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

2

  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

3

Electronsinanatom   Analogy:

  SatelliteorbiIngtheEarthcontainsgravitaIonalpotenIalenergy

  SatellitecanorbittheEarthatanyheight.Or,itcancontainanyamountofgravitaIonenergy—itsgravitaIonalpotenIalenergyisconInuous

  Similarly,electronorbiIngnucleuspossesseselectricpotenIalenergy.Butitcanonlystayinafinitenumberofdiscreteenergylevels(ororbits)

  =>energylevelsofatomsare‘quan8zed’

4

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

8

Capitalledersusedformany‐electronsystems

Whenincludinginterac8onwithnucleusofspinI:TotalangularmomentumF;FquantumnumberF=|I‐J|,…,I+J

Electronconfigura8on

9

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

12

  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

43

  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.

50

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