Time‐dependent close‐coupling methods for …€dependent close‐coupling methods for...
Transcript of Time‐dependent close‐coupling methods for …€dependent close‐coupling methods for...
Time‐dependentclose‐couplingmethodsforelectron‐atom/
moleculesca6ering
JamesColgan1,MitchPindzola2
1Theore9calDivision,LosAlamosNa9onalLaboratory,LosAlamos,NM2DepartmentofPhysics,AuburnUniversity,Auburn,AL
Outlineoftalk• Theore9calapproachestoelectron‐impactioniza9on–briefdescrip9ons– Time‐dependentclose‐coupling(TDCC)method
• Strengthsandweaknesses• Considera9onsofconvergenceissues
– Distorted‐wave(DW)approaches• EIIcrosssec9ons:overviewofcalcula9onsperformedtodate– Selectedexamplesofioniza9onofneutralatoms,ionsandafewmolecules
• EIEcrosssec9ons–lessdoneinthisareausingTDCCbuttherearesomeexamplesofLiandBeq+ions
• Inclusionofioniza9ondatainpublicdatabases• Conclusions&outstandingissues
– Whats9llneedstobedone– Apathforward?
TDCC approach to electron-impact ionization • The TDCC method centers around solution of the time-dependent Schrödinger
equation for two interacting electrons
• The electron-electron interaction between the outgoing electrons from an ionization process is treated exactly; a close-coupling, or non-perturbative approach
• In electron-impact ionization all possible LS final states are possible (1,3S, 1,3P, 1,3D, …), and one needs to monitor carefully the convergence with respect to the number of states – For moderate projectile energies, the number of partial waves which is required for
convergence is usually quite manageable. • Probabilities for ionization may be extracted at some final time via standard
projection methods • For multi-electron targets, the interaction of the remaining electrons with the
two outgoing electrons is treated through additional direct and local exchange potential terms
i!PLS
(r1, r2, t)
!t= T
l1l2PLS(r1, r2, t)+ V
l1l2l '1 l '2PLS(r1, r2, t)
l '1 l '2
"
Why is a time-dependent approach useful? • The TDCC approach avoids the troublesome boundary condition
associated with the three-body Coulomb problem by propagating the equations that describe the electron motion until the interactions are small, and so that converged probabilities for a given scattering process may be extracted.
Plots of the radial component of the total wavefunction show how the two electrons interact
t=0 t=25
• Suchissuesinclude– Radialmeshchosenbyuser– Numberofpar9alwavesretainedinexpansion– Whethertop‐up(withDWpar9alcrosssec9ons)wasusedandatwhatpar9alwavethesewereapplied
– Choiceofcorepoten9alforoneortwo‐electroncalcula9onsoutsideofafrozencore
• Anexperiencedusershouldbeabletominimizetheuncertaintyarisingfromsuchconsidera9ons,buts9lltediousand9me‐consumingtes9ngistheonlywaytochecktheseissues
• Theseare“numerical”issues;othermore“physics‐based”issuesalsoexist
UncertaintyissuesinaTDCCcalcula=on
UncertaintyissuesinaTDCCcalcula=on
• Theinterac9onofoutgoing(ac9ve)electronswiththeremainingcoreelectronscanleadtouncertaintyinthetotalcrosssec9onpredic9onfromTDCCcalcula9ons
• TheTDCCapproachtoioniza9onisaconfigura9on‐averagedapproachandsotermdependenceoftheinterac9onoftheoutgoingelectronswiththecoreisnotproperlyincluded
• ExamplesofthiswillbepresentedforNe
• Thedistorted‐waveapproachtoelectron‐impactioniza9on(orexcita9on)isawell‐establishedmethod– Theincident,sca[ered,andejectedelectronicwavefunc9onsareall‘distorted’bythepoten9al
ofthetargetatom(includingnuclearandelectronpoten9alterms)– Theradialdistortedwavesareevaluatedusingaone‐electronHamiltonianofaformsimilarto
– ThesedistortedwavesarethenusedtocomputeSlaterintegralswhicharesummedappropriatelytocalculatethesca[eringprobability
