1965Apj. . .141. . 364M TWO-ELECTRON EXCITATION

Home , Autoionization

1965ApJ. . .141. . 364M l + + 1 -13-14 zZ z2 3 the 165-200-ÂregionusingsynchrotronradiationfromNBS180-MeVelectronasa able theoreticalestimates.Theabsorptionprofileofthestrongestresonance,dueto2s2pP°state, background source.Twenty-oneresonanceshavebeenobserved,formingfourserieswhichcanbeasso- photoionization continuumabsorptionofhelium.Thestatesresponsibleforthelowest- found manyadditionalautoionizingstates.Allofthesestatesliemorethan35eVabove has beenstudiedindetailandfoundtobewellpredictedbytheory. n —4statesofHe,respectively.Theobservedenergiestheseresonancesarecomparedwithavail- of theseseriesconvergeontothen—2statesHe,whileothertwow=3and ciated withtransitionsfromthegroundstatetotwo-electronexcitationstatesofneutralhelium.Two forward scatteringofelectronsbyhelium.Simpson, Mielczarek,andCooper(1964), helium (MaddenandCodling1963a);atthattimetheobservedenergy-levelstructure kept pacewithexperimentaldevelopments.Theenergy andautoionizationprobabilityof ported findingadditionalresonances,corresponding toopticallyforbiddentransitions. region foropticalexcitationfromthegroundstate.Thesetransitionshavebeenob- was theoreticallyinterpreted(Cooper,Fano,andPrats1963).Subsequentlywehave using moremonochromaticelectronbeamsthanpreviously attainable,haverecentlyre- recently bySilvermanandLassettre(1964)from discreteelectronenergylossesinthe onances intheopticalabsorptionspectraobserved inthepresentworkwasfirstob- helium wasobtainedbyComptonandBoyce(1928)Kruger(1930).sug- siderable interest.Indeed,thesimplicityofheliumitselfplacesimportanceonde- This simplifyingconditionmakesthestudyofprofiletheseresonancescon- lying seriesofobservedresonancescaninteractwithonlyonecontinuum(\sepP°). by autoionization(typically,inlO-!!)sec).Theinteractionleadstoresonancesthe served inabsorptionbyutilizingthe“synchrotronlight”continuumradiationfrom the firstionizationlimitforhelium(24.6eV)andrequireradiationin165-200-Â excitation ofbothelectrons.Thestatesinteractwithadjacentcontinuaanddecayrapidly mains inthe2sshell(2s2pP°-2sndP,w=3,4,and5). 3601 Âwereduetotransitionsindoublyexcitedhelium,wheretheinnerelectronre- gested thattheemissionlineinheliumat320Âmightbeexplainedbytransitions: tained byWhiddingtonandPriestley(1934),Priestly andWhiddington(1935),more Rosenthal’s (1930)suggestion,sincediscarded,thatthecoronalinesat5303,3987,and tailed evaluationandunderstandingofthesephenomena. classification. Earlyinterestindouble-electronexcitationwasfurtherstimulatedby 180-MeV electronsynchrotronattheU.S.NationalBureauofStandards. \slp P°-2pP.SubsequenttheoreticalcalculationsbyWu(1944)supportedthis © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem Resonances inthephotoionizationcontinuumofheliumhavebeenobservedspectroscopically Recently, wereportedtheobservationofautoionizingneutralatomenergystatesin The developmentofthetheorytwo-electronexcitation statesinheliumhasroughly Helium isofspecialinterestbecausesuchhigh-lyingstatesrequirethesimultaneous Evidence fortheexistenceofthéstatesresponsibletwomostprominentres- Early experimentalevidencefortheexistenceoftwo-electronexcitationstatesin * WorksupportedinpartbytheU.S.AtomicEnergyCommission. TWO-ELECTRON EXCITATIONSTATESINHELIUM* National BureauofStandards,Washington,D.C. R. P.MaddenandK.Codling Received September11,1964 I. INTRODUCTION ABSTRACT 364 1965ApJ. . .141. . 364M here isapproximatelytwentytimesthatavailableintheelectronenergylossexperiments several ofthepossibledouble-electronexcitationstateshavebeencalculated(Fender The resultspresentedinthispaper,additiontobeingconsiderablymoreextensive, val asafunctionofwavelength,calculatedforsinglemonoenergeticelectron.The supersede theearlierresultsinseveralimportantdetails. and Vinti1934;Wu1934,1944;CadyWilson1935;Ma1936;Bransden monoenergetic electronforenergiesof120and180MeV. electrons duetotheirstrongradialaccelerationwhileorbitingwith170-MeVenergyin served, andtheshapesofbroadeststructureshavebeenstudiedinsomedetail. and Dalgarno1953;Propin1960;Cooper1963;Burke,McVicar,Smith1963).A radiation fromthisunconventionalsource,namely, itsangulardistributionandpolariza- calculation hasbeenperformedfortwo-electronenergies, usingtheradiusofNBS and theradiusoforbit.Figure1showspowerradiatedperunitwavelengthinter- with thespectralregionofgreatestradiantintensitydependingonelectronenergy tinuum absorptionofheliumduetotwo-electronexcitationstates.Theresolutionused and applied(Fano1961)totheelectronlossdataofSilvermanLassettre. detailed theoryfortheabsorptionprofileofautoionizingtransitionshasbeenformulated the synchrotron.Theinstrument issolidlyconstructedwithasfewadjustments as electric vectorintheplaneoforbit. of thelightisutilized,radiationroughly85 percentplane-polarized,withthe dependence isverydifferentforthetwopolarizations. Iftheentireverticaldistribution synchrotron. Atanelectronenergyof180MeVthe powerperunitwavelengthjpeaksat the NBS180-MeVelectronsynchrotron.Thisradiationiscontinuousinwavelength, tion (CodlingandMadden1965).Theintensityof theradiationdecreasesbyafactorof about 340Â,andtheusableintensityisknownto extenddowntoatleast75A. (radius 0.84meters).Theordinateisthepowerradiatedintoallanglesperunitwavelengthforasingle (Silverman andLassettre1964).Consequentlymanymoreresonanceshavebeenob- 10 withinafewtenthsofdegreeaboveorbelow theorbitalplane,andangular © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem The backgroundsourceforthepresentabsorptionexperimentwaslightradiatedby The presentpaperpresentsthefirstspectroscopicstudyofstructureincon- A preliminaryreportonthisresearchhasbeengiven(MaddenandCodling1963¿>). A specialgrazing-incidence spectrographwasdesignedandconstructedfor usewith In additiontoitscontinuousnature,therearetwo otherunusualpropertiesofthe Fig. 1.—Spectraldistributionofthe“synchrotronlight”computedforNBSelectronsynchrotron TWO-ELECTRON EXCITATIONSTATES365 II. EXPERIMENTALDISCUSSION a) SynchrotronLightSource b) Spectrograph 1965ApJ. . .141. . 364M possible. Thoseadjustmentswhichweredeemedessentialdesignedtowithstandthe dispersion at200Âisapproximately1Â/mm.Thespectralslitwidthusedinthisexperi- instrument usesa600line/mmgratingof3-mradius.Theincidentangleis84.5°andthe ment isapproximately0.06Â. cated ofonlyonematerial(aluminum)inanattempttoavoidtemperaturestresses.The considerable vibrationscreatedbythesynchrotronmagnet.Thespectrographisfabri- 366 R.P.MADDENANDK.CODLING passing throughawindowandopticalfilter.Anintegrationofthisvisiblelightsignal Another portionisinterceptedbyamirroranddetectedphotomultiplierafter system, throughthetangenttubeconnectiontoentranceslitofspectrograph. in theintensityofradiatedlight. radiation. Thistechniqueissuperiortoatimeintegrationsincethenumberofelectrons serves asanindexoftheexposurephotographicplatetovacuumultraviolet the lightfromorbitingelectronstravelssynchrotron’storus-shapedvacuum captured inorbitthesynchrotronvarieswithtime,causingaproportionalvariation spectrograph. A3-meter,6001/mmconcavegratingisusedat84.5degreesangleofincidence.Foilfilters The integratedphotomultipliersignalisusedasanexposureindex.gastobestudiedfillstheentire A thickwasused.Thisfiltertransmittedwellinthe200-Âregion,butstronglyab- of thetwo-electronexcitationstateinabsence ofinteractionwithadjacentcontinua mental reliability,andrepresentsneitherthe“center” oftheresonancenorlocation long wavelengthwereavoided. sorption maxima(seeFig.3).Thispointinthe resonancewaschosenforexperi- graph wasmeasuredwithaMcLeodgaugeandcontrolled byanautomaticleak.The gen-cooled carbontrapbeforeenteringthespectrograph. Thepressureinthespectro- sorbing below170Âandabove825Â.Thussecond-orderspectrastrayradiationof (not shown)canbeinsertedinfrontofthespectrographentranceslit. gas, thusmaintainingahighvacuuminthesynchrotron torus. arrangement wassuchthattheonlygasleakfrom the spectrographintosynchrotron through theuseofaquantum-defect plotandagratingequationwhichhasproven highly section betweenthespectrographandsynchrotron tangenttube,removedtheleakage tangent tubewasthroughtheentranceslit.A4-inch diffusionpump,operatinginthe optical shutterorafilterholder.Inthepresentexperimentsanaluminumfoil1140 (Fano 1961). © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem The arrangementoftheexperimentalapparatusisindicatedinFigure2.Aportion The lightwhichfallsuponthespectrographentranceslitcanbeinterceptedbyan The positionsoftheabsorption peaksweredeterminedrelativetotheirseries limits The gasusedwascommercialtankhelium,which waspassedthroughaliquid-nitro- Fig. 2—Experimentalarrangementforutilizingthe“synchrotronlight”absorptionspectroscopy. The positionsoftheabsorptionresonanceswere determined atthepeakofab- c) Procedure 1965ApJ. . .141. . 364M © American Astronomical Society Provided bytheNASA Astrophysics DataSystem

a reduced-absorption zone or “window” in the continuous photoionization background absorption. 1965ApJ. . .141. . 364M © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem

Fig. 4.—An enlarged photograph of the absorption spectrum of helium in the region 190-210 Â. Here the weak and narrow resonances due to l the states (sp} 2n~) P° can be more easily seen. 1965ApJ. . .141. . 364M 4 1 + viously determinedincident-energyratioforthetwopositions.Thisprocedure,while knowledge oftheH-D-curveforphotographicemulsion. The problemofthevariabilityH-D-curvefromonephotographicplatetoanother reliable forthisspectrograph.Theknownserieslimitthenputsthewavelengthsonan vertically displacedpositionsonthephotographicplate,andgaspressure.Thein- in thetwospectraatwavelengthofinterest.Forthisabsorption recorded withthespectrographfilledhelium,toapressurewhichrangedfrom0.06 graphic plateatthetwoverticallydisplacedpositions.Anotherphotographicwas developed emulsionatthewavelengthofinterest.Theratioexposuresusedfor absolute basis.Estimatederrorsforthesenumbersareincludedwiththeresults. tedious, allowedtheabsorptioncoefficientofgastobedeterminedwithoutanexact coefficient ofthegascouldbecalculatedfromknownexposureratioandpre- to 0.3mmHg.Onceagaintheexposureswereadjusteduntilequaldensitywasobtained two spectrathenrepresentedtheratioinintegratedenergyincidentonphoto- exposures forthetwospectrawereadjusteduntilequaldensitiesobtainedin each platebymovinganoccultervertically.First,withnogasinthespectrograph, was avoidedbyutilizingadensitycoincidencetechnique.Twospectrawereexposedon primarily byoutgassingofthephotographicplatesandwereminimizedpredrying gauge andinadditionsufferedfromthefactthatadynamicpressurebalancewasre- gas-absorption run. due tothisvariationwasminimizedbydeterminingitsvaluebothbeforeandaftereach cient havebeentheevaluationofratioincident-lightintensityattwo then exposedatthesesametwopositions;however,thistimeoneofthespectrawas The lowest-lyingresonancehasitsabsorptionpeak at206.21+0.05Â(60.1eV)andis Hg andapathlengthofapproximately84cm.Theobservedresonancesaresuperim- helium intheregion165-200Â.Thisspectrumwastakenforapressureof0.5mm quired tomaintainaconstantamountofgasinthespectrograph.Itwasfounddifficult limits then=3andw 4statesofHe*. from themostprominentseries.Theseresonances canbefittedintoserieshavingas for theseresonancesaregiveninTable1. posed uponthecontinuumphotoionizationabsorptionwhichexiststhroughoutthis to avoidsmallvariationsinpressureduringarun.Samplegasimpuritieswerecaused tensity ratiohasbeenfoundtoundergoasomewhatregulardailyvariation.Theerror scattering experiment(60.0±0.1eV).Theremaining resonancesinthemostprominent region. Asaresultoftheinterferencetwo-electronstateswithcontinuum the platesinaseparatevacuumsystem. absorption spectrum,existing intheregionofmostprominentseries.The firstmem- series canbefittedtoaRitzformula.Weassumethe limittobe189.58A(65.4eV),i.e., associated withthe2s2pP°stateofneutralhelium. Thepositiongivenhereisingood states, eachresonanceshowsaregionofenhanced absorptionandaregionofreduced the n=2stateofHe.Thepositions,estimatederrors, andeffectivequantumnumbers agreement withthevalueobtainedbySilverman and Lassettre(1964)intheirelectron- absorption immediatelyadjacent(the“Beutler-Fano” profile[Beutler1935;Fano1935]). © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem The absorptionprofilesofthestrongestresonancesobservedwerestudiedindetail. The twomostimportantsourcesoferrorindeterminingtheheliumabsorptioncoeffi- The gas-pressuredeterminationsincorporatedtheusualreadingerrorofaMcLeod Figure 3isaphotographoftheabsorptionspectrumwhichhasbeenobtainedfor A numberofweakerresonancescanbeseeninFigure 3lyingtoshorterwavelengths One furtherseriesofvery weakandnarrowresonancescanbeseeninthis helium- TWO-ELECTRON EXCITATIONSTATES367 a) PositionandIdentificationofResonances in. RESULTS 1965ApJ. . .141. . 364M 1 +l 21 l1 + 2 + 2 210 1 namely 2pndP°.Burkeetal. (1964)havecalculatedthepositionofadditionalresonances duetothe pected goingtothelimitHe(n=2)(eachhaving2s2pP°asacommonfirstmember) fied withthetransitionIs^2s2pP°.However,twoseriesoflevelsmightbeex- The lowest-lyingandmost-prominentresonanceobservedcanbeunambiguouslyidenti- has thesamelimitasprominentseries,andresonancesaresimilarinprofile, 368 R.P.MADDENANDK.CODLINGVol.141 existence ofsuchstates. states 2snpP°and2pnsmixstronglyinapproximatelyequalamounts.In which timeonlytheprominentserieshadbeenobserved.Theydeterminedthat problem wasconsideredbyCooperetal.(1963),duringanearlierexperimentalstage,at ber ofthisweakseriesliesbetweenthefirstandsecondmembersprominentseries, since eitherthesorpelectroncouldprogressinprincipalquantumnumber.This although narrowerthanthecorrespondingmembersofprominentseries. and canbeobservedmoreeasilyintheenlargementshownFigure4.Theweakseries numbers determinedfromabestseriesfittothe He(w=2)limit.Thedifferencein superimposed ontheprominentseries(seeFig.4) canbeidentifiedwiththetransitions been experimentallyestablishedascanbeseen from