Application of the Second Born Approximation to Excitation o

We present and compare total cross sections for excitation in collisions of protons and antiprotons with hydrogen atoms in the 2s state. Calculations are performed in the framework of the second Born approximation, in the energy range of 5--1000keV. We app

CHIN.PHYS.LETT.Vol.25,No.10(2008)3635

ApplicationoftheSecondBornApproximationtoExcitationofHydrogenAtoms

byProtonsandAntiprotonsImpact

RedaS.Tantawi2 ,SamiaM.Said1

2

DepartmentofMathematics,FacultyofScience,ZagazigUniversity,Zagazig,Egypt

DepartmentofBasicEngineeringSciences,FacultyofEngineering,Sana’aUniversity,Sana’a,Yemen

1

(Received10February2008)

Wepresentandcomparetotalcrosssectionsforexcitationincollisionsofprotonsandantiprotonswithhydrogenatomsinthe2sstate.CalculationsareperformedintheframeworkofthesecondBornapproximation,intheenergyrangeof5–1000keV.WeapplytheusualapproachofthesecondBornapproximation,whichapproximatesthesummationraisedbyretainingfewterms,aswellasanotherapproachapproximatesallenergiescorrespondingtotheintermediatestatestothatcorrespondingtotheinitialstate.Theannihilatione ectinthecaseoftheantiprotoncollisionisinvestigated.Wecomparetheresultswiththeprevioustheoreticalcalculations.

PACS:34.10.+x,34.50.Fa

Collisionprocessesinvolvingexcitedatomicstateshaverecentlybecomesubjectsofconsiderableinterest.Collisionprocessesofprotonsandantiprotonsonhy-drogenatomsareoneofthemostimportantandthesimplestcasesofatomiccollisionresearch.Acompar-isonofthetwoprocessesshouldgivedetailedinfor-mationonthefundamentalmechanismoffew-particledynamicprocesses.Hydrogenatomsareoffundamen-talinterestfortestingtheoreticalmethodsandmodelsinion-atomcollisions,andhavebeenofconsiderableinterestboththeoreticallyandexperimentallyforalongtime.[1,2]Noexperimentaldataareavailablefortheantiprotoncollisionsystemsyetduetothelackofappropriatelow-energyantiprotonsources.Thismayalsobethereasonfortherelativelysmallinter-estinantiprotoncollisionscomparedtotheirprotoncounterpartsuntilnow.However,theupcomingFa-cilityforAantiprotonandIonResearch(FAIR)withitsincorporatedFacilityforLowenergyAntiprotonandIonResearch(FLAIR)[3]willprovidetheneces-saryexperimentalconditionsinthenearfutureandisthereforeexpectedtoattractfurtherattentiontothe eldofantiprotoncollisions.BesidesthetraditionalBornapproximationmethodinhighenergycollisions,forexcitationprocessbyprotonimpact,thereisalsotheclose-couplingmethod.

Therearefewtheoreticalworksconcerningthein-elasticcollisionswithexcitedhydrogenatoms.Rein-holdetal.[4]usedthesymmetrizedeikonalapproxi-mationtocalculatecross-sectionsforthen=2(3)→n =3,4(4)transitions.JanevandKrstic[5]usedtheasymptoticadiabaticmethodandtheconceptofhid-dencrossingsofadiabaticpotentialenergysurfacesinthecomplexplaneofinternucleardistancetocarrysimilarcalculations.Fordetal.[6]reportedcrosssec-tionsfortheindividual2sand2pinitialstatesaswellasthecrosssectionsaveragedoveralln=2initialstatesublevelsforthep+H(n=2)collisionsystem.Theyusedasingle-centreedexpansionmethodbasedontheabilityofthetarget-centreedbasistopresent

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projectilecentreedorbitalsforasu cientrangeofprojectile-targetseparations.Themethodrepresentsthewavefunctionofthesystemintheinteractionpic-ture.Thetransitionamplitudesarecalculatedbyatime-developmentoperatorwherethebasisstatesarethematrixeigenvectorsofthetargetHamiltonianandareobtainedbydiagonalizingthisHamiltonianonanunderlyingbasis.Atwo-statemodelapplicabletotop-of-barrierprocessesinion-atomcollisionsatlowve-locityisinvestigatedinRef.[7].AnexpressionfortheMasseyparameterofthetransitionn→n+1wasderivedandusedittocomputeionization,cap-ture,andexcitationfromstatesofhighprincipalquan-tumnumberinproton-hydrogenatomcollisions.Animpactparameterapproach,basedonasingle-centreexpansioninatomicorbitals,isappliedtostudyim-pactexcitationsofhydrogenatomsbeinginitiallyintheexcitedinitiallyintheexcited2s-state[8,9]and2p-state[10]byprotonsandantiprotonsimpact.Pindzolaetal.[11]calculatedexcitationcrosssectionsforthep+H(2s)collisionsusingeachoftime-dependentlat-ticemethodwhichisbasedondirectsolutionoftheelectrontime-dependentSchr¨odingerequationonathree-dimensionalCartesianlatticewhereastraight-lineclassicaltrajectoryfortheprotonacrossthelat-ticeischaracterizedwithasingleimpactparameter,close-couplingcalculationswithatomicorbitalsonthetwocollisioncentreswithpseudocontinuumstatesplacedontheatom,andtheclassicaltrajectoryMonteCarlomethodisasimulationoftheion-atomcollisioninwhichalargeensembleofprojectile-targetcon g-urationissampledsubjecttotheclassicalevolutionofinitialstatescreatedtoapproximatethequantum-mechanicalatomicdistribution.

The rstBornapproximationtakesintoaccountdirecttransitionsbetweentheinitialand nalstatesandhastheadvantageofleadingtosimpli edanalysis.TheenergyrangeofvalidityofBornapproximationisdi culttodetermineanddependsonthetransitionofinterestandtheaccuracyrequired.Theearliestwork

redatantawi1@http://www.77cn.com.cn

c2008ChinesePhysicalSocietyandIOPPublishingLtd

We present and compare total cross sections for excitation in collisions of protons and antiprotons with hydrogen atoms in the 2s state. Calculations are performed in the framework of the second Born approximation, in the energy range of 5--1000keV. We app

3636RedaS.Tantawietal.Vol.25

onexcitationofgroundstatehydrogenatomsbypro-tonsisprobablyduetoBatesandGri ng[12]usingthe rstBornapproximation.Dewangan[13]presentedamethodforevaluatingthe rstBornamplitude,inacompactform,fortransitionbetweenarbitraryexcitedstatesoflargevaluesoforbitalangularmomentumandmagneticquantumnumbers(l,m).HeobtainedacompactexpressioncontainingaJacobipolynomialfortransitionwhenallthequantumnumbers(l,m)oftheinitialand nalstateshavetheirmaximumvalues.ThesecondBornapproximationimprovesthe rstBornapproximationbyallowingcouplingstointerme-diatestatestotheinitialand nalstatesandextendstheenergyrangeofthevalidity.Forion-hydrogencollisionssecondBornapproximationin …… 此处隐藏：15341字，全部文档内容请下载后查看。喜欢就下载吧 ……