– Theincident/sca[ered/ejectedelectronradialorbitalseachcanbecomputedineitheraVNorVN‐1poten9al• AcommonchoiceistousetheVNpoten9alfortheincidentandsca[eredorbitalsandaVN‐1
poten9alfortheejectedorbital• Alterna9vesincludecompu9ngallorbitalsinaVN‐1poten9al,thisleadstobe[er
orthogonalityproper9esforthewavefunc9ons• Athighenergiesorforhighlyionizedtargets,eitherchoiceproducessimilarioniza9oncross
sec9ons– Atlowenergies,orforneutral/near‐neutralsystems,thetwochoicescanproducedifferent
results– Distorted‐wavemethodsareconsidered‘perturba9ve’inthattheinterac9onbetweenthe
electronsisnottreatedtoallorders
Distorted‐waveapproachtoelectron‐impactioniza=on
Electron‐impactioniza0onofH:TotalCrosssec0ons
• EarliestTDCCcalcula9onsweremadefor(e,2e)ofH
• Close‐couplingcalcula9ons(CCCandthenTDCC)wereshowntoprovidesignificantlybe[eragreementwithmeasurementthandistorted‐wave(DW)calcula9ons
• ForH,theDWcalcula9onsare~20‐30%largerthanthemeasurements;atrendthatpersistsformanyneutralsystems
• Progressmadesincethiswork‐includingaccuratedescrip9onsoftheangulardistribu9onsoftheoutgoingelectrons(TDCS)–leadstotheacceptancethat(e,2e)ofH(andH‐likesystems?)isasolvedproblem
Pindzola&Robicheaux,PRA54,2142(1996)
H(1s)
• Latercalcula9onsdrama9callyshowedhowdistorted‐wavemethodsbecomelessaccurateformoreexcitedstatesofatoms
• StudywasmadeforHandH‐likesystems
• Thisworkalsoclearlyshowshowthecrosssec9onfromexcitedatomicstatesismuchlargerthanfromthegroundstate
Griffinetal,JPB38,L199(2005)
Electron‐impactioniza0onofH:TotalCrosssec0ons H(ns)
• Alsoinves9gatedweresomeH‐likeions(Li2+);
• DW1(mixedpoten9als)doesverywellforgroundstate
• Althoughthisisnotnecessarilytrueforexcitedstates,whereDWapproachesappearlessaccurate
Electron‐impactioniza0onofLi2+:TotalCrosssec0ons
Griffinetal,JPB38,L199(2005)
Li2+(ns)
• TDCCcalcula9onsforelectron‐impactioniza9onofHefindsimilarconclusionstotheHioniza9onwork
• AgainDWover‐es9matesmeasurementforneutralsystemsby~20‐30%
Pindzola&Robicheaux,PRA61052707(2000)
Electron‐impactsingleioniza0onofHe:TotalCrosssec0ons He(1s2)
• Cau9onarytale:– Experimentisnotguaranteedtobeperfect(!)
• Forioniza9onfromexcited‐stateHe,measuredcrosssec9onshavebeenques9oned:– Threeclose‐couplingcalcula9onsareingoodagreementwitheachotherbutnotwithmeasurement• MeasurementbyDixon,Harrison&Smithmadein1976
• Anewmeasurementherewouldbemosthelpful
Colganetal,PRA66,062707(2002)
Electron‐impactsingleioniza0onofHe(1s2s) He(1s2s)
• Cau9onarytale:– Experimentisnotguaranteedtobeperfect(!)
• Forioniza9onfromexcited‐stateHe,measuredcrosssec9onshavebeenques9oned:– Threeclose‐couplingcalcula9onsareingoodagreementwitheachotherbutnotwithmeasurement• MeasurementbyDixon,Harrison&Smithmadein1976
• PWBcalcula9onsinthe70sagreedwellwiththemeasurement;seeminglyanunfortunatecoincidence
Colganetal,PRA66,062707(2002)
Electron‐impactsingleioniza0onofHe(1s2s) He(1s2s)
• Electron‐impactioniza9onofLigroundstate;againtheoriesagree(TDCC/CCC)butarelowerthanmeasurement– Measurementmadein1960s– Anothermeasurementwouldbeusefulalso
• ForexcitedstateRMPS,TDCCandCCCcalcula9onsareallinexcellentagreementaswell–butnomeasurements
Colganetal,PRA63,062709(2001)
Electron‐impactsingleioniza0onofLi(1s22s)Li(1s22s)
• Asystema9cstudywasperformedusingTDCCofelectron‐impactioniza9onofallBeions,includingexcitedstates
• ForneutralBe,3methodsareinreasonableagreement– Butnomeasurements
Colganetal,PRA68,032712(2003)
Electron‐impactsingleioniza0onofBe(1s22s2) Be(1s22s2)
• ForBe+measurementsdoexist
• Threetheore9calapproachesagreewellwitheachotherbutareagainlowerthanmeasurement
• Perhapsitis9meforacampaigntore‐measuretheioniza9onfrommanyoftheselightatomicsystems?
Electron‐impactsingleioniza0onofBe+(1s22s)
Colganetal,PRA68,032712(2003)
Be+(1s22s)
• TDCCandRMPScalcula9onsinverygoodagreement
• DWapproachesappearreasonableforthistwice‐ionizedion– ButDWlessaccurateforexcitedstateioniza9on
Electron‐impactsingleioniza0onofBe2+(1s2)
Colganetal,PRA68,032712(2003)
Be2+(1s2)
• Electron‐impactioniza9onofB(1s22s22p)
• TDCCcalcula9onsareconsiderablylowerthanDWcalcula9ons–althoughnomeasurementswithwhichtocompare– DWcalcula9onswithmixedpoten9alsexhibitashaperesonanceatlowenergies(unphysical)
– BinaryencountermethodduetoY‐KKiminreasonableagreementwithTDCCresults
Electron‐impactsingleioniza0onofboronanditsions
Berengutetal,PRA76,042704(2007)
B(1s22s22p)
• OldermeasurementsmadebyJILAgroupofGordonDunn
• Measurementsdidnotknowfrac9onofmetastablecomponent(1s22s2p3P)intheionbeam
• NewmeasurementsatORNL(Fogle&Bannister)wereabletodetermineametastablefrac9onof~9%
• TDCCandRMPScalcula9onsingoodagreementwiththenewmeasurements
• Furthercalcula9ons(notshown)appeartoconfirmthe9%metastablecomponent
Berengutetal,PRA78,012704(2008)
B+(1s22s2)
Electron‐impactsingleioniza0onofB+
• Singleioniza9onofneutralC• TDCCcalcula9ons(squares)agreewellwithmeasurement
• DWaround15%largerthanTDCCcalcula9onsatcrosssec9onpeak
• AmorerecentTDCCcalcula9onbyAbdel‐Nabyetal,PRA87,022708(2013)alsoexaminedexcited‐stateioniza9on
Electron‐impactsingleioniza0onofcarbon C(1s22s22p2)
Pindzolaetal,PRA62,042705(2000)
• Singleioniza9onofexcitedC+(1s22s23l)
• TDCCcalcula9onspredictadirectioniza9oncrosssec9on~20%lowerthanDWcalcula9on
• RMPScalcula9onssignificantlyhigherduetostrongexcita9on‐autoioniza9oncontribu9onfromtermsarisingfromthe1s22s2p3sconfigura9on
Electron‐impactsingleioniza0onofexcitedcarbonions C+(1s22s23s)
Ballanceetal,PRA84,062713(2011)
• Jointtheory/experimentalstudyofsingleioniza9onofC2+(1s22s2)
• Experimentwasabletoes9matefrac9onofionbeaminametastablestate(around60%)
• RMPS/TDCC/CCCcalcula9ons,allmadeforbothgroundandmetastablestates,agreewellwithmeasurementusingthe40/60%ionbeammixture
Electron‐impactsingleioniza0onofC2+ C2+(1s22s2)
Lochetal,PRA71,012716(2005)
• O1+toO4+
• Müllergroup(Giessen,Germany)performedaseriesofioniza9onmeasurementsfromlow‐chargedOions
• ForO+,TDCCcalcula9onsareingoodagreementwiththemeasurements
Lochetal,PRA67,042714(2003)
Electron‐impactsingleioniza0onofoxygenions O+(1s22s22p3)
• TDCCcalcula9onsaresystema9callylargerthanthemeasurements,asareDWcalcula9ons
• Howeverterm‐dependentDWcalcula9ons(dashedline)lowerthecomputedcrosssec9ontoclosetotheexperimentalresult– Thisterm‐dependentcalcula9onusedthe
2p5kd1PHFpoten9alsintheDWcalcula9on
– insteadofthe2p6configura9on‐averagedpoten9al
• Demonstratesthattheterm‐dependenceoftheoutgoingelectronswiththe2p5coreneedstobetreatedaccurately
• ItwouldbedesirabletoincludesuchHartree‐Fockinterac9onsinaTDCCapproach
Electron‐impactsingleioniza0onofneon
Pindzolaetal,PRA62,042705(2000)
Ne(1s22s22p6)
Electron‐impactsingleioniza0onofneon Ne(1s22s22p53s)
Ballanceetal,JPB37,4779(2004)
• Excited‐state2p53s3PtermofNe
• RMPSdoeswellcomparedtomeasurement;whenaveragedoverterms,RMPSagreesverywellwithTDCC
• Excited‐state2p53s3PtermofNe
• RMPSdoeswellcomparedtomeasurement;whenaveragedoverterms,RMPSagreesverywellwithTDCC
Electron‐impactsingleioniza0onofneon Ne(1s22s22p53s)
Ballanceetal,JPB37,4779(2004)
• GroundstateofSi• DWsignificantlyover‐es9matesmeasuredioniza9oncrosssec9on
• BEBmethodduetoY‐KKiminreasonableagreement
• NoTDCCmeasurements(yet)
Electron‐impactsingleioniza0onofsilicon
Si(1s22s22p63s23p2)
Colganetal,PRA77,062704(2008)
• GroundandexcitedstatesofSi7+
• Highlyionizedion–wecomputecontribu9onsfrom2s&2psubshells
• DWcalcula9onisinverygoodagreementwithmeasurement
Electron‐impactsingleioniza0onofsiliconions
Si7+(1s22s22p3)
Colganetal,PRA77,062704(2008)
• VeryrecentTDCCcalcula9onsweremadeforioniza9onofNaandMg
• Calcula9onsmadeusinganewerTDCCversionwithabe[errepresenta9onofnon‐ionizedcoreelectrons
• Tocompareagainstmeasuredangulardistribu9ons(TDCS)madebyManchestergroup– Goodagreementfoundinbinary&recoilpeaksintheTDCS
• Totalcrosssec9onagreedwellwithpreviousmeasurements
Electron‐impactioniza0onofNa&Mg
Armstrongetal,PRA88,042713(2013)
Na(1s22s22p63s)
• 3‐electronTDCCcalcula9onsweremadefordoubleioniza9onoftheH‐ion
• Notveryrelevantformodeling,butagoodexampletodemonstratehowtheorycandiscriminatebetweenconflic9ngmeasurements
• TDCCcalcula9onsinmuchbe[eragreementwithmeasurementsofDefrancegroup(1992)thanwitholdermeasurementsfromPeart&Dolder(1971)
• Otherthree‐electronTDCCcalcula9onshavebeenmadefordoubleioniza9onofHe&Be
Electron‐impactdoubleioniza0onofatoms:H‐
Pindzolaetal,JPB39,L127(2006)
• FirstmolecularTDCCcalcula9onofelectron‐impactioniza9onexaminedH2
+,thenH2• TDCCcalcula9oninexcellentagreementwithmeasurement
• Angulardistribu9onsalsoavailableforioniza9onofH2byelectron‐impact– Thesecomparequitewellwithcoincidencemeasurements
Electron‐impactioniza0onofmolecules:H2
Pindzolaetal,PRA73,052706(2006)
• TDCCcalcula9onwellsuitedtoprovidingexcita9oncrosssec9onsforone‐electronsystems
• ComprehensivestudyofLiexcita9oncrosssec9onsdemonstratedgoodagreementbetweenthreeclose‐couplingmethods:RMPS/TDCC/CCC
• ConvergenceinRMPScalcula9onswasalsoinves9gated
Electron‐impactexcita0onofLi
Griffinetal,PRA64,032718(2001)
• RMPScalcula9onsprovidedcomprehensivesetofdataforallBeions
• TDCCwasusedtobenchmarkthecrosssec9onsforBe+
• Agreementagainverygoodbetweenallthreemethods
Ballanceetal,PRA68,062705(2003)
Electron‐impactexcita0onofBe+
ConclusionsofqualityofTDCCioniza=ondataformodeling
• TheAuburngrouphasdemonstratedthatuseofimproved(close‐coupling)crosssec9onsforHandHedoesmakeadifferencetoplasmatransportstudies– Theyalsoinves9gatedtheapproxima9onofusingsemi‐classicalapproachesorDWapproachesinsteadofclose‐couplingdata
– Thisstudyallowedanassessmentofhowwellsuchapproachesmightworkforcaseswherenoclose‐couplingdataareavailable
– Thesemi‐classicalapproachwaspreferredforneutralsbuttheDWapproachwaspreferredforions
Lochetal,PPCF51,105006(2009)
Ioniza=ondatawithindatabases• Allioniza9ondata(fromTDCCandothersources)forlightelementsfromHthroughBhavebeenincludedintherecentversionsoftheADASdatabase– GeneralizedRatecoefficientsaswellasrawcrosssec9onsarestored
– Excita9onratesalsoincluded– Publishedinaseriesofdetaileddatapapers:
• Lochetal,PPCF51,105006(2009);“Theroleofexcitedstateioniza9ondataonHandHegeneralizedcollisionalradia9vecoefficients”
• Lochetal,ADNDT92,813(2006);Generalisedcollisional‐radia9vemodelforlightelements.A:datafortheLiisonuclearsequence
• Lochetal,ADNDT94,257(2008);Generalizedcollisionalradia9vemodelforlightelements:B:datafortheBeisonuclearsequence
• Lochetal,JPhysConfSeries(2014);Generalizedcollisionalradia9vemodelforlightelements:C:datafortheBisonuclearsequence
• Papersforthcomingontheratesforthecarbonisonuclearsequence
ConclusionsofuseofTDCCioniza=ondataformodeling
• Wecandis9nguishbetweenthreeareasofioniza9ondataforatoms:
– Neutralatoms– Excited‐statesofneutrals&near‐neutrals– Mul9ply‐chargedIons
ConclusionsofuseofTDCCioniza=ondataformodeling
• Neutralatoms– Forone‐electronandtwo‐electronsystemsTDCCperformswellandhasbeenshowntogiveaccurateresults
– Compareswelltootherclose‐couplingapproaches– DWapproaches,invariousforms,typicallyover‐es9matecrosssec9onby20‐50%,dependingontarget
– TDCCismoredifficultforatomsinwhichsignificanttermdependenceisexhibitedintheini9alstate• i.e.whereconfigura9on‐averageapproachislessapplicable
ConclusionsofuseofTDCCioniza=ondataformodeling
• Excited‐statesofneutrals&near‐neutrals– TDCC(alsootherclose‐couplingcalcula9ons)areowenmoredifficultforexcitedstates• Duetoslowerconvergenceproper9eswithrespecttoradialmesh,par9alwaveexpansions,etc
– Calcula9onsperformedtocompletenessshouldbeaccurateforone‐electronandtwo‐electronsystems
– DWcalcula9onshavebeenshowntobecomelessaccurateforexcitedstatesofneutralsandfew‐chargedions
ConclusionsofuseofTDCCioniza=ondataformodeling
• Mul9ply‐chargedIons– DWapproachesrapidlybecomemoreaccurateasthechargeontheionincreases
– Lessneedforclose‐couplingapproacheswhenthenuclearchargedominates
– Broadlyspeaking,thisistrueforionsthataremorethantwiceionized• Butsuchassump9onsmustbechecked–especiallyifexcitedstateioniza9onisimportant!
BroaderConclusionsforioniza=ondata(1)
• Usuallyweassumethatexperimentistheul9matearbitertodis9nguishbetweencalcula9onsandtoassessaccuracyofdata
• Howeverinsomecasesthereiscompellingevidencethatsomemeasurementsneedtobelookedatagain– Forcasesforwhichtwoorthreeclose‐couplingapproachesagreewellwith
eachother,butnotwithmeasurement– OccursforneutralHe*,Li,Be*,and….
• Weencouragemoremeasurements,especiallyforneutralsystems• Thesearedifficultmeasurementsthatmustbeperformedcarefully
– determina9onofmetastablecomponentofionbeamisachallenge– alsofundingconstraintsareasignificanthurdle
• Howeveritisdifficulttobetrulyconfidentinadatasetunlessseveralcalcula9onsandseveralmeasurementshavebeenperformed– Isthiswishunrealis9ctoday?!
BroaderConclusionsforioniza=ondata(2)
• Tungsten– Wehavemostlyignoredheavierelementsinthistalksofar– However,Wisofprimeimportancetofusionmodeling,andtransi9onmetals
areowenkeytounderstandingastrophysicalplasmas– DWcalcula9onshavebeenperformedforallionsintheWisonuclear
sequence• S.D.Loch,etal,Phys.Rev.A72,052716(2005)
– Similarcalcula9onsalsomadefortheArisonuclearsequence– TheDWcalcula9onsarelikelytobeaccurateformoderatelyandhighly‐
chargedions,butmuchlessaccurateforneutral&near‐neutral• Someevidencethationiza9onofW4+orW5+ionsisreasonablywelldescribed
– However,noclose‐couplingmethodhasbeenshowntobefeasibleforneutral/near‐neutralW
– Thesignificantcomplexityoftheatomicstructureofsuchionstagesisthemainreason
– TDCCmethodsareunlikelytobeappliedtosuchionstagesinthenearfuture
– RMPScalcula9onsmightbepossiblebutares9llextremelydaun9ng!
Pathforward
• Abenchmarkstudywouldbeausefulwayforwardfortheatomiccollisioncommunity– TDCCmethodscancontributetosuchastudyviaaccurateioniza9oncrosssec9ons,givenasuitablesystem.
– Unfortunately,ionsthatmightbeofmostinteresttofusion,suchaslow‐chargedTungstenions,areoutofreachfromTDCC(andotherclose‐coupling?)calcula9onsatpresent
– AlowerZneutralatomorlow‐chargedionmightbemostviablecandidateforsuchabenchmarkstudy