Nuclear/Particle Physics

Transcription

1 Revsc Prce Dyncs: The Bsc de o Qunu Fed Theory n Prce Physcs: Progresson o seps n he heorec rewor up o now: Revsc Prces Drc eqn. = ½ K-G eqn. = 0 resus n posve nd negve energy souons Expnd Drc nd K-G sons. n qunu hronc oscor nor ode pudes ny prce proe prces n prces Drc se ec. Prces represened y qunu eds Phys 450 nro ucer Physcs

2 For now: Assue h neurons nd proons re he proper degrees o reedo nd h her nercons cn e odeed wh poens. Connue o use he Lppnn-chwnger nd/or he chrödnger equon o nd souons o he ound nd scerng ses. To do hs we need o nd ss n whch he reevn qunu echnc oserves hose h coue wh H cn e suneousy dgonzed nd consruc he wveuncons ro h. Le s coun he reevn oserves Phys 450 nro ucer Physcs

3 Proon euron p p z p p n n z n n L Pry s deerned y L. = p + n = p + n o J = L + J z = L z + z nd = p + n re he correc qunu nuers whch coue wh he honn Phys 450 nro ucer Physcs

4 04-0- Phys 450 nro ucer Physcs 4 For he snge nuceon se we hve wo posse ss o choose ro: Or The er res he neuron nd he proon s deren ses o snge prce he nuceon... 0 e n e p n p n p

5 04-0- Phys 450 nro ucer Physcs 5 For he snge nuceon se we hve wo posse ss o choose ro: Or The er res he neuron nd he proon s deren ses o snge prce he nuceon... 0 e n e p n p n p

6 The second ss w e useu here s n underyng syery h does no dsngush eween he neuron nd he proon. Ths s rue or he srong nercon u no he we or eecrognec nercons! Ths s reerred o s nvrnce under so-spn syery or he nucer / srong orce! Ths syery s sghy roen ecuse o he s ss derence eween he neuron nd he proon or h o he underyng up nd down qurs. or our purposes he oen we cn use: Phys 450 nro ucer Physcs 6

7 04-0- Phys 450 nro ucer Physcs 7 For n orhonor ss we us hve ong he nd es snce hose re xed: o we cn wre he snge nuceon wve uncon s: Wh ou or ngur oenu? r r r

8 Every prce hs n or ngur oenu L ssoced wh. Ler when we specy he wo nuceon se we w consder ony he reve L. Bu or now we w wre he snge nuceon wveuncon n pr wve ss whch speces s ngur oenu expcy: Bu ony he o or ngur oenu coues wh he honn wh qunu nuers ˆ J ˆ ˆ L s s Phys 450 nro ucer Physcs 8

9 o we wre or he wveuncon wh o ngur oenu: r r s To ge useu expresson one hs o expnd hs n soe poson ss e.g. spherc coordnes nd n ers o he uncouped ngur oenu ses Phys 450 nro ucer Physcs 9

10 Wh h we on he snge nuceon wve uncon: r 4 r Y s s s To nsh hs we woud hve o evue he Gesch-Gordon coecens sung over he spn ses nd he or ngur oen o neres nd specy whch prce we re deng wh neuron: = -½ or he proon: = ½ However hs s ree snge nuceon nd we wn o nvesge he properes o he wo nuceon nercon. o e s ove on o nd wveuncon h descres h syse Phys 450 nro ucer Physcs 0

11 The Two uceon Wveuncon: We specy he se n ers o couped o spn reve or ngur oenu L nd o ngur oenu J. Render: you oo up he spn-pry o gven nuceus you w nd noon o he or: J 0 ec... Where spn reers o o ngur oenu! Phys 450 nro ucer Physcs

12 04-0- Phys 450 nro ucer Physcs The Two uceon Wveuncon : o he wo nuceon se cn e copeey speced y: Where nd L J ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ J L s s s s s s s

13 04-0- Phys 450 nro ucer Physcs The Two uceon Wveuncon : The wo nuceon wve uncon s hn: wh s s J L J L L L r r Y r r u L r

14 yeres o he nercon: Exchnge syery or denc prces: uceons re erons nd we re reng he s denc ecuse o sospn syery. Honn us e syerc wr. prce exchnge e exchnge: Wveuncon us e n-syerc wr. prce exchnge e exchnge: L J r r r J L J L Phys 450 nro ucer Physcs 4

15 yeres o he nercon: Exchnge syery or denc prces: x x Bu nd he properes o he spherc hroncs under reecon re: Y rˆ Y Y Y r ˆ Then x L J L J x Wh ou he spn nd so-spn es under prce exchnge? Phys 450 nro ucer Physcs 5

16 yeres o he nercon: Exchnge syery or denc prces: we use he noon: We ge he r snge nd rped conons or wo prces: = Trpe: = 0 = - nge: = Phys 450 nro ucer Physcs 6

17 04-0- Phys 450 nro ucer Physcs 7 yeres o he nercon: Exchnge syery or denc prces: o he n syery o he wveuncon under prce exchnge depends on he spn nd so-spn se o he wo nuceon syse! o under prce exchnge we hve: r r J L J L

18 yeres o he nercon: Exchnge syery or denc prces: o he o wve uncon s: L J r r L J And we us hve: odd or he wveuncon vnshes! Phys 450 nro ucer Physcs 8

19 yeres o he nercon: For srong.e. here nucer s resdu srong nercons under pry he L even ers n he wve uncon do no x wh he L odd ers ecuse he wve uncon s n egense o pry: e.g. [H P]=0 nce he srong nercon does no voe pry! The honn s roony nvrn snce [HJ]=0. 4 The honn s chrge ndependen or sospn nvrn snce he srong nercon doesn depend on ; enng h [H]=0. The presence o he Couo nercon whch s no sospn nvrn doesn chnge hs snce ony cs n he pp se whch hs dene sopn coupng =! Phys 450 nro ucer Physcs 9

20 yeres o he nercon: ury so r: J J nd re good conserved qunu nuers nd he correspondng operors or x se o coung operors ogeher wh he honn. As usu we hve s s c s = 0 hen = we ge n uncouped pr wve. s = nd = nd we ge n uncouped pr wve snce cnno x wh he = ses y pry. s = nd = hen we ge couped pr wve nd L s no good qunu nuer Phys 450 nro ucer Physcs 0

21 yeres o he nercon: ury so r: We cn now essh s o owed wo nuceon ses. Usng he usu specroscopc noon: s wh = PDFGH... We hve: ee nex sde Phys 450 nro ucer Physcs

22 yeres o he nercon: ury so r: nge =0 = even pry 0 D G 4... =0 odd pry P F H 5... Trpe = =0 even pry - D D D - G G 4... = odd pry P 0 P P - F F... The Deueron ound se s oserved n he - D = 0 couped se! Phys 450 nro ucer Physcs

23 The nercon o he Drc uceon Fed wh cr eson Fed: The nercon nd he eson exchnge pcure: so-spn J pc ev ev * ev o ev ev ev ev K K 0 K 0 ½ 0-49 ev pseudo scr cr no physc vecor pseudo scr srnge And ny ore hgher energes Phys 450 nro ucer Physcs

24 The nercon o he Drc uceon Fed wh cr eson Fed: Ared wh he U grngn we now hve revsc descrpon o se o spn ½ prces nercng wh scr exchnge ed. We now ep o descre he nercon eween nuceons v exchnge esons usng: L g A We re ony neresed n he nercon er snce we re deng wh he nercon eween nuceons v eson exchnge no he ree oon o nuceons Phys 450 nro ucer Physcs 4

25 The nercon o he Drc uceon Fed wh cr eson Fed: nce here re no dervves he Honn densy s oned ro he energy-oenu ensor s H T 00 g 00 L g A We cn deny he eds A wh he pons u we hve o e ew dusens. There re hree proes o ddress:. As hey snd he A do no rnsor n we dened wy under so-spn roons.. Pons re pseudo-scrs nd wh we hve s our-vecor poen.. We so hve vecor nuceon curren rher hn scr or eer ye pseudo-scr curren Phys 450 nro ucer Physcs 5

26 The nercon o he Drc uceon Fed wh cr eson Fed: nce we re ng ou he srong nercon here we wn he Honn o e pry even operor whch s n vrn under so-spn roons. To cheve hs we us hve noher pseudo-scr pry odd operor or he nuceon whch cn coupe o he pseudo-scr pon operor. o we spy repce he Lorenz vecor wh Lorenz pseudo-scr honn: g H A g 5 To ge hs honn whou hvng o consruc s we dd here one woud hve o sr ro QCD whch s expcy pseudo-scr Phys 450 nro ucer Physcs 6

27 04-0- Phys 450 nro ucer Physcs 7 The guge eds A ge redened no soehng h rnsors we under so-spn: Fro: To: + - so dene A A A A A A A pn so 0 The nercon o he Drc uceon Fed wh cr eson Fed:

28 The nercon o he Drc uceon Fed wh cr eson Fed: We hen wre he honn s H g d x x x x 5 nd 0 0 Ths s he correc honn o descre he coupng nercon o pon nd nuceon Phys 450 nro ucer Physcs 8

29 The nercon nd eson Exchnge: o Exne We go c o ecure 6 noes nd sr ro here: The oowng sdes re en o oune he u ccuon presened n he noes. You re no expeced o ren ny o hs! s en o show you wh re ccuon n nucer physcs s e o show he seps nvoved n ndng he n poen or pon exchnge nd o prove h he Yuw poen cn e oned n hs wy Phys 450 nro ucer Physcs 9

30 The nercon nd eson Exchnge: o Exne Dervon o he one-pon exchnge poen n he nercon: o n order o descre he u nercon eween wo nuceons we need wo o hese pon-nuceon verces; one or esson nd one or sorpon: o we rec he second order er n he Lppnn-chwnger eqn: T nd T nd Hˆ H E E ˆ Phys 450 nro ucer Physcs 0

31 04-0- Phys 450 nro ucer Physcs Dervon o he one-pon exchnge poen n he nercon: For he n nd n wo nuceon ses we use he se or o he wve uncons we derved erer u now n oenu spce: We wor n ses o we dened o ngur oenu J o so-spn nd reve oenu eween he wo nuceon syse: We expnd he gener n nd n ses n ers o copee se o hronc oscor egenses usng creon nd nnhon operors see hronc oscor revew noes: W J J 0 odd s o Exne The nercon nd eson Exchnge:

32 04-0- Phys 450 nro ucer Physcs Expcy: x x e v e u E V x x x e v e u E V x Hronc Oscor prces nnor ode pudes: prces uons re resu ro n expnson n copee se o pne wve souons o he Drc equon hs s Fourer rnsor ro oenu o poson represenon. o Exne The nercon nd eson Exchnge:

33 04-0- Phys 450 nro ucer Physcs e Concep or he K-G ouons chrged osonc prce: q x q q x q q q e c e c V x * q x q q x q q q e c e c V x Hronc Oscor prces nnor ode pudes: prces Chrged osons re uu n-prces! o Exne The nercon nd eson Exchnge:

34 The nercon nd eson Exchnge: o Exne Prce creon nd nnhon: c q c q Crees prce +. Desroys prce +. Crees n n-prce -. Desroys n n-prce -. Crees prce 0. Desroys prce Phys 450 nro ucer Physcs 4

35 04-0- Phys 450 nro ucer Physcs 5 Prce creon nd nnhon: The expnson coecens c c re qunzed operors wh zero nd posve negers s egenvues whch we nerpre s he nuer o prces n gven ode. They ssy he couon reons: o Exne The nercon nd eson Exchnge: c c c c c c 0

36 04-0- Phys 450 nro ucer Physcs 6 Dervon o he one-pon exchnge poen n he nercon : And he wve uncons re gven y ; W J L J J J L J L L J L J Y w W ; o Exne The nercon nd eson Exchnge:

37 04-0- Phys 450 nro ucer Physcs 7 Dervon o he one-pon exchnge poen n he nercon : The nerede ses so hve n ddon pon n he: wh 0 q q c 0 q c o Exne The nercon nd eson Exchnge:

38 04-0- Phys 450 nro ucer Physcs 8 Dervon o he one-pon exchnge poen n he nercon : Wh hese denons we go ro: To: where des n he noes nd E E T H H ˆ ˆ q nd q d d d T H H ˆ ˆ 9 q q o Exne The nercon nd eson Exchnge:

39 04-0- Phys 450 nro ucer Physcs 9 Dervon o he one-pon exchnge poen n he nercon : o we hve o oo he he rx eeens he wo verces! For he n verex: The n se hs wo nuceons nd he nerede se hs wo nuceons nd pon: ˆ ˆ 6 W d d H H g H g o Exne The nercon nd eson Exchnge:

40 04-0- Phys 450 nro ucer Physcs 40 Dervon o he one-pon exchnge poen n he nercon : For he n vercex: The n se hs wo nuceons nd he nerede se hs wo nuceons nd pon: W d d ˆ ˆ 6 H H g ˆ H g o Exne The nercon nd eson Exchnge:

41 04-0- Phys 450 nro ucer Physcs 4 Dervon o he one-pon exchnge poen n he nercon : o he o nercon s Where: Whch s n negr/su over nuceon degrees o reedo. g g q q nd g g q d d d T ] [ 9 ] [ * 6 6 W W d d d d o Exne The nercon nd eson Exchnge: