 473 4972 ;8 8: 8P4H 8:;456 @:9:45788: 6 48 5 12 4 :3 1 B22 6: 2 ;87 7 : 5 53 @J:" : :5 :7 527 4:2 42 42 ;2867 ;55 9 8 455 : 8:2 8:7 22 :7 49 675 5 57 65 657 8; ; .8 8 4227 ;2 7 48: 142 2 2 7 48 955(:542 45%*42;84 445 12 :5 84 :2 6:528 5 8 48 :2 27 55 : 9127 53 81 127 88 68: 95 142 577 523 82 1; 152 ;27 ;55 :2 48 ;584;955;6945:4:2 5 :2 65 8 2 43 "# :58 95 ;8 89 6 4 68: ;5 17 +44995 85 97 2 87 86 49 812 2% 5( 27$( ( * " % "# ()),) !"% )% %) ( #))! "- ## ! )" "%! "( ! $ $ $ $ $" $m>∆m =j=1jj=1NXPmjKj ≥ 0QKj = −∆m · c2 .∆m > 0∆m · c2Nε = ∆m · c2 .;57%4:)288872 952 7 4:2 42 1;527 4957 7 65 :2 42 : 6:5 :2 4: 4 6:227 :5(3 97 5 : 482 52 4955 6 ,189 953"4:% 82% ;95 453"6:% :55% 845 :5% 495 2 8 ( 887 8#7 2 6: 6 : 2 !52 6 95 ; "4# :8;82 6 8 42 ;89 7 4 6 !5 67 2 7 8( )2 9 2 :5 8: 48 1/ 2( :5 *"/ 27-87 ;8 9)-8 5 ;: :2( ;2 4523 897 6:2 87 :2 ;5 82 9) 65 82 5 657 2%7 445 9" 5989587(477( 8 # 557865695978557 8 89 495 95 # 4 48 12 49 553 :22 89 8: 8 8 ( 657 2( 95( 12 95(- 8 15 ;! 5 95 2 : 85 2 4- :2 4 : ;2 88 5 5 4 52 2% 48 8;2 87 5 8;2 67 4:2 95 5 452 4 7 6: 97 #7 84 48 :2 84 5% 12 5 4:2 857 895 22/ 8# 1 8122 2/ 45% 8122 *2 4:)2 +7 889 59 8!5 6: 44 5 6:# ;57 ;8# 4:)2 ;5%7 "# 88 "8 5 " 222 48 ;52 +:5 ;)2 8#57 4%)2 5 88 4)2 5 !2 ;)2 ;2 482 57 48 8: 85 8: "4 !2 8: "4 42 :5 $ 9 $ 8 # $8#$ $ mj − mQ=NXj=1mj c2 + Kj ,s̀Kjj=1mjεj =NX ", #+.