Positron/Electron Annihilation via the Two-Photon Pathway @ Copyright by

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Positron/ElAencntirhoinl ation
vitah e
Two-PhoPtaotnh way
by
IsabeGlaluet hier
A thessiusb mittiencd o nformwiittyth h er equirements
fort hed egreoefM asteorfS cience
DepartmeonfPt h ysics
LakeheUandi versity
@CopyriIghsabeltle G abuythier 2,0 11
Lakehead
UNIVERSITY
OFFICEO F GRADUATES TUDIES
NAME STUDENT:
OF IsabeGlaluet hier
DEGREEA WARDED: Sc.
M.
ACADEMIC UNIT: Physics
TITLE THESIS:P ositron/EAlnencithriolvnai ttaih Toewn o -Photon
OF
Pathway
Thitsh eshiass b eenp repared
undemry supervision
andt hec andidhaatsec omplied
witht heM aster's regulations.
SignatoufrS eu pervisor
Abstract
Whena positron/elpeaciatrnr noinh ilvaitate h et wo-phoptaotnh watyh,ee mittpehdo toanrse
momentucmo rrelaTtheidcs.o rrelaetnisounr tehsa tth emyo vea lonags trailgihntpe a tihn o pposite
directiAonn esx.p erimpeenrtf ormien2d 0 04b yD r.V .DI.r bmye asurtehdet imien terbveatlw een
detectoifot nh ep hotonHse. o bservaed de caiyn t hen umbeorf c ountwsi tihn creasdientge ction time
intervwahli,c hhe d escribed auL soirnegn tztihaenl ,i nwei dtohf w hicaht f ull-wihdatlhf -maxiimsu m
measurteodb e1 20psT.he d atcao llecbtyeI dr biys i nteresbteicnagu csuer retnhte orpyr editchtast
becautshee s ourciess ol ocali(ztehdee f fectsiovuer cwei dtuhs ebd yI rbiys s afewliyt hi5nrnrn ) the
photosnhso ulbded etectweidt hiant imien terovfa� lt =d/wch erde i st het hicknoefst sh es ourcTeh.i s
timien tercvoarlr espotno1d 7sp sT.h itsh esfiistt sh er esulttoas n e xponentainadsl h,o wtsh atth is
exponentidaelclayy innagt uorfet hec oincidetnicmeie n terivsac lh aracteroifts hteei nct anglemoefn t
thet wop hotonWse. f intdh atth ew avefunctoifot nhsep hotodnesc oherienss p acaec corditnohg o w
lontgh e parptaiicrl et toodo ekc a(yw hicihse xponentainaldt) h,at th ep robabiolfis tiym ultaneous
detectdieopne ndosnt hee xponentoifta hlep roduocftt hel ifetoifmp eo sitronainudtm h ed etection
timien terval.
TABLOEF C ONTENTS
Page
ACKNOWLEDGEMENTS
ii
LISOTFF IUGRES
iv
CHAPTER
1 INOTDRUCTION 1
2 THEl RYBE XPEMREINT 6
3 THED IRAECQ UATION 14
3.D1E RVAITI.ON. 14
3.P2L ANWAEV ES OULITONS 16
4 CHANGBIANSG.E S. . . .. . . . 31
5 THEYOO RFS PONNTEUAOSE MISSION 34
6 DIUSSCSI.O N. . . . 38
6.A1P LPICATION 42
6.F2U UTREEX PERITMIEONNT A 43
7 APPEND.I C.E S . . . . . . . . 4.6 . .
7.A1. P LANWAEV ES OULITON 46
7.B2. S IGMMAA TRICES 48
BIBLIOG.RA.P.HY. . .. . . . . 49
lll
LISOTFF IGURES
2.C1o incriadtevensSsc o eu procsei tTihsoehn o.r t-ldiarnseehp erde ­
senctosi ncdiedteenoctfta di eocnpa hyo twointe hi tahp ehro ton
frotmht eh ree-dpehcpoartyoo conert s htsew- ophodtceoapnyr ocess.
Thleo ng-ldiarnsehepe rdec soeinnttcd sie dteenocftt hipeoh no tons
creabtyte hde twoa-npnahitohitipoolrnno cTehsseso .ll iirdne ep ­
resetnottcsao li ncidnedteenccAtesit ohndees t.e acrtmeoo rvse d
farftrhotemhrs eo ucrocien,c diedteenectvt esian ortdneo minbayt ed
two-pahnontiohni[ .l6 a]t.i o.n . . . . . 9. . . . . . . . . . . .
