PHYSICAL REVIEW VOLUME 183, NUMBER 1 5 JULY 1969

Multiple Photo-Ionization of Xenon

R. B. Cairns, Halstead Harrison, and Richard I. SchoenGeo-AstxoPhysics Laboratory, Boeing Scientific Research Laboratories, Seattle, Washington 98124

(Received 26 February 1969)

The photoionization cross sections for the production of Xe, Xe, and Xe+++ have beenmeasured in the energy range 28-83 eV. At energies between the thresholds for Xe pro-duction 33.3 eV and 4d-electron removal 67.55 eV, the Xe cross section reaches about one-third of the total cross section. This cannot be accounted for by an independent electronmodel in terms of an electron shake-off process. At energies greater than 67.55 eV, boththe Xe and Xe++ cross sections increase; here the singly charged ion should be accompaniedby fluorescence and the doubly charged ion can result from a simple Auger process. Thetriple ionization is attributed to a process which involves first the removal of a 4d electronand then an Auger event in which two electrons are emitted simultaneously.

I. INTRODUCTION

In previous work we have used modulatedcrossed beam techniques to measure relativephoto-ionization cross sections of atoms to ahigh-energy limit of 50.2 eV. ' More recently,we have been able to extend these measurementsto 82.7 eV. In so doing, it was necessary toknow of changes in detection efficiency of thesodium-salicylate sensitized photomultiplier.The quantum conversion efficiency of sodiumsalicylate is known to be constant over the en-ergy range 13-40 eV, but a decrease is ob-served at higher energies. '~' To investigatethis decrease, to extend the range of measure-ments of the quantum conversion efficiency ofsodium salicylate and to calibrate our particularsystem, we undertook a comparison of the rateof production of singly charged ions in raregases with the current from our sensitized photo-multiplier. This comparison, made at a numberof wavelengths, was to be used with the knownphoto-ionization cross sections of the rare gasesto obtain the relative quantum conversion effi-ciency as a function of wavelength. Xenon wasfirst used for this purpose, since it has a largephoto-ionization cross section in the vicinity of80 eV, and it was well separated in the massspectrometer from residual gas contaminants.However, Xe was shown to be unsuitable by theobservation that when photons with energiesgreater than the threshold for Xe++ production(33.3 eV) were absorbed, a large fraction of theions formed was multiply charged. This obser-vation led to the present investigation of multipleionization processes and to the realization thaterrors can be incurred if rare-gas ionization isused for absolute photon-flux determinations inregions where multiple ionization processes areenergetically possible.

The known energy thresholds for double ioniza-

tion of all atomic species are within the range15-82 eV (826-115 A). Despite theoretical treat-ments' and the many measurements of photo-ionization processes in this spectral range, fewdata are available on multiple photo-ionizationprocesses. A literature survey showed thatComes4 has indeed reported measurements ofXe++ production to a high-energy limit of 44 eV,and Carlson et al. ' have examined the chargespectrum of Xe'under x irradiation. It has beenknown for some time that multiply charged ionsare produced by electron impact a few voltsabove the threshold for multiple ionization. '~'

At energies in excess of 500 eV, Schram et al. 'have reported electron bombardment measure-ments in Xe, but in this work, as in that of Carl-son et a/. , Auger processes could dominate themultiple ionization spectrum. The results re-ported here span the region from the Xe++ energythreshold through the first threshold for doubleionization involving the Auger effect.

II. EXPERIMENTAL TECHNIQUES

The apparatus used is shown schematically inFig. 1. Vacuum ultraviolet (vuv) radiation wasproduced in a triggered capillary spark sourceand dispersed with a 1-m focal length Seya-Nami-oka monochromator, which incorporated aplatinizedgrating (Bausch and Lomb model No. 35-52-28-840). The line spectrum obtained was of usableintensity to a short wavelength limit of 150 A(82.7 eV). The instrumental bandpass was setat 2 A. However, the spectral bandpass was de-termined by the widths (~ 0.1 A) and spectraldistribution of individual emission lines withinthe instrumental bandpass. The dispersed radia-tion passed into the ionization chamber and be-tween the pusher plate and entrance aperture ofa time-of-flight mass spectrometer. It was thendetected with a sodium-salicylate sensitized

183 52

53

Seya - Namioka Mortochrometer

Light Sourc

Power Supply

Trigger

rticle

itttiass Spectrometer

~Phato multiplier

ower Supply

Pre Amp.

Pulse 5,'

PulseGerterator i P mplifier

Delayed Pulse

Recorder

Electrometer

Post Amp

DelayedGate

Power Supply Sealer

0Scope

PIG. l. Apparatus for relative photo-ionizationcross-section measurements.

photomultiplier. Spectroscopically pure Xe wasRdnlltted to the lonlzRtloD chamber Rt R constRntpressure not exceeding 10 ' Torr. At this pres-sure, the open EMI 96438 particle multiylierassociated with the mass spectrometer could beoperated at 6000 V without breakdown, and no

complications were expected from charge exchangereactions. The base pressure in the liquid-ni-trogen-ionization chamber was about 5x 10 'Torr. The puls8 applied to the ion yusher platewas delayed appxoximately 4 p.sec anth respectto the light-source trigger pulse. ID this manner,iona were collected after the completion of eachlight flash (which lasted about 2 p, sec) but beforethey had diffused from the collection volume ofthe mass spectrometer. The magnitude and widthof the pushlx1g pulse %'818 such that the Dlomenta.given to differently charged ions of the same ele-ment wex'8 px'opox'tloDRl to thelx' chRx'ges; that lsthe arrival times of Xe+, Xe++, and Xe+++ at theparticle multiplier mere in the ratios 6 3:2, re-spectively. Pulses from this multiplier corre-syonding to single-ion arrivals mere amplified,processed through an electronic gate of adjustablewidth and delay, which was set to yass only therequix'ed syecies, Rnd counted. In this manner,unwanted counts from ionized background gaseswere minimized. The ratio of the number ofcounts in a prescribed number of radiation flashesdlvlded by the measured radiation lntenslty wRS

determined at a number of wavelengths, correc-tions being made for background ionization causedby scattered radiation. These corrections mere

small except for measurements of Xe+ in the en-ergy range 45-65 eV, where the effective crosssectloD for the scRttex'ed radiation, which wRS

composed mainly of less energetic vuv photons,greatly exceeded the cross section being mea-sured, This situation was improved by placinga collodion filter over the exit slit of the mono-chromator. The transmittance of this filter,shown in Fig. 2, was low at energies less tha, n

45 eV, where the Xe+ cross section is large. At

energies between 50 and 83 eV, use of this filtergave up to a tenfold improvement in the signal-to-background count ratios. The collodion filter wasalso used to ensure that second-order radiationdid not invalidate the data obtained at the longerwavelengths.

As previously mentioned, it was necessary toknow of changes in the quantum convex sion effi-ciency of sodium salicylate at energies greaterthan 40 eV. This information was obtained by in-troducing Ne into the system and repeating thetype of measurement made with Xe. Carlsong hasdetected Ne++ and found its abundance relative toNe+ to be approximately 5 artd V% at average pho-ton energies of 72 and 85 eV, resyectively. Thisinformation, together with values of the total pho-to-ionization cross section'o of Ne, allowed frac-tional changes in quantum conversion efficiency

)00

e~

I10

—10

II ~~ e ~

~ ~e

NU

~ ~C000

CL

1.0—

] 0

20l I

Photon Energy (eV)

FIG. 2. The total photo-ionization cross section ofXe: ~, the sumoftheXe, Xe++, and Xe +cross sectionsnormalized to the data of Samson (Ref. 10); ———(Ref. 10); ~, Kderer (Ref. 11), recentexperiments byEderer have suggested that his earlier data shorvn above,are too large in the energy range 45-65 eV (privatecommunication);~, Lukirskji (Ref. 12) . The solid curverepresents the transmittance of the collodion filter.

CAIRNS, HARRISON, AND SCHOEN

to be determined. The quantum conversion effi-ciency was found to decrease by 25% in the region40-83 eV. A previous calibration of a differentsodium-salicylate coating had shown a 50% de-crease over the same energy range, and Samson2quotes about a 40% decrease between 36 and 62 eV.The differences in these results are of the order ofthe combined ex rors, and it is premature to assessthe reproducibility with which sodium-salicylatecoatings can be made. It should be mentionedthat the effect ascribed to a change in the quan-tum conversion efficiency of sodium salicylatecould be caused by a change in the spectral distribu-tion of its fluorescent radiation. However, the sim-ilarity between our data and those of Samson suggeststhat this is not the case, since we used a filter(Wratten No. 36) between the fluorescent screenand the multiplier, whereas Samson did not.

III. RESULTS

The measured cross sections of Xe+, Xe++,and Xe+++ over the energy range 28-83 eV areshown in Fig. 3. In general, about 1000 netcounts were recorded at each observation, so thatsimple statistical errors were about 3%. Radia-tion intensity measurements were reproducible to5'%%uo. Any error in the sodium-salicylate calibra-tion would not alter the ratios of the three crosssections at any one wavelength but would alterthe spectral shape of each cross section. At 28.6

Thresh oids Xe

'p 'D 'S2 0 2, 'l,0

X ++

0

0Q

~ IMP

C0~ ~00

0

Photon Energy (eV)

FIG. 3. Photo-ionization cross sections for the

production of Xe+, Xe++, and Xe~+

eV, where only Xe+ was formed, the cross sec-tion was normalized to the data of Samson, 'thereby placing this cross section on an absolutescale throughout the entire energy range. The magni-tudes, but not the spectral shapes, of the Xe++and Xe+++ cross sections, however, dependedon the relative detection efficiencies for singlyand multiply charged ions of the combination ofmass spectrometer and particle multiplier.These efficiencies were assumed to be equal.and the three cross sections were summed andthe resulting values compared with publishedtotal-ionization cross sections. The results areshown in Fig. 2, whexe the sums of the Xe+,Xe++, and Xe+++ cross sections have been plot-ted with their associated errors and shown to bein agreement with the data of Ederer, "Lukir-skii, "and Samson. " Since the Xe+ cross sec-tion equals the total cross section at 28.6 eV(our point of normalization, whereas it is only20'%%ug of the total at 63 eV), it can be concludedthat the detection efficiencies for differentlycharged ions were indeed nearly equal. Conse-quently, the Xe++ and Xe+++ cross sections arealso placed on an absolute scale.

IV. DISCUSSION

Three sets of thresholds for double ionizationprocesses are of interest here. The first in-volves the removal of two 5P electrons. Thisprocess leaves Xe+ in the 'P ground state(33.327 eV), the 'D metastable excited state(35.4 eV), or the metastable excited state '8(37.96 eV). It is ionization to these states whichgives rise to the appearance of double ionizationnear 35 eV. Since two outgoing Coulomb wavesare involved, no sharp jump at threshold is ex-pected and none is observed. The slow rise fromthreshold made lt impossible ln this experimentto estimate the relative contributions from thethree ionic states.

Removal of both a 58 and 5P electron becomespossible at 45.5 eV. No rise in cross sectioncorresponding to the formation of either thesinglet or the triplet I' states of the ion is ob-servable in the cross section. Similarly, atabout 60 eV, removal of both 5s electrons isenergetically possible, and again no increase inthe double ionization is observed.

In the energy region 55-60 eV, about one thirdof the ions produced are Xe++. In order to checkthe possibility of shake off, one-electron wavefunctions of Xe and Xe+ were calculated by theHermann-Skillman program, " and the innerproduct was taken. The deviation from 1.00 w'as

less than 2% when the 5p electron was removedand less than 3% when a 5s electron was removed.Thus, the double ionization appears not to be asimple shake-off process and requires an ap-

183 MULTIPLE PHOTO-IONIZATION OF Xe

proximation better than the one-electron approxi-mation for its explanation.

The appearance of such strong double ioniza-tion makes it seem likely that processes in whichone electron is removed from the atom andanother is excited are present. These shouldmanifest themselves as a series of thresholdsin the Xe+ cross section, discrete lines in theelectron energy spectrum, fluorescence ofvarious wavelengths from the Xe+ ions, andpossibly variations in the angular distributionsof the electrons emitted in single ionization. Thefact that no such thresholds have been observedin the ionization cross of Xe indicates that noone of the cross sections for any of these pro-cesses at its threshold exceeds 15% of the totalcross section in the spectral region 12-60 eV.

Hydberg series leading to two thresholds at67.55 eV ('DM, ) and 69.52 eV ('D„,) have beenreported by Codling and Madden' at energiesabove 65.11 eV (see Fig. 3) . We observe a sharpincrease in double ionization near 67 eV, wherethe wavelength of the radiation used overlapsseveral Bydberg states. The apparent smallrise in the Xe cross section near 64 eV is pos-sibly not real, since the point lies within experi-mental error of the point of next lower energy.Above the 'D thresholds for 4d electron removal,both the Xe+ and Xe++ cxoss sections increasemarkedly. The increase in the latter can beascribed to a simple Auger process, and the in-crease in the former indicates that fluorescenceof energies 55.42, 56.08, and 57.39 eV is alsoproduced. We note that the electron-energyspectrum from Xe++ produced by 4d-electronremoval followed by an Auger process shouldconsist of discrete lines. In contrast, Xe++produced at lower energies, at which no Augerprocess is possible, wiQ give rise to a continuum.These processes have been discussed previouslyby Krause et a/. " The lack of an abrupt rise inionization at the 'D thresholds has been explainedby Cooper" in terms of the effect of the centrifu-gal pseudopotential.

The threshold for Xe+++ production is 65.4 eV,but this ion was not observed below the thresh-old for removal of a 4d electron. No cascade ofsimple Augex events, each causing the emissionof a single electron, is energetically possible.

The most likely explanation of the triple ioniza-tion is that the photoemission of the 4d electronis followed by an Auger process which releasestwo electrons per event. Double electron emis-sion in an Auger process has been described byCarlson and Krause. " The electron-energy spec-trum from this process will consist of a singleline for the 4d photoelectron and a continuum forthe Auger double ionization process. From Fig.3, it is possible to estimate the cross sectionsfor single and double ionization which involved-electron removal. This is done by extrapolat-ing from 60 to 85 eV the cross sections for di-rect double ionization and for single ionizationof 5P and 58 electrons and subtracting the ex-trapolated from the measured values. Follow-ing this procedure, we conclude that at 84 eV,d-electron removal is followed in about 16% ofall cases by fluorescence, in about 61% by asimple Auger process leading to double ioniza-tion, and in about 23 /q by a double Auger processleading to triple ionization. It is to be notedthat the simultaneous removal of two electronsby the fall of a single electron into the 4d shellis comparable in probability to the radiation ofan x ray by the fall of a single electron into the4d shell. That is, the probability of the processforbidden in the independent-paxticle model is atleast as probable as the allowed radiation pro-cess.

From the foregoing, it can be concluded thatat energies above the double ionization threshold,photo-ionization of many electron atoms cannotbe adequately described by the usual one-electroncentral-field picture. Further data on crosssections for multiple ionization, electron energydistributions from such processes, and fluores-cence from processes of ionization and excitationwould be useful in mapping deviations from theone-electron picture across the Periodic Table.

ACKNOWLEDGMENTS

We thank Dr. D. Ederer for values of the Xetotal photo-ionization cross section and Dr. J.Cooper fox helpful comments on our work. Inaddition, we acknowledge the skilled labox atoryassistance of Claude Austin, Max Shupe, andKeith Torluemke.

H. Harrison, R. I. Schoen, R. B. Cairns, and K. K.Schubert, J. Chem. Phys. (to be published).

J. A. R. Samson, Techniques of Uacuum UltravioletSpectroscopy (Wiley-lnterscience, Inc. , 1967), p. 215.

3M. Pano and J. W. Cooper, Rev. Mod. Phys. 40,441 (1968).

F. J. Comes, in Proceedings of Thirteenth Annual

Conference on Mass Spectrometry and Allied Optics,16-21 May 1965 (unpublished), p. 12.

T. A. Carlson, W. E. Hunt, and M. O. Krause,Phys. Rev. 151, 41, (1966).

R. E. I'ox, Advances in Mass Spectroscopy I.

CAIRN, HARRISON, AND SCHOEN 183

(Pergamon Press Ltd. , New York, 1959), p. 403.

F. A. Stuber, J. Chem. Phys. 42, 2639 (1965).

B. L. Schram, Physica ~32 197 (1966).

T. A. Carlson, Phys. Rev. 156, 142 (1967).

J. A. R. Samson, in Advances in Atomic and Molec-ular Physics, edited by D. R. Bates and I. Estermann(Academic Press Inc. , New York, 1966), Vol. 2, p.177.

D. L. Ederer, Phys. Bev. Letters 13, 760 (1964);and private communication.

A. P. Lukirskii, I. A. Brytov, and T. M. Zimkina,

Opt. Spektroskopiya ~12 438 (1964) fEnglish transl. :Opt. Spectry. (USSR) 17, 234 (1964)].

13F. Hermann and S. Skillman, Atomic Structure Cal-culations (Prentice Hall, Inc. , Englewood Cliffs, New

York, 1963).K. Codling and R. P. Madden, Phys. Bev. Letters

12, 106 (1964).M. O. Krause, T. A. Carlson, and R. D. Dismukes,

Phys. Rev. 170, 37 (1968).J. W. Cooper, Phys. Rev. Letters 13, 762 (1964).T. A. Carlson and M. O. Krause, Phys. Rev. Letters

14, 390 (1965).

PHYSIC AL REVIEW VOLUME 183, NUMBER 1 5 JULY 1969

Theory of Atomic Structure Including Electron Correlation.III. Calculations of Multiplet Oscillator Strengths and Comparisons with Experiments

for Cll. Nl, Nil, Nlll, Oil, Obli, Ol v, Fll, Nell, and Nail!Paul Westhaus

DePartment of Physics, Oklahoma State University, Qillzoater, Oklahoma 74074

Oktay SinanogluSterling Chemistry Laboratory, Fale University, ¹soHaven, Connecticlt 06520

(Received 20 February 1969)

The theory of atomic structure developed in the two preceding papers which treats electroncorrelation accurately in excited as well as ground states is applied to the evaluation of multi-plet absorption oscillator strengths for a number of transitions of the type of 1s 2s 2pn

1s 2s2pn in Crr, Nr, Nzr, Nrrr, Orz, Orrr, Orv, Fzr, Nerz, and Nazrr. Those types ofcorrelation effects necessary to obtain accurate oscillator strengths are clearly indicated bythe theory. The usual improvement on the Restricted Hartree-Fock (BHF) calculation, the

mixing of those few configurations nearly degenerate with the BHF configuration, is by itselfincapable of bringing the oscillator strengths into agreement with experimental values. All

the nondynamical correlation effects given in the first paper of this series mustbe considered.Very detailed wave functions which contain those important nondynamical correlations wereobtained in that paper and here are used to compute oscillator strengths. The results arecompared extensively with recent experiments. The calculated values are usually in verygood agreement with experimental data. Many more transitions for which no experimentalresults are yet available are also tabulated here.

I. INTRODUCTION

In the first two papers' of th.'.s series a theorywhich includes electron correlation effects inboth the ground and excited states was developedand applied to several atomic properties. Meth-ods for predicting and analyzing the N-electroncorrelation energies in states of nonclosed shellconfigurations were given and applied to 113states of the ls22s "2P~(0 &n &2, 0 &m &6) con-

figurations in atoms and ions with nuclear charge5 «Z «11. Some of the excited configurationssuch as 18'2s2p' and 1s'2p' contain inner holes.Theoretical electron affinities and excitation en-ergies were obtained and compare favorably withexperiment.

In this paper we present a way of applying thistheory to predict allowed electric-dipole transi-tion probabilities. Multiplet absorption oscillatorstrengths of 29 far-ultraviolet transitions of the