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123456789102-1111-11-1125sm/3-1RR→22Rnrvp2=R=250mmn=382.2r/minR=250mmn=382.2r/min3-1tQP=pkEEQ+=kEEp2221212121mvmvEEEk+=+=mgRmghEp==∴)(212221gRvvmQ++=13)(212221gRvvtmtQP++==1v=1m/s2v=15m/sR=0.5m)(212221gRvvtmtQP++===(0.302+67.95+2.96)W=71.212wP500wPdh1h2hV2221hhh+==-0.8668hwdPP=700W1.5kW2n=382.2r/min14min/14001rn=min/2.382/12rinn==222295.05.1×=×=hdPP=1.35kwmNnPT.732.33/9550222==1nicaPAKcaPPKAcaP1nmmdd751=mmmmdiddd725.27475663.312=×=×=15smsmnddv/498.5/10006014007510006011=×××=×=ppsm/498.5maxv=sm/254a)(2)(7.021021ddddadddd++mma7000=0212210'4)()(22addddddddadL-+++=p=1972.36mmVmmLd2000=ammmmdLLdaa82.713)236.1972700(2'0=+=-+=51aoooo12068.1605.5782.713752801801=×--=a6VzlcakkPPPza)(900Δ+=min/14001rn=,mmdd751=ikwP68.00=kwP17.00=Δ95.0=aK03.1=lK0FNqvKvzPFca436.125)15.2(50020=+-=apF2sin210azFFp=16pFdddbminahminfh2110+-2110+-δadjo38o1±o38o1±0d1d1b1h2h1D17min/2.382/12rinn==222295.05.1×=×=hdPP=1.35kwmNnPT.732.33/9550222==1050=AmmnPAd99.152.38235.110533220min===23-23-231V1-22-323d=22mmD=22mmV35mm1-2mml3212=2mmd2223=6205,18aDBminsradaDasr62042552151314611200016000mmd6045=mml54245=420mmVmml40=mml6023=5mma20=mml4034=mml2656=6Vmmd1612=55×=×hbl22mmV6/7nH6k7o452×3-33-319451-1.5mmHRC56-628mm×=500mm×129mm250mm26mm120mm140mm40mm×20mmM103-43-4HT2002010f538mm1-1.5mmHRC56-6210mmmm516f20HT200L63*63*621,:1.:,2.:,,,,,,,,!3.,,,,,,,,!222003.11992.6200620041999.32001..2004.12324,,,,:;;;;;;;1.,16091687.·,1765,.,,,,1836,[1],(),()(),m,MT()MPKj[1],,1,()2,(),,,,[2]25,,,,18unsolvablet,,,19,2.,,,,,,,,,:,,,,,,,[3,4],,coplanar(i.e.=0)acollinearmotion(i.e.=0and?1=?2),,26,,3.,,,anticusp,,,4.,,,,--,,,internuclear,27Ui,vi,Wf28wavefunction,C3Dj[5],[6],Brauner[7],,,,GaribottiMiraglia,Berakdar(1992),5.,1keV2,:292(ECC)CrooksRudd[8][9],1kECC,,,,,,,,,,,collinearKoverLaricchia1998dr/dEedXkdXKcollinear,H2100keV[10],Berakdar[11],Sarkadi75keV30collinear,ECC,[12]6.H21keV45,1993Brauner,90[13],,451000eV100eV,45,,22.57.22.5,,,1772,Wannier,[14-18],,ei,,,a,901354.,,3134QDCS345,tp,,3258.,,,,,33Theoryofionizationprocessesinpositron–atomcollisionsAbstractWereviewpastandpresenttheoreticaldevelopmentsinthedescriptionofionizationprocessesinpositron–atomcollisions.Startingfromananalysisthatincorporatesalltheinteractionsinthefinalstateonanequalfootingandkeepsanexactaccountofthefew-bodykinematics,weperformacriticalcomparisonofdifferentapproximations,andhowtheyaffecttheevaluationoftheionizationcrosssection.Finally,wedescribetheappearanceoffingerprintsofcapturetothecontinuum,saddle-pointandotherkinematicalmechanisms.Keywords:Ionization;Collisiondynamics;Scattering;Electronspectra;Antimatter;Positronimpact;Saddle-pointelectrons;Wannier;CDWPACSclassificationcodes:1.IntroductionThesimpleionizationcollisionofahydrogenicatombytheimpactofastructurelessparticle,the“three-bodyproblem”,isoneoftheoldestunsolvedproblemsinphysics.Thetwo-bodyproblemwasanalyzedbyJohannesKeplerin1609andsolvedbyIsaacNewtonin1687.Thethree-bodyproblem,ontheotherhand,ismuchmorecomplicatedandcannotbesolvedanalytically,exceptinsomeparticularcases.In1765,forinstance,LeonhardEulerdiscovereda“collinear”solutioninwhichthreemassesstartinalineandremainlined-up.Someyearslater,Lagrangediscoveredtheexistenceoffiveequilibriumpoints,knownastheLagrangepoints.Eventhemostrecentquestsforsolutionsofthethree-bodyscatteringproblemusesimilarmathematicaltoolsandfollowsimilarpathsthanthosetravelledbyastronomersandmathematiciansinthepastthreecenturies.Forinstance,inthecenter-of-massreferencesystem,wedescribethethree-bodyproblembyanyofthethreepossiblesetsofthespatialcoordinatesalreadyintroducedbyJacobiin1836.Allthesepairsarerelatedbylinealpointcanonicaltransformations,asdescribedin[1].Inmomentumspace,thesystemisdescribedbytheassociatedpairs(kT,KT),(kP,KP)and(kN,KN).SwitchingtotheLaboratoryreferenceframe,thefinalmomentaoftheelectronofmassm,the(recoil)targetfragmentofmassMTandtheprojectileofmassMPcanbewrittenintermsoftheJacobiimpulsesKjbymeansofGalileantransformations[1]34Fordecades,thetheoreticaldescriptionofionizationprocesseshasassumedsimplificationsofthethree-bodykinematicsinthefinalstate,basedonthefactthat•inanion–atomcollision,oneparticle(theelectron)ismuchlighterthantheothertwo,•inanelectron–atomorpositron–atomcollision,oneparticle(thetargetnucleus)ismuchheavierthantheothertwo.Forinstance,basedonwhatisknownasWick’sargument,theoverwhelmingmajorityofthetheoreticaldescriptionsofion–atomionizationcollisionsusesanimpact-parameterapproximation,wheretheprojectilefollowsanundisturbedstraightlinetrajectorythroughoutthecollisionprocess,andthetargetnucleusremainsatrest[2].Itisclearthattoassumethattheprojectilefollowsastraightlinetrajectorymakesnosenseinthetheoreticaldescriptionofelectronorpositron–atomcollisions.However,itisusuallyassumedthatthetargetnucleusremainsmotionless.Thesesimplificationsoftheproblemwereintroducedintheeighteenthcentury.Theunsolvablethree-bodyproblemwassimplified,totheso-calledrestrictedthree-bodyproblem,whereoneparticleisassumedtohaveamasssmallenoughnottoinfluencethemotionoftheothertwoparticles.Thoughintroducedasamean