2006 J. Opt. Soc. Am. B/Vol. 5, No. 10/October 1988

High-resolution absorption spectrum of Ne I in the region of565-595 A

Kenji Ito

Photon Factory, National Laboratory for High Energy Physics, Oho, Tsukuba, Ibaraki-ken 305, Japan

Kiyoshi Ueda and Takeshi Namioka

Research Institute for Scientific Measurements, Tohoku University, Katahira, Sendai 980, apan

Kouichi Yoshino

Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, Massachusetts 02138

Yumio Morioka

Institute of Physics, University of Tsukuba, Tennodai, Tsukuba, Ibaraki-ken 305, Japan

Received December 4, 1987; accepted May 17, 1988.

The absorption spectrum of Ne I was observed photographically in the wavelength region of 565-595 A with thehigh-resolution spectrograph at the Photon Factory in Japan. From the observed term values, the first ionizationpotentials I(2p5

23,2) and I(2p5 2P1 /2 ) were found to be 173 930.0 + 0.2 and 174 710.4 + 0.2 cm-', respectively.Furthermore, the five-channel quantum-defect theory is applied to the analysis of the present experimental termvalues. It is found that the multichannel quantum-defect theory describes well the absorption spectrum of Ne Iobserved in the present measurement.

INTRODUCTIONDipole-allowed photoabsorption of Ne in the ground stateproduces five Rydberg series, i.e., transitions to the levels'2p5 (2P3/2 )ns[3/2] l, 2p5 (2P3/2 )nd[1/2]l, 2p5 (2P3/2 )nd[3/2] ;,2p5(2 P1/2 )ns'[1/2]l, and 2p5(2P1/2 )nd'[3/2]1 (hereafter abbre-viated as ns(3/2);, nd(1/2),, nd(3/2), ns'(1/2),, and nd'(3/2)', respectively). The first three series converge to the firstlower ionization limit, I3/2, and the other two series convergeto the first upper limit, I1/2. These two limits correspond tothe ground doublet levels, 2p5 2P3/2 and 2p5 2P,1 2, of Ne II.

High-resolution (10-mA) spectroscopic studies of Ne Iinvolving Rydberg levels were carried out by several investi-gators. Kaufman and Minhagen 2 accurately measured theresonance line at 743 A, 2p6 So-3s(3/2)1, in the fifth order ofthe National Bureau of Standards' 10.7-m spectrograph anddetermined its wavelength to be 743.71955 0.000 2 A.With this value, they calculated the term values for theobserved 2p 5nl levels relative to the ground state and de-rived the first lower ionization limit I3/2 = 173 929.75 ± 0.06cm-'. They calculated, to an accuracy of a few tenths of amilliangstrom, the wavelengths of 46 lines in the region of743-576 A by using the combination principle. Baig andConnerade3 observed the absorption spectrum in the regionof 700-570 A by using synchrotron radiation and a 3-m off-plane Eagle-type spectrograph equipped with a 5000- or6000-groove/mm holographic grating. The five Rydberg se-ries were observed to high members, e.g., up to n = 44 for the

nd(3/2); series, yieldingI3/2 = 173 929.9 + 0.2 cm'1 andl1/2174 709.8 + 0.2 cm-'.

The 20Ne 2p 5ns, 2p5nd Rydberg levels with J = 0-4 werestudied by Harth et al.4 5 by means of resonant two-photonexcitation of a highly collimated metastable Ne beam. Theydetermined the ionization potentials relative to the metasta-ble level 3s(3/2) (s5 in Paschen notation): I312 -E(ls5 )39 887.932 6 cm-' and I1 2 -E(1s5 ) = 40 668.359 5 cm1.

Theoretical investigations of the Ne I spectrum are mostlybased on multichannel quantum-defect theory (MQDT) 6

because much spectroscopic information can be deducedfrom a few parameters obtained by MQDT analysis. Star-ace 7 performed two-channel analysis on the 2p 5(2P3/2 ,1/2 )ns,J = 1 and the 2p5(2 P3/2 ,1/2 )n'p, J = 0 levels and calculated theabsolute line strength for the transition between these twochannel series with n, n' = 3, and n' = 4. Harth et al.5

carried out the two- and five-channel fittings to the mea-sured term values for J = 0 and J = 1, respectively.

We have observed the absorption spectrum of Ne I in theregion of 565-595 A by using the 6VOPE facility8' 9 -thehigh-resolution vacuum UV spectrograph-monochromatorat the Photon Factory-and have extended the five Rydbergseries to higher members, e.g., n = 65 for the nd(3/2)' series.After we submitted a paper on the result of this study, acomprehensive paper on the odd Rydberg spectrum of 20Ne Iwas published by Harth et al.10 In view of their results, wehave revised our original paper. In this paper we report the

0740-3224/88/102006-09$02.00 © 1988 Optical Society of America

Ito et al.

Vol. 5, No. 10/October 1988/J. Opt. Soc. Am. B 2007

wavelengths of the observed Rydberg series members andthe first ionization potentials, I3/2 and I1/2, determined fromsingle-channel quantum-defect analysis. We also give a setof eigenchannel MQDT"1 12 parameters obtained throughfive-channel quantum-defect analysis of our data on thespectrum of Ne I.

EXPERIMENT

The 6VOPE facility consists of a 6.65-m vertical dispersionoff-plane Eagle spectrograph-monochromator and a uniquepredisperser system of zero-dispersion type; its details aredescribed elsewhere. 9

The absorption spectrum of Ne gas was registered on 2 in.X 10 in. (5.1 cm X 25.4 cm) Kodak SWR plates in the 565-595-A wavelength range in the tenth spectral order of a6.65-m, 1200-groove/mm, 5500-A blaze, Os-coated grating(Bausch & Lomb). The resolving power of the facility wasestimated to be -3 X 105 in this spectral region. A wave-length portion of 565-595 A of synchrotron radiation fromthe 2.5-GeV electron storage ring at the Photon Factory wasproperly filtered with the predisperser and was focused uponthe 10-Am entrance slit of the main spectrograph. Tank Neof research grade was flowed, without further purification,through the main spectrograph tank at a pressure of 10-3-10-5 Torr. Exposure time was 30-100 min.

To provide comparison lines for the wavelength determi-nation, emission lines of the CO fourth positive bands in thethird spectral order were superimposed upon the tenth-or-der absorption spectrum of Ne gas. The CO bands were

30 25

produced by passing dc discharge through CO2 in a U-shaped discharge tube, and the light from the discharge tubewas directed onto the entrance slit of the main spectrographby a switching mirror. Four photographic plates were mea-sured with a Grant Instruments spectral line comparator.The error in the absolute positions of the absorption andemission lines was estimated to be less than 2 im, whichcorresponds to an absolute wavelength accuracy of <0.3 mA.

RESULTSFigure 1 shows a 574-578-A portion of the absorption spec-trum of Ne taken in the tenth order of the main grating. Nepressure in the spectrograph was 1 X 10-3 Torr, and theexposure time was 45 min. We observed five Rydberg se-ries: The ns(3/2);, nd(1/2);, and nd(3/2); series convergingto the '3/2 limit and the ns'(1/2); and nd'(3/2); series con-verging to the I1/2 limit. Baig and Connerade3' observedthese five series for n as great as 30s(3/2), 11d(1/2)l, 44d(3/2);, 29s'(1/2)l, and 36d'(3/2)l; in the present experiment weextended these series to n = 44, 15, 65, 45, and 57 for therespective series. Harth et al.10 reported that they detectedseries members as great as 80s(3/2)l, 71d(1/2)1, and 73d(3/2), for the three series converging to I3/2. As for the seriesconverging to I/2, they observed only a few members be-cause of the limitations in their experimental technique.

To determine the absolute wavelengths of the observedNe I lines, we followed the same standard procedure as weused for the wavelength determination of the He I lines.13In doing so we used rotational lines of the CO fourth positive

20 19 18 7 16 15 14 13 12 nd'(3/2)

ns'(l/2)

I I I I I I, I , , I I I I I I

573

lid' 12s'

I I00

215

574

10d' lls'

20

9d'

15 141

575

1Os'

13 12nd(1/2)1

nd(3/2)0

ns(3/2)0

I I I I I I I I I I I I I

575 576 577 (A)Fig. 1. Photoabsorption spectrogram of Ne taken in the tenth order of the main grating. Exposure time was 40 min, Ne pressure was 1 X 10-3Torr, and the entrance slit width was 10 um.

