Física Nuclear e Partículas Subnucleares - Capítulo 5 – S. S. Mizrahi & D. Galetti

7/31/2019 Fsica Nuclear e Partculas Subnucleares - Captulo 5 S. S. Mizrahi & D. Galetti

1/32

Dnz|sih 3

N ghvn ksdicnv

3 N ghvn ksdicnv >3:3+> Ok|vhlsh + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + >3:3+6 Zvhzvoclnlct ln ghvn ksdicnv c dhkt|n|nct c}zcvoeck|not n

fno}nt ckcvaont + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + >363+4 Ehlciht lc ghvn ksdicnv + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + >3313+3 Kn|svcpn lnt ghvnt tsfksdicnvct + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + >763+7 Zvhficent + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + >733+1 Nzklodc N0 Zh|ckdonot gckheckhiaodht + + + + + + + + + + + + + + + + + + + + + + + >71

3+1+> Zh|ckdoni lc Znvot + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + >713+1+6 Ghvn lc |vt dhvzht + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + >7=

3+= Nzklodc F0 \chvon ln ghvn ksdicnv lc _sbnqn + + + + + + + + + + + + + + + + + + >16

3+? Fofiohavnn + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + >=:

3+> Ok|vhlsh

H dhkdco|h lc ghvn) hvosklh ln gtodn dittodn) gsklneck|n%tc kn olon lc sen nh lcdhk|n|h) hs ck|h lc sen nh lot|kdon ck|vc lhot hs enot dhvzht+ Ht dntht enot vcz%vctck|n|owht lct|n i|oen dhktolcvnh th n ghvn avnwo|ndohkni) ~sc n|sn ck|vc dhvzht

zhv |cvce enttn) c n ghvn dhsihefonkn ~sc nac ck|vc hf`c|ht ~sc th cic|vodneck|cdnvvcanlht+ Dhokdolck|ceck|c) hs |niwcp kh) nefnt nt ghvnt |e lczcklkdon dhe h~snlvnlh lh okwcvth ln lot|kdon ~sc tcznvn ht lhot dhvzht) G -v> v6/ ( yv> v6y

4

-v> c v6 th ht wc|hvct zhtoh/) ds`n nh tc l nh ihkah ln iokmn ~sc ht ioan) c n ok%|cktolnlc lc dnln |ozh lc ghvn lczcklc hs lh zvhls|h lnt enttnt lht dhvzht hs lc

tsnt dnvant ci|vodnt+ Ct|c tcvon h dhkdco|h kcq|hkonkh lc ghvn2 enot |nvlc) EodmnciGnvnlny vckhs cttc dhkdco|h) tsft|o|soklh n khh lc nh lot|kdon zcih dhkdco|hlc dnezh lc ghvn) hs tc`n) kh dnth ln ghvn dhsihefonkn se dhvzh cic|vodneck|cdnvvcanlh ct|cklc tsn whi|n se dnezh lc ghvn c ~sni~scv hs|vh dhvzh) |nefe dnv%vcanlh) ~sc znttc kn vcaoh lcttc dnezh tck|ovon tsn zvctckn c vctzhklcvon eslnklh

>3:

T+T+ Eopvnmo ' L+ Anic||o


2/32

3+> Ok|vhlsh >3>

tsn |vn`c|von+N e lc |ck|nv c}ziodnv n dhcth lht dhkt|o|sok|ct ksdicnvct) n Gtodn Ksdicnv nlh|hs

|nk|h h dhkdco|h lc ghvn n lot|kdon dheh h lc dnezh+ Stnklh n zvoecovn dhkdczh)ghvne gco|nt lowcvtnt zvhzht|nt znvn lctdvcwcv n kn|svcpn ln ghvn ~sc enk|e n dh%cth lht kdichkt kh kdich>+ Kct|c tck|olh) nh ihkah ln ldnln lc >?4: logcvck|ctc}zvcttct ghvne zvhzht|nt dheh dnkloln|nt znvn h zh|ckdoni ksdicnv lc lhot dhvzht)~sc vcdcfone ht khect lc tcst zvhzhkck|ct) dheh Mcotckfcva) Qoakcv) En`hvnkn) c|d+Dnln zh|ckdoni dhkt|o|slh lc sen gskh ~sc lczcklc ln lot|kdon ck|vc ht kdichkt)ent zhlc lczcklcv |nefe lht tcst tzokt) ghvenieck|c won se gn|hv lc ok|cvnh tzok%tzok) hs ck|h zhlc |cv dnv|cv |ckthvoni dhe n oktcvh lc se gn|hv ctzcddh dhk|cklhtzokt c wc|hvct zhtoh+

@ n olon lc ~sc n ghvn ksdicnv zhlcvon |nefe tcv lctdvo|n) ce nknihaon nh cic|vh%

enakc|oteh) dheh se dnezh c ~sc n ok|cvnh ksdicnv tc enkogct|nvon zcin |vhdn lcsen znv|dsin lc dnezh ce nknihaon nh g|hk) znvn h dnth ln ghvn ck|vc znv|dsintcic|vodneck|c dnvvcanlnt znv|os lc _sbnqn+ Ce >?43) cic zvhzt sen |chvon -h tcslc|nimneck|h ckdhk|vn%tc kh Nzklodc F lct|c dnz|sih/ tcasklh n ~sni n znv|dsin lcdnezh |cvon sen enttn ck|vc >3: c 6:: EcW(d6 c) wot|h ~sc n~scin cvn sen enttn ok%|cveclovon ck|vc n lh ci|vhk -:) 3 EcW(d6/ c n lh zv|hk -?4= EcW(d6/) n znv|dsinvcdcfcs h khec ethk+ Kct|c dckvoh) h dhkdco|h ~sc vcac h ecdnkoteh ln ghvn ks%dicnv tcasc h znvnloaen ln ghvn cic|vhenak|odn) ot|h ) nleo|c%tc c}ot|ov se dnezhksdicnv c n ok|cvnh ck|vc ht kdichkt hdhvvcvon zcin |vhdn lc se -hs enot/ ethk2 khhft|nk|c) ht zv|hkt) lcwolh ok|cvnh dhsihefonkn) |nefe ok|cvnaovone) nlodohkni%eck|c) n|vnwt ln |vhdn lc g|hkt+ _sbnqn lclspos h zh|ckdoni lc ok|cvnh ck|vc lhotkdichkt) ~sc lczcklcvon ln lot|kdon ck|vc ht ecteht) v 5 yv> v6y) dheh tcklhln ghven Wksd -v/ 5 a6 c}z-v/ (v) hklc se znvec|vh dhe loeckth lc

okwcvth lc dhezvoeck|h > tcvon h nidnkdc eloh ln ghvn c a n dhkt|nk|c lc

dnvan ksdicnv) ce nknihaon n dnvan ci|vodn c+ H gn|hvc}z-v/ vctzhktwci zcihdnv|cv lc dsv|h nidnkdc ln ghvn ksdicnv) dheznvn|owneck|c nht zh|ckdonot dhsihe%

fonkh c avnwo|ndohkni ~sc |e nzcknt h gn|hv>(v+ N|snieck|c) ck|cklc%tc ~sc n ghvnksdicnv -ok|cvksdickodn/) vctzhktwci zcin dhcth c ct|nfoiolnlc lh kdich) sen dhe%

zhkck|c vctolsni ln dmnenln ghvn ghv|c) hs ok|cvnh ghv|c) ~sc nac ck|vc ht ~snvbt) htdhkt|o|sok|ct lht kdichkt+

Nie ln ok|cvnh ghv|c m sen hs|vn ghvn ~sc tc gnp tck|ov kht kdicht) ~sc vc%tzhktwci zcin fstdn lc tsn ct|nfoiolnlc c zhv |vnktes|nct ksdicnvct) enkogct|nklh%tc won |vt zvhdcttht0 o/ kht lcdnoeck|ht lc se ks|vhk hs zv|hk lh kdich m lhot

zvhdcttht logcvck|ct lc lcdnoeck|h ) ~sc tc lot|okasce zcin ceotth lc se ci|vhk-/ hs lc se zto|vhk -"/) ~snklh ceo|olh `sk|neck|c se nk|okcs|vokh -c/ hs

se kcs|vokh -c/) vctzcd|owneck|c) ~sc zhttsce sen enttn eso|h eckhv ~sc n lhci|vhk hs lh zto|vhk2 oo/ n dnz|svn cic|vkodn) hs dnz|svn B) ~sc dhktot|c kn dnz|svn)zcih kdich) lc se ci|vhk ln dnenln cic|vkodn B -hvfo|ni enot zv}oeh lh kdich/)

>Ce wcp lc stnv n c}zvctth ghveni lc ghvn) ~sc sen ~snk|olnlc wc|hvoni) stn%tc) dhvvo~scovneck|c)n gskh ckcvaon zh|ckdoni) enot toezicteck|c dmnenln gskh zh|ckdoni hs zh|ckdoni) ~sc sen gskhctdninv+



3/32

>36 Dnz|sih 3+ N ghvn ksdicnv

~snklh ck|h se zv|hk tc |vnktghven ce se ks|vhk c m ceotth lc se kcs|vokh-z " c k " c/+ Cttc |ozh lc ghvn gho dmnenln gvndn hs ok|cvnh gvndn) zhv|cv ok|cktolnlc eso|h eckhv ~sc n ghvn ksdicnv) cefhvn eso|h enot ok|cktn ~sc n ghvncic|vhenak|odn ~sc n|sn ck|vc znv|dsint cic|vodneck|c dnvvcanlnt+ Ck|vc|nk|h) zcih ~scn|snieck|c tc dhkmcdc thfvc ghvnt ksdicnvct) h dhkdco|h lc &ghv|c&hs &gvndn&lczcklcvonln ckcvaon ckwhiwoln) hs tc`n) ce ckcvaont -lc dhiotct ck|vc znv|dsint/ eso|h ni|nt) nghvn gvndn zhlc tc |hvknv |h hs enot ok|cktn ~sc n ghv|c+

Cefhvn n |chvon zvcwnick|c znvn n lctdvoh lc dheh n en|von dhkt|o|sln cetcst ciceck|ht enot gsklneck|not kcdctto|c lc se |vn|neck|h ghveni cefntnlh kn |ch%von lc dnezht ~sk|odht vcin|owt|odht) n Gtodn Ksdicnv n fno}nt ckcvaont |ce tc hdsznlhmot|hvodneck|c lc dheh h kdich tc enk|e dhcth c ct|wci) tc`n ce tcs ct|nlh gskln%eck|ni hs ce tcst ct|nlh c}do|nlht) tce icwnv ce dhk|n n ct|vs|svn ok|cvkn lc zv|hktc ks|vhkt dhktolcvnlht dheh znv|dsint ciceck|nvct zhk|snot+ Zhv dhktcasok|c) c}%|cklcklh n woth kcq|hkonkn lc ghvn) nleo|c%tc ~sc nt ghvnt c nt gskct lc ckcvaon

zh|ckdoni tc`ne c}zvcttnt ce |cveht lnt dhhvlcknlnt ctzndonot lc lhot hs enot k%dichkt) lht tzokt c lc se hs|vh avns lc iofcvlnlc dmnenlh othtzok hs tzok oth|zodh+Dhk|slh) znvn ckcvaont ok|cveclovont) dhktolcvn%tc ~sc n ghvn ksdicnv tc enkogct|n

zcin |vhdn lc ethkt ck|vc ht kdichkt) sen c}|ckth lh dhkdco|h lc dnezh lc Gnvn%lny+ thfvc otth ~sc |vn|nvceht knt tcct tcasok|ct+