thespectrainFigures3and4. the (+)and(—)transitionsaregiveninTable 1alongwiththeeffectivequantum would bemuchgreaterthantothe(2n—)states. They suggestedthat“futureobserva- ground state(Is)wavefunction,thatthetransitionprobabilityto(2n+)states tron wavefunctions,themixedstatesarerepresentedby their formulation,whereU(2snp)andU(2pns)arethesymmetrizedindependent-elec- the lowest-lyingtoHe(^=2)limitcanbeidentified withthetransitionsIs^—» Using thenotationofCooperetal.,prominent seriesofresonancesextendingfrom tion ofweakandverynarrow(2n—)levelsisconceivable^ andthat“the(+)levelof each pairliespresumablyabovethe(—)level.”The validityofthesecommentshasnow Is ^—»(sp,23—),24—),and25—)P. The observedwavelengthpositionsfor 10 (sp, 2n-{-)P°,whilethethreeveryweakandnarrow resonanceswhichhavebeenobserved 4 . 9 3 2 . 8 . 6 . 5 . 7.. 1 1 1 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem Thisclassificationschemeneglects theinfluenceofadmixtureotherpossibleP° upper states, In thisexperimentonlytransitionsfromthegroundstatetoP°statescanbeexpected. Cooper etal.concluded,fromananalysisoftheoverlap^{sp,2n±)with Experimentally DeterminedWavelengthsandEffectiveQuantumNumbers 1l FOR THE(sp,2n+)P°AND2n~)ABSORPTIONRESONANCESINHELIUM 206 21(±005) 194 78(± 189 98(±002) 190 22(± 191 29(± 192 33(± 190 08(± 190 43(± 190 75(± A(À) .02) 02) 02) 02) 02) 02) 02) c sp, 2n±)=^2[^(2snp)±U(2pns)]. (sp, 2»+)iP 9 8 85 606(±0 002) 82 82 82 (± 812(+ 85 791(± 005) (±0 2) (± (± (± (± TABLE 1 07) 04) 02) 012) 15) ID 197 56(±003) 191 73(±005) 193 30(±05) X(Ä) {sp, In-)iP° 4 30(±005) 3 29(+02) 2 269(±0004) 1965ApJ. . .141. . 364M 2l 0 21l02 + l l 2 No. 2,1965TWO-ELECTRONEXCITATIONSTATES369 higher-lying states,however,mayagaincorrespondtothepositivecombinationof mixed independent-electronwavefunctions.Thus,theidentificationofcorresponding sociated withtransitionsIs—+3s3pP°andS—>IP,respectively.The indicating thelargedifferenceinelectron-electroninteractionbetween“in-phase” position andeffectivequantumnumberoftheobservedresonancesin(sp,3n-\~) transitions areIs^—»(sp,3#+)P°andlsS-+4w+)IP,respectively.The the (sp,2n±)series.Thelowest-lyingmembersoftwoseriesmaycoursebeas- 3) andHe(w=4)limits,cannowbeidentifiedusingtheargumentofCooperetal.for and the“out-of-phase”modeofoscillationtwoelectrons(Cooperetal.1963). effective quantumnumberforthecorrespondingmembersoftwoseriesis0.52, (spj 4^+)seriesarelistedinTable2. 3dnfP°. prominent {sp,2w+)series.TheresultsareshowninFigure5forthespectralregion ionization limitsforthesecases.However,thedetailed physicalinterpretationofthis Lassettre (1964)andbyKuyattSimpson(1963) fromelectron-lossexperiments. resonances becomerapidlynarrowerwithincreasingprincipalquantumnumber.The profile awaitedtheanalysisofelectronlossdata ofSilvermanandLassettre(1964)by quite narrowwithrespecttothespectrometeroptical slitwidth. Tomboulian (1965)andinfairagreementwith the determinationbySilvermanand Section II,theabsorptioncoefficientwasdeterminedatvariousfrequenciesnear optical slitwidth,andthereforethehighermembersbecomerapidlylessdistinct. Fano (1961)forthe2s2pP°resonanceinhelium. In thatpaper,theformalismwaspre- absorption spectrumofAr,Kr,andXebetween the Pz/

Here (excited state, (

ELECTRON VOLTS

WAVELENGTH (ANGSTROMS) Fig. 5.—The absorption coefficient of helium in the 175-245-Â region. The solid curve connects the points at which the data were reduced in the present experiment. The dashed curve indicates the result of Lowry et al. (1965).

E', as y (Tv would be the true final state in the absence of an interfering discrete state) ; VE’ is the matrix element for autoionization of the discrete state; P and F are quantities which depend on the evaluation of the interaction between the discrete state and the continuum states of non-equivalent energy. The resonance, according to equation (1), may be thought of as centered at £' + F (F therefore represents a shift of the resonance from the position of the zero-approximation discrete state). The mean lifetime of the discrete state before autoionization is h/lirI PVl2> and therefore the resonance can be thought of as having a “width,” F, equal to 27t|F^] 2. Thus, € can be seen to be a measure of energy, in units of F/2, relative to the resonance center, while q is an index which determines the profile of the resonance according to equation (1). The height of the absorption maximum relative to the background absorption is given by (q2 + 1), and this maximum is displaced from the center of the resonance by Ae = \/q.

© American Astronomical Society • Provided by the NASA Astrophysics Data System 1965ApJ. . .141. . 364M -1 3 l l 1 above. assumed tobethoseindicatedonthefigure.Noslitfunctioncorrectionhasbeenappliedthesedata the statisticaldeterminationofvalueabsorption atthispoint.Whilethepeakof the absorptioncoefficientwasdeterminedtobe (272 ±25)cm(atS.T.P.),andthe F =0.033eV.Purificationof the samplegasinsubsequentmeasurementsresulted valuesgiven the absorptionatresonanceminimum.Sixindependent runsweremadetoimprove the errorforindividualdatapoints.Particular emphasiswasplacedondetermining data areindicatedaspoints.Thesolidcurverepresents thebestfitofrelation(1)to points representthevaluesobtainedfromcontinuousdataby“densitycoincidence”technique the experimentaldata,whichhavebeenobtained foravalueof<7=—2.80+0.25and error intheobservedabsorptionovermostof resonance. the spectralslitwidth,indicatedinFigure6,issufficiently narrowastocausenegligible (Sec. IL).Thesolidcurverepresentstheprofilepredictedbyequation(1)ifvaluesofqandYare tion goescompletelytozeroatonepointintheresonance. (the opticalslitwidthofthespectrographisindicatedonfigure).Note,inparticular,thatabsorp- T =(0.038±.004)eV.Noslitfunctioncorrection hasbeenmadeinthisanalysis,since was devotedtotheexperimentaldeterminationofabsorptionprofileforthisreso- nance. Figure6isanexpandedviewofthe2s2pP°resonanceinwhichexperimental ment wassmallerthanthewidthof2s2pP°resonance.Henceaconsiderableeffort condition doesnotholdifmorethanonecontinuumcaninteractwiththediscretestate.) No. 2,1965TWO-ELECTRONEXCITATIONSTATES371 the absorptioncompletelyvanishatonepointinresonance,namelye=—q.(This the aboverelationshold,shouldbeanadequatedescriptionforcaseofheliumnear or morethanonecontinuummustbeconsidered;however,thesimplepicture,forwhich the 2s2pP°resonance.Ofparticularinterestisfactthatrelation(1)requires 3 l © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem Inapreliminaryreport(Madden andCodling1963&)thesevalueswerereportedtobe ^=—238, The profileformulatedbyFanofitstheexperimental dataverywell,certainlywithin Fig 6—Absorptionprofileoftheresonancecausedbytwo-electronexcitationstate,2s2pP°.The 3. Experimentalresonanceprofile.—Thespectralslitwidthavailableinthisexperi- The situationismorecomplicatediftheinteractionofthanonediscretelevel 10 05-0-10 DISPLACEMENT FROMPEAKABSORPTION(ANGSTROMS) ELECTRON VOLTS 1965ApJ. . .141. . 364M 14 2 l 2 -1 l l0 reported whichwascausedby impuritiesdueprimarilytooutgassingphotographicplates. background absorptioncoefficientextrapolatedtotheresonancecenterisapproximately 372 R.P.MADDENANDK.CODLINGVol.141 be (0±3.0)cm“(atS.T.P.) series—i.e., theyhaveanegativevalueoftheshape index,q.Further,aninspectionof x] slitfunctiongaveaquitesimilarresult;however,therectangularisprobably nique (Sec.lie).Thedashedcurverepresentstheprofilepredictedbyequation(1)ifvaluesofqand resonance, atheoreticalprofilegivenbyrelation(1)forq=—2.0andP0.008eV, approximation. Figure7showstheexperimentalabsorptiondataobtainednearthis a slitfunctioncorrectionmustbemadealthoughthisisonlyknownincrude to eitherthe(sp,29+)or {sp,210+)resonances. the originalphotographindicatesthat(sp,23—) resonanceissimilarinappearance ment. Theobservedmembersofthe(sp,2n—)series aremuchnarrowerthantheircoun- 4w+) P°series.However,afewfeaturesofthese otherresonancesareworthyofcom- The pointsrepresentthevaluesobtainedfromcontinuousdataby“densitycoincidence”tech- these resonancesareasymmetricinthesamesense asthemembersof(sp,2n-\-) the spectrometerspectralslitwidth(0.02eV).However, itcanbeseeninFigure4that per cent. terparts inthe(sp,2n-\-)series—theobservedbreadths beingdeterminedprimarilyby mental dataindicatesthatthevaluesofqandP used areprobablygoodtoatleast50 dashed curvebyarectangularslitfunctionofwidth0.02eV. F areassumedtobethoseindicatedonthefigure.Thesolidcurverepresentsresultofsmearing the theoreticalprofilesmearedbyarectangularslitfunctionof0.02-eVwidth.(A[sinx/ (33 ±5)cm(atS.T.P.),theabsorptioncoefficientatminimumwasdeterminedto of the(sp,2n-\~)P°seriesormembers (sp, In—)P°,3^+)IP,or a betterapproximation.)Theroughagreementofthesmearedprofilewithexperi- {sp, 23+)resonanceinanattempttodeduceqandP.Thedifficultyencounteredisthat 4 1 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem A roughanalysiswasperformedontheexperimentalcross-sectionprofileof Inthepreliminaryreport(Madden andCodling19636),aresidualabsorptionintheminimum was No attempthasbeenmadetodeterminetheresonance profileofthehighermembers Fig. 7.—Absorptionprofileoftheresonancecausedbytwo-electronexcitationstate,(sp,23+)P°. 0.3 0.20.10-0.1-0.2-0.3 DISPLACEMENT FROMPEAKABSORPTION(ANGSTROMS) ELECTRON VOLTS 1965ApJ. . .141. . 364M l 1 1 C 1 c c 0 No. 2,1965TWO-ELECTRONEXCITATIONSTATES373 interpretation ofthisreversalinthesignqhasrecentlybeenaccomplished(Cooper and (sp,4w+)P°seriesaretheonlyexperimentalvaluespresentlyavailableforthese differ fromthecorrespondingmembersof(sp,2n-\-)series. higher-lying resonancescontrastmuchlessnoticeablywiththebackgroundabsorption. helium spectrum.Sincethen, anumberofadditionalcalculationshavebeen performed mentally observed.Fano(1961),afteranalyzingthe effectoftheslitfunctionsmearing states inheliumwerecarriedoutbyanumberof workers (FenderandVinti1934;Wu 60.1 eV.Weestimatethatthetrueabsorptionpeak lieslessthan0.01eVbelowtheen- studied byelectron-scatteringexperiments.Forthesetworesonances,thepresentspec- and Fano1964).Theobservedwidthsofthesehigher-lyingresonancesdonotgreatly q fortheobservedmembersofbothhigher-lyingseriesarepositive.Thephysical resonance minimum.Thisistobeexpected,sincethemixedcontinua(sp,2e±)P°,as on theelectron-scatteringdata,concludedthat the “center”ofresonancelayat resolution of0.4eV,therealabsorptionpeaklies athigherenergythanthatexperi- scattering measurementsareshowntobeingoodagreement withthepresentdetermina- experiments ofSilvermanandLassettre(1964).In Table3theresultsofelectron- achieved; also20timesgreaterresolutionwasavailable thanintheelectron-scattering states, withtheexceptionof2s2pP°and(sp,23+)levelswhichhavebeen (sp, 25+)LP well asthe(Isep)P°continuum,areinvolvedininteraction. In particular,noticethatthereisaconsiderableamountofresidualabsorptionatthe other butdifferfromthe(sp,2w+)seriesincertainimportantaspects.First,these ergy oftheresonancecenter. troscopic resultsshouldbethemostreliable,sinceabsoluteaccuracyismoreeasily (sp, 24+)P (sp, 23+)P 2s2p P. asymmetric intheoppositesensewithrespectto(sp,2n+)series—i.e.,valuesof tions, particularlyinviewofthefactthat electron-lossmeasurements,witha 1934; CadyWilson 1935)inanattempttoclassifyobservedemission linesinthe (Wu andMa1936;Wu1944; BransdenandDalgarno1953;Propin1960;Cooper 1963; 1 l 1 Two-Electron Experimentally DeterminedandTheoreticallyCalculatedEnergiesofAbsorp- © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem The valuesgiveninthispaperfortheenergylevelsof(sp,2n-\-)P°,3w+) The resonancescorrespondingtothe(sp,3n+)and4w+)seriesaresimilareach The earlytheoreticalcalculationsofthepositions ofcertaintwo-electronexcitation A furtherobservationofinterestisthattheresonances(sp,3w+)and4w+)are * Valuesgivenarethemeasuredpositionofpeakabsorption(ratherthanresonance“center”) Î Valuesquotedareaveragesofthosecalculatedfor2snpP°andns2pstates. f Calculationperformedfor2sSpP° States tion ResonancesinHeliumduetoTwo-ElectronExcitationStates 64 813(±0007) 64 462(±007) 63 651(±007) 60 123(±0015) : Experimental Energies(eV) Present Study 63 5(±02) 60 0(±01) Silverman Lassettre (1964) and IV. DISCUSSION TABLE 3 Fender (1934) 61 3 Vinti and (1934) 60 3 Cady Theoretical Energies(eV) Wilson (1935) 61 2 (1936) 63 6f 61 3 Ma and Wu Propin (1960) 60 4 (1963) 63 6f 64 4f Coo- per (1963) Burke 64 82 63 68 60 23 64 49 et al 1965ApJ. . .141. . 364M 1 Z 13-1l 13-1 2 2 2 0 l 2 1 l 1 Bransden, B.H.,andDalgarno, A.1953,Proc.Phys.Soc.London,A,66,904. Beutler, H.1935,ZsPhys.,93, 177. lent agreementwiththeexperimentaldeterminations. values calculatedbyBurkeetal.(1963)fortheautoionization probabilitiesareinexcel- Bransden andDalgarnoisinerror.Asthecase ofthepositionresonances, culations andtheexperimentalvaluesseemto indicate thatthevalueobtainedby Bransden andDalgarno(1953)forthe2s2pP°state. Themorerecenttheoreticalcal- Wu (1944)forthe2s2pP°stateisinseriousdisagreement withthatcalculatedby 5.8 (±0.6)X10secforthe2s2pP°state and 1.2(±0.6)X10secforthe excess transitionprobabilitycross-sectionforthisresonancewas0.15creVcm(where is 0.41(±0.13)