PAIR AND TRIPLET PRODUCTION REVISITED FOR THE
Downloaded from www.ajronline.org by University of Arizona Health Sciences Library on 02/24/14 from IP address 150.135.114.244. Copyright ARRS. For personal use only; all rights ONRADIOLOGIST*RALPHD.REYMOND,BALTIMORE,‘I.-’ HEinaandradiologist,pairof thisdardsimplemannertripletpaperis to elucidatethe processesoftripletproductionfor the curioususingconceptsknownto thetextssimplyisconsideredwithOF RADIATIONElectromagneticmatterby 6radiationdistinctcontributiontomechanismis nisms.interactionservetionof lectron,respec-A modelblackis whyby theandana andthetripletnearboxpair.to con-boxof whatispresented.and how sintoan electron positronpairof a photonwithenergygreaterthan1.02mev.locatednearan atomicnucleus.Tripletproduction,similarly,isthe materializationintoan electron-positronpairof a photonwithenergyof atleast2.04mev.locatedneara freeorweaklyboundelectron.Becauseof theircentralimportancein scatteringare wellexplainedin the stanSthepairto eAlso shownconservedproduction;()triplet(6) photodisintegration.The first and last mechanismsare of littleor no importancein medicalradiology.Inthephotoelectriceffect,a lowenergyphoton(10-90key.)is absorbedbyanatomicplanetaryelectronthatis thenejectedfromthe atom.The thirdprocess,Comptonscattering,operatesovera widerangeof photonenergies(25key.to 35mev.),butis mostimportantwithiookey.to 2 mpartssomeofitsenergyto a free or weaklyboundelectronwiththe emergenceof a scatteredscattering;productionenteringexit of an electron positronis told,but not shown,thatoccursscattering;Comptonasthetivelyon photonenergy.orderof increasing(I) coherenteffect;()of radiologicphysics.Pairandon the otherhand,aregiventhe “blackbox” treatment.Aof energyabovea lizationFromtheDepartmentof umand energy)(b)Fio.z. box”approachand (1’) tripletto:(a)production.pairpro-
RalphDownloaded from www.ajronline.org by University of Arizona Health Sciences Library on 02/24/14 from IP address 150.135.114.244. Copyright ARRS. For personal use only; all rights reserved640D. ReymondMARCH,1972“ordinary”electron on .h-i)1M0C2Uiz--M0C2Ui.0A-. T.E8-0-,,,,hole (a)110.Energy2.in notonly accommodateIncidentphotonthe free electronofwithE ,theE kineticenergymomentum1.02theofto the E.mev.electronnucleusand(d)to the Diracstatesare filled with “quantumto oblivion.All the negativeelectron.(c)Photonannihilationa singleenergy,excessaccordingenergyto transithi’ where(c)(b) positronor electron.(d)theory.(a) Dirac’selectron-vacuumelectrons.”(6) “Ordinary”are filled and each statecanof an electron-positronpair.mechanicalenergystatesand creationEp,respectivelyandPositron-electronEp energytransferredwithannihilationcreationof2 Pairmentallyinusingequationtheinof2 quantum,and(Fig.statesthewherem0c velocityrest energy.to an electronrestof light,andm0c2 anThe anto freeintheareareenergybecomeandsight! e;2’3(i)all negativestates( - m0c2 to ) forwitha difficulty,assumptionsfilled,electrona lyavoidif antoof quantumanelectronbeenis facedWhata “quantumspontaneouslyreleaseTono lectrons,quantumDiracimpendingwould no permissibleis a Theycan bewith quantummechan-presentenergyhas- field.Solutionof the Diracthatfree electronscan existstates“ordinary”inanalogy.for an electron sticsets of ple.Sincewithonlythei
Downloaded from www.ajronline.org by University of Arizona Health Sciences Library on 02/24/14 from IP address 150.135.114.244. Copyright ARRS. For personal use only; all rights nbandenergya itiveenergyfromfilledTripletProduction moc2) or withnear zero kineticenergytofall intoa “hole”of energynear-m0c2,i.e.,a nergystatesdo not tdonotcontributemomentumoris eseactandpairtripletproductioninterms of the above model.The absorptionof an incidentphoton(an externalelectroniagneticfield) with an energygreaterthan2m0c2 na nstateis like a “hole”is interpretedasin a israys.’(Fig.wasdiscoverysubstancemoveinto tionas amodelthe blackand inAlthoughenergyOFMOMENTUMAND TRIPLETPLACEOUTINSPACEof momentumisWITHPRODUCTIONin anypro-.“materialization”ofwavesor photons,as inproduction,is difficult.Thisdifficultystemsfrom the fact that photonsof all the “particles”of the sametotalenergy(restand kinetic)havethe greatestmomentum.Thisis best demonstratedasfollows.Therestmomentumm0 is.of a materialparticleofmass0P, rnv (I)(v2\h12c2)thedescribed3 yearsinpriorcosmicmodeldescribesthe disappearandithesimultaneousapan electronand positron,of both pair and tripletpro-wherevelocityThec is the speedof lightand v is theof the materialparticle.energyof the materialparticleis:0Emme2 duction.reversetransition,withelectronfallinginto a “hole”tive energybandis d2 photons,annihilation.to be conserved,werewhat-electromagneticpairand tripletanceof a photonpearanceof boththeof2a thirdshownwhereanceof a positiveelectron,withkineticenergy,sinceit representstheabsenceof a negativeelectronwith a as requiredfromelectron-positronchargewasofappeara heenergyTheTAKINGa negativecharge,and leus.Thisquantumdescribesthe occurrencesbox in pairand tripletin a negaraisesthatappearancedinary”electronwithand a given momentumenergy,E(Fig.2c).anPAIRin yband.Thistransitionis interpretedphysicallyas thedisappearanceof hekinetichavem0c2Abe consideredas thatelecwhereall negativeenergyarefilledand noneof thestatesare manenergy.smallpositronof a system.mechanical“quantumthe64!an ordinaryin the negaas the electron-positronpairannihilation.The transition probabilityis highestfor an electroninits lowestpositi% e energyratioforgivesthethe material(P\kEmomentumparticle:v)mC2perunit
RalphDownloaded from www.ajronline.org by University of Arizona Health Sciences Library on 02/24/14 from IP address 150.135.114.244. Copyright ARRS. For personal use only; all rights photonorD.elec-is:its energy-‘is:ratiogivesthe(4)photonmomentumper unit energy:IE)c v always,then/P\IP(-I 1-\E/\EI f energyis conservedE Em, thenthemomentaare P Pmand rvedandthereforea photonout inspacecannotundergopairor tripletproduction.An additionalmasssuchas anatomicnucleusor electronis neededtoabsorbthe excessphotonmomentuminpair and he“m nviainsideoccurs‘ ‘thefortripletproduction.wherem c2kinetic)tron,energytheto thetotoforpairthephotonproduction.Itzero,i.e.,in reality,wouldm air,forinfortheenergyEquationin ilationisTheexcessphotonmomentumwhichis transferredto the atomicnucleusmay be sizablebut the kineticenergy,E,transferredto the nucleusis infinitesimallysmalldue to the verylargenuclearmasswithrespectto the electronmass.Hencethethresholdfor pairproductionis Thisdifferenceis veryenergynotionphotonnucnoteenergy,mayofbe. Thisthresholdin henoneTheThistripletconservationofproductionof E,incidentphoton,arethetotalof the rentproduction.energyfortripletis: ifl’e C2E0 m’c2energyofduction.sumedNogeneralit\thatthe electrontheisthe iflf C2wheretotalelectron mc2(restE1,andprior(5)kinetic)to tripletpro-is lostif itis stationaryisasandthe first term on the left of Equation5 becomesm0c2. The kineticenergytransferredto the is eassumedand mec2.itthatat thresholdenergy,the stationaryelectronand the positron-electronpair areall ejectedin the forwarddirection(i.e.,directionof incidentparticleswith( 5ofenergyConservationproductionusing E thatthethe3energyThe conserva5 becomes:in Equation(6)3mc2.of momentumEquationsforiand3tripletiS:E -Ckineticphotonpractically,is moreconsidersmc2 m c2i f notproduction.is: nucleusis assumedandelectronv v oductiontransferkineticTheE is transferredIt is importantwithoutenergyfieldor anicallynucleusstrongit is notisstrongatomicmomentumor electron.FORPRODUCTIONboxto thethisjacentis viaatomic1972maximal.fP\Sinceto n.‘4’,P#{231} Reymondwhere3 V/C.3mv 3mf3c,(7)
Downloaded from www.ajronline.org by University of Arizona Health Sciences Library on 02/24/14 from IP address 150.135.114.244. Copyright ARRS. For personal use only; all rights reservedVOL.PairNo. 3114,E,, fromEliminatingm,c2 and6 andEquations3mI3C2Triplet7,3mc2 m0-(I 31352)1/2-(I/32)5/2 643It shouldstandpoint,be notedthatelectron-positronresultthefromprotonsm0mo 3(I -Productionbothsides:3 ositronElectron-positron7 C-considered,transition4m0C-.energyis ssumptions”Whentheelectronturnasthisreason,hadto be madeenergiesand scatteringparticles,to calculatefor tripletproduction.in 4atomicnucleusoris includedin thesystem,is s thefromastateto gativeis ormassvacatedis inasationtheas in tripletmomentumor assystemkineticduetotheproduction.Theis transferredviatheirmechanicaltobe anor anexcessto ergyisverylargeinanother,momentum.The mass maynucleusas in pair ai r formelectronsmallHence“particles”pera ormationin common.pairformationcanbebecomingmassisall energies,momentaand scatteringcanbe assignedexactvaluesdeterminedby usingconservationlawsofenergyand momentum.Thereis, therefore,aninherentindeterminationin pairandtripletproductionandthe ��well sumliteratureenergyComptonthe momenta,of the ejectedthe thresholdenergyThisindeterminationetc., ePair and tripletproductionare multibodysystemsinvolvingtheinteractionof anincidentphoton,an electron-positronpairand an atomicnucleusor din “closedform,”whereall variablesare assignedexactvalues.For ctionassigned“intuitiveincidentl/2/5\4. 31,- m0j\3/5incidenttripletonof pair25)in EquationE,pair.dependencenumberof the absorber,marizedin the radiologicand will not be discussed tphoton-photonThem0ofparticleswithin an electron positron3.rn a nor clearmass.the incidentphotonenergythreshold for pairproductionininfinitesimallygreaterthan 2m02.Withtripletproductionthe excess photonmomentumis transferredto an electron,and the associatedkineticenergytransferredis considerable.Thecalculatedold is m0c2assumptionsincidentphotonenergythresh-after makinga few “intuitive”on the system.Theseassump-
Downloaded from www.ajronline.org by University of Arizona Health Sciences Library on 02/24/14 from IP address 150.135.114.244. Copyright ARRS. For personal use only; all rights reserved644RalphtionstripletwhichareD.are necessarysincebothpairandproductionare multibodysystemscannotbe solvedso that all variablesassignedexactReymondof preciationJ sshisH. Morganeditorialhelp.1972REFERENCESC. D. Phys.ANDERSON,values.DepartmentThe .,TheFourthedition.Press, Oxford,1958.W. The Quantumedition.ChapterOxford,1954.H.TheoryIII, andE. ThePhysicsCharlesC Thomas,Ill., 1964, pp. 160.H.1933,PrinciplesE. Private43,491-498.ofQuantumof Radiation.V. Universityof pring-
may besizable but thekinetic energy, E, transferred tothenucleus isinfinitesimally small due tothe very large nuclear mass with respect tothe electron mass. Hence the threshold for pair production isin-finitesimallv greater than 2m0c2 but not equal to 2m0c2. This difference is very importa
MATH ASSIGNMENT NO. 1 SQUARES AND SQUARE ROOTS CLASS-VIII Q1. (i) If one number of the Pythagorean triplet is 6, then find the triplet. (ii) If one number of the Pythagorean triplet is 9, then find the triplet. Q2. Find the square root of the followi
1.2 Advantages of Triplet-State Helium The use of triplet-state helium has many advantages over singlet-state helium. One reason for using triplet-state helium is its long lifetime of around 7900s [4] compared to singlet-helium, whose lifetime is about 20ms [5]. The Rydberg-states of triplet-state helium are thus also longer lived than those of .
Volume 47, Number 24 September 14, 1999 CENTERS FOR DISEASE CONTROL AND PREVENTION U.S. DEPARTMENT OF HEALTH AND HUMAN SERVICES . 1980 and 1997, the twin birth rate increased 42 percent (from 18.9 to triplet/ birth rate more than quadrupled, climbing from 37.0 to 173.6 Triplet births rising faster than quadruplet and quintuplet
By making triplets, one triplet of 3 and 1 triplet of 7 is found. Therefore cube root of 9261 is . 3 7 21u (vii) Solution: Prime factorization of 5324 is 2,2,11,11,11. By making triplets, one triplet of 11is found but two factors are still lef
v Using triplet tracks from first few leading vertices 4. Patatrack pixel tracks (3clean/all-tight 4all) – option-2D v Using quadruplet tracks from any vertex v Using triplet tracks from first few leading vertices as usual v Add triplet
Herringbone gear pair is composed of two matched herringbone gears. It can be classified into two types: external herringbone gear pair and internal herringbone gear pair. Involute herringbone gear pair of external gearing with parallel axes It consists of two matched involute herringbone gears of external gearing.
Biodiversity Revisited research and action agenda 4 REVISITING BIODIVERSITY RESEARCH AND ACTION Carina Wyborn, Jasper Montana, Nicole Kalas, Santiago Izquierdo Tort, Victoria Pilbeam This chapter examines the rationale and approach of the Biodiversity Revisited agenda. We first consider what biodiversity is and why it might need to be revisited.
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