3+6 Zvhzvoclnlct ln ghvn ksdicnv c dhkt|n|nct

c}zcvoeck|not n fno}nt ckcvaont

Nahvn wneht c}zhv h ~sc tc nzvcklcs thfvc n ghvn ksdicnv6 n znv|ov lc lnlht cezvodht

hf|olht lc dhiotct n fno}nt ckcvaont) n znv|ov ln ldnln lc >?4:) ce tk|ctc0 n ghvn ksdicnv kh lc kn|svcpn cic|vhenak|odn) zhot oklczcklc ln dnvan ci|vodn

c nac dhe n ecten ok|cktolnlc ck|vc zv|hkt c ks|vhkt) nttoe dheh nzcknt ck|vczv|hkt hs ck|vc ks|vhkt+

N ghvn ksdicnv |nezhsdh lc kn|svcpn avnwo|ndohkni) zhot ct|n ghvn vcin|own%eck|c eso|h gvndn) cin zvhlspovon sen ckcvaon lc ioanh ln hvlce lc 4 >:41 E cW

znvn h ls|cvhk) ck~snk|h ~sc n ckcvaon lc ioanh ecloln lc dcvdn lc 6) 6 E cW+Zhv|nk|h) n ghvn ksdicnv tszink|n n ghvn avnwo|ndohkni zhv se oezvcttohknk|c gn|hv lnhvlce lc >:41+

N ghvn ksdicnv lc dsv|h nidnkdc) ot|h dhs cwolck|c ` knt zvoecovnt c}zcvokdontlc ctznimneck|h) ~snklh Vs|mcvghvl dhkt|n|hs ~sc n >: g e ->:>6 de/ lh dck|vh lhkdich n ghvn ksdicnv zhlcvon tcv lctdhktolcvnln ce dheznvnh dhe n ghvn dhsihe%

fonkn+ Zhve) n dsv|nt lot|kdont n ghvn ksdicnv) lckh|nln zhvWQ -v/ -v 5 yv> v6y h wc|hv lot|kdon vcin|own hklc v> c v6 th nt zhtoct ctzndont lht kdichkt/ thfvczs`n

6Zhv wcpct ckdhk|vn%tc ct|c |cveh kh zisvni) ghvnt ksdicnvct) zhot -n/ tsn c}zvctth enot dhezic|n dhk%t|o|sln lc wvoht |cveht+ Zhve) n~so wneht kht vcgcvov ghvn ksdicnv dheh n then lht |cveht kcdcttvohtznvn sen fhn vczvhlsh lc zvhzvoclnlct ksdicnvct cezvodnt+



4/32

3+6 Zvhzvoclnlct ln ghvn ksdicnv c dhkt|n|nct c}zcvoeck|not n fno}nt ckcvaont>34

n ghvn dhsihefonkn ~sc nac ck|vc zv|hkt+ Dhkwe icefvnv ~sc ce sen ehidsin nok|cvnh ck|vc ht kdicht lht |heht cttckdonieck|c dhsihefonkn+ N ghvn ksdicnv ck|vc lhot kdichkt iowvct kh oasni ~scin ~sc tc enkogct|n

~snklh cict th znv|c lc se -lh/ kdich+ Lc dcv|n ghven) n zvctckn lht lcenot k%dichkt ni|cvn n ghvn ~sc nac ck|vc kdichkt iowvct) zhot) ce eckhv ctdnin) c}ot|ce ok|cv%nct ~sc lh hvoace n se dnezh ksdicnv eloh enot dhvvcinct ~sk|odnt lc eso|htdhvzht+

Ht ci|vhkt kh zhlce c}ot|ov lck|vh lh kdich c |nefe th oeskct ghvnksdicnv) cict kh n tck|ce+

H zh|ckdoni ksdicnv ck|vc lhot kdichkt lczcklc lc tcst tzokt2 znvn v 5 yv> v6y)se lht |cveht ln gskh zh|ckdoni ksdicnv) n ok|cvnh tzok%tzok) |hen n ghven

Wt-v/ 5 wt-v/t> t6+ -3+>/

N|snklh thfvc se ns|hct|nlh lc tzokt dhk`sk|hTEt ->) 6/) hf|e%tc -wc`n h NzklodcN lh dnz|sih 6/

Wt-v/TEt ->) 6/ 5 wt-v/

4< :: ->) 6/

>< >Et ->) 6/ +

Zhv|nk|h) n ok|cktolnlc c h tokni lh zh|ckdoni ksdicnv wnvonvh dhe h kasih vcin|owhck|vc ht tzokt+ Tc wt-v/ ghv se zh|ckdoni n|vn|owh -tokni kcan|owh/) h zh|ckdoni Wt-v/ tcvvczsitowh znvn ht tzokt lht kdichkt nzhk|nklh ce tck|olht hzht|ht -T 5 :) tokaic|h/ cn|vn|owh ~snklh ht tzokt nzhk|nvce kh ecteh tck|olh -T 5 >) |vozic|h/+ Ce nefht htdntht n ok|cktolnlc lc wt-v/ vclspoln zhv se gn|hv4(< hs >(/) stnklh h hzcvnlhvZ 5

> " < t> t6

(6) ce wcp lc t> t6) ds`n c~snh lc

ns|hwnihvct ZTEt ->) 6/ 5 ->/

>TTEt ->) 6/ )

w%tc ~sc) lczcklcklh lh wnihv lc Ttcv znv hs eznv) m nzcknt sen logcvckn lc toknilh ct|nlh lc tzok) kcan|owh znvn h tokaic|h c zhto|owh znvn h |vozic|h4+ Nttoe) sen ghvnok|cvkdichk ln ghven wt-v/Z nac eslnklh h tokni lh ct|nlh lc tzok lht kdichkt)

tce ngc|nv n ok|cktolnlc+ \nefe) oeclon|h zcvdcfcv ~sc

Z6

5 >+

N znv|ov lc lnlht lc ctznimneck|h ct|nfcicdcs%tc ~sc n ghvn ksdicnv lcwc tcv vc%zsitown n dsv|ttoen lot|kdon -lop%tc ~sc ht kdichkt nzvctck|ne se dnvhh vczsitowh/)

4Zhlc%tc |nefe ctdvcwcv n nh lh hzcvnlhv thfvc ht ct|nlht oklowolsnot dheh

Z

et>

->/ et6-6/

5 et6

->/ et>-6/ )

wcvodnklh%tc ~sc ht ct|nlht lht kdichkt ghvne |vhdnlht) nttoe Z dnvnd|cvopn%tc dheh se hzcvnlhv lc|vhdn+



5/32

>3< Dnz|sih 3+ N ghvn ksdicnv

h ~sc gnp dhe ~sc ht kdichkt enk|ckmne sen dcv|n lot|kdon elon ck|vc to lck|vh lhkdich) h ~sc `st|odn n dhkt|n|nln tn|svnh ln lcktolnlc ksdicnv+ N ghvn ksdicnv lcwc |nefe dhk|cv sen dhezhkck|c kh%dck|vni) dmnenln ghvn

|ckthvoni) tcklh ln ghven

W\-v/ 5 w\-v/T>6 -v(v/ ) -3+6/

hklc h hzcvnlhvT>6 -v(v/ 5 4-t> v/ -t6 v/ (v

6 t> t6 -3+4/

|ce dnv|cv |ckthvoni) tcecimnk|ceck|c ok|cvnh ck|vc lhot lozhiht+ N ghven ln c}%zvctth -3+6/ gho tsacvoln zciht tcasok|ct lnlht c}zcvoeck|not hftcvwnlht kh ls|cvhk0->/ h eheck|h lc lozhih enak|odh ioacovneck|c logcvck|c ln then lht eheck|htenak|odht lh zv|hk c lh ks|vhk) dhktolcvnlht dheh znv|dsint oklczcklck|ct2 -6/n c}ot|kdon lc se zc~sckh eheck|h lc ~snlvszhih ci|vodh2 -4/ h eheck|se nkas%

inv ksdicnv-|ce/ ntthdonlh @ 5 >+ Cttct gn|ht oklodne ~sc h ct|nlh gsklneck|ni lhls|cvhk lcwc tcv lctdvo|h dheh sen tszcvzhtoh lc lhot ct|nlht) se dhe eheck%|se nkasinv hvfo|ni i 5 : -lheoknk|c/ c hs|vh dhe i 5 6 -zc~sckn dhk|vofsoh/+ Heheck|se nkasinvi lcwc tcv znv) zhot kcdcttvoh ~sc ->/i 5 > znvn ~sc n znvolnlclh ct|nlh tc`n dhktcvwnln) lc ndhvlh dhe n hftcvwnh c}zcvoeck|ni+ Znvn vczvhlspovct|ct lnlht n hzcvnh lc T>6 -ctdvcwcklh) lc ghven enot dheznd|n) T>6 ce wcp lcT>6 -v(v// lh zh|ckdoni ksdicnv oeziceck|n n eslnkn lh eheck|se nkasinv hvfo|ni|h|ni c lht tzokt lc dnln kdichk zhot I6 c nt zvh`cct Ip c Tp kh th ~snk|olnlctdhktcvwnlnt) m

I6) T>6

o75 :)

mIp) T>6

o75 : c

mTp) T>6

o75 : + -3+ " t6 th ht eheck|n nkasinvct hvfo|ni c lc tzok) |h|ni) lht lhot kdichkt+3H |heh dmnenlh lcs|voh c se ot|hzh lh |heh lc molvhakoh+



6/32

3+4 Ehlciht lc ghvn ksdicnv >33

3+4 Ehlciht lc ghvn ksdicnvDht|secovneck|c) ht ehlciht zvhzht|ht dnznpct lc vczvhlspov zvhzvoclnlct c}zcvo%eck|not acvnot lht kdicht tc fntcone kn dhkt|vsh lc zh|ckdonot ksdicnvct lc lhot c|vt dhvzht+ Cttct dhk|e |cveht lczcklck|ct lnt wnvowcot vcicwnk|ct) c ~sc c}ofce) lcghven c}zido|n) niaskt zhsdht znvec|vht n tcvce n`st|nlht znvn vczvhlspov) h ecimhv

zhttwci) niasent zhsdnt zvhzvoclnlct lht kdicht hs lnlht lc ctznimneck|h kdichk%kdichk+ Nttoe) tcv ecimhv n~scic ehlcih ~sc zslcv tcv enot nfvnkack|c) o+c+) ~sc

zslcv vczvhlspov h enot cieck|c zhttwci se avnklc kecvh lc zvhzvoclnlct znvn henohv kecvh zhttwci lc ksdilcht+ Ck|vc|nk|h) nzctnv lc tcv fnt|nk|c |oi) ct|c |ozhlc gckheckhihaon |ce tsnt ioeo|nct2 logcvck|ceck|c ln gtodn n|eodn ds`n ghvn)~sc n|sn ck|vc ci|vhkt c ck|vc ct|ct c h kdich n dhsihefonkn ) kh c}ot|c kn Gtodn

Ksdicnv se kodh ehlcih lc ghvn ~sc l dhk|n lc |hlnt nt zvhzvoclnlct ce |hlht ht

ksdilcht+ Lc gn|h) n ghvn ~sc n|sn ck|vc lhot kdichkt -dhe n |vhdn lc ethkt/ senenkogct|nh vctolsni ln ok|cvnh ghv|c ~sc n|sn) zhv |vhdn lc aihkt) ck|vc ht ~snvbt)ht dhkt|o|sok|ct lht kdichkt+ lcttn ghvn vctolsni ~sc n Gtodn Ksdicnv lc fno}ntckcvaont tc hdszn+ Ot|h gnp dhe ~sc c}ot|ne eso|ht ehlciht) dnln se enot nzvhzvo%nlh znvn se dhk`sk|h lc ksdilcht c(hs znvn vczvhlspov lc|cveoknlnt zvhzvoclnlct+ Nenohv znv|c lnt ghvnt zvhzht|nt tc vcgcvc nzcknt nh tot|cen toezict lc lhot kdichkt)cefhvn c}ot|ne ehlciht ~sc okdisce se |cveh lc ghvn lc |vt dhvzht+

H zvoecovh ehlcih lc ghvn ksdicnv gho zvhzht|h zhv Mcotckfcva) tcklh nzvctck%|nlh ce sen tvoc lc |vt nv|oaht h zvoecovh lcict ce `skmh lc >?46) ~sn|vh ectctnzt n lctdhfcv|n lh ks|vhk zhv Dmnlqodb ds`nt olont tc |hvknvne gsklneck|not

znvn n okwct|oanh ce Gtodn Ksdicnv kh lcdhvvcv lht nkht tcasok|ct+ Cttckdonieck|c)Mcotckfcva zvhzt ~sc ht kdicht cvne dhkt|o|slht lc zv|hkt -h zv|hk dheh sen

znv|dsin ciceck|nv/ c ks|vhkt -h ks|vhk wot|h dheh sen znv|dsin dhezht|n) sendhefoknh lc se zv|hk c se ci|vhk/+ N ct|vs|svn ksdicnv zhlcvon tcv c}ziodnlnzcin icot ln ecdkodn ~sk|odn) ce |cveht lc ok|cvnct ck|vc nt znv|dsint) c n ok|cv%nh tc lnvon dheh se |ozh lc |vhdn) ce nknihaon dhe n ok|cvnh ck|vc se |heh lcmolvhakoh >M c se hk M"+ Ihah lczhot) ce >?44) Qoakcv c En`hvnkn zvhzstcvnetcst vctzcd|owht ehlciht znvn c}ziodnv ht wnihvct c}zcvoeck|not lnt ckcvaont lc ioa%nh lh ls|cvhk) ln znv|dsin ) nttoe dheh n tn|svnh ln lcktolnlc ksdicnv+ Ht |vtehlciht th vczvctck|nlht zciht |vt |ozht lc ok|cvnh

Mcotckfcva 0 WM-v/ Z)

Qoakcv 0 WQ -v/ ) -3+1/

En`hvnkn 0 WE -v/ ZE)

hklc Z 5

> " {> {6

(6 c Z) nk|cvohveck|c do|nlh) th hzcvnlhvct lc |vhdn lcct|nlht lc othtzok c lc tzok ck|vc lhot kdichkt+ Nttoe dheh eht|vnlh kh vhlnz 6)

znvn lsnt znv|dsint dhe othtzok | 5 >(6 |ceht

Z

e>->/ e6

-6/

5 e6->/ e>

-6/ +



7/32


^snk|h nh hzcvnlhvZE) tsn nh dhktot|c ce |vhdnv nt zhtoct lnt dhhvlcknlnt ct%zndonot knt gskct hvfo|not)

ZE>-v>/6-v6/ 5 6-v>/>-v6/+

Dheh ht kdichkt th znv|dsint gcveokodnt n gskh lc hkln dhk`sk|n lcwc tcv nk|ot%toe|vodn) tcklh nttoe) nziodnklh h zvhls|h lht hzcvnlhvct ZZZE thfvc se ct|nlhlc lsnt znv|dsint |ce%tc ZZZE -s>) s6/ 5 -s6) s>/ 5 -s>) s6/) hklc svczvctck|n ht dokdh avnst lc iofcvlnlc0 |vt ctzndont v) se lc tzok c se lc othtzok+Ck|h) dheh ZZZE 5 >) tcasc ~sc tc zhlc ctdvcwcvZE 5 ZZ+

Dnln sen lnt |vt ok|cvnct ce -3+1/ gho okwck|nln c ok|vhlspoln kn |chvon ks%dicnv oklczcklck|ceck|c lnt hs|vnt+ Mcotckfcva zvhzt n ok|cvnh WM-v/ Z) dhk%

`cd|svnklh ~sc n ghvn ksdicnv lczcklcvon lc sen hzcvnh lc |vhdn vczvctck|nln zhvWM-v/ ZZE WM-v/ Z -dhe WM-v/ ; :/+ Ct|c |cveh dhs dhkmcdolh dheh|cveh hs ghvn lc Mcotckfcva) cic nac ck|vc se zv|hk c se ks|vhk gnpcklh n |vhdnz k) dheh tc se ci|vhk ct|owcttc hvfo|nklh lhot zv|hkt+ Ghvenieck|c) cttc |cvehvczvctck|n n |vhdn lh avns lc iofcvlnlc lc othtzok7) ent ce tcs |cvdcovh nv|oah cic dhk%t|n|hs ~sc n ghvn lc |vhdn kh icwnwn tn|svnh ln lcktolnlc ksdicnv hftcvwnln+ Nt%toe) Mcotckfcva ok|vhlspos sen znv|c ghv|ceck|c vczsitown kn ghvn ck|vc ht kdichkt

znvn sen lot|kdon ok|cvksdickodn v eckhv ~sc sen dcv|n lot|kdon dv|odn vd) hs tc`n)cic zht|sihs n c}ot|kdon lc se dnvhh vczsitowh+

Znvn |ck|nv c}ziodnv n dnstn ln ndck|snln logcvckn lc ckcvaon lc ioanh ck|vc hls|cvhk -Fl 6) 6 E cW/ c n znv|dsin -F 6= E cW/) ce >?44 Qoakcv zvhztsen ok|cvnh K K -kh|nh dheznd|n znvn kdichk%kdichk/ ~sc lczcklcvon nzckntln lot|kdon ck|vc ht kdichkt) WQ -v/+ Icwnklh ce dhktolcvnh nzcknt nt ok|cvnctzk) c lctzvcpnklh nt ok|cvnct1zz c kk) cic dhkt|n|hs ~sc n logcvckn ln ckcvaon

lc ioanh zhv kdichk) znvn dnln kdich) zhlcvon tcv c}ziodnln nzcknt tc n ok|cvnhghttc dhktolcvnln lc dsv|h nidnkdc+ Enot |nvlc) Mcotckfcva eht|vhs ~sc sen ghvn

zsvneck|c dck|vni) dheh n~scin zvhzht|n zhv Qoakcv) kh zhlcvon lnv dhk|n thpokmnlh cgco|h lc tn|svnh) zhv|nk|h kh zhlcvon tcv vctzhktwci zcin ckcvaon lc ioanh khtkdicht+ Ck~snk|h znvn Mcotckfcva n ghvn ksdicnv lcwcvon zhttsov sen znv|c vczsitown nlot|kdont enot dsv|nt) znvnEn`hvnkn ct|n c}ziodnh kh cvn tn|otgn|von c kce ct||odn)

zhot ce tsn dhkdczh tcvon sen |cecvolnlc ok|vhlspov enot sen znv|c vczsitown knghvn) lc ok|cktolnlc ln hvlce lc dck|cknt lc E cW) ~snklh nokln kh tc dhkmcdon nhvoace ln znv|c n|vn|own2 tcs ok|so|h cvn lctdhfvov ~sni tcvon n ok|cvnh enot toezictck|vc kdichkt ~sc icwnttc tn|svnh+

Ce se nv|oah lc >?44) En`hvnkn nzhk|hs ~sc n ghvn lc Mcotckfcva tcvon dnznp lcc}ziodnv n zvhzvoclnlc lc tn|svnh tce n kcdcttolnlc lc dhktolcvnv se &dnvhh vc%

7Znvn dhezic|nv n dnvnd|cvopnh ln ghvn kdichk%kdichk) Mcotckfcva okdisos sen ghvn ks|vhk%ks|vhkenot gvndn c |nefe n ghvn dhsihefonkn ~sc nac ck|vc ht zv|hkt+ Ihah lczhot) Qoakcv c En`hvnkn lot%zcktnvne n ghvn ck|vc ht ks|vhkt c dhktolcvnvne ~sc n ok|cvnh dhsihefonkn zhlcvon tcv lctzvcpnln cekdicht icwct) dnklh nzcknt dhe n ghvn ck|vc zv|hkt c ks|vhkt+ Ent otth ct|nwn cvvnlh2 ce >?47 c}zcvo%eck|ht lc ctznimneck|h lc kdichkt eht|vnvne ~sc n ghvn ksdicnv zvn|odneck|c n ecten) oklczcklck|c%eck|c ln kn|svcpn lht kdichkt) zz) z k hs k k+

1H ~sc okdhvvc|h zhot n ghvn ksdicnv oklczcklc ln dnvan ci|vodn lh kdichk+



8/32

3+4 Ehlciht lc ghvn ksdicnv >31

zsitowh& t tc h zh|ckdoni WM-v/ ghttc dhktolcvnlh tcezvc kcan|owh znvn |hlh v ce-:) /+ Ck|vc|nk|h) tc cttn ctdhimn tn|otgnpon n dhkloh lc tn|svnh) cin kh c}zio%dnwn n avnklc ckcvaon lc ioanh ln znv|dsin + Cic kh|hs ~sc znvn se zh|ckdoni lh|ozh WM-v/ ZZE) dhe WM-v/ 9 :) h didsih ln ckcvaon lc ioanh vctsi|nwn tcv eso|heckhv dcvdn lc < EcW ~sc h wnihv hftcvwnlh) 6=) 4 EcW+ Kct|c dnth) n znv|dsin tcvon ni|neck|c okt|wci c ihah nzt n tsn ghvenh tc doklovon ce lhot ls|cvhkt)gn|h ~sc kskdn ghvn hftcvwnlh kht c}zcvoeck|ht+ Otth icwhs En`hvnkn n dhktolcvnv h

zh|ckdoni lc |vhdn WE -v/ ZE dhe WE -v/ 9 :) hklc h ns|hwnihv lc ZE zhto|owh znvnct|nlht hvfo|not toe|vodht c kcan|owh znvn ht nk|ottoe|vodht+ Kct|n ok|cvnh) dnln zv%|hk ln znv|dsin ok|cvnac dhe ht lhot ks|vhkt) vctsi|nklh nttoe ce ~sn|vh ioanctn|vn|ownt c n ct|nfoiolnlc ln znv|dsin -dn/ c}ziodnln+ Zhv tsn cicakdon c toeziodo%lnlc n |chvon lc En`hvnkn gho oeclon|neck|c ndco|n c Mcotckfcva nfnklhkhs tsn |chvonlc ok|cvnh dhe dnvhh vczsitowh+ Theck|c ce >?36) ~snklh vctsi|nlht lc c}zcvoeck%|ht lc ctznimneck|h z z kh zhlone tcv c}ziodnlht nzcknt dhe n ghvn lc En`hvnkn) ~sc n |chvon lc Mcotckfcva lc dnvhh vczsitowh gho vcttstdo|nln+ N|snieck|c) c}ot|cdhktckth lc ~sc lhot kdichkt tc vczcice n lot|kdont eckhvct ~sc :) = g e+

N ok|cvnh ksdicnv dck|vni enot acvni znvn lhot kdichkt sen dhefoknh lntok|cvnct nk|cvohveck|c lotds|olnt) h dhk`sk|h -3+1/) nlodohknln lc enot se |cveh lc|vhdn lc tzok) WF -v/ Z) ok|vhlspolh zhv@+ M+ Fnv|ic|| ce >?47 R>U) ~sc lczcklc lhct|nlh lc tzok lht lhot kdichkt

WA -v/ 5 WQ -v/ " WE -v/ ZE " WF -v/ Z WM-v/ Z+ -3+=/

Zht|cvohveck|c) ce >?) Qoakcv c Cotckfsl R6U zvhzstcvne se zh|ckdoni lc lhot%dhvzht enot acvni) ~sc dhk|owcttc se |cveh kh%dck|vni c ~sc kh dhk|owcttc |cveht

dhe -ht lcenot |cveht kh dhk|owcttce h/ eheck|se iokcnv lc zh|kdon enohv ~sc >+\nefe oezstcvne n dhkloh lc ~sc h zh|ckdoni lcwcvon tcv dhktot|ck|c dhe nt icotlc dhktcvwnh lh eheck|se nkasinv) ln znvolnlc) c tcv okwnvonk|c thf n hzcvnh lcvcwcvth |cezhvni2 tsn ghven

W -v/ 5 WQ -v/ " W6 -v/ {> {6 " W\-v/T>6 -v(v/ " WTH -v/ I T

dhe t 5 (6+ Ct|n sen dhefoknh lc sen ghvn lc Qoakcv) sen ghvn dck|vnilczcklck|c lc tzok) sen ghvn -kh%dck|vni/ |ckthvoni c knieck|c sen ghvn lc ok|cv%nh tzok%vfo|n) zhot dhk|e h zvhls|h ctdninv I T+ Lczhot lotth eso|ht zh|ckdonotksdicnvct ghvne zvhzht|ht) dnln se dhkt|vslh znvn vczvhlspov se dhk`sk|h lc lnlhtc}zcvoeck|not ctdhimolht zciht tcst zvhzhkck|ct+ Kh Nzklodc N ovceht lotdhvvcv th%

fvc lhot lcict0 h zvoecovh se zh|ckdoni lc lhot dhvzht ~sc nzvctck|n sen ct|vs|svn

fnt|nk|c tht|odnln c dhkmcdolh dheh zh|ckdoni lc Znvot2 h hs|vh) nie lht |cvehtlc ghvn lc lhot dhvzht dhk|e -m/ se |cveh lc ghvn lc |vt dhvzht) ~sc znvn lc|cv%eoknlht kdicht -K 5 P 5 znv/ tc vclsp n se |cveh lc ghvn lc lhot dhvzht wcpct nlcktolnlc ksdicnv+



9/32

>3= Dnz|sih 3+ N ghvn ksdicnv

3+< Ethkt dheh znv|dsint lc dnezh ksdicnvH dhkdco|h lc ok|cvnh won |vhdn lc znv|dsint lc dnezh ct|nwn zvctck|c kn gtodn lctlc>?61) ~snklh Lovnd R=U lctckwhiwcs n |chvon ~sk|odn lh cicd|vhenakc|oteh) c lczhot)ce >?46) ~snklh Gcveo R?U gcp nt dhk`cd|svnt lc ~sc n ok|cvnh ck|vc znv|dsint cic|%vodneck|c dnvvcanlnt tc lnvon zcin |vhdn lc g|hkt c lc ~sc ct|ct kh c}ot|ovone nk|ctln ok|cvnh) ent tcvone dvonlht kh n|h+ Zhv dhktcasok|c) ce se dcv|h zvhdctth) seci|vhk zhlc nfthvwcv se g|hk lh dnezh cic|vhenak|odh ~sc h zcvecon) c cic lco}nvonlc c}ot|ov -lop%tc ~sc cic gho lct|vslh/2 zht|cvohveck|c) h ecteh ci|vhk zhlcvon ceo%|ov se hs|vh g|hk -lop%tc ~sc cic dvonlh/+ Ct|c zvhdctth zvctdoklc ln kcdcttolnlclc olck|odnv h g|hk ceo|olh dheh tcklh h ecteh g|hk nk|cvohveck|c nfthvwolhhs niase hs|vh2 dheh ht g|hkt kh th olck|odwcot oklowolsnieck|c kh tc imctn|vofso v|siht ~sc zhttne lot|okaso%iht se lh hs|vh+ Ce >?4:U ct|cklcs h

dhkdco|h lc dvonh c nfthvh lc g|hkt znvn hs|vnt znv|dsint) ce tsn |chvon lh lcdno%eck|h cic nvehs ~sc h ci|vhk c h kcs|vokh kh c}ot|ovone nk|ct lh lcdnoeck|h) ent~sc tcvone dvonlht kh eheck|h ce ~sc cic hdhvvc+ Zhv|nk|h) nttoe dheh ndhk|cdc dheht g|hkt) ht kecvht lc zv|hkt) ks|vhkt c ci|vhkt kh tc enk|cvone dhkt|nk|ct khlcdnoeck|h + oezhv|nk|c tniock|nv) zhve) ~sc ce |hlht ht zvhdcttht ksdicnvct) ndnvan ci|vodn |h|ni sen ~snk|olnlc dhktcvwnln+

\nefe ce >?4?3=/ c L+ Oqnkckbh R>>U dhk%`cd|svnvne n c}ot|kdon lc sen ghvn lc |vhdn znvn n ok|cvnh ck|vc zv|hk c ks|vhk-tcvone |vhdnlht h znv ci|vhk%kcs|vokh/) ds`h zh|ckdoni cgc|owh tcvon ln ghven S-v/ 5

a6G({d

v3) hklc aG n dhkt|nk|c lc ndhzineck|h stnln zhv Gcveo ce tsn |ch%von lh lcdnoeck|h + Ck|vc|nk|h) ct|n ghvn eht|vhs%tc eso|h gvndn znvn zhlcv vc%

zvhlspov ht wnihvct c}zcvoeck|not lnt ckcvaont lc ioanh lh ls|cvhk c ln znv|dsin

+ Nzhonklh%tc knt olont lc Mcotckfcva) nttoe dheh knt lc \nee c Oqnkckbh) ce>?43) _sbnqn zvhzt tsn |chvon thfvc n kn|svcpn ln ghvn ksdicnv gnpcklh n tcasok|c ts%zhtoh0 ce nknihaon |chvon cic|vhenak|odn hklc ht g|hkt ok|cveclone n ok|cvnh)lcwcvon mnwcv sen znv|dsin ok|cveclonklh n ok|cvnh ksdicnv+ N okhwnh dhktot|os cenvenv ~sc cttn znv|dsin lc dnezh kh tcvon h ci|vhk hs h kcs|vokh -n znv|c ghveni ln|chvon ct| nzvctck|nln kh Nzklodc F/) ent sen khwn znv|dsin dhe enttn ck|vc >


10/32

3+< Ethkt dheh znv|dsint lc dnezh ksdicnv >3?

fstdn ln znv|dsin kht vnoht dteodht=

+N fstdn lh ethk lc _sbnqn |cveokhs ce >?4U lctdhfvovne) ce cesitct c}zht|nt kh ehk|c Dmndni|nyn) kn Fhiwon)|vnht dhe cwolkdont ln zvctckn lh ethk -hs zhk) dheh gho fn|opnlh h ethk lc_sbnqn/) |cklh n enttn ct|oenln ce ed6 >3: EcW(d6) wc`n h dnz|sih >+ N znv|ovlnt hftcvwnh lnt cesitct nttcwcvhs%tc ~sc h ethk ~sc cvn |nefe dmnenlhethk zctnlh lcdnn ce hs|vn znv|dsin -se ethk icwc/) ~sc gho olck|odnln dhehh ethk ) h ecteh ~sc ghvn lctdhfcv|h ce >?41+ Enot |nvlc) dhkt|n|hs%tc ~sc ct|ckh cvn se ethk) ent sen znv|dsin ciceck|nv c zntths n tcv dmnenln toezicteck|cehk c kh enot ethk + N lot|okasofoiolnlc lnt lsnt znv|dsint gho eso|h oezhv|nk|c

zhv |cv zcveo|olh sen ok|cvzvc|nh enot hvlcknln c dhezvccktwci lht eso|ht lnlhtc}zcvoeck|not ~sc mnwone tolh zvhlspolht2 ot|h nfvos sen khwn zaokn kn okwct|oanhlnt znv|dsint tsfn|eodnt+ Ce >?


11/32

>7: Dnz|sih 3+ N ghvn ksdicnv

lot|kdon zcvdhvvoln

V 5 d| 5{

ed5

c6

-c6({d/ ed65

>?1) 4

e RE cWUg e+

Nttoe) znvn ghvnt ksdicnvct lc nidnkdc lc > g e n enttn ln znv|dsin ~sc ok|cveclonn ok|cvnh e >?1) 4 EcW(d6+ \ni zvhdctth ce ~sc hdhvvc n wohinh ln dhktcv%wnh ln ckcvaon ce se dsv|h zcvhlh lc |cezh dmnenlh wov|snic nt znv|dsint thdmnenlnt znv|dsint wov|snot -cefhvn ct|c`ne zvctck|ct kh ghvenioteh) cint kh zh%lce tcv lc|cd|nlnt c}zcvoeck|nieck|c/+ Lop%tc ~sc ht ethkt hs zhkt dnvvcane nghvn ksdicnv+

H ethk lc eckhv enttn lc vczhsth vctzhktwci zcin ghvn ksdicnv lc enohvnidnkdc -> n >) 3 g e/ lh zh|ckdoni kdichk%kdichk2 kct|c dnth) n ok|cvnh hdhvvc dhe

n |vhdn lc se kodh ethk+ Dheh n ok|cvnh ksdicnv tc l ck|vc ht znvct zz) kz) zk ckk) dhkdiso%tc ~sc lcwc mnwcv |vt |ozht lc zhkt dhe dnvant ci|vodnt) ">) : c >) ~scth ") :) + Tsnt zvhzvoclnlct ghvne eclolnt c wcvodhs%tc ~sc cict |e tzok :)

znvolnlc ok|vktcdn kcan|own c enttnt e 5 >4?) 7 E cW c e: 5 >43) : EcW+ Htethkt " c th se n nk|znv|odsin lh hs|vh2 nttoe) kh m tck|olh ce lopcv ~snilcict en|von c ~sni nk|oen|von+ Zhv tsn wcp h ethk : kh zhttso ctzcdodneck|csen nk|oznv|dsin) zhv cic tcv tsn zvzvon nk|oznv|dsin+

N c}zvctth znvn n ckcvaon zh|ckdoni lc ok|cvnh kdichk%kdichk lclspoln zhv_sbnqn

WKK -v/ 5 a6 cv

v) -3+?/

hklc v 5 yv> v6y n lot|kdon ck|vc ht kdichkt) h znvec|vh lc dnvan ksdicnv a |ceznzci tcecimnk|c nh ln dnvan ci|vodn c kh cic|vhenakc|oteh) c > h nidnkdc ln ghvn+