22. PulHseehi tDg istrifbourMt iiaco rno ChanDneetle-cTPthloear t.e
solliidn e rtehpperu elhsseeein dgtihsst t rfiobmrui tdi-oen(n 1e rgy
kVe electTrhdoean sslh.ie rdne ep retshpeeun lhtsesei d gihst-t ribu
)
tifoon.r 5 M1e1Vp hot[o.6n ]s. . . . . . .1 1. . . . . . . . . . . . . . .
23. Finraels buylI trsb2 y0 0.4 Tdhaitisfias t w itaLh o rennf zutnica-
( )
tiownh,ear d eo uebxlpeo nle rnietsqi uatiodr eesdc prsoiibter onium
deyc.a. . . . . . . . . . . .1 2. . . . . . . . . . . . . . . . . . . . . . .
3.A1p osipt+raonnad n e lecpt-rmoonv iantlg os wp eaeraden ni­
( ) ()
hilaattx e1ad nx d2 A.v irptauratlmi ocvfleresoo mna en nihilation
lotciatoont hoet her, rbeyqp .Tr weops heonttooefknd 1as n kd2
flyo ffa lonlgi n.ae .. . . . . . . . 2.9 . . . . . . . . . . . . . . . . . .
IV
v
4.1A visualoiftz hcaeot mipoons oift thcieeo nnt eenre (roxgfacy n) d
rela(Xtr i)cv oeo rdiTnhabetl ebusoer.x e pretsheen tssTo huer ce.
krk,c ,a nPdca re conssitmri.ul catreldy 33
Pn
6.I1r brya'dwsa tsah,o wviranigof uusn cfittitsoi.Tnn hgdeo uebxlpeo ­
nenitsib aealt fittte otr h pee ak,t hteaan fidol lstl hoLewo rentzian
fitgt.iT nhset anddeavridoa ftt hideoo nu ebxlpeo nieasnp trioaxli ­
mat0e.ly4w 5i,tFh W HMo fa bo1u0ts3 .p. . . . . .4 1 . . . . . . . . .
6.2Ad iagirlalmu stthrdeae ttieoncfogt n ieo np maoimre noctfou rmr e­
latpehdo tons forrotimhgt eiw pnoha-otptioonsngi troann/neil­ectron
hilaptrioocInem sas(g.aei ) l lustthtria anPt EeTls,o caitnifoonr ma­
tiiodsni streiqbuuaatllelodtyn h Lge O .RI ma(gbei) l lustthtra ates
inT OFP ETs,o ulroccea itnifoonr imsa tliootcnoaa s leigzmoeefdn t
thLeO R[ 16. ].. . . . . . . . . .4 4 . . . . . . . . . . . . . . . . . . . .
CHAPTER 1
INOTDRUCTION
Quantum meficrhdsaitns ieccroasevs adsw oalsu tiporno btolofbe lmtashoc edk yb
ratdiiaonp,h otthoe- eeffleeaccntotd tr hipechr e nosmuecnhah oaawst oemmsi t
radioantliyo na te ndeirsIgctpirr eeostv.ei g doeoesdx pnala atoifao tno mic and
photonic ipnvh aecnuoaumnmwed in tath hifenr ameowfio nrtke rfaocrtcieosn.
Thidse scroifrp etaidlooincet osym wei tcohn cedpitffiutcaiuhlelo sw,ee rvA.r ising
ouotft hqeu anmteucmh adneisccarloi ftp htweio oranlr dte h ied eoafas c t-aito-n
ad-istnaonnc-el,ao ncedan ltiatnyg alleolmfw ehnistceh,et moo perianct oeu nter­
intiuvaient mdys tieorwuayss M.a ngyr esacti e(natlniodst tss ofo nmetesod,oi )o cre
havheag dr edaitffi cuilantc iceestp htqaiutna gn mteucmh amnaibyc ecs o mpilne te
itdse scroifrpe taialonintdt h yia ittrs e atlhitiat csyo nsfiung.
In tohfeti-rpc aipt"eeCrda Qnu antMuemc-haDneisccarloi fpP thiyosni cal
RealBiet yC onCsoimdpeelr?[ee"t1dE ]is ntePiond,o alnsRdko ys ceonn template
thied oefna o n-commoupteartapitefnirogor nmosena d ne ntansgylsetTdeh me.y
looaks yastt em daet swcpora iwrbatve uednf cbt\[!yi(x oixn2,) = L n1/J( xUin()x2 )
n
wher(ex id)e scornicebo emsp o(nwehncitoc uhbl epd h otooren lse cett.rco)n s
1/Jn
anUdn( 2. )iT tsh seeo tfe igenfoufQn c(ttpihooesn isot pieornaa ntddoe rs)c ribes
thsee ccoonmdpe on.ntM easutrhien gp oofos nioetft i hoen pacrotmipclleetse ly
detertmhiwean veuesnf ctoifto hsnee cpoanrdt Miecalseu.r cionmgp ltehmee ntary
propmeormteyn atlucsmoo m pletely wdaeevtfeurnmcoitftn ihesoesen c otnhde
pairctolnel,iy nt hciasts hede e terwmaivunenefcdt iinsoo nw eaing enfoufn tion
1
2
thmeo menotpuemr Pa.tS oirnP c aen Qda rneo n-cuiotnmgm toop,rpe sorsaition
anmdo menctaunmbn oottbh ed esccroimbpeldae ttt heel yts iammTeeh. uE si n­
stePiond,o alnsRdko ys ceonn ctlhutadhtedi ess croifrp etaimlouinstb tyef aulty
sintchseee csoynsdht aensmo bte einn terwaictIthnte. hd ew iorr ds
"Thmiask tehsre e aolfPia tnyQd d epeunpdon p rtohcoemef esass ure­
mencta rrioentd h fieor usstyt s wtheimdc ohen sod ti sttuhsreeb c ond
sysitnaen mwy a yN.o readseofinnaoibfrtl eieao clnoi utblyeed x pected
top ertmhiits .
11
Asi hta eppntsh,Ee P Rpa raodtro hixed tehatia nterwaicottnhpie an rgtm iacyl e
alttehsret aotfae n otdhiaesnrptt a rtiincnsltteaa neionsuo sawfl aym icloinacre pt
iqnu anmteucmh arneiflicevsoce fat p roperteyn tcaanltgl."lWe ehdme etnnw oor
11
morteh i(nlegpi shk otaorncesr )e fatreotdmhs ea me procaenas nsn i(hsiulcaht iaosn
eve)an ntmdu tsc onsseormvpeer opbeerttwyte hee(nms uacsmh o menttuhme)
twoob jemcatybs ee ntanAg flaemdri.e l xiaamopfel net angalreem Betenhltel
tohugehxtp eri[.m2I e]nn ttseh xepseetr istm,wee oln ecwthriomcnuhssc to nserve
angumloamre nbtteuwme tehnea mrs ee inndt i fferent dtihdreie ffcetrieonnts and
spactoimaplo onfse pnaitrnsme e asuarsei dnt hSet erernl-eaGxcphe trsiTm.he en
measuroetfmh eesnsptea ctoimaplo cnoernrtests onpo onn-dcsio nmogmp uetrrsa,to
juassit tn he eExPaRem .p l
Oncweem eastuhrxee- compoofsnp eoinfontn o ef ptahretu iscialnS eegtsr n­
Gerlamcanhge ,wt ec ainn ftehxre- coonmeponfst p oiftn h oet hpearr tIiwfce l e.
bleietvhEeePd R a rguimwteon utbl erd e asotnoaas bslutemht wea e c oumleda sure
thxe- comtpo ofsn peoinfon n oeft hpea rtainctdlh zee-s c ompoofsn peoinftnt h e
othpearr tainicdnl fteeh creo rressppocinondm ipnogfn oeerna tcpsha rtTihcelne .
wew ouhladvs eh otwhnta htse p accoimaplo onfse pncitansin nf abcetm easured
simultaanntedho tqau usalnyt um minesoc athv alanitidhc eso ry.
3
Howeerva,p pliocfBa et'listlo hne oarnendmo lno-lciattoty h EiPsR t hought
expiemresnhtot whsma eta suacr oimnpgo onsfep noitofn n oetf h pea rtcihcalnegse s
thwea vuenfctoifto hne iontashnatetnre oaunsdl yst,uh baste mqeuaesnutro efm ent
thsee cpoanrdt sipciilnsre e 'flsie voceftt hailst erendo tths oetr aitgseip nianl­
consesrttvaeMe.ad n eyx eprimheanvbtees ep ne rfotrotm eeBsdlet l i'nse quality
anndo n-l[o[c3[4a].5]lN ]iomt ayt tthederi stbaentcwete heeenn tanegllenec,sdt ro
theayrd ee scrbiya bs eidnw galvueen fctainodnc haa nignte h awtaf vuenction
caeudbs ya measuorfte hpmere onpteo rfet iitpehaser rti incnsltteaa neaoeffucstlsy
thset aotfte ho et hTehrii.tss h ees seonfecn et ang.lT ehwmeae evnftuntcahtti on
desctrhieebn etsa sntglacetaden sbn eos te pairnattthoepe dr odoutfch iten dividual
composnteantTteh se.yl ianrakette hdme o sbta sliecv el.
