Absorption spectrum of Pb I between 1350 and 2041 Å
13
cause it can now be argued that electron densities in heavy metal break arcs should be comparable to or greater than those for magnesium. Arc temperatures are generally higher for the heavier metals and there- fore one might reasonably expect LTE to obtain for such elements in break arcs. On that basis, the observed in- tensities of the emission lines can be used to determine improved values of oscillator strengths. A study of this kind involving Pd, Ag, Pt, and Au has been completed and the results will be reported shortly. In the mean- time, the oscillator strengths for these elements are available on request. 9 *To whom correspondence should be addressed. 'W. F. Meggers, C. H. Corliss, and B. F. Scribner, Tables of Spectral Line Intensities, 2nd ed. Nat. Bur. Stand. (U.S.) Monog. 145, (U.S. Printing Office, Washington, D.C., 1975). 2 J. M. Bridges and W. L. Wiese, "The Oscillator Strength Scale for Fe(I), " Astrophys. J. 161, L71 (1970). 3B. Warner and C. R. Cowley, "On Systematic Errors in Oscillator Strengths Measured in a Free Burring Arc, " J. Quant. Spectrosc. 7, 751 (1967); "Influence of Systematic Errors in Laboratory Oscillator Strengths on the Interpreta- 4tion of Stellar Spectra," Observatory 87, 117 (1967). 4 E. 0. Degenkolb and J. E. Griffiths, "Temperature of the Meggers-Corliss-Scribner copper arc, " J. Opt. Soc. Am. 65, 315 (1975). 5W. L. Wiese, M. W. Smith, and B. Miles, "Atomic Transi- tion Probabilities II, " Natl. Stand. Ref. Data Ser. Natl. Bur. Stand. 22, (1969). 6 V. Vujnovic, "Use of the Saha Equation for the Simultaneous Determination of Temperature and Electron Concentration," Fizika (Zagreb) 3, 105 (1971). 7 C. H. Corliss, "A Review of Oscillator Strengths for Lines of Cu(I), " J. Res. Nat. Bur. Stand. Sec. A 74, 781 (1970). 8 H. R. Griem, Spectral Line Broadening by Plasmas (Aca- demic, New York, 1974), pp. 340-341. 9 J. E. Griffiths and E. 0. Degenkolb (unpublished results). ' t H. R. Griem, "Validity of Local Thermal Equilibrium in Plasma Spectroscopy, " Phys. Rev. 131, 1170 (1963). W. L. Wiese, Plasma Diagnostic Techniques, edited by R. H. Huddlestone and S. L. Leonard (Academic, New York, 1965), Chap. 6. 1 2 T. Utsumi, "Measurements of cathode spot temperature in vacuum arcs, "1 Appl. Phys. Lett. 18, 218 (1971). Absorption spectrum of PbI between 1350 and 2041 A C. M. Brown* and S. G. Tilfordt E. 0. Hulburt Centerfor Space Research, Naval Research Laboratory, Washington, D.C. 20375 Marshall L. Ginter E. 0. Hulburt Center for Space Research and Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742 (Received 21 March 1977) The high resolution absorption spectrum of Pbi is reported between 1350 and 2041 A. Transitions are observed from the 6p 2 (1/2,1/2),, (3/2,1/2),, and (3/2,1/2)2 levels to levels with J < 2 associated with 6pns and 6pnd configurations. Energy levels have been determined with n * values as high as 74. More than 500 spectral features and 370 odd parity energy levels are reported, a major part of which are new. These observations include five electric quadrupole transitions and 31 nuclear-spin-induced transitions from the 20'Pb isotope. Ionization limits of 59819.57 4 0.10 cm-' and 73900.64 4 0.10 cm-' have been determined for levels converging on the 6p 2P'P2 and 6p 2P3,2 levels of Pb ii, respectively. An analysis of these data in terms of Lu-Fano graphical methods and multichannel quantum defect parametrization also is presented. INTRODUCTION The electronic spectrum and structure of Pbi have been investigated extensively. Much of the data from earlier investigations summarized by Moore' were superseded in the late 1960's by data presented by Garton and Wil- son 2 and by Wood and Andrew. 3 Wood and Andrew rein- vestigated the Pbi emission spectrum and reported im- proved lists of wavelengths (emission lines in the 1733- 39 039 A region) and energy levels (59 with even and 58 with odd parity). Garton and Wilson reinvestigated the Pb I absorption spectrum in the 1100-2500 A region and observed a number of new transitions from the ground level 6p2 3Po. They reported two discrete series [6p 23 3po- 6pns 'P' (n = 8-32) and 6p 23 PO-6pnd'Do, (n=6-53)] con- verging on the lowest (6p'P 5 1N 2 ) limit of Pb Ii, three auto- ionized J= 1° series converging on the 6p 2 P3/ 2 limit, and over 100 odd parity energy levels not included in Wood and Andrew's list. Although subsequent publications"4 7 1240 J. Opt. Soc. Am., Vol. 67, No. 9, September 1977 contained information of interest to the present work, they have left the spectral line positions and energy lev- els presented in Refs. 2 and 3 substantially unmodified, The present investigation emphasizes the absorption spectrum of lead in the - 1350-2041 A region. The spec- trum reported here is more extensive and highly resolved than previously published absorption spectra 2 ' and has improved wavelength accuracy. The essentially com- plete assignment of the observed Pbi spectrum leads to a substantial increase in the number of odd parity levels which have been experimentally characterized and to the identification of a number of transitions forbidden by electric dipole selection rules. The absorption spectrum of PbI under discussion here consists of transitions between levels [designated 3Po, 3 P 1 , and 'P2 or (*, 2), (2, )1,. and (3, 2)2 in LS or J nota- tion, respectively] from the ground configuration 6p 2 and Copyright ©O 1977 by the Optical Society of America 1240
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Transcript of Absorption spectrum of Pb I between 1350 and 2041 Å
cause it can now be argued that electron densities inheavy metal break arcs should be comparable to orgreater than those for magnesium. Arc temperaturesare generally higher for the heavier metals and there-fore one might reasonably expect LTE to obtain for suchelements in break arcs. On that basis, the observed in-tensities of the emission lines can be used to determineimproved values of oscillator strengths. A study of thiskind involving Pd, Ag, Pt, and Au has been completedand the results will be reported shortly. In the mean-time, the oscillator strengths for these elements areavailable on request. 9
*To whom correspondence should be addressed.'W. F. Meggers, C. H. Corliss, and B. F. Scribner, Tables
of Spectral Line Intensities, 2nd ed. Nat. Bur. Stand. (U.S.)Monog. 145, (U.S. Printing Office, Washington, D.C., 1975).
2 J. M. Bridges and W. L. Wiese, "The Oscillator StrengthScale for Fe(I), " Astrophys. J. 161, L71 (1970).
3B. Warner and C. R. Cowley, "On Systematic Errors inOscillator Strengths Measured in a Free Burring Arc, " J.
Quant. Spectrosc. 7, 751 (1967); "Influence of SystematicErrors in Laboratory Oscillator Strengths on the Interpreta-4tion of Stellar Spectra," Observatory 87, 117 (1967).
4E. 0. Degenkolb and J. E. Griffiths, "Temperature of theMeggers-Corliss-Scribner copper arc, " J. Opt. Soc. Am.65, 315 (1975).
5W. L. Wiese, M. W. Smith, and B. Miles, "Atomic Transi-tion Probabilities II, " Natl. Stand. Ref. Data Ser. Natl. Bur.Stand. 22, (1969).
6V. Vujnovic, "Use of the Saha Equation for the SimultaneousDetermination of Temperature and Electron Concentration,"Fizika (Zagreb) 3, 105 (1971).
7 C. H. Corliss, "A Review of Oscillator Strengths for Linesof Cu(I), " J. Res. Nat. Bur. Stand. Sec. A 74, 781 (1970).
8H. R. Griem, Spectral Line Broadening by Plasmas (Aca-demic, New York, 1974), pp. 340-341.
9 J. E. Griffiths and E. 0. Degenkolb (unpublished results).'t H. R. Griem, "Validity of Local Thermal Equilibrium in
Plasma Spectroscopy, " Phys. Rev. 131, 1170 (1963).W. L. Wiese, Plasma Diagnostic Techniques, edited by R.H. Huddlestone and S. L. Leonard (Academic, New York,1965), Chap. 6.
12T. Utsumi, "Measurements of cathode spot temperature invacuum arcs, "1 Appl. Phys. Lett. 18, 218 (1971).
Absorption spectrum of PbI between 1350 and 2041 A
C. M. Brown* and S. G. TilfordtE. 0. Hulburt Center for Space Research, Naval Research Laboratory, Washington, D.C. 20375
Marshall L. GinterE. 0. Hulburt Center for Space Research and Institute for Physical Science and Technology, University of Maryland, College Park,
Maryland 20742(Received 21 March 1977)
The high resolution absorption spectrum of Pbi is reported between 1350 and 2041 A. Transitions areobserved from the 6p 2 (1/2,1/2),, (3/2,1/2),, and (3/2,1/2)2 levels to levels with J < 2 associated with 6pnsand 6pnd configurations. Energy levels have been determined with n * values as high as 74. More than 500spectral features and 370 odd parity energy levels are reported, a major part of which are new. Theseobservations include five electric quadrupole transitions and 31 nuclear-spin-induced transitions from the20'Pb isotope. Ionization limits of 59819.57 4 0.10 cm-' and 73900.64 4 0.10 cm-' have been determined forlevels converging on the 6p 2P'P2 and 6p 2P3,2 levels of Pb ii, respectively. An analysis of these data in termsof Lu-Fano graphical methods and multichannel quantum defect parametrization also is presented.
INTRODUCTION
The electronic spectrum and structure of Pbi have beeninvestigated extensively. Much of the data from earlierinvestigations summarized by Moore' were supersededin the late 1960's by data presented by Garton and Wil-son2 and by Wood and Andrew. 3 Wood and Andrew rein-vestigated the Pbi emission spectrum and reported im-proved lists of wavelengths (emission lines in the 1733-39 039 A region) and energy levels (59 with even and 58with odd parity). Garton and Wilson reinvestigated thePb I absorption spectrum in the 1100-2500 A region andobserved a number of new transitions from the groundlevel 6p2 3Po. They reported two discrete series [6p233po-6pns 'P' (n = 8-32) and 6p23PO-6pnd'Do, (n=6-53)] con-verging on the lowest (6p'P5 1N 2 ) limit of Pb Ii, three auto-ionized J= 1° series converging on the 6p 2P3/2 limit, andover 100 odd parity energy levels not included in Woodand Andrew's list. Although subsequent publications"47
1240 J. Opt. Soc. Am., Vol. 67, No. 9, September 1977
contained information of interest to the present work,they have left the spectral line positions and energy lev-els presented in Refs. 2 and 3 substantially unmodified,
The present investigation emphasizes the absorptionspectrum of lead in the - 1350-2041 A region. The spec-trum reported here is more extensive and highly resolvedthan previously published absorption spectra2 ' and hasimproved wavelength accuracy. The essentially com-plete assignment of the observed Pbi spectrum leads toa substantial increase in the number of odd parity levelswhich have been experimentally characterized and to theidentification of a number of transitions forbidden byelectric dipole selection rules.
The absorption spectrum of PbI under discussion hereconsists of transitions between levels [designated 3Po,3P1, and 'P2 or (*, 2), (2, )1,. and (3, 2)2 in LS or J nota-tion, respectively] from the ground configuration 6p2 and
Copyright ©O 1977 by the Optical Society of America 1240
levels associated with the excited electron configurations6pns and 6pnd, which have the ground term 6p 2PI ofPbii as their core. For the analogous transitions in thespectra of CI, 8 Si i, 9 Ge I, 10 and SnI, 11 the only selectionrules observed to apply were the general electric dipolerules even- odd, and AJ= 0, ± 1 (J= 04- J= 0). The sit-uation is similar for Pb i, except that a number of weaktransitions with AJ=+2 and J"=0-J'=0 also are ob-served.
For 6pns and 6pnd configurations, there are 12 oddparity channels (level series plus their continua) with J< 2 based on the 6p2P /2 or the 6p2P'/ 2 level of Pb ii.Consideration of the jj- coupling terms produced by add-ing ns or nd to 3/2 or 2P1/2 indicates that one J= 0,three J= 1, and three J= 2 channels belong to the 2P,12(upper) ion core, and one J= 0, two J= 1, and two J= 2channels belong to the 2P1/2 (lower) ion core. The AJselection rule limits the electric dipole allowed transi-tions between 6p2 3P and the 12 channels listed above to27 spectral series. The Pb i ground term more nearlyapproaches jj than LS coupling3 and is regular with(3, 2)-(2, 2)0 and (2, 2)2- (22 2) separations3 of 7819. 263cm' and 10650.327 cm1 , respectively. The Pbi'6P2P°,2-2 P1o 2 spacing12 is 14081.074 cm-'; hence, sev-eral of the 27 spectral series mentioned above will con-verge to each of six apparent convergence limits between1353.17 and 2033.80 A.
The multichannel two limit approach to the problem ofinterpreting interactions among the energy levels con-verging on the two ground-state levels of Pb ii is thesame as that discussedl0 "1 in detail for the analogouschannels in GeI and Sni. Briefly, the interactions be-tween channels13 '16 are periodic because level series be-longing to channels converging on different ion core lim-its periodically cross. The restriction that interactinglevels have the same parity and J value permits the con-sideration of the resulting channel mixings for each Jvalue as an individual problem. The possible energylevels correspond to the points of intersection of func-tions nt = G(n2*) and nt = f(n2*). The first function can berepresented by
nt= G(n2*) = n2*(1 - A)*2) /2 (1)
while nt = f (n2*) is the solution of
F(nt, n4) =detI Ui0 sin(n - j)I =0 . (2)
In Eq. (1) the quantities nh and n2* are the effective quan-tum numbers for each level based on the two possibleionization energies, El. (for 6p2P ,2 ) and E2,
(for 6p 2 P3/ 2 ), with A = (E2 ,. - ElO)R-' = 0. 128 316 53 usingR= 109 737. 024 cm-. In Eq. (2) the Ui,'s are matrixelements for the transformation between the close-cou-pled and loose-coupled representations, 17 the pla areeigenquantum defects17 for the close-coupled eigenstates,and n0' is nt or n* depending upon which state of the ionthe ith loose-coupled state is built.
The mixing coefficients Man which specify the specificlinear combination of close-coupled states making up theRydberg level, can be computed from the expansion's5 "
3 -1/2)Ma = CiOp oE Am,) vo 7
1241 J. Opt. Soc. Am. Vol. 67, No. 9, September 1977
where the Ci 's, which are functions of nP and n*, arethe cofactors of the ith row and ath column of the deter-minant in Eq. (2).
EXPERIMENTAL PROCEDURES
The apparatus and experimental procedures used inthis work have been described in detail1 and are similarto those employed to obtain highly dispersed absorptionspectra of other fourth group atoms. 9-11 Briefly, lead'9
was heated to temperatures in the range 850-1350 °C inan evacuable King furnace system with a 122 cm longhot zone.. Absorption spectra were obtained from asingle pass through the furnace using microwave-excitedxenon or krypton lamps to provide background continua.Spectra were photographed on Kodak SWR plates using a6. 6 m spectrograph in either the third (for X > 1500 A)or fourth (for X< -1500 A) orders with reciprocal dis-persions of - 0. 41 or 0. 31 A/mm, respectively. Mostof the experiments were performed with flowing argon inthe furnace at pressures less than 0. 1 Torr, although ina few cases argon pressures as high as 100 Torr wereemployed.
Reference standards, plate measurement, and data re-duction procedures are similar to those described previ-ously. 18 The wavelength uncertainty in sharp unblendedlines is estimated to be ± 0. 002 A or less, which is equalto ±0.08 cm-' at 1500 A and - ±0. 06 cm-' at 1800 A.However, the wavelengths of diffuse or blended lines aremore uncertain.
RESULTS
Temperatures were limited to less than '-1350'C inour experiments by the vapor pressure of lead. At thesetemperatures, the 6p
2(3, 2)2 and 6p 2 (3, 2), levels are pop-
ulated sparsely relative to the ground level 6p2( , 2)Hence our spectrum of Pb I is dominated by transitionsfrom 6p2 (2, 12) to a greater extent than were similarspectra 9 "11 for the lighter fourth group elements. It alsoshould be noted that our spectrum of Pb i is simpler thanthe corresponding spectra for SiI, Gel, or SnI because(a) below the 6p2Pl1 2 limit there are fewer perturbationsbetween levels in channels with different core levels and(b) above the 6p 2 P1°/2 limit the extremely intense auto-ionizing transitions from 6p2(1, '), to J= 10 channelsassociated with 6p2P3/2 mask spectral transitions from6p 2 (2, 12) and (2, 12) to all other channels associated with6p2p /
Although a number of spectrograms were taken in theA > 2040 k region in an attempt to locate transitions fromthe 6p2(2, 2)2 level to excited levels with J= 1, 2, or 3,only very faint absorptions were observed. Since suchtransitions were the only allowed combinations with J= 3levels, no new data on J= 3 levels were obtained in thiswork. This negative result was anticipated since the6p2(3, ')2 lies 10650 cm-' (kT=14 000 'K) above the groundlevel and hence has a negligible population at 1350 'C.
Table I contains the relative intensities, wavelengths,and transition assignments of the absorption spectrumof Pbi observed in the present work. Table II lists allof the odd parity energy levels of Pb I which have been
Brown et al. 1241
TABLE I. Observed absorption lines of Pbr.
Wave UpperWavelength number Transition Lovolc
Comm.a Int.b (A, vac) (cm-t) J1 J' n*
0000321252d254132176318674
15121845942
1239183
17193
252
103
202
10225
4039
301382s
32136
2041. 7982040. 1292039.2782036.0582035.9962035. 7142026.4742023.3282022.6742022.0692015. 9362015. 1032014. 0202006.6702005.3822025.2381992. 9591992. 3181991. 6081985. 8281985. 7581977. 8751977. 0881976. 6111972. 5451972.4471966. 6581966. 3741966. 0681963. 0971959. 0121958. 3701956. 1361953. 2081952. 5761950. 8481948. 7481948. 2251948. 1031946. 7391945. 2661944. 6731944. 5781943.4811942. 5621941. 8221941. 7471940. 8561940. 3501939. 5021939.4431938. 7041938. 5821938. 5621937. 5921937. 5411937. 0111936. 9251935. 9911935. 9521935. 6891935. 6281935.4321934. 6461934. 614
48 976.4549 016. 5149 036. 9749 114. 5249 116. 0149 122. 8149 346.7949 423. 5249 439. 549 454. 349 604.7649 625.2649 651. 9349 833. 8149 865. 8149 869. 3950 176. 6450 192.7850 210. 6850 356. 8250 358.650 559.3050579.4450 591.6450 695. 9250 698.4550 847. 6850855.0250 862. 9450 939. