PHYSICAL REVIE% A VOLUME 34, NUMBER 5 NOVEMBER 1986

Two-photon laser spectroscopy of the ns' and nd' autoionizing Rydberg series in xenon

Liang-guo %ang and R. D. KnightDepartment ofPhysics, Ohio State Uniuersity, Coiumbus, Ohio 43210

(Received 22 May 1986)

%e have studied the odd-parity autoionizing levels in xenon by two-photon laser spectroscopy

from the 6s[ 2 ]q metastable level via various J=1,2 6p' intermediate levels. Observed Rydberg

series are ns'[2 ]o ~, nd'[ z ]~,2, and nd'[

2 ]2 3 with n ranging to, in some cases, n & 80. This is the

first observation of J&1 odd-parity autoionization in xenon. These spectra are notable for the ab-

sence of the very intense, broad transitions to nd [ z ]~ which dominate photoabsorptiou from the

J=O ground state. %e here present energy-level measurements for 140 levels. These extensive new

data should be useful for further multichannel quantum-defect theory analysis of xenon.

I. INTRODUCTION

The highly excited states of the rare gases have attract-ed experimental and theoretical attention for years. Bothbound and autoionizing Rydberg states have been of in-creasing interest, especially since the development of mul-tichannel quantum-defect theory (MQDT). Analysis ofthe J= 1 odd-parity states of xenon was, in fact, the firstmajor application of MQDT. ' Further measurements ofautoionization in the rare gases are of value both for ap-plications, such as excimer lasers, and as further tests ofMQDT.

The excited states of the heavy rare gases, including xe-non, are best characterized by the jl coupling scheme, inwhich the orbital angular momentum / of the excited elec-tron is strongly coupled to the angular momentum jof theion core, forming a resultant angular momentum K. E isthen weakly coupled to the electron spin s, giving totalangular momentum J. The core states are np I'~&2 and

P3~2 (with inverted fine structure), giving j= z, —', . Ryd-berg states converging to the lower I'3/2 ionization limitare bound, while those converging to the Pi&2 limit are,except for the very lowest members, autoionizing. Nota-tion is nl [E]z, with a prime ( ) on I indicating j= —,.

The even-parity bound Rydberg series np and nf of xe-non have been studied by one-photon laser spectroscopyfrom the metastable 6s'[ —,']o level, both in an atomicbeam ' and also with optogalvanic spectroscopy, Exten-sion into the autoionization regime was first reported byRundel et al., s who photoionized metastable 6s'[ —,

']o and

6s[—,'

]2 in an atomic beam. They observed the np' seriesfor n =7,8 and also low members of the nf' series. Morerecently, the np' series has been extended in our laborato-ry to n =17 by one-photon laser spectroscopy from6s'[

2 ]o.'The odd-parity J= 1 levels have long been studied by

direct vacuum ultraviolet (vuv) absorption from the J=0ground state, with recent work by Yoshino and Freemanimproving and extending the earlier measurements. Theyobserve the ns'[ —,

']i and nd'[ —,

']i series with n ranging to

n=39 and n =65, respectively. Isolated s' and d' au-

toionizing resonances have also been studied at high reso-lution by extreme-ultraviolet laser techniques. Thebound ns and nd series have been measured using optogal-vanic spectroscopy.

Unfortunately, selection rules restrict one-photon ab-

sorption from the ground state to odd-parity, J=1 levels

only. Resonant two-photon excitation from the metasta-ble levels, on the other hand, allows the observation ofRydberg series with J ranging from 0 to 4 and thus pro-vides extensive new information on the highly excitedstates of the rare gases. Two-photon optical excitation in

krypton has been reported by Delsart et al.," but only forthe bound Rydberg series. Very recently, a two-photonstudy of both bound and autoionizing s and d series ofneon with J=0, 1 has been reported. '

In this paper we report the study of resonant two-photon autoionization in xenon. We have observed theseries ns'[ —,

']o i, nd'[ —,

']i 2, and nd'[ —,

']2 &

with n ranging

to, in some cases, n & 80 by two-photon excitation fromthe inetastable 6s[—,']2 level through intermediate levels

6p'[ —,'

]i and 6p'[ —', ]i z. To our knowledge, this is the firstobservation of J&1 odd-parity autoionization in xenon.We present the measurement of 140 energy levels, 91 ofthem being reported for the first time.

II. EXPERIMENT

A second dye laser has been added to upgrade our pre-vious ability to perform one-photon spectroscopy withfield ionization or autoionization detection. The basic ex-perimental procedure, which is laser spectroscopy of' ametastable atomic beam, has been described elsewhere. '

A thermal atomic beam of xenon is formed by an effusivenozzle and passes through a transverse electron gun,where a small fraction is excited to the metastable 6s'[ —,

']o

and 6s[—', ]z levels. Only the J=2 levels are used in these

experiments. The metastable beam passes through a 3-mm aperture into a second, differentially pumpedchamber, where it is intersected at right angles by twoNd:YAG-pumped dye laser beams (where YAG denotesyttrium aluminum garnet). Ions produced by autoioniza-tion are dragon through a grid in the parallel-plate interac-

34 3902 1986 The American Physical Society

T%'0-PHOTON LASER SPECTROSCOPY OF THE ns' AND nd'. . . 3903

tion region and accelerated into a microchannel platedetector. The extl'actloil pulse is Ilot applied lliltll afterthe laser has fired, to avoid Stark effects at the higher n,and is sufficiently low that the arrival times of ions are in-dividually resolvable. The output is amplified, then rout-ed through a discriminator and into a high-speed gatedsealer.

The first dye laser excites the intermediate level of6p'[ —,

']i or 6p'[ —', ] i z. These three levels lie close together,

making it convenient to change quickly from one toanother without changing laser dye. Depending on choiceof intermediate level, as described in the next section,various ns' and nd' autoionizing levels can be reachedwith the second laser. The two laser pulses, each =10nsec duration, are essentially synchronous.

In contrast with our previous one-photon spectroscopy,careful geometric alignment is here found to be critical.Best signal-to-noise ratio is obtained when the second dyelaser beam is larger than and completely overlaps the firstbeam. This assures that all atoms excited to the inter-mediate level can then be photoionized. Our major limita-tion is keeping the first laser intensity sufficiently low tominimize the background from resonant two-photon ioni-zation to the continuum states by that laser alone. Thereis no background from the second dye laser operatingalone.

A commercial neon hollow cathode discharge tube isused for wavelength calibration of the second dye laser viathe optogalvanic effect. Our estimated uncertainty in thewavelength calibration is +0.3 cm

III. RESULTS

By use of the three intermediate levels 6p'[ —,'

]„6p'[ —', ]„and 6p'[ —', ]i we have been able to observe all ofthe ns' and nd' autoionizing Rydberg series. These havevalues of angular momentum J ranging from 0 to 3.Some typical spectra are shown in Figs. 1 and 2. Notethat the resonances are symmetric and that there is httlecontinuum intensity. The major component of the ap-parent continuum is, in fact, due to a two-photon ioniza-tion background from the first laser alone. These qualita-tive features are readily understood from the fact that the

l6'

~d[S~Z],

d'[e~Z],

s'[iiz],~~i Q m~saJ L ~ I~

TW +pe~~ & g y~ H ~Tl

600 500Energy {crn ')

FIG. 1. A portion of the xenon odd-parity autoiomzationspectrum from intermediate level 6p'[ z ]q.

m] el l81 l7]

l l I I

l51

d [5/2]~~~

s[iiz]d[Wa],+

,-l.dl ]

intermediate 6p' levels have a nearly pure j=—, core. Di-pole matrix elements with the j=—,'continuum are thus

quite small. The lack of interference between discrete andcontinuum transitions leads to symmetric peaks centeredon the resonances and having widths [full width at halfmaximum (FWHM)] equal to the autoionization rates I .

Another important aspect of these spectra is the ab-sence of the intense, broad resonances to nd'[ —', ]& whichdominate the vuv absorption spectra from the groundstate. Indeed, these levels are barely seen at all in ourspectra. Consequently, our data provide a more straight-forward measurement of resonance positions and widths,without the need for a MQDT analysis of line shapes.

The transitions we have observed with this techniqueare as follows:

6p'[ —,'], ns'[ —,']o, n =9—14

~ns'[ —,']i, n =10—54

~nd'[ —,' ]i, n =21—26

nd'[ —', ]i, n =8—84

6p'[ z ]i~ns'[ i ]o, n = 10—15

~ns'[ —,]i, n =9—46

~nd'[ —,]i, n =12—30

~nd'[ —', ]i, n =8—79

6p'[ —', ]p~ns'[ —,']i, n=10—52

~nd'[ , ]i, n =8——26

~nd'[ —, ]&, n =8—80 .

It is clear that many final levels can be accessed frommore than one intermediate level, which provides redun-dancy for our energy-level measurements.

We have utilized three types of information to identifythe transitions which we observed.

(1) Electric dipole selection rules in jl coupling areAj =0, Lt'C =0,+ 1, and 5J=0, + 1. All observed transr-

l07900 800 700 600 500 400 500Energy {cm ')

FIG. 2. A portion of the xenon odd-parity autoionizationspectrum from intermediate level 6p'[T]~. The apparently in-

creased width of the s lines, in comparison with Fig. 1, is dueto the unresolved presence of both J=0 and 1 components.

3904 I.IANG-GUO %'ANG AND R. D. KNIGHT 34

TABLE I. Quantum defects p for the six odd-parity autoion-

izing Rydberg series in xenon (n &13) and a comparison ~iththe bound-state quantum defects of each series.

ns'[ —,'

]0ns'[

2 ]ind'[

2 ],nd'[ —,

']i

«'[ —,'

hnd'[ —', ]3

Quantum defect p

4.021 +0.002

4.013+0.002

2.32+0.01

2.451+0.004

2.474+0.004

2.435+0.004

Bound state p

4.0S5 (n =7)4.045 (n =7)2.273 (n =5)2.454 (n =5)2.475 (n =5)2.432 (n =5)

tions obey these rules, although some allowed transitionswere not seen. (The apparent violation in the initial6s~6p' transitions arises from configuration interactionin 6s, which destroys j as a good quantum number. ) Themissing transitions can be explained on the basis of ex-pected intensity, as discussed below. Note in particularthat use of 6p'[ —,]2 gives unambiguous identification ofnd'[ —,]i, which is reached only through this intermediatelevel, and of ns'[ —,

']i, since its J=o fine-structure partner

cannot be reached this way. Also that use of 6p'[ —,']ieliminates transitions to K= —,

'levels.

(2) Calculation of expected intensities further clarifiesthe situation. Dipole matrix elements in jl coupling canbe calculated in a manner which we have previously out-lined in conjunction with Stark effect measurements. '

Only relative intensities are needed here, so evaluation ofradial integrals is not necessary. Our calculations indicatethat the transitions 6p'[ —', ]i ~nd'[ —,

']z and

6p'[ —,' ]2~nd'[ —', ]i should be much stronger than any oth-

ers, and indeed that is what we observe. Further, for thetransitions 6p'[ —,']i~nd'[ —,']i 2 the J=2 branch should

dominate. The allowed but unseen transitions are all cal-culated to be very weak. The correspondence between cal-culated and observed intensities is not perfect, likely dueto configuration interaction in the 6p' levels, but is ade-

quate, in conjunction with other information, to furtherguarantee the reliability of our assignments.

(3) Finally, previous measurements confirm the tenta-tive assignments made on the basis of the last two para-graphs. Yoshino and Freeman have made extensive mea-surements of the J= 1 levels, but care has to be exercised

TABLE II. Energy levels and effective quantum numbers for the ns'[ Y]0 1 series. Uncertainty in the

energy is %0, 3 cm

91011121314151617181920212223242526

28293031

333435

37383940

ns'[ —,'

]0

Energy (cm ')

103927.0105 294.3106 115.3106646.1

107009.5107268.9107460.5

4.9695.9726.9757.9778.9789.979

10.980

ns'[ —,'

]1

Energy (cm ')

103943.6105 303.3106 121.0106649.7107012,0107270.6107461.8107 606.9107 720.3107 809.8107 882.5107 941.4107990.7108032.2108066.6108096.2108 121.7108 143.7108 163.5108 180.4108 195.1108 208.1

108 219.8108230.3108 239.9108 248.3108 256.3108 263.5108 269.9108 27S.7108 281.0108 286.0

4.9795.9816.9847.9858.9879.987

10.98711.98612.98813.98614.99115.98616.99118.0018.9919.9920.9921.9823.0124.0124.9925.9726.9627.9528.9529.9330.9631.9832.9833.9734.9635.97

34 T%G-PHGTGN LASER SPECTRGSCGPY GF THE ns' AND nd'. . . 3905

TABLE III. Energy levels and effective quantum numbers for the nd'[ —', ]~ q and nd'[z jq i series. Uncertainty in the energy is

+0.5 cm ', except for the I=1 series where it is +2 cm

101112131415161718192021222324252627282930313233

353637383940

«'[ i liE (cm-')

107201.3107408.7107 S67.9107686.7107 780.4107 861.5107923.4107976.2108018.8108054.6108086.6108 114.3108 137.5108 158.3108175.5108 190.5108 203.9108215.9108227. 1

9.6910.6811.6912.6713.6314.6815.6616.6817.6618.6319.6520.6821.6922.7223.7024.6725.6426.6227,63

nd'[ —', ]iE (cm ')

104796.0105 809.5106441.8106869.3107 166.2107 383.5107 547.4107673.5107772.9107 852.3107917.2107970.910801S.6108052.5108084.4108 110.8108 134.4108 155.3108 173.2108 188.5108202.3108214.7108 225.8108 235.7108244.9108253.0108 260.6108267.3108 273.3108 278.7108 283.8108288.5108 293.1

5.5416.5467.5428.5499.545

10.54311.54412.54513.54814.5515.5516.5717.5818.5719.5720.S421.5522.5723.5724.5325.5226.5127.5128.5029.S230.5231.5632.5633.5534.5235.5236.5237.58

«'[ i ]2

F. (cm ')

104 775.3

106433.9106861.2107 161.6107 380.3107 544.7107 671.5107 771.4107 850.4107915.9107 968.6108013.3108051.6108082.7108 110.0108 133.5

5.525

7.5278.5269.526

10.52611.52612.52713.53114.5215.5316.5217.5218.5419.5220.5121.51

nd'[ ', ]—3

E {cm ')

104 827.5105 825.6106455.0106 875.4107 171.3107 387.7107 550.4107 676.0107 774.8107 853.2107918.1107 970.2108014.8108052.9108083.8108 110.7108 134.4108 155.0108 173.1108 189.5108 203.0108215.1108 226.2108 235.9108 244.8108 252.7108 260. 1

108 266.9108 273.0108 278.7108 284.0108 288.7108 293.1

5.5656.5667.5688.5669.56S

10.56511.56512.56713.56914.561S.5716.5517.5618.5819.5520.5421.5522.5523.5624.602S.5726.5527.5528.5229.5130.4831.4832.5033.5034.5235.5636.5637.58

in md ing comparisons since they repo~ the wavelengthof maximum absorption as seen on photographic plates,For ns'[ —,] i this is acceptable since they see narrow, high-

ly symmetrical resonances. Our measurements forn =10—39 differ from theirs by only, on average, 0.15cm ' with a dispersion of 0.2 cm '. This is well withinthe probable error. The nd'[ ,']i abso—rption from theground state, on the other hand, shows highly asymmetricFano-like profiles with the peak absorption shifted fromthe resonance position. %'e have estimated the Pano q pa-rameter from Yoshino and Freeman's line profiles andthus determined approximately the resonance positionsfrom their data. They are in good agreement with our as-signment of nd [—,]& and are inconsistent with our assign-ment of any other series. Finally, we can compare quan-tum defects from the highest bound members of theseseries, taken from Moore's tables, ' with those determinedfrom our series by a weighted average for levels withn &13. Lower levels were excluded because of possiblevariations with energy. This comparison is shown inTable I. Differences between the bound and Rydberg

quantum defects will be discussed later, but we note thatthe agreement is sufficiently good, in conjunction with theprevious evidence, to make the assignments completelycertain.

Tables II and III present our results for the measuredenergy levels and effective quantum numbers for the sixodd-parity series in xenon. The energy levels were ob-tained from adding our calibrated laser frequency to theenergies of the intermediate levels. On the basis of revisedvuv measurements in xenon, ' these energies lie 0.5 cmlower than listed in Moore's table. ' For those final levelsobserved via different intermediate levels, we checked thateach set of measurements was consistent with the othersand then averaged the values. In particular, the ns'[ —,]iseries was seen strongly through all three intermediate lev-els, providing a good self-consistency check and a reliablemeans for estimating probable errors. Effective quantumnumbers are calculated on the basis of the revised value of108370.8 cm ' for the I']&& limit. Our calibration inthis experiment does not allow us to improve upon thisvalue.

3906 LIANG-GUO %'ANG AND R. D. KNIGHT

All collected data were used in the averaging except forone series of 6p'[ —,'],~nd'[ —', ]i measurements. An un-

known error in that series, probably in the calibration, re-sulted in effective quantum numbers which are not self-consistent nor consistent with those obtained for nd'[ —,]ithrough the 6p'[ —', ]z level. Restriction of the nd'[ —,']idata to that obtained through 6p'[ —,']i forces the n=9level, which fell between two laser dyes, to be omitted.Data are given only to n =40, even if the series was ob-served beyond that point. For larger n the measurementuncertainty becomes a sizable fraction of the spacing be-tween levels, and more accurate energies can be deter-mined with the use of the quantum defects. The lowestmeasured values of n were set by the long-wavelength lim-it of our dye laser. It is unfortunate that the lowestmembers of these series could not be reached.

Estimated probable errors in the ns' series are +0.3cm ', due almost entirely to the uncertainty in calibra-tion. The nd' series, except for J= 1, have an additionaluncertainty in locating the center of somewhat broaderlines. For these we estimate a probable error of +0.5cm '. The J= 1 nd' series was much weaker and broaderthan the others and also infiuenced by a stronger neigh-boring peak, making the measurements much more uncer-tain. We estimate a probable error of +2 cm ' for thisseries. The resulting probable errors in the effective quan-turn numbers is given by

b, n'=(n' IZR)h&,

where 8 is the Rydberg constant. For the ns' series, hn'ranges from +0.001 at n =10, to +0.02 at n=25, to+0.09 at n=40. The probable error for the J&1 nd'series is 1.7 times this, and for the J= 1 nd series is 6.7times this.

The quantum defects for these series, calculated as aweighted average using the probable error in n', weregiven in Table I. For n &13 they are constant, to withinexperimental error, in all series. For lower n they exhibitsome variation with energy, which is not unexpected. Theagreement with the bound levels of each series is extreme-ly good for nd'[ —', ]2 and for nd'[ —', ]2 &. The agreement isnot so good for nd'[ —', ], or ns'[ —,

']i, but the bound levels

of these series are known to be heavily perturbed by theJ= 1 channels converging to P3&2, so a change as theseseries go above the ionization limit is to be expected. ' Thechange in the quantum defect of ns'[ —,

']0 between bound

and autoionizing levels is likely due to perturbation of thebound level by the single nd[ —,

']0 channel. Harth et al. '

assert that the s-d interaction should be most visible inthe J=O channels. This is a two-channel problem andshould be readily tractable with MQDT.

We have not determined autoionization rates I withhigh precision. Such measurements require more exten-

TABLE IV. Autoionization rates I for the ns' and nd' seriesin xenon, given in terms of the effective quantum numbers n

Estimated error is +30%.

Series

ns'[ —,'

]0ns'[ —,

' ],nd'[ —,

']i

nd'[ —', ],nd'[ —,

']2

nd'[ —', ]3

I (cm ')

1400/n *

1300/n

35 000/n

12000/n

4000/n

6000/n

IV. CONCLUSION

Two-photon laser spectroscopy of a metastable atomicbeam of xenon has provided measurements of all the ns'

and nd' autoionizing Rydberg series with angular mo-menta J ranging from 0—3. Of the six measured series,four are here reported for the first time. We anticipatethat these extensive new data, along with previous mea-surements of the bound state data, will provide an oppor-tunity for further MQDT analyses of the J&1 series inxenon.

ACKNOW LEDGMENTS

We would like to thank Professor C. Heer and Profes-sor C. Nielsen for loan of equipment. This research wassponsored by the National Science Foundation underGrant No. PHY-8503424. Some of the equipment wasprovided by the Research Corporation and the PetroleumResearch Fund of the American Chemical Society.

sive control over laser parameters than we could maintainwhile scanning such wide ranges with several laser dyes.We can, however, infer approximate I"s from the lowermembers of each series, and these are shown in Table IV.The accuracy is estimated to be +30%. Within this levelof accuracy, our results are consistent with the previousdata for the J= 1 levels. For the other four series, this isthe first determination of any width information at all. Itis interesting to note that the nd'[ —,]i series has by far thelargest rate, with the nd'[ —,

']2 3 series nearly a factor of 10

less. Fortunately the intensities of the nd'[ —', ], resonanceswere very small, since otherwise the other nd' serieswould have been overwhelmed. We note that the widthsof all of these series could be measured much more accu-rately with the present technique by using an intercavityetalon in the dye laser and restricting the scan range tojust a few resonances.

~K. T. Lu, Phys. Rev. A 4, 579 (1971}.2R. F. Stebbings, C. J. Latimer, %. P. %'est, F. B.Dunning, and

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(1985}.4J. P. Grandin and X. Husson, J. Phys. 8 14, 433 (1981).5R. D. Rundel, F. B. Dunning, H. C. Goldwire, Jr., and R. F.

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34 T%'O-PHOTON LASER SPECTROSCOPY OP THE ns' AND nd'. . . 3907

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