Fundamental processes: Atomic Physics -...
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Fundamental processes: Atomic Physics CERN Accelerator School: Ion Sources Senec, Slovakia 2012 Magdalena Kowalska CERN, PH‐Dept.
Transcript of Fundamental processes: Atomic Physics -...
Fundamentalprocesses:AtomicPhysics
CERNAcceleratorSchool:IonSources
Senec,Slovakia2012
MagdalenaKowalska
CERN,PH‐Dept.
Outlineandintro Electronsinanatom
ElectronconfiguraIons Periodictableofelements
IonizaIonenergies NegaIveions–electronaffinity
Atomicprocessesinionsources
Waystoionizeatoms:
Hotsurface ParIcleimpact Photons
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Interestofatomicphysics: studyoftheatomasanisolated
systemofelectronsandanatomicnucleus
Processes:atomionizaIonandexcitaIonbyphotonsorcollisionswithparIcles
Atomicphysicsforionsources: EnergyrequiredforionizaIon EfficiencyofionizaIon
Physicalquan88esandunits KineIcenergyofchargedparIclesismeasuredinelectronvolts(eV).
1eV:energyacquiredbysinglychargedparIclemovingthroughpotenIalof1Volt.
1eV=e*(1Volt)=1.6022*10‐19J
Massofelectron:me=9.109*10‐31kg
Massofproton:mp=1.672*10‐27kg
Atomicmassunit=1/12carbon‐12mass:1u=1.6606*10‐27kg
ElementarychargeofparIcleise=1.6022*10‐19C(orA*s)
Electronwith1eVkineIcenergyismovingwithavelocityofabout594km/s 1eV=thermalenergyat11600K
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Electronsinanatom Analogy:
SatelliteorbiIngtheEarthcontainsgravitaIonalpotenIalenergy
SatellitecanorbittheEarthatanyheight.Or,itcancontainanyamountofgravitaIonenergy—itsgravitaIonalpotenIalenergyisconInuous
Similarly,electronorbiIngnucleuspossesseselectricpotenIalenergy.Butitcanonlystayinafinitenumberofdiscreteenergylevels(ororbits)
=>energylevelsofatomsare‘quan8zed’
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Earth‐satellite:
Nucleus‐electrons
Allowedstates
Electronsinanatom Electronsorbittheatomicnucleusonorbitsoffixedenergy
Energyofeachelectronlevel/orbit/shellisdeterminedmostlybyadracIonofthenucleusandtoasmallerdegreebytherepulsionofotherelectrons
Factorsinfluencingelectronenergy:nucleus,el‐elinterac8on,spin‐orbit
Quantummechanicsisbehindtheexistenceofshellsandthenumberofelectronsoneachshell
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Atomicshellstructure
Spin‐orbitinterac8on:interacIonbetweenelectron’sspinandorbitalangularmomentum(i.e.magneIcfieldgeneratedbytheelectron'sorbitaroundnucleus)Hyperfinestructure:nuclearspinexperiencesmagneIcfieldduetocurrentloopofelectronanddipolarinteracIonoftheelectronicandnuclearspins
(hyperfinestructure,isotopeshih)
Electronquantumnumbers
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Electronquantumnumbers
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Capitalledersusedformany‐electronsystems
Whenincludinginterac8onwithnucleusofspinI:TotalangularmomentumF;FquantumnumberF=|I‐J|,…,I+J
Electronconfigura8on
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Orbitalnames:s,p,d,f,g,h..:
sharp,principal,diffuse,fundamental,andthenalphabeIc
Electronorbitals
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Electronterms
Comingfromvalenceelectrons(thoseinoutermostorbit)
F=|J‐I|toJ+I
Hydrogenterms
(nuclearspin)
Electronconfigura8on
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Examples:
Electronbindingenergies
Periodictableofelements
ChemicalproperIesdictatedbyvalenceelectrons
Periodictableofelements1(1A)‐alkalimetals(1s1‐7s1)2(2A)‐alkalineearthmetals(1s2‐7s2)17(7A)‐halogens(2p5‐6p5)18(8A)‐noblegases(1s2,2p6‐6p6)14(4A)‐theCarbonfamily
Ioniza8onenergy Ioniza8onenergy(IE):minimumenergyrequiredtoremoveanelectronfrom
gaseousatomorion(notsolidorliquid)
FirstionizaIonenergy:minimumenergyneededtoremoveanelectronfromthehighestoccupiedsub‐shell(outermostelectron)ofgaseousatom
SecondionizaIonenergy:minimumenergyneededtoremovethesecondelectronfromthehighestoccupiedsub‐shellofgaseousatom
Third,fourth,…ionizaIonenergy–analogous
“Total”ionizaIonenergy:minimumenergyrequiredtoremoveallelectronsfromgaseousatom
Naming:knownalsoasionizaIonpotenIal
Units:eVorkJ/molinchemistry ItgovernschemicalproperIesofatoms
Ioniza8onenergyandshellstructure IEshowshoweasyitistopullelectroncompletelyfromatomicnucleus
IEisinfluencedby(inorderofimportance): Nuclearcharge–nucleus‐electronadracIonincreaseswithnuclearcharge Numberofshells–inpresenceoflevelsclosertonucleusoutermostelectronsare
furtherfromnucleusandarenotsostronglyadracted Shielding–electronsonorbitsclosertonucleusshield/protectoutermostelectron
fromadracIonofnucleus
AtomicradiiandIEareconnected
Whathaslower1stIE: MgorNe
KorCa KorRb PorAr Etc…
Atomicradii
Ioniza8onenergyandshellstructure
Atomicradii
AtomicsizeincreasesdownaPeriodicTablegroupwhileionizaIonenergydecreases,asnegaIvevalenceelectronisfurtherfromposiIvenucleus
1stionizaIonenergygenerallyincreasesacrossperiodsofPeriodicTableduetoincreaseinnuclearcharge:addiIonalelectronsgointosameshell,areaboutthesamedistancefromnucleus,butposiIvenuclearchargeincreases
2ndionizaIonenergyislargerthan1st,aselectronisremovedfromposiIveion
AsnumberofelectronsinoutermostshellsincreasesacrossaperiodsotoodoesthefirstionizaIonenergy,thereforeahighfirstionizaIonenergyindicatesshellorsub‐shellthatisalmostfull
Whathaslower1stIE: MgorNe
KorCa KorRb PorAr Etc…
Firstioniza8onenergy Closed‐shellatoms
Firstioniza8onenergy
Ioniza8onenergy IonizaIonenergyformulIplychargedions
Ioniza8onenergy e‐shellsvisibleinIEjumps easiesttotakefurtheste‐(smalleradracIonbynucleus) IEforgivenorbitincreaseswithZ(largeradracIon
Numberofelectronsremaininginorbits
IE:Ion
izaI
onene
rgyforlastelectron(eV)
1s 2s 1p 2p 1d 4s 3porbits 3s
Experiment,sosomevaluesmissing
Ioniza8onenergy WhenionizaIonenergiesformoreboundelectronsarenotknown,
Carlson‐correc8onisused: IonizaIonenergyPq,iiscalculatedfromionizaIonenergyWi(q)ofion
withchargestateqandtheatomicbindingenergiesofelectrons(measuredorcalculated)
E0i:bindingenergyofanelectroninthei‐thshellofanatom
E0q:atomicbindingenergyoftheelectron,whichistheweakestboundelectronintheionofthechargestateqWi(q):ionizaIonenergyoftheion(describesalwaystheweakestboundelectron)
innerelectroni,toberemoved
weakestboundelectronq(ionizaIonenergyisknown)
Ion:Aq+
E0q‐E0i
Nega8veions:electronaffinity
Atomicradii
Electronaffinity(EA):energygivenoffwhenneutralatomingasphasegainsextraelectrontoformnega1velychargedion
IEisinfluencedbythesameeffectsasEI: Nuclearcharge Numberofshells
Shielding
AtomicradiiandIAareconnected
Electronaffinity Electronaffinity<0–negaIveionisnotstable
ElectronaffinitypaOerns ElectronaffiniIesgetsmallerwhengoingdownacolumnofperiodictable:
electronaddedtoatomisplacedinlargerorbitals,whereitspendslessImenearnucleus
numberofelectronsonatomincreasesaswegodownacolumn,sorepulsionbetweenelectronbeingaddedandelectronsalreadypresentonaneutralatombecomeslarger
Electronaffinitydataarecomplicatedbecauserepulsionbetweenelectronaddedtoatomandelectronsalreadypresentdependsonatom’svolume
Vapourpressure vaporpressures:equilibriumpressureofvapouraboveitsliquid(orsolid);
pressureofthevapourresulIngfromevaporaIonofaliquid(orsolid)aboveasampleoftheliquid(orsolid)inaclosedcontainer
vaporpressuresatambienttemperaturesincreasewithdecreasingboilingpoints
Importantespeciallyinsurfaceionsources
Vapourpressure
Atomicprocessesinionsources
O.Kester
Atomicprocessesinionsources
O.Kester
Atomicprocessesinionsources
• Ioniza8on‐single‐ionizaIon‐double‐ionizaIon
Theproduc1onofhigherchargestatesisasuccessiveprocess
Theioniza1onhasenergythreshold→higherchargestatesneedhigherprojec1leenergies(electronenergies)
• Chargeexchange(forlowchargestates)
• Recombina8on‐radiaIverecombinaIonThecrosssecIonislargerforlowerelectrontemperatures
‐dielectronicrecombinaIon(resonantprocess)
• Chargeexchange(forhighchargestates)
dependingontheneutralpar1cledensityresidualgas)
crosssec1onarelargerforhigherchargestates
Waystoionizeatoms PosiIveions:
Electronimpact
Photons Hotsurfaces
NegaIveions: Electronadachment
ChargeexchangeofaposiIveiononahotsurfaceorinmetalvapour
(MoleculedissociaIon)
(MoleculeexcitaIon)
Waystoionizeatoms IonizaIoncrosssecIonsforArvsenergyofionizingcollisionswith:
Photons Electrons protons
Surfaceioniza8on Surfaceioniza8on:ioniza8onbycontactwitha(metal)surface
Requirements: AtomsIcks(isadsorbed)tothesurfacelongenoughtoreachthermodynamic
equilibrium=>atomvalenceelectronis“broadened”andcanmovebetweenatomandsurface
SurfaceishotenoughtodesorbparIcles:someareneutralatoms,orposiIve/negaIveions
MaterialworkfuncIon(W)=minimalenergyrequiredforanelectrontoescapethematerialsurface
WorkfuncIonforelementsfollowsatrendsimilartoionizaIonenergy
AdsorpIon Thermalequilibrium(1e‐7‐1e‐5s)
DesorpIonand
ionizaIon
Surfaceioniza8on DegreeofposiIvesurfaceionizaIon:Saha‐Langmuirequa8on
Materialworkfunc8on
Atomioniza8onenergy
MaterialtemperatureBoltzman’sconstant
ConstantdescribingatomproperIes
J=0,1,…=quantumnumber(electrontotalangularmomentum)r=0to1,reflecIoncoefficient
gi/gA=1/2forgroupIand2forgroupII
Notimportant:Chargestatebeforeadsorbingonthesurface(duetoequilibrium)
Important:materialworkfuncIonandstateofparIclesbeforedesorpIon(butaheradsorpIon),i.e.atomionizaIonenergy
PidecreaseswithincreasingTifW‐Ei>0
SurfaceionizaIonpossiblealsoforW‐Ei<0
Tmustbesufficientlyhightoevaporategivenelement(e.g.Li,Na).
Onthecontrary,thediffusionofsurfacematerialmustbelowenough(<10%ofamono‐layer),tokeeptheionizaIoncondiIonsasconstantaspossible
=>trade‐offrequired
Surfaceioniza8onpar8cle Ei(eV) W‐Ei(eV) Pi(1000K) Pi(1500K) Pi(2000K) Pi(2000K)
Cs 3.88 0.64 790 72 20 10
K 4.32 0.20 6.3 2.2 1.6 1.3
Na 5.12 ‐0.60 5e‐4 5e‐3 1.6e‐2 3e‐2
Li 5.40 ‐0.88 2e‐5 6e‐4 3e‐3 8e‐3
Surfacenega8veioniza8on
See1stlecture
Resonantioniza8onbyphotons
Excita1onschemesusedforresonantlaserioniza1on
OrdersofmagnitudesforthecrosssecIons:
• non‐resonant(directionizaIon): σ=10‐19–10‐17cm2
• resonant: σ=10‐10cm2
• AIS(auto‐ionizingstates):σ=1.6x10‐14cm2
• Rydbergstates:σ~10‐14cm2
RILIS(Resonantioniza8onlaserionsource)
Non‐resonantphoto‐ioniza8on
Chargestatevslaserpower
IncontrasttoresonantionizaIon,ions/plasmawithinthissourceisgeneratedviaenergydeposiIon
Laserfrequencycouplestofreeelectronplasmafrequency(eitherinmaterial,orformedplasma)
Thelaserbeampenetratesmaterial
LocalheaIngofelectronsbyinverseBremsstrahlung+excitaIonofatoms
Materialisablatedandanexpandingplasma‐plumedevelops
Ifplasmadensityisloweredandcut‐offfrequencydropsbelowlaser‐frequency,laserlightcanre‐enterplasma.
=>Electronsinsideplasmaareacceleratedupto100keV
Ioniza8onbypar8cleimpact
ImpactionizaIonisbyordersofmagnitudeshigherthancrosssecIonforphotoionizaIon
CrosssecIondependsonmassofcollidingparIcle:energytransferofaheavyparIcleislower,protonneedsforanidenIcalionizaIonprobabilityanionizaIonenergythreeordersofmagnitudeshigherthanelectron
Thus,electronsaremostcommonionizingparIcles
Processesinvolved: DirectknockoutionizaIon Indirectprocesses(basedoninner‐shellexcitaIonandsubsequentautoionizaIon);
moreimportantforheavieratoms
Ioniza8onbyelectronimpact
ElectronimpactSingleionizaIon
ElectronimpactDoubleionizaIon
CrosssecIo
n
electronenergy electronenergy
ForenergeIcreasonsmostprobableprocessisionizaIonreleasingonlyoneelectronfromatomicshell
Toproducehighlychargedions,kineIcenergyofprojecIleelectronshastobeatleastequivalentton‐thionizaIonpotenIal
IonizaIoncrosssecIon:electronenergyhastobe>ionizaIonenergy
Ioniza8onbyelectronimpact
with
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ApproximaIonofcrosssecIonandionizaIonImeforproducIonofbareionsfromH‐likeionsusingMosley’slaw,forX‐rayfrequenciesemidedintransiIonsfromconInuumtoK‐shell:
Ioniza8onbyelectronimpact
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Lotzformula:semi‐empiricalformulaforcross‐secIonofmulIpleionizaIonIonizaIo
nfactorj e*τfo
rdiffe
rentcharge
statesofX
ede
pend
ingon
electronen
ergy
W.Lotz,ZeitschrihfuerPhysik206,205(1967)
HigherE
MinimumcorrespondstohighestionizaIoncrosssecIon
Ioniza8onbyelectronimpact
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Lotzformulaindetail: 3parameterstorepresentcrosssecIonsforsingleionizaIonfromground‐state
Approximatesalmostalldatawithin10%andwithinexp.errorsforupto10keV‐electrons
Empiricalformula,butwithpropertheorybasis:followsearliertheoreIcalworkone‐escadering,usesapproximaIonofstarIngandfinalwavefuncIons,getsparametersfromfits
W.Lotz,ZeitschrihhirPhysik206,205(1967)
EclosetoPi
E>>Pi
ai=2.6–4.5e‐14cm2(empirically)
TotalionizaIoncross‐secIon #ofelectronsinsubshell
#ofsubshell
E<E(maxcrosssecIon):
Op8malelectronenergy
=>OpImalenergyisnearlye‐ImesionizaIonenergyoflastelectronremovedfromionwithchargestatez45
Whereσ(E)hasmaximum,ionizaIonfactorje*τhasminimumthere
CrosssecIonforthelastelectron,whichisremoved,determinesionizaIonIme
OpImalenergyoflastelectron,whichisremoved:
Ion.factorandop8malelectronenergy
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Electron
ene
rgy
IonizaIonfactor
Summary
Atomicphysicsgovernsmanyaspectsofionsources
Electronshellstructuredeterminesenergyrequiredtoexciteelectronsandeventoejectthemfromatoms(ionizaIon)
TheseenergiesdictatechemicalproperIesofelements
TherearedifferentpathstoatomionizaIon(surface,parIcle,photonimpact)
Theirdetailsdependonelectronstructureofionizedatomsandinvolvemanyatomicphysicsprocesses
Literature
B.Wolf,Handbookofionsources,CRCPress1995 G.Brown,Thephysicsandtechnologyofionsources,2004,WileyVCHVerlag
GmbH,ISBN3‐527‐40410‐4 F.J.Currell,ThePhysicsofMul1plyandHighlyChargedIonsVolume1:Sources,
Applica1onsandFundamentalProcesses,2004,Kluwer O.Kester,LecturesonIonSources:
h^p://acc.physik.uni‐frankfurt.de/vorlesung/vorlesung.html Ch.Foot,AtomicPhysics,OxfordUniversityPress2005
Addi8onalslides
Ioniza8onbypar8cleimpact
Examples:Argoncanbeionizedby10keVelectrons,ionsoftheheavyelementsbyupto100keVelectronsandUraniumby150keVelectrons.TheresulIngvaluesfortheionizaIonenergy,crosssecIonandionizaIonfactoraresummarizedinthetableonthelehside.
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Electronconfigura8ons
Hund’sruleofMaximumMulIplicity
Chargeexchange
FortheapproximaIonofthechargeexchangecrosssecIon,commonlytheequaIonbyMüllerandSalzbornisused:
ThereinidescribesthechargestateofthehighlychargedionandEion,gasistheionizaIonpotenIalofthegasatomsinteracIngwiththeion.
Example:Reachablechargestatesdependingonthecurrentdensityandthepressure
Chargeexchange:
Radia8verecombina8onFortheapproximaIonoftheRRcrosssecIonsthesemi‐classicalexpressionbyKimundPradisused.TheirformulabasesonthefirsttheoreIcaldescripIonoftheRadiaIveRecombinaIonbyKramers(1923):
with
Ry:Rydbergenergy13,6eVα:finestructureconstantω0raIobetweenthenumbersofoccupiedandunoccupiedstatesZ:nuclearchargeq:chargestaten:mainquantumnumber(λe)r:reducedCompton‐wavelengthE:electronenergy
with:
• theeffecIvenuclearchargetotakeintoaccounttheshieldingofthenuclearpotenIalbytheboundelectrons
• theeffecIvemainquantumnumber
toincludethecaptureintostateswithdifferentangularmomentums
Ioniza8onenergies
Z
IE:Ion
izaI
onene
rgyforlastelectron(eV)
electron
num
ber(1:1
stionizede‐)
Electronshellstructurecanbevisualisedevenbeder–seenextslide
Spin‐orbitcoupling
Ioniza8onbyphotons
Atomsofagascanbeionizedbyanintensivebeamofphotonswiththeadequateenergy(photoioniza8on).Thereforethephotonenergyhastobe.
Theenergyofaphotoelectronis:
ThereacIonis:
• ForagivenatomicshellthecrosssecIonσpisthelargestclosetothreshold,meaningwherethephotonenergyreachestheionizaIonenergyI(resonance/thresholdbehavior):
CrosssecIonσp:• σphasastrongdependenceonthephotonenergyandthenuclearchargeZ:
• DescripIonofσpasIme‐inverseeffecttotheradiaIverecombinaIonbytheMilne‐formula:
• ForhighphotonenergiestheionizaIonofthes‐orbitalismostprobableandtheK‐shellionizaIondeliversthedominantcontribuIon:
withg:sta1s1calweights
→
σpn:crosssec1onforRRintotheK‐shelln:mainquantumnumber
Atomicshellstructure
Atomicshellstructure
Energyspectrum:Heexample
Ioniza8onenergy