Thitsh eiscsio sn cewrinttehhwd ea vuenfcttihtoca nab neu setdod esctrhieb e
entasntgalotefde p t hhoete omnistv titeahad en nihoitflh ameta itotne r/anti-matter
paoifar n e lecatnradop no sitWrhoeannn.e lecatnradpo ons iatrrieonc n l ose
enouprgxohi mtihtceyay an n niheialocathth Teeh rai.ns n ihpirloaccteoiesnorvsnt s
theen earsgsyo cwiiatthme adts hsem oatnoidtfo h npe a rtiincrtlaoed isio aTnth.e re
are ptrwoobp aabhtwlaefy ostr h eem intctoeaft hriasd iioanTt.hfi er psatt hway
itska ewnh enp otshieet lrreoocnpnta/ hi aras t otsaploi nna en,sd e tehsee n ergy
releiasnte hdfe o romft hrpeheo toTnhsse.e copantdh iwstak aye wnh etnh e
posietlreocpnta/rhi oarsns p zienr os,e easen ndte hrreegl ye iants hfeeod ro mf two
photWoena sri.en terients httewe podh- otporno cess.
Thtew poh otcornesaf treotdmha insn ihpirloactaeirdoseens s cursiibtnehgde
theoofwra yv uenfctcioolnl[ a.lBp ]tesweetehne m mtuhscetoy n stehreevn ee rgy
and momoeftn htmeua mt tnetri/t-atmpeaari Trh.ee n ecrognyas iteorpnvr operty
ensutrhebasot t phh otaornes xaipmpar.to51e1MleyiV ne nerTghyme.o mentum
coenrasivtopnr opmeerattnyhs at th etswepo h ottorvnaesil no ppodsiiriteoecn ts,
antdh aen gumloamre ntuma itcoponrn ospeierwsrvh taryte sutlhttesw p ohi-ont on
4
procwehseosrn ee s piuispna ntdh oet hseprdi wonn T.h etsherp ereo perties taken
tgoetmhaektreh pioss itrotnw/oe-lpeshcyotstratooneinn md ecaaln ditdosat tued y
thnea touftr heee inrt ang,al nedme extnaotm wihnapeth enommeanayor nif sreo m
theinst angTlhememe eanstu.r oefom neoenft t hp eh o'tmsoo nmeunmrt esiunl ts
thceo lloaftp hwseae v uenfctoifo snte hcepo hnodt on.
Thitsh eorweotreikxc aamlti hneeens t angdliesmeceronebvtdya nA merican
scieVnitciDts.Iot rr [b .y6H ]ep erfoarnem xerpdie mtehnuatst ve edfr ayds et­t ec
tieoqnu iptmode enttte hctetw p oh ottoocn osn fitrhhmey o pthtehstai st hese two
photonbse d ceotueslcidtm eudl taTnheeeox uepsrliyma.el nltoI wrebtdyom ea­
sure acctuirmadetie effrleybn tecwteeh deeen t eecvtesino.Htn eo brsveewdh at
wec laiiasmn e xpondeenctfaiuyan lcc thiacortnae rtihzdeii nffge riendn ectee ction
timveesr nsuubmse orfc ounTthsim.se atnhsaa tl thsooumgpehh otpoania rrse
detected almomsotsa trss eie mpualrbtayaat s neiedgo nnuittsfi ilcmyiae,ne trval.
Thneu mebrof d ecays d eevcerneetxapsoense wnitttihhate li limyne t aeblr evtween
deteocftt ihcoeon r replhaottIeordnbe sys. t imaca htacertsae rliiswntieid octf h
aroulnOdO ps.
Thiesxn peontdeicaialnty h neu mebro fc ouwnittishn credaestientcgit mieo n
intaelir sivn terbecesatucisunerg r tehneto ry tphrabeted ciatcuhtsseseo urce is
sol oca(ltiehzffeeei dcv steo urceu swebidyd tIhr by is saiwftae sl y within 5mm)
expetchtatethda e r rtiivamdleie ffrenceb ets hhteoi umilettd a kteots rv aerse
thseo uflrct=ed /w hedr eti hste h icokfnt ehsseos u rIctte a.k esa bloiugth t
c
1p7st ot rvaer5smem A. nu ncienrottfyta hmiasg niwtouudalecd c ofuotnrht e
annihiolcactuiraotran in n ge xetnrodeft m hese o urHcoewe.er v,l itwnhieed th
oft heexo pnendteicaaatlfy u ll-hwaildft-hm iatxsei tnmiu mgmer se attheatrnh is
soulroccea tiaoinn mtueyna,cs eurrted by1 2Ip0rsLb.iy gt hkaatest s h laiobsno gu t
ttor av3e6.rcsme.c lWateih tmta heex ponednetciaaylilnoygtf hcneoa itnucried ence
timienrt veiacslh aerraicostftt hieecn tangolfte hmteew pnoht o tons.