H wnihv lc a6zhlc tcv ct|oenlh n znv|ov ln ckcvaon lc ioanh c}zcvoeck|ni lh ls|cvhk)Cl ! 6) 64 EcW) tcklh ln hvlce lc >:: EcW ge+ Ln w%tc ~sc a6(c6 1:) h~sc eht|vn ~sc n ghvn ksdicnv eso|h enot ghv|c ~sc n ghvn dhsihefonkn) c sen enttnlc nzvh}oenlneck|c > ! >) < g e+ ok|cvcttnk|c kh|nv ~sc h nidnkdc ln ghvn okwcvtneck|c zvhzhvdohkni enttn lcvczhsth ln znv|dsin lc dnezh2 kh dnth ln ghvn cic|vhenak|odn) h g|hk |ce enttnksin) h ~sc dhvvhfhvn h nidnkdc okko|h ln ghvn+

Ce >?3>) h gtodh E+ \nbc|nko c tcst dhinfhvnlhvct R>3U zvhzstcvne sen ok|cv%nh cgc|own ck|vc kdichkt znvn lot|kdont ndoen lc 6) > g e) ~sc dhs dhkmcdolndheh HZCZ -hkc%zohk%c}dmnkac%zh|ck|oni/) ~snklh hdhvvc |vhdn lc se zhk nzcknt)ds`n ghven

W-v/ 5>

4 a6e

6E

6 ed6

> 6

&> 6 " T>6

> "

4

v "4

-v/6.$ cv

v +

-3+>:/^snk|h lczcklkdon ctzndoni kct|n c}zvctth) kh|n%tc ~sc ct|h zvctck|ct |cveht dhec}zhck|ct kcan|owht lc v) n lot|kdon ck|vc ht kdichkt) nttoe dheh se zh|ckdoni lh |ozhlc _sbnqn cv(v) ~sc tc gnp zvctck|c dheh se gn|hv esi|oziodnklh |hln n c}zvctth+



12/32

3+< Ethkt dheh znv|dsint lc dnezh ksdicnv >7>

Nie lotth) m sen lczcklkdon lc |vhdn lc tzok > 6) lc |vhdn lc othtzok > 6 c se gn|hv |ckthvoni T>6+ Ht znvec|vht gckheckhiaodht ~sc ct|h zvctck|ct th0n enttn lh zhk e) h nidnkdc eloh ln ghvn >) n vnph ck|vc n enttn lh zhkc lh kdichk e(E) nttoe dheh n dhkt|nk|c lc dnvan ksdicnv a+ Ht wnihvct enotdheseck|c stnlht th 5 >) g e c a6 -e(6E/

6 5 :) :=: :) ::6) ~sc h wnihv~sc ecimhv vczvhlsp nt tcct lc dmh~sc lc ctznimneck|h z z c z k znvn ckcvaontkh VDE ck|vc 6>1 c 43: E cW+ Znvn lot|kdont ok|cveclovont) > ge 9 v 9 6 g e) nghven lh zh|ckdoni gho ct|oenln n znv|ov ln |chvon lc zcv|svfnh) n| |cveht lc ~snv|nhvlce) hklc dheznvcdce |cveht lc |vhdn lc lhot ethkt+ Goknieck|c) znvn lot|kdontnfno}h lc > g e) ht zvhzhkck|ct dhktolcvnvne se zh|ckdoni gckheckhiaodh+

Wneht nahvn dhktolcvnv dcv|ht |ozht lc avdht) dheh n~scict eht|vnlht kn Goasvn3+>) znvn hf|cv sen &wotsniopnh&lht zvhdcttht lc ok|cvnh+ Cict ghvne ok|vhlspolht

zhvVodmnvl Z+ Gcykenk R>7U kn cic|vhlokeodn ~sk|odn znvn vczvctck|nv zvhdctthtlc ok|cvnh ck|vc znv|dsint cic|vodneck|c dnvvcanlnt c h dnezh cic|vhenak|odh) ~schdhvvce dhe n |vhdn lc g|hkt c n zvhlsh lc znv|dsint tsfn|eodnt) dheh se znvci|vhk%zto|vhk+ Zcin tsn dhkwckokdon lc hvlce zv|odn znvn n vcniopnh lc didsiht)cttct avdht |hvknvne%tc lc sth dhvvo~scovh znvn n lctdvoh lc zvhdcttht kn |chvonlc znv|dsint ciceck|nvct c tsfksdicnvct) c |nefe ghvne nlnz|nlht znvn n gtodn lceso|ht dhvzht) |nk|h ce |chvont ln en|von dhklcktnln dheh ce Gtodn Ksdicnv+

T|vod|s tckts) kht avdht ln Goasvn 3+> nt iokmnt dmcont) nt |vndc`nlnt c ht wv|odct|e sen dhk|vnznv|oln en|ce|odn fce lckoln+ Lc ghven acvni) dnln avdh vczvc%tck|n se |cveh ln c}znkth lc sen nezio|slc lc sen zvhfnfoiolnlc lc |vnktoh) cehvlce dvctdck|c ln -ce/ tvoc zcv|svfn|own) ln ok|cvnh KK |cklh zhkt nt znv|dsintlc dnezh+ Dhk|slh) ovceht dhktolcvnv ht avdht lc ehlh in|s tckts) ds`n nzvctck%|nh n~so |ce h ok|so|h lc ghvkcdcv sen woth zod|vodn c ~snio|n|own lh zvhdctth lc

ok|cvnh+ Dnln iokmn dmcon vczvctck|n se kdichk) ~sc zhlcvneht ok|cvzvc|nv dhehsen |vn`c|von kn wnvoclnlc ctznh%|cezh) dnln zhk|h ln iokmn vczvctck|n n zhtoh lhecteh ce se lnlh |cezh2 nt tc|nt knt iokmnt oklodne n zvhavctth |cezhvni) lh znt%tnlh znvn h gs|svh) h eheck|h okodoni ln cwhish ct| to|snlh ct~scvln c h kni lo%vco|n+ Sen iokmn |vndc`nln vczvctck|n se ethk) ~sc |vhdnlh ck|vc lhot kdichkt+ Zhvc}cezih) kh zvoecovh avdh) icklh ln ct~scvln znvn n lovco|n kh tck|olh lc zvhavctthlh |cezh) nt iokmnt -n/ c -f/ vczvctck|ne lhot ks|vhkt ~sc ok|cvnace won ghvn ksdicnv)h ks|vhk n lcdno ceo|oklh se ethk :) zhve) tce lco}nv lc tcv se ks|vhk) se|cezh lczhot h ks|vhk f nfthvwc h :) c |nefe dhk|oksn dheh ks|vhk+ Ck|vc|nk|h)

zcin nkiotc lnt |vn`c|vont tcv oezhttwci ct|nfcicdcv ~sce ~sce nzt n ok|cvnh)zhv tcvce ht ks|vhkt znv|dsint olk|odnt+ Znvn ht hs|vht avdht wnic n ecten ok%|cvzvc|nh2 nt iokmnt dmcont -n/) -d/) -c/ c -a/ vczvctck|ne zvhdcttht lc lcdnoeck|h lc

se kdichk -k hs z/ dhe ceotth lc sen znv|dsin lc dnezh) ck~snk|h ~sc nt iokmnt-f/) -l/) -g/ c -m/ vczvctck|ne zvhdcttht lc nfthvh lc sen znv|dsin lc dnezh zhv sekdichk+ Kh|c ~sc kht zvhdcttht ~sc ckwhiwce n ok|cvnh z k c k z) ht ethkt|vhdnlht |e dnvan ci|vodn+

Ht zhttwcot lcdnoeck|ht) vczvctck|nlhtzciht wv|odct) ct|h nzvctck|nlht kn \nfcin4+>+ Kh|c%tc n nstkdon lht zvhdcttht " k } c " " z y) ~sc) lc gn|h) kh



14/32

3+3 Kn|svcpn lnt ghvnt tsfksdicnvct >74

3+3 Kn|svcpn lnt ghvnt tsfksdicnvctSen avnklc ~snk|olnlc lc znv|dsint dhe |cezh lc woln%elon eso|h dsv|h) dheznv%n|owneck|c nh |cezh lc woln%elon lh ks|vhk iowvc?) ghvne lctdhfcv|nt n znv|ov lnldnln lc >?3: ce c}zcvoeck|ht gco|ht ce infhvn|voh dhe ndcicvnlhvct lc znv|ds%int) ckwhiwcklh ckcvaont dnln wcp enot ni|nt) c |nefe n znv|ov lh ct|slh lc vnohtdteodht+ Dheh ghvn wcvodnlh ~sc ht kdichkt |e ct|vs|svn) o+c+) kh th zhk|s%not>:) |hvkhs%tc oezcvn|owh c}ziodnv n ghvenh c dhkt|o|soh lnt znv|dsint ~sc tc vcw%cinwne kht c}zcvoeck|ht+ Mnwon n kcdcttolnlc iaodn -dhktolcvnklh%tc ~sc n kn|svcpnlcwn tcv znvdoehkohtn kn wnvoclnlc lc znv|dsint/ lc ckdhk|vnv sen |chvon kn ~sni sent

zhsdnt znv|dsint -ecteh kh hftcvwnlnt lovc|neck|c/ tcvone vcnieck|c ciceck|nvct)dhe zvhzvoclnlct fce lc|cveoknlnt) c ~sc tc dhkt|o|sovone kht fihdht gsklneck|notkcdcttvoht znvn dhezhv nt lcenot znv|dsint lc|cd|nlnt+

Cttn zvhdsvn icwhs nh ehlcih n|snieck|c woack|c kn gtodn lc znv|dsint c dne%zht) ~sc h dmnenlh Ehlcih Znlvh -T|nklnvl Ehlci/) kh ~sni dhc}ot|ce nt |vtok|cvnct) n ghv|c) n gvndn c n cic|vhenak|odn) cefhvn n gvndn c n cic|vhenak|odn tcsko~sce kn dmnenln ghvn cic|vhgvndn) ~snklh nt ckcvaont dok|odnt lnt znv|dsintckwhiwolnt th eso|h ni|nt -LNV NIASE WNIHV ZNVN CGCO\HDHEZNVN\OWH/+ N ckcvaont dok|odnt enot fno}nt -dheh kn Gtodn Ksdicnv/n ghvn gvndn vctzhktwci zcih lcdnoeck|h c n cic|vhenak|odn tc logcvckdone+

Kh Ehlcih Znlvh |hlht ht mlvhkt dn|cahvon lc znv|dsint ~sni zcv|ckdce ht k%dichkt c ht ethkt th ct|nlht ioanlht lc znv|dsint ciceck|nvct dmnenlnt ~snvbt

~sc th ht fihdht gsklneck|not ) c nt ok|cvnct ghv|c) gvndn cic|vhenak|odn n|sneck|vc cict+ Ht ethkt ~sc woeht tcvce znv|odsint lc dnezh ln ghvn ksdicnv n ck%cvaont ok|cveclovont th ct|nlht ioanlht dhezht|ht lc se ~snvb c lc se nk|o~snvb)

ck~snk|h ~sc ht fvohkt -zv|hk) ks|vhk c hs|vnt znv|dsint lc enttnt enohvct/ thdhkt|o|slht lc |vt ~snvbt+ Ht ~snvbt |e tzok >(6 c hfclcdce zhv|nk|h ct|n|t%|odn gcveokodn+ Nt znv|dsint lc dnezh ln ghvn ghv|c th ht aihkt -~sc |e znzcitcecimnk|c ~scic lht g|hkt kn ok|cvnh cic|vhenak|odn/) ht ~snvbt ok|cvnace ck%|vc to |vhdnklh aihkt2 ct|ct |e tzok >) hfclcdce zhv|nk|h ct|n|t|odn fhtkodn c |eenttn ksin+ Ck|vc|nk|h) logcvck|ceck|c lh cic|vhenakc|oteh ~sc sen ghvn lc ihkahnidnkdc c ht g|hkt |e enttn ksin) n ok|cvnh ghv|c |ce dsv|h nidnkdc ecteh dhk|nklhdhe znv|dsint lc dnezh lc enttn ksin+ Znvn c}ziodnv cttn dhk|vnloh) okwck|hs%tc seecdnkoteh dhkmcdolh zcih khec lc dhkkneck|h) cic tcvon h vctzhktwci zhv oezclov~sc ~snvbt c aihkt tc |hvkce znv|dsint iowvct+

Kh zvctck|c ct|aoh lh ehlcih znlvh nleo|oln n c}ot|kdon lc >= |ozht lc ~snvbtc) hfwoneck|c) >= nk|o~snvbt) zhot kcdcttvoh c}ziodnv n c}ot|kdon lc nk|oen|von+ Cictth dinttodnlht zcih kecvh ~sk|odh dmnenlh tnfhv-ce kecvh lc tcot/ c zcih wnihv

?Lh zhk|h lc wot|n zv|odh) h ci|vhk c h zv|hk th dhktolcvnlnt znv|dsint ct|wcot ~sc kh lcdnce)cefhvn n ct|oen|own znvn h zv|hk tcasklh h ehlcih woack|c ~sc tcs |cezh lc woln%elon tcvon tszcvohvn >:6? nkht2 ` znvn h ks|vhk cic lc ==7 t+

>:C}zcvokdont dhe ctznimneck|h lc ci|vhkt eht|vnvne ~sc h vnoh eloh ln lot|vofsoh lc dnvan ci|vodnlh zv|hk ln hvlce lc :) = g e2 |nefe wcvodhs%tc kh ks|vhk n c}ot|kdon lc sen lot|vofsoh lc dnvanci|vodn zhto|own dck|vni) dhezcktnln zhv sen dnvan ci|vodn kcan|own lot|vofsln enot c}|cvkneck|c+



15/32


lc se hs|vh |ozh ctzcdoni lc dnvan -nie ln dhsihefonkn/ ~sc cict dnvvcane) dmnenlndhv -ce kecvh lc |vt logcvck|ct/) ~sc vctzhktwci zcin ghvn ~sc ht enk|e dh%ctht+ Ht ~snvbt |nefe zhv|ne gvnct ln dnvan ci|vodn gsklneck|ni c) ~sc zhlce tcv"6(4 c hs >(4 c+ Ht ~snvbt th dinttodnlht ce |vt gneiont hs acvnct) dnln sendhkt|o|sln lc se znv0 n zvoecovn acvnh -s) l/) n tcaskln -t) d/ c n |cvdcovn -f) |/) dheenttnt dvctdck|ct2 ht nk|o~snvbt th lckh|nlht dhe sen fnvvn thfvc n ic|vn ~sc ht toe%

fhiopn -s) l/) -t) d/) -f) |/ c nt dnvant ci|vodnt zhv|nlnt |e tokni hzht|h t lht ~snvbtdhvvctzhklck|ct+ Ht |vt logcvck|ct |ozht lc dnvan dhv th lckh|nlht f) a c v) znvn npsi-f) lc fisc/) wcvlc -a) lc avcck/ c wcvecimh -v) lc vcl/+ Nttoe dheh n dnvan ci|vodnkcan|own zhlc tcv ck|ckloln dheh n nk|odnvan ln dnvan zhto|own) |nefe c}ot|ce ntnk|odhvct) ~sc th nt dnvant lc dhv zhv|nlnt zciht nk|o~snvbt c th lckh|nlnt f) a c v+

^snk|h t znv|dsint lc dnezh ln ok|cvnh ghv|c) c}ot|ce ho|h |ozht lc aihkt) dnlnse dnvvcan lsnt skolnlct ln dnvan dhv0 sen dhv -d/ c sen nk|odhv -d/) c th vczvctck%|nlht ghvenieck|c zhv ct|nlht lc tszcvzhtoct lc zvhls|ht |ckthvonot ydo ydo2 enohvctlc|nimct th lnlht kh dnz|sih >(4/lcdno ce se ~snvbs -dnvan ci|vodn ^s 5 6(4/ ceo|oklh sen znv|dsin lc dnezh lnghvn gvndn) se fthk wc|hvoni Q ~sc) zhv tsn wcp) lcdno ce se znv lc iz|hkt c cc+ Kh|n%tc ~sc kh zvhdctth dhktcvwne%tc0 h kecvh fnvokodh) h kecvh icz|kodh cn dnvan ci|vodn+ Zhve) h tnfhv lht ~snvbt kh dhktcvwnlh) hs tc`n) n ghvn gvndn khdhktcvwn h tnfhv lht ~snvbt+ N ghvn gvndn |nefe tc enkogct|n kh lcdnoeck|h lc seethk) zhv c}cezih) h ~sc dhktot|c lc se ~snvbl c lc se nk|o~snvbs ) -~sc/lcdno ceo|oklh se fthk wc|hvoni Q ~sc) ce tcasoln) lcdno ce lhot iz|hkt0 h ehk c h nk|okcs|vokh + Ct|c zvhdctth zhlc tcv ecimhv ck|cklolh wotsniopnklh h avdhln Goasvn 3+


18/32

3+1 Nzklodc N0 Zh|ckdonot gckheckhiaodht >71

1+ Ce didsiht ce |chvon lc zcv|svfnh kn cic|vhlokeodn ~sk|odn) oklowolsni%eck|c ht dnezht lc ~snk|n ce lc|cveoknlh tsfzvhdctth kh ct|h ts`co|ht nht wkds%iht ln dhktcvwnh ln ckcvaon c lh eheck|se iokcnv -th ct|aoht ok|cveclovoht cevcnct lc znv|dsint tsfn|eodnt c ciceck|nvct/) cefhvn h zvhdctth dheh se |hlh|ckmn ~sc dhktcvwnv nefht+ Ct|c |ozh lc wohinh zcveo|olh zcin vcinh lc okdcv|cpnlc Mcotckfcva) ~sc nven ~sc n ckcvaon Czhlc dnv oklc|cveoknln ce sen gno}n Clsvnk|c se ok|cvwnih lc |cezh | C(u+ Ct|ct zvhdcttht th dmnenlht zvhdct%

tht wov|snot) tsnt zvhfnfoiolnlct lc hdhvvkdon lcwce tcv thenlht) dhk|vofsoklh nttoeznvn h zvhdctth vcni) ido|h+ Se c}cezih lc zvhdctth wov|sni n nko~soinh lh znvci|vhk%zto|vhk lnklh -znvn lnv/ hvoace n se g|hk+ N ckcvaon lh znv lcwc tcv

Ccc" 5 ~e6c

d< " d6z6

c

" ~e6c

d< " d6z6

c" )

ck~snk|h ~sc n ckcvaon lh g|hk C 5 zd+ Kh ck|nk|h) kh zhttwci |cv nefnt nc~snct

Ccc" 5 C c zc "zc" 5 z -3+>>/tn|otgco|nt) zhv dnstn ln enttn lc vczhsth lh ci|vhk -zto|vhk/+ Ot|h toakodn ~sc h g%|hk wov|sni t zhlc c}ot|ov dheh se ct|nlh ok|cveclovoh kh hftcvwnlh) c cic ndnfn tcokdhvzhvnklh nh -kh/ zvhdctth aihfni lc ok|cvnh+ Kh hft|nk|c) ct|c |ozh lc zvhdctthc " c" zhlc tcv hftcvwnlh -o+c+) vcni/ knt oeclonct lc se kdich ~sc zhttnnfthvwcv sen znv|c lh eheck|se c ln ckcvaon lh zvhdctth+ Tc h kdich ghv fce ent%towh) CK 5 Ed6) c tsn ckcvaon kh esln kh zvhdctth) cic zhlc nfthvwcv sen znv|c lheheck|se iokcnv c) zhv|nk|h) nt c~snct -3+>>/ th ctdvo|nt dheh

Ccc" 5 C) zc "zc" 5 z "zK+ -3+>6/

Vcthiwn nt C~t+ -3+>>/ c -3+>6/ c lotds|n ht vctsi|nlht+

=+ Znv|oklh ln C~+ -3+>7/ dmcasc ckcvaon -3+>1/ dhktolcvnklh se kdich lc miohvczvctck|nlh zhv se lc|cveoknk|c lc gskct lc hkln lc znv|dsint oklczcklck|ct+

3+1 Nzklodc N0 Zh|ckdonot gckheckhiaodht

3+1+> Zh|ckdoni lc Znvot

Kh okdoh ln ldnln lc >?1: R4U) se avszh lc gtodht gvnkdctct zvhzt sen c}zvctth

znvn se zh|ckdoni kdichk%kdichk gckheckhiaodh ~sc

dhs dhkmcdolh dheh h zh%|ckdoni lc Znvot dhk|cklh lowcvtht |cveht ds`ht dhcdock|ct ghvne dnidsinlht n znv|ovlc lnlht lc ctznimneck|h K c dsolnlhtneck|c ctdhimolht+ Ct|c zh|ckdoni ghon`st|nlh lc ghven n vczvhlspov lnlht c}zcvoeck|not lc dhiotct KK -n`st|nklh lctih%dneck|ht lc gntc n| eheck|se nkasinv` 5 7) dhfvoklh se ok|cvwnih ckcvaon vcin|ownn| 44: E cW c wcvodnklh zvhzvoclnlct lh ls|cvhk/ hf|olht icwnklh ce dhk|n n |vhdn



19/32


lc se zhk) lhot zhkt c lc se ethk + N zvokdzoh) h ehlcih zvhzht|h wnicvon znvnlot|kdont ok|cvksdickodnt v ' :) = g e -vcaoh lc ihkant c elont lot|kdont/) sen wcp~sc nfno}h lcttn lot|kdon) kn dmnenln vcaoh lc dsv|nt lot|kdont |nefe dhkmcdolndheh vcaoh lh dnvhh ) zvhdcttht tsf%mnlvkodht ckwhiwcklh ~snvbt c aihkt lcwc%vone tcv icwnlht ce dhk|n+ Kh hft|nk|c) ht zvhzhkck|ct lh zh|ckdoni lc Znvot lcvnesen lctdvoh gckheckhiaodn znvn n~scin vcaoh) dhktolcvnklh) znvn v 9 :) = g e) sewnihv dhkt|nk|c znvn h zh|ckdoni2 h zhk|h v 5 :) = g e se zhk|h tokasinv) hklc ntlsnt dsvwnt lh zh|ckdoni dhokdolce ce wnihv) ent kh ce tsn lcvownln+ H zh|ckdoni

zhttso sen zc~sckn lczcklkdon kn ckcvaon lc dhioth lht kdichkt+ Zhve) h zh|ck%doni gho znvnec|vopnlh znvn zhlcv tcv stnlh ce zvhficent lc eso|ht dhvzht) kh didsihlc zvhzvoclnlct ksdicnvct) dhkt|o|soklh%tc) lc ndhvlh dhe tcst ns|hvct) dheh h enottht|odnlh c zvcdoth zh|ckdoni ksdicnv cezvodh+ Ghvenieck|c cic c}zvctth dheh

W

v) z6

5 W>

v) z6

" W6

v) z6

> 6 " WIT-v/ I -> " 6/"W\ -v/ \ " WTH6 -v/ TH6 -3+>4/

znvn othtzok |h|ni \ 5 :) >2 ht zh|ckdonot W>

v) z 6

c W6

v) z 6

|e lczcklkdon dheh eheck|se iokcnv vcin|owh lht lhot kdichkt) ck~snk|h WIT-v/) W\ -v/ c WTH6 -v/ th

zh|ckdonot dck|vnot c I 5 i> " i6 h eheck|se nkasinv |h|ni lht lhot kdichkt+ Ce-3+>4/ h zvoecovh |cveh oklczcklc lh tzok lht kdichkt) h tcasklh lcwolh ok|cvnh

tzok%tzok) h |cvdcovh lcwolh ok|cvnhtzok%vfo|n ce nknihaon gtodn n|eodn) entkct|c dnth cic kh zvhwe ln ok|cvnh enak|odn) ent tcvon lcwolh ok|cvnh ghv|c )h ~snv|h h |cveh |ckthvoni dhe

\ 5 4> v 6 v(v6

> 6

c h ~sok|h vczvctck|n sen ok|cvnh tzok%vfo|n ~snlv|odn)

TH6 5

> I 6 I " 6 I > I

(6+

Znvn h ct|nlh tokaic|h) T 5 :) dhe \ 5 >) nzcknt h |cveh W>

v) z 6

thfvcwowc+ Zhvlczcklcvce lh eheck|se iokcnv nt gskct W

v) z 6

th lo|nt tcvce lczcklck|ct

ln wcihdolnlc)

W

v) z 6

5 Wn -v/ "z 6

e\Wf -v/ " Wd -v/

z 6

e\)

hklc e\ nzvh}oenlneck|c n enttn lh zv|hk) ~sc lczcklc lh othtzok \ -e: 5?4=) ?:33 EcW(d6) e> 5 ?4=) 63?6 EcW(d6/+ \hlnt nt gskct Wb -v/ dhk|e thentlc |cveht dhegskct lh |ozh lh zh|ckdoni lc _sbnqn -3+?/) dhe ei|oziht znvec|vht+

Knt Goasvnt 3+3 n 3+? zhlceht wcv niasent dsvwnt vczvctck|n|ownt lh zh|ckdoni+ C}dc|h

znvn n ok|cvnh |ckthvoni -Goasvn 3+=/ nt dsvwnt eht|vne se ghv|c dvctdoeck|h ln ok%|cktolnlc lh zh|ckdoni ce |hvkh lc :) 3 g e) h ~sc vctsi|nlh ln zvctckn lh dnvhhksdicnv+

Kn io|cvn|svn ckdhk|vne%tc hs|vht zh|ckdonot dheh) zhv c}cezih h dmnenlh zh|ck%doni lc Fhkk R8U) ~sc th stnlht znvn h didsih lc zvhzvoclnlct ksdicnvct) ent ~sc khtcvh lotds|olht n~so+



20/32

3+1 Nzklodc N0 Zh|ckdonot gckheckhiaodht >7?

Goasvn 3+30 Zh|ckdoni lc Znvot) dhezhkck|c dck|vni) \ 5 >+

3+1+6 Ghvn lc |vt dhvzht

Znvn se tot|cen lc N kdichkt) h didsih lc zvhzvoclnlct ksdicnvct dhe lc ghvnt lc|vt dhvzht sen |nvcgn enot vlsn lh ~sc dhe ghvnt lc lhot dhvzht) ecteh stnklhe|hlht lc didsih dhezs|ndohkni+ Ck|vc|nk|h) gho dhkt|n|nlh ~sc znvn kdicht ~sc |e

se ecteh kecvh znv lc zv|hkt c ks|vhkt) dcv|ht zh|ckdonot lc |vt dhvzht) kn ghvenznv|odsinv lc se zvhls|h lc lsnt gskct lh |ozh lci|n lc Lovnd>>) tc vclspce n sezh|ckdoni lc lhot dhvzht dhe lczcklkdon kn lcktolnlc ksdicnv+ \ni zvhzht|n znvn hzh|ckdoni ksdicnv gho gco|n ce >?37 zhv\+ M+ V+ Tbyvec R " }:Z

-v/ ">

6|>m

-v/ b 6 " b6-v/o

" |6b -v/ b

"oQ: -> " 6/ b -v/ b) -3+> b6

(6 5 -> 6/ (6o h hz%

cvnlhv lc eheck|se vcin|owh c Z h hzcvnlhv lc |vhdn lc tzok+ Zhv dnstn lnt lot%>>N ghvn dmnenln lc dhk|n|h) zhot G -v v:/ 5 -v v:/ 5 "

vv:yvv:y

-yv v:y/) hklc -}/ n gskh lc Mcnwytolc0

-}/ 5

> znvn } ; :: znvn } 9 :+



21/32

>1: Dnz|sih 3+ N ghvn ksdicnv

Goasvn 3+70 Zh|ckdoni lc Znvot) dhezhkck|c dck|vni) \ 5 :+

|vofsoct lci|n lc Lovnd>6 esi|oziodnlnt zciht hzcvnlhvct ) n c}zvctth -3+>) v6) v4/ 5 |4-v> v6/ -v6 v4/ -3+>3/

c ht wnihvct lht znvec|vht lcwce tcv n`st|nlht lc ghven ~sc tc`ne vczvhlspolnt zvh%zvoclnlct lc niaskt kdicht |not dheh nt ckcvaont lc ioanh lc dcv|ht ksdilcht ~scnzvctck|ne dnenlnt gcdmnlnt ce Pc K) ht vnoht ksdicnvct) c|d+ N ||sih oist|vn|owh nz%vctck|neht kn \nfcin 3+> dhk`sk|ht lc znvec|vht tcasklh logcvck|ct ns|hvct R3) 7) 1U+

>6Ce tsn ghven |voloecktohkni)

-v v:/ 5 -} }:/ -y y:/ -p p:/ )

dnln gn|hv sen gskh lci|n lc Lovnd2 ck|vc|nk|h) -} }:/ kh zvhzvoneck|c sen gskh kh tck|olh|vnlodohkni) cin zhttso tck|olh nzcknt ce se dhk|c}|h enot nezih) dheh gskh ackcvniopnln+ Znvn sthzv|odh) cin zhttso h tcasok|c toakodnlh0 ksin znvn } 75 }: c |ce wnihv oklckolh ce } 5 }:) n|vofso%tctoefhiodneck|c + Ck|vc|nk|h) n lcvownln lc -} }:/ ce vcinh n } sen sen gskh vcasinv) c}dc|hkh zhk|h } 5 }: hklc cin tokasinv+ Ok|cavnklh dhe sen gskh vcasinvg-}/) h vctsi|nlh

Uf

n

-} }:/ g-}/ l} 5

g -}:/ znvn }: -n) f/: hs|vhttoe

l%imc se toakodnlh enot znizwci +



22/32

3+1 Nzklodc N0 Zh|ckdonot gckheckhiaodht >1>

Goasvn 3+10 Zh|ckdoni lc Znvot) dhezhkck|c lc tzok%vfo|n) T 5 >+

Kh|c ~sc nzctnv lc |cvce tolh stnlnt zvhzvoclnlct logcvck|ct) ht znvec|vht |henewnihvct ~sc) n avhtth ehlh) th ln ecten hvlce lc enako|slc+

Tbyvec WF%O WF%OO HE

|:

> :16 > :31) 4 > >7?) ? > >>3) 3|> 643) ? 3=3) 7 4> >:7) 1|4 = :61 >< ) > >< ??6) =Q: :) 37 :) 4< :) =: >6: >:3 7=) >

\nfcin 3+> ^sn|vh dhk`sk|ht lc znvec|vht znvn h zh|ckdoni -3+>3/) ctdhimolht znvnn`st|nv niaskt lnlht c}zcvoeck|not+ Ht dhk`sk|ht lc wnihvct logcvce ck|vc to zhv~sc ghvne ctdhi%molht logcvck|ct lnlht c}zcvoeck|not+ Ht didsiht lht Tbyvec) WF%O) WF%OO c HE th ckdhk|vn%lht knt vcgcvkdont ++++++++++++++++

Znvn kdicht K 5 P 5 znv) kh ehlcih lc znv|dsin oklczcklck|c) n ghvn lc |vtdhvzht -3+>3/ c~sownick|c n sen ghvn lc lhot dhvzht) |ozh lci|n lc Lovnd) esi|oziodnln

zcin lcktolnlc kh dck|vh lc enttn lht lhot kdichkt)

W4 -v>) v6) / 5>

7|4 -> " Z/ -v> v6/

v> " v6

6

+ -3+>7/

Zhv|nk|h) h zh|ckdoni -3+>3/ tc toeziodn) |hvknklh%tc se zh|ckdoni lczcklck|c ln lck%tolnlc+ Stnklh n ok|cvnh -3+>3/ hs n -3+>7/ znvn h didsih ln dhk|vofsoh ln ok|cvnh



23/32


Goasvn 3+=0 Zh|ckdoni lc Znvot) dhezhkck|c |ckthvoni) T 5 >+

lc |vt dhvzht znvn n ckcvaon |h|ni lc se kdich dhe K 5 P 5 znv) cttn tc c}zvcttndheh sen ok|cavni ckwhiwcklh h zvhls|h lc |vt gskct lcktolnlc)

C4 5|41/

hklc z -v/ c k -v/ th nt lcktolnlct lc zv|hkt c ks|vhkt) vctzcd|owneck|c

z)k -v/ 5hd]

-)et/

z)ket -v/

6+

N lcktolnlc |h|ni n then lnt lcktolnlct lc zv|hkt c ks|vhkt) -v/ 5 z -v/"k -v/)c z)ket -v/ n gskh lc hkln lc se kodh zv|hk hs lc se ks|vhk) dnidsinln n znv|ovlc se zvhficen lc eso|ht dhvzht) dheh) zhv c}cezih) h ehlcih lc dnenlnt hs zhvniase e|hlh ns|hdhktot|ck|c+

3+= Nzklodc F0 \chvon ln ghvn ksdicnv lc _sbnqn

N |chvon lc |vhdn lc ethkt znvn c}ziodnv n ok|cvnh ck|vc kdichkt gho zvhzht|n zhv_sbnqn c zsfiodnln ce >?43+ Tsn dvonh fntchs%tc kn |chvon ~sk|odn lh cic|vhena%kc|oteh) hklc nt znv|dsint lc dnezh th ht g|hkt+ Lct|n ghven) wneht eht|vnv dhehn nknihaon kht icwn ok|vhlsh lht ethkt dheh znv|dsint lc dnezh ln ghvn ksdicnv+

Lh cic|vhenakc|oteh vcdhvlceht ~sc h zh|ckdoni ctdninv lh dnezh -v) |/) kn zvc%tckn lc sen ghk|c lc dnvant ci|vodnt lc lcktolnlc -v) |/) hf|olh n znv|ov ln thish



27/32


h hzcvnlhv nl`sk|h lc

+ Ht hzcvnlhvct " c

th hzcvnlhvct lc othtzok ~scn|sne thfvc ht ct|nlht lc zv|hk c lc ks|vhk |vnktghvenklh se ks|vhk kse zv|hk cse zv|hk kse ks|vhk) vctzcd|owneck|c) dheh tcasc0

"k 5 :) "z 5 kk 5 z) z 5 :+

Nt gskct lc hkln znvn ks|vhkt c zv|hkt htdoine mnvehkodneck|c dhe h |cezh)k -v) |/ 5 sk -v/ c

oCk|({ c z -v) |/ 5 wz -v/ coCz|({) hklc Ck c Cz th nt ckcvaont

lh ks|vhk c lh zv|hk) vctzcd|owneck|c+ Dmnenklh n logcvckn ck|vc nt ckcvaont

Ck Cz

{5

-Ek Ez/ d6

{)

|ceht

z -v) |/ k -v) |/ 5 w

z -v/ sk -v/ co| c k -v) |/ z -v) |/ 5 s

k -v/ wz -v/ co|+

Ctdvcwcklh -v) |/ 5 S:-v/co| nt C~t+ -3+66/ c -3+6) v:/ 5

>

v:y

yv> v:y+

>?/ gho tsft|o|slh zhvo knt C~t+ -3+63/%-3+67/+



28/32


Ht zh|ckdonot ksdicnvct ~sc zvhlspce ht dnezht lc ethkt ht gn|hvct ck|vc znvk|c%tct knt ok|cavnot lc -3+61/ c -3+6=/ th ctdvo|ht dheh

Wkz-v>/ 5 a

v6y

yv> v6y -6/ -3+6?/

Wzk-v>/ 5

Wkz-v>/

5 a

v6y

yv> v6y" -6/ ) -3+4:/

ds`h wnihv kn zhtoh v> lcwolh zvctckn lc se ks|vhk hs lc se zv|hk kh zhk|hv6) vctzcd|owneck|c+

Ht zh|ckdonot -3+6?/ c -3+4:/ th ok|vhlspolht kn c~snh lc Tdmvlokacv>3 znvnvczvctck|nv n ok|cvnh ck|vc h zv|hk c h ks|vhk+ Nttoe) n ok|cvnh zv|hk%ks|vhk

zhlc tcv ctdvo|n dheh

Wzk -v>) v6/ 5 Wkz-v>/ " ->/ " Wzk-v>/ ->/

5 a

v6y

yv> v6y-" ->/ -6/ " ->/ " -6// ) -3+4>/

hklc h zvhls|h lovc|h lht hzcvnlhvct " ->/ -6/ n|sn thfvc se znv zv|hk%ks|vhk|vnktghvenklh%h ce se znv ks|vhk%zv|hk) wop+)

" ->/ -6/zk -v>) v6/ 5 kz -v>) v6/ )

ck~snk|h) zhv tsn wcp) h hzcvnlhv ->/ " -6/ cgc|sn n hzcvnh okwcvtn) |vnktghvense znv ks|vhk%zv|hk ce se znv zv|hk%ks|vhk+ Kh|c%tc n toec|von lh zh|ckdoniWzk -v>) v6/ 5 Wzk -v6) v>/+

N c~snh lc Tdmvlokacv zvhzht|n zhv _sbnqn znvn se znv zv|hk%ks|vhk ck|h->> >6

o{

|

"

{6

6

&> " 46Ek

6

.>

>6 " >>

> 46Ez

6

.6

$

&> " 4

6Ekd

6

.>

>6 " >>

> 4

6Ezd

6

.6

$

aWzk -v>) v6/h-k

z/ -v>) v62 |/ 5 :) -3+46/

hklc ht lhot |cveht lck|vh lht dhidmc|ct kn zvoecovn iokmn dhvvctzhklce nh hzcvnlhvckcvaon dok|odn) ht |cveht kn tcaskln iokmn dhvvctzhklce t ckcvaont ntthdonlnt tenttnt lc vczhsth lht kdichkt c h i|oeh |cveh h zh|ckdoni lc ok|cvnh -3+4>/+ > h hzcvnlhv skolnlc+

Zhlceht ck|h ctdvcwcv n C~+ -3+46/ dheh

o{

|-k

z/ -v>) v62 |/ 5 M->) 6/-k

z/ -v>) v62 |/ )

>3Kh|c%tc ~sc cefhvn nt znv|dsint lc dnezh lcdhvvce lc se didsih vcin|owt|odh -n c~snh lc Bicok%Ahvlhk/) ht kdichkt th |vn|nlht dheh znv|dsint kh%vcin|owt|odnt) ln stnv%tc n c~snh lc Tdmvlokacv+



29/32


hklc h hzcvnlhv mneoi|hkonkh

M->) 6/ 5 {6

6

&> " 4

6

6Ek

$>

>6 " >>

&> 4

6

6Ez

$6

.

"

> " 4

6Ekd

6

.>

>6 " >>

> 4

6Ezd

6

.6

a6cyv>v6y

yv> v6y-->/ " -6/ " " ->/ -6// + -3+44/

wot|h ~sc

a -S-v>/->/ " S-v>/"->// 5

5 a6cyv>v6y

yv> v6y-->/ " -6/ " " ->/ -6// +

Tszhklh%tc nahvn ~sc n gskh lc hkln lc se tot|cen ks|vhk%zv|hk tc`n lnghven

-kz/-v>) v62 |/ 5 -v>) v6) |/

k ->/ z -6/ " z ->/ k -6/

-3+4 " 4

6k

5 k

c> " 4

6z

5 :)

> 46

k 5 : c> 4

6z 5 z+

N nh lht hzcvnlhvct zvctck|ct kh hzcvnlhv mneoi|hkonkh thfvc h tzokhv -3+4> " 4 ->/

6Ek

6> >6

.-kz/

-v>) v62 |/ 5>

Ek

6> -v>) v6) |/

k ->/ z -6/ )

>>

>6 4 -6/

6Ez

66

.-kz/

-v>) v62 |/ 5>

Ez

66 -v>) v6) |/

k ->/ z -6/ )

c

-->/ " -6/ " " ->/ -6//

k ->/ z -6/ " z ->/ k -6/

5 -->/k ->//

" -6/ z -6/

" -"->/k ->//

-6/ z -6/

"

->/z ->/

-" -6/ k -6// "

"->/z ->/

- -6/ k -6//

5 z ->/ k -6/ " k ->/ z -6/ +



30/32

3+= Nzklodc F0 \chvon ln ghvn ksdicnv lc _sbnqn >1?

Zhv|nk|h h ct|nlh k ->/ z -6/"z ->/ k -6/ ns|h%ct|nlh lh hzcvnlhv->/" -6/"

" ->/-6/ dhe ns|hwnihv>+En|vodonieck|c

4 5

> :: >

c > 5

> :: >

)

-kh|c%tc ~sc ht hzcvnlhvct >) 4) " c ghvene se dhk`sk|h dhezic|h lc en|vopctkh ctznh lc loeckth 6 th c}n|neck|c nt en|vopct lc Znsio/+ Nziodnklh h hzcvnlhvmneoi|hkonkh -3+44/ kh tzokhv |ce%tc

M->) 6/-kz/-v6) v>2 |/ 5

{6

6

>

Ek

6> -v>) v6) |/ "

>

Ez

66 -v>) v6) |/

k ->/ z -6/ " -Ek " Ez/ d6 -v>) v6) |/ k ->/ z -6/

a6cyv>v6y

yv> v6y -v>) v6) |/

k ->/ z -6/ " z ->/ k -6/

)

c) dhktolcvnklh ht |cveht ~sc esi|oziodne k ->/ z -6/) n c~snh lc Tdmvlokacv|hvkn%tc

o{ -v>) v6) |/

|5

{6

6

>

Ek

6> "

>

Ez

66

" -Ek " Ek/ d6 -v>) v6) |/ a

6 cyv>v6y

yv> v6y -v>) v6) |/ +

Ctdvcwcklh n gskh lc hkln dheh

-v>) v6) |/ 5 -v>) v6/ coC|({o--Ek"Ek/d6/|({

dneht dhe sen c~snh oklczcklck|c lh |cezh znvn h tot|cen z k)

{6

6

>

Ek

6> "

>

Ez

66

" a6

cyv>v6y

yv> v6y

-v>) v6/ 5 C -v>) v6/ )

hklc C h ns|hwnihv lc ckcvaon+ Dheh h zh|ckdoni nzcknt lczcklc ln logcvcknyv> v6y) zhlceht ctdvcwcv n c~snh lc Tdmvlokacv tcznvnklh h ehwoeck|h lh dck%|vh lc enttn -DE/ c h vcin|owh -v/) dhe v 5 v> v6) V 5 -v> " v6/ (6 c -v>) v6/ 5

-v/

V

) zcih ~sc hf|ceht n tcznvnh ln c~snh lc Tdmvlokacv ce lsnt) sen

znvn n dhhvlcknln lc DE c hs|vn znvn n dhhvlcknln vcin|own)

{6

Ede

6VV 5 CdeV ) -3+43/

{6

ev

6v " a

6 cv

v

-v/ 5 Cv -v/ ) -3+47/

hklc

C 5 Cv " Cde2 ev 5EkEz

Ek " Ez2 Ede 5 Ez " Ek+



31/32

>=: Dnz|sih 3+ N ghvn ksdicnv

H dck|vh lc enttn lh tot|cen z k cwhiso iowvceck|c) C~+ -3+43/) ck~snk|h ~sc nc~snh lh ehwoeck|h vcin|owh dhk|e h zh|ckdoni ksdicnv) ~sc dck|vni) C~+ -3+47/+N ok|cktolnlc ln ok|cvnh kdichk%kdichk lczcklc ln dhkt|nk|c a -ce nknihaon dnvan ci|vodn c kh cic|vhenakc|oteh/0 Ck~snk|h n ckcvaon lc ok|cvnh lc lsnt dnvantci|vodnt lc toknot hzht|ht

Qce>6 5 c6

v)

kh dnth ln ok|cvnh ksdicnv ck|vc ht kdichkt |ce%tc

Qksd>6 5 a6 cv

v

dhe v 5 yv> v6y+ H wnihv lc a6 zhlc tcv ct|oenlh n znv|ov ln ckcvaon lc ioanh

c}zcvoeck|ni lh ls|cvhk) Cv 5 6) 64 E cW) c ln hvlce lc >:: EcW ge) ihaha6(c6 1:) h ~sc eht|vn ~sc n ghvn ksdicnv eso|h enot ghv|c ~sc n ghvn dhsihe%

fonkn+ H nidnkdc ln ghvn ksdicnv ln hvlce lc V 5 > 5 {(e}d) zhv|nk|h h ethkzvhzht|h zhv _sbnqn |cvon sen enttn ln hvlce lc e}d6 {d(V+ Ce >?3: EcW) h ~sc tsacvc se nidnkdc nzvh}%oenlh lc >) 4 g e znvn n ghvn ksdicnv+

3+? Fofiohavnn

R>U Fnv|ic|| @+ M+) >?47) Zmyt+ Vcw+


32/32

3+? Fofiohavnn >=>

R>:U Gcveo C+) >?47>+

R>>U \nee O+ c Oqnkckbh L+) >?46?) ?=>+

R>6U Nklcvthk D+ L+ c Kcllcvenycv T+ M+) >?41) Zmyt+ Vcw+ 3>) ==4U In||ct D+ A+ E+) Esovmcnl M+) Hddmonioko A+ Z+ T+ c Zhqcii D+ G+) >?3?) 7??:1) 61:+

R>3U \nbc|nko E+) Knbnesvn T+ c Tntnbo E+) >?3>) Zvhav) \mchv+ Zmyt+ 7) 3=>+

R>7U Gcykenk V+ Z+) >?

Física Nuclear e Partículas Subnucleares - Capítulo 5 – S. S. Mizrahi & D. Galetti

Documents

Transcript of Física Nuclear e Partículas Subnucleares - Capítulo 5 – S. S. Mizrahi & D. Galetti