.Ito et al.

2008 J. Opt. Soc. Am. B/Vol. 5, No. 10/October 1988

bands as comparison lines' 3 and the wavelengths of certainNe I lines given by Kaufman and Minhagen 2 as the wave-length standards. After being corrected for so-called coinci-dence error, the wavelengths of the observed Ne I lines wereaveraged over the four plates measured. Our final wave-lengths thus determined are listed in Tables 1-5 togetherwith those given by Kaufman and Minhagen 2 (KM) and byBaig and Connerade3 (BC). Errors in our absolute wave-lengths listed in these tables are estimated to be +0.6 mA.In Table 6 our term values below the first lower ionizationlimit I3/2 are compared with those calculated from the transi-tion energies measured by Harth et al.'0 and from the termvalue of the 3s(3/2); level given by Kaufman and Minhagen. 2

Table 1. Observed Wavelengths for2p6 ISO_2p5(2P312 )ns[3/2]j (in angstroms)

n

3456789

1011121314151617181920212223242526272829303132333435363738394041424344

KMa

743.7196629.7388602.7263591.8303586.3141583.1261581.1220579.7711578.8224578.1270577.6047

BOb

743.7195629.7388602.7263591.8302586.313583.127581.123579.772578.822578.126577.604577.203576.882576.627576.419576.247576.103575.983575.882575.794575.717575.650575.593575.541575.495575.454575.418575.386

ThisWork

591.8306586.3138583.1257581.1215579.7704578.8220578.1262577.6038577.2024576.8816576.6262576.4184576.2481576.1032575.9822575.8796575.7912575.7149575.6483575.5902575.5406575.4933575.4530575.4169575.3844575.3551575.3291575.3050575.2831575.2632575.2451575.2284c575.2127c575.1979c575.1855c575.1733c575.1624c575.1516c575.1420c

a Rof 2b Refl 3.I Partially overlapped with the (n - 1)d(3/2); lines.

Table 2. Observed Wavelengths for2p6 1So-2p5(2P312 )nd[ 1/2]; (in angstroms)

Thisn KMa BCb Work

3 619.1024 619.10234 598.8908 598.88975 590.0108 590.009 590.01096 585.3042 585.304 585.30407 582.5065 582.506 582.50598 580.7138 580.714 580.71319 579.4888 579.488 579.4880

10 578.6185 578.619 578.617511 577.9749 577.976 577.974012 577.4886 577.487213 577.1090 577.108014 576.808315 576.5645c

a Ref. 2.b Ref. 3.I Partially overlapped with the 15d(3/2), line.

The term values by Harth et al. in Table 6 are, thus, fornatural Ne.

QUANTUM-DEFECT ANALYSIS

Single-Channel Analysis: Determination of IonizationPotentialsIf the Rydberg series is not perturbed, the term values forthe Rydberg levels are given by the Rydberg formula

I - En = Ry/(n -A)', (1)

where I is the limit to which the Rydberg series converges, Enis the term value for the energy level with the principalquantum number n, Ry is the Rydberg constant (Ry =109 734.34 cm-'), and ,u is the quantum defect. Using theterm values obtained for the ns(3/2); and nd(3/2), levels anda trial value of 13/2, we calculated g's with Eq. (1) and plottedthem in Fig. 2 as a function of energy. In such a graph itnever occurs, regardless of trial values, that one curve movesup (or down) and the other moves down (or up). Contrary tothis, the curves in Fig. 2 come closer to each other as nincreases.

This false behavior stems from an effect of developmenton the photographic emulsion, i.e., the expansion of high-density parts of the spectrum on development. This effectcauses two lines whose separation is comparable with theinstrumental width to approach each other on a photograph-ic plate. For example, the 39s(3/2)l and 38d(3/2); lines areclearly resolved, as can be seen in Fig. 1, and their separationis measured to be 17 m or 2.1 mA (or 0.63 cm-') on thephotographic plate, showing a resolving power of -2.7 X 105in the sense of Rayleigh's criterion. Because of the narrow-ing effect mentioned above, the measured separation doesnot necessarily reflect the true separation of 1.14 cm-' or 3.8mA (or 30 Am), which was given by Harth et al.'0 A similareffect is seen for the line pair ns(3/2); and (n - 1)d(3/2)1with n - 37, ns'(3/2)1, and (n - 1)d'(3/2), with n _ 33, andnd(3/2)' and nd(1/2)' with n 15 (for n _ 16 they arecompletely blended).

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Vol. 5, No. 10/October 1988/J. Opt. Soc. Am. B 2009

Comparison of the present term values with those given byHarth et al.10 clearly shows the consequence of this effect,aside from a constant deviation of -0.2 cm-'. We thereforedetermined the ionization potentials I3/2 and I1/2 in the fol-lowing manner. We used the term values of the ns(3/2)1levels with 6 _ n _ 36 and those of the nd(3/2)1 levels with 16_ n < 35 in the determination of 13/2. Furthermore, wediscarded several members in these two series that are per-turbed by the interactions among the five series. In deter-mining I/2 we employed the two autoionizing series ns'(1/2);with n = 14-32 and nd'(3/2), with n = 12-31. The single-channel quantum-defect fitting'4 was applied to the fourseries mentioned above. In these fittings the quantum de-fect of each series was represented by a polynomial of ener-gy. Details of the fitting procedure are described in anotherpaper.' 3

The two limits I3/2 and I1/2 thus determined are given inTable 7 with conservative estimates of possible uncertain-ties. The differences in the series limits obtained from thetwo different series converging to the same limit were 0.06and 0.15 cm-' for 13/2 and I1/2, respectively. The standarddeviations in the fitting procedure were less than 0.1 cm-'

for the two cases. The values of I3/2, I/2, and the fine-structure splitting A = 11/2 - I3/2 determined by Baig andConnerade3 and by Harth et al.'0 are also given in Table 7 forcomparison.

Five-Channel AnalysisIn determining ionization potentials we did not take accountof the interactions among the five Rydberg series. However,any pair of the series converging to the different limits mayinteract with each other, as in the case of heavier rare-gasatoms."",12 To describe such interactions it is necessary toperform five-channel quantum-defect analysis.

On the basis of the conventional eigenchannel representa-tions,' 0-'2 five eigenchannels, a = 1, 2, ... , 5, are expected tohave approximately LS-coupled features and are designatedby conventional spectroscopic notation (p5s) 3P, (p5s) 1P,(p5d)3P, (p5d)1P, and (p5d)3D, respectively, whereas the fivedissociation channels, i = 1, 2, ... , 5, are expected to havejj-coupled features designated as (2P3/2)d5/2, (2P3/2)d3/2,(

2P3/2)sj/2, (

2Pj/2 )s/ 2 , and (2 P,/ 2 )d3 /2.Expressing the five eigenquantum defects by the first-

order polynomial of energy

Table 3. Observed Wavelengths for 2p6 1S0-2p5(2P3 /2 )nd[3/2]; (in angstroms)This This

n KMa BCb Workc n KMa BCb Workc

3 618.6717 618.6716 35 575.242 575.24064 598.7056 598.7056 36 575.226 575.2247e5 589.9114 589.912 589.9114 37 575.211 575.2095e6 585.2473 585.246 585.2472 38 575.197 575.1958e7 582.4691 582.469 582.4687 39 575.184 575.1832e8 580.6894 580.691 580.6887 40 575.173 575.1716e9 579.4722 579.473 579.4712 41 575.162 575.1606e

10 578.6056 578.607 578.6049 42 575.151 575.1506e11 577.966 577.9649 43 575.142 575.1408e12 577.482 577.4803 44 575.133 575.132413 577.107 577.1034 45 575.124014 576.807 576.8048 46 575.116315 576.567 576.5658d 47 575,109116 576.370 576.3685 48 575.102117 576.206 576.2048 49 575.095618 576.070 576.0684 50 575.089819 575.955 575.9530 51 575.084220 575.855 575.8544 52 575.078521 575.770 575.7691 53 575.073622 575.697 575.6958 54 575.068823 575.632 575.6316 55 575.064024 575.576 575.5755 56 575.060025 575.527 575.5256 57 575.056126 575.483 575.4816 58 575.052427 575.445 575.4425 59 575.048328 575.409 575.4076 60 575.044729 575.377 575.3762 61 575.041530 575.350 575.3480 62 575.038831 575.323 575.3223 63 575.034432 575.301 575.2988 64 575.031333 575.279 575.2777 65 575.029234 575.262 575.2583

a Ref. 2.b Ref. 3.c The lines with n _ 44 are blended with the (n + 1)s(3/2); lines, and the lines with n _ 16 are blended with the nd(1/2)i lines.d Partially overlapped with the 15d(1/2); line.I Partially overlapped with the (n + 1)s(3/2), lines.

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2010 J. Opt. Soc. Am. B/Vol. 5, No. 10/October 1988

Table 4. Observed Wavelengths for2 p6 1SO-2p5(2PI12)nsI[1/2]l (in angstroms)

Thisnca KMa BCb Workc

Table 5. Observed Wavelengths for2p6 LSo..2p5(2Pi/2)ndi[3/2]l (in angstroms)

Thisna . KMa BCb Workc

3456789

101112131415161718192021222324252627282930313233343536373839404142434445

735.8963626.8232600.0366589.1793583.6893580.5120578.5129577.1692

735.8962626.8232600.0365589.177583.689580.512578.513577.168576.226575.538575.014574.614574.295574.043573.839573.669573.525573.404573.303573.216573.139573.077573.020572.970572.923572.882572.846

3456789

101112131415

589.1792583.6891580.5113578.5123577.1687576.2255575.5347575.0158574.6144574.2982574.0447573.8383573.6679573.5257573.4056573.3037573.2159573.1403573.0741573.0164572.9654572.9204572.8806572.8444572.8122572.7833572.7572572.7336572.7118572.6923572.6742572.6579572.6428572.6283572.6156572.6041572.5930572.5822572.5730572.5641

a Ref. 2.b Ref. 3.c The lines with n = 33-45 are partially overlapped with the (n - 1)d'(3/2);

lines.

(2)

and ignoring the energy dependence of transformation ma-trix element Ua, we have carried out a least-squares fit byusing the well-known MQDT formula' 2 to the measured J =1° term values below I3/2. The term values of ns(3/2) with n_ 37 and nd(3/2)' with n _ 15 were removed from the fittingbecause of the false behavior described above (see also Fig.2).

The resulting MQDT parameters, pa) yu(), and Ui., aresummarized in Table 8. The calculated five ya(°'s are inreasonable agreement with the values of the energy-inde-

615.6283595.9200587.2128582.5982579.8411578.0715576.8650576.0052

161718192021222324252627282930

615.6283595.9200587.213582.598579.839578.072576.864576.006575.375574.892574.517574.222573.982

573.786573.625573.490573.376573.280573.195573.122573.058573.004572.956572.911572.872572.837572.806572.779

313233343536373839404142434445

572.753572.730572.709572.690572.672572.656

464748495051525354555657

587.2127582.5977579.8406578.0710576.8643576.0045575.3703574.8912574.5172574.2208573.9821

573.7873573.6252573.4889573.3754573.2775573.1937573.1210573.0573573.0015572.9523572.9089572.8703572.8353572.8044572.7762

572.7508572.7279572.7064572.6876572.6702572.6537572.6398572.6258572.6127572.6010572.5905572.5804572.5708572.5622572.5543

572.5466572.5391572.5324572.5268572.5204572.515572.510572.505572.500572.496572.494572.491

o Ref. 2.b Ref. 3.I The lines with n = 32-44 are partially overlapped with the (n + 1)s'(1/2),

lines, and those with n _ 45 are blended with the (n + 1)s'(1/2)1 lines.

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Aa _` Ace (0) + AC'M/(2P312 2)

Vol. 5, No. 10/October 1988/J. Opt. Soc. Am. B 2011

Table 6. The J = 10 Term Values of Ne I below the First Limit I3/2

This WorkT(obs) T(calc) T(obs) - T(calc)

Designation Ta (cm-') (cm-,) (cm-') (cm-')

0.22-0.11-0.35-0.02-0.09-0.01-0.14-0.09-0.09-0.26-0.63-0.49-0.26-0.25-0.33-0.27-0.12-0.13-0.10-0.12-0.02

0.01-0.01-0.02

0.02-0.12-0.09-0.04-0.05-0.04-0.05-0.15-0.09-0.12-0.16-0.22-0.20-0.25-0.15-0.28-0.25-0.22-0.24-0.16-0.14-0.19-0.20-0.10-0.13-0.11-0.02-0.08-0.12-0.16-0.02

0.01-0.01-0.14

0.300.370.19

(table continued)

5d[3/2]1b6789

1011121314151617181920212223242526272829303132333435363738394041424344454647484950515253545556575859606162636465

172 570.920172 829.300173 020.704173 165.937173 279.013173 368.861173 441.150173 500.359173 549.422173 590.520173 625.374173 655.052173 680.607173 702.755173 722.079173 739.033173 753.996173 767.270173 779.084173 789.655

173 807.743173 815.487173 822.518173 828.924173 834.769173 840.123173 845.035173 849.556173 853.733173 857.586173 861.143173 864.450173 867.524173 870.387173 873.057173 875.549173 877.883173 880.067173 882.117173 884.045173 885.854173 887.560173 889.170173 890.688173 892.122173 893.478173 894.761173 895.980173 897.137173 898.231173 899.274173 900.267173 901.209173 902.110173 902.966173 903.786

169 516.98170 867.96171 683.05172 209.32172 571.12172 829.51173 020.88173 166.09173 279.17173 368.89173 440.76173 500.10173 549.41173 590.49173 625.29173 655.02173 680.72173 702.86173 722.21173 739.14173 754.21173 767.50173 779.30173 789.86173 799.35173 807.86173 815.63173 822.71173 829.10173 834.96173 840.30173 845.11173 849.69173 853.83173 857.64173 861.15173 864.48173 867.50173 870.46173 873.00173 875.53173 877.89173 880.05173 882.18173 884.13173 885.89173 887.59173 889.30173 890.78173 892.24173 893.68173 894.91173 896.09173 897.20173 898.44173 899.51173 900.49173 901.30173 902.64173 903.57173 904.21

169 516.76170 868.05171 683.40172 209.34172 571.21172 829.52173 021.02173 166.18173 279.26173 369.15173 441.39173 500.59173 549.67173 590.74173 625.62173 655.29173 680.84173 702.99173 722.31173 739.26173 754.23173 767.49173 779.31173 789.88173 799.33173 807.98173 815.72173 822.75173 829.15173 835.00173 840.35173 845.26173 849.78173 853.95173 857.80173 861.37173 864.68173 867.75173 870.61173 873.28173 875.78173 878.11173 880.29173 882.34173 884.27173 886.08173 887.79173 889.40173 890.91173 892.35173 893.70173 894.99173 896.21173 897.36173 898.46173 899.50173 900.50173 901.44173 902.34173 903.20173 904.02

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2012 J. Opt. Soc. Am. B/Vol. 5, No. 10/October 1988

Table 6. Continued

This WorkT(obs) T(calc) T(obs) - T(cac)

Designation Ta I(cm-') (cm-,) (cm-')

66676869707172735d[1/2];6789

1011121314686970716s [3/2] lb789

1011121314151617181920212223242526272829303132333435363738394041424344454647

173 904.569173 905.316173 906.029173 906.712173 907.365173 907.991173 908.591173 909.169

173 906.015173 906.699173 907.351173 907.943

171 489.473172 080.925172 481.881172 764.517172 972.356173 128.858173 249.200173 345.606173 422.343173 484.865173 536.200173 579.782173 616.184173 647.187173 673.814173 696.850173 716.904173 734.466

173 763.744173 755.928173 786.826173 796.608173 805.425173 813.391173 820.614173 827.187173 833.183173 838.667173 843.698173 848.324173 852.590173 856.525173 860.170173 863.547173 866.682173 869.604173 872.325173 874.868173 877.242

169 488.41170 851.38171 672.09172 202.08172 566.13172 825.74173 018.17173 164.01173 277.79173 367.83

168 967.27170 557.13171 489.60172 081.05172 482.06172 764.68172 972.60173 129.06173 249.44173 345.80173 422.59173 485.08173 536.36173 580.02173 616.46173 647.41173 674.07173 697.08173 717.18173 734.72173 749.69173 763.98173 776.15173 787.04173 796.84173 805.71173 813.56173 820.85173 827.47173 833.48173 838.94173 843.98173 848.75173 853.19173 856.97173 860.63173 863.94173 867.21

173 870.10

169 488.27170 851.42171 670.04172 202.05172 566.10172 825.73173 018.12173 164.02173 277.67173 367.71

168 967.24170 556.96171 489.59172 080.92172 481.90172 764.61172 972.53173 129.01173 249.33173 345.83173 422.53173 485.06173 536.39173 579.99173 616.38173 647.40173 674.03173 697.06173 717.12173 734.68173 749.75173 763.97173 776.15173 787.05173 796.83173 805.65173 813.61173 820.84173 827.41173 833.41173 838.89173 843.92173 848.55173 852.81173 856.75173 860.39173 863.77173 866.91

173 869.83

0.14-0.04

0.050.030.030.010.05

-0.010.120.12

0.030.170.010.070.160.070.070.050.11

-0.030.060.02

-0.030.030.080.010.040.020.060.04

-0.060.010.00

-0.010.010.06

-0.050.010.060.070.050.060.200.380.220.240.170.300.27

Ito et al.

Vol. 5, No. 10/October 1988/J. Opt. Soc. Am. B 2013

Table 6. Continued

This WorkT(obs) T(calc) T(obs) - T(calc)

Ta (cm'1) (cm-') (cm-,)

173 879.469173 881.556173 883.516173 885.358173 887.091173 888.727173 890.270173 891.727173 893.104173 894.410173 895.644173 896.815173 897.927173 898.987173 899.992173 900.948173 901.864173 902.730173 903.558173 904.348173 905.103173 905.825173 906.512173 907.167173 907.726173 908.461

173 909.583173 910.118173 910.632173 911.127173 911.604173 912.062

172 461.023

173 609.498

172 261.738172 856.973173 259.352173 542.960173 749 .5 5 7b173 908.038

170 296.04171 645.02172 461.19172 989.15173 350.99173 609.75173 801.11169 727.63171 324.10172 261.94172 857.18173 259.56173 543.18173 751.47173 908.25

170 295.44171 644.73172 461.29172 989.13173 351.00173 609.77173 801.14169 727.60171 323.83172 261.90172 857.16173 259.55173 543.15173 751.44173 908.25

0.600.29

-0.100.02

-0.01-0.02-0.03

0.030.270.040.020.010.030.030.00

a Calculated from the transition energies obtained by Harth et al.' 0 and from the term value of the 3s(3/2)2 obtained by Kaufman and Minhagen.2 These termvalues and the present ones are, thus, both for natural Ne.

b The ns(3/2), lines with n _ 37 and the nd(3/2), lines with n _ 15 were excluded in the MQDT fitting procedure.I Should be assigned to the 26s(3/2), level.

pendent ,$a's given by Harth et al.,4 i.e., It = 0.3155, $2 =

0.2845, A = 0.0332, 4 = 0.0217, and A = 0.0049. The U'sin Table 8 are calculated by taking 013 = -0.0489, 014 =

0.0066, 15 = -0.0090, and 024 = 0.0315, all in units of radians;the same notations as defined by Harth et al.10 are used forthe coupling angles. The present coupling angles, 0kk', areagain in reasonable agreement with 013 = -0.050 and 024 =0.008, as obtained by Harth et al.10 It should be noted,

however, that these sets of k' are merely one of the finitenumber of possible sets."

In Table 6 the term values calculated from the MQDTparameters in Table 8 are also compared with observed termvalues for the energy levels below the I3/2 limit. As is seen inTable 6, the parameters reproduce the measured term valueswell: the differences are of the order of 0.1 cm-' for most ofthe levels fitted in this analysis.

Designation

484950515253545556575859606162636465666768697071727374757677787980

5d'[3/216789

10116s'[1/2]f789

10111213

Ito et al.

2014 J. Opt. Soc. Am. B/Vol. 5, No. 10/October 1988

* ns(3/2)1

* * * *um

uuum-u-5 30 3I5 * 0

U.

0

24 nd(3/2)' 30 3 0, * . * * 00. 0 .7

173 800term value

ACKNOWLEDGMENTS

We are grateful to the staff of the Photon Factory. KiyoshiUeda is grateful to M. L. Ginter for helpful discussionsconcerning the quantum-defect analysis. This work hasbeen carried out under the approval of the Photon FactoryProgram Advisory Committee (proposal 85-088) and sup-ported in part by Japan Society for Promotion of Scienceand National Science Foundation under a Japan-USA Co-

173900 operation Research Program.Icm'

Fig. 2. The quantum defect, u, plotted as a function of energy forthe ns(3/2); and nd(1/2); series. The 's were calculated from Eq.(1) with the observed term values and a tentative value of 173 930.0cm-' for 13/2. The quantum defect of the 26s(3/2); line deviatesbecause of the interaction with the 12s'(1/2); line.

Table 7. Ionization Potentials I3/2 and I/2 for Ne I

and the Fine-Structure Splitting A = '1/2 - 3/2(in cm-')

ThisParameter Work BCa Hb

I3/2 173 930.0 4: 0.2 173 929.6 + 0.2 173 929.773 0.040I1/2 174 710.4 + 0.2 174 709.8 + 0.2 174 710.200 + 0.043A 780.4 780.2 780.4296 + 0.0036

a Ref. 3.b Ref. 10. The ionization potentials by Harth et al.10 were calculated by

using 134 041.840 + 0.040 cm-' for T(3s 3P2) by Kaufman and Minhagen 2 andare for natural Ne.

Table 8. Eigenchannel MQDT Parameters for FiveJ = 1 Channels of Ne I

a 1 2 3 4 5

Ja(O) 0.3155 0.2842 0.0338 0.0229 0.00325yA) 0.1893 0.0756 -0.1001 -0.1341 0.0676

0.034729 0.024390 -0.547068 0.774019 -0.315928-0.028299 0.008139 0.729424 0.258301 -0.632736

Ui, 0.576624 0.815972' 0.028221 -0.029519 0.0051900.815470 -0.577233 0.039911 0.012804 0.007339

-0.022508 0.018187 0.407760 0.577183 0.706933

REFERENCES

1. C. E. Moore, Atomic Energy Levels (National Bureau of Stan-dards, Washington, D.C., 1949), Vol. 1.

2. V. Kaufman and L. Minhagen, "Accurate ground-term combi-nations in Ne I," J. Opt. Soc. Am. 62, 92 (1972).

3. M. A. Baig and J. P. Connerade, "Centrifugal barrier effects inthe high Rydberg states and autoionizing resonances in neon,"J. Phys. B 17, 1785 (1984).

4. K. Harth, M. Raab, J. Ganz, A. Siegel, M. W. Ruf, and H. Hotop,"Spectroscopy of neon Rydberg states detected by electrontransfer to SF6 molecules," Opt. Commun. 54, 343 (1985).

5. K. Harth, J. Ganz, M. Raab, K. T. Lu, J. Geiger, and H. Hotop,"On the s-d interaction in neon," J. Phys. B 18, L825 (1985).

6. M. J. Seaton, "Quantum defect theory," Rep. Prog. Phys. 46,167 (1983).

7. A. F. Starace, "Absolute line strengths by analysis of Lu-Fanoplots with application to excited state transitions in neon," J.Phys. B 6, 76 (1973).

8. T. Namioka, H. Noda, K. Goto, and T. Katayama "Designstudies of mirror-grating systems for the use with an electronstorage ring source at the Photon Factory," Nucl. Instrum.Meth. 208, 215 (1983).

9. K. Ito, T. Namioka, Y. Morioka, T. Sasaki, K. Goto, T. Ka-tayama, and M. Koike, "High-resolution VUV spectroscopicfacility at the Photon Factory," Appl. Opt. 25, 837 (1986).

10. K. Harth, M. Raab, and H. Hotop, "Odd Rydberg spectrum of20Ne I: high resolution laser spectroscopy and multichannelquantum-defect theory," Z. Phys. D 7, 213 (1987).

11. K. T. Lu, "Spectroscopy and collision theory. The Xe absorp-tion spectrum," Phys. Rev. A 4, 579 (1971).

12. C. M. Lee and K. T. Lu, "Spectroscopy and collision theory. II.The Ar absorption spectrum," Phys. Rev. A 8, 1241 (1973).

13. K. Ito, K. Yoshino, Y. Morioka and T. Namioka, "The is2 1So-lsnp 'P; series of the helium spectrum," Phys. Scr. 36, 88(1987).

14. M. J. Seaton, "Quantum defect theory. II. Illustrative one-channel and two-channel problems," Proc. Phys. Soc. LondonSer. A 88, 815 (1966).

n=24

0.3

_ 0.2

0

E0.1

21

23

Ito et al.

I n=22

113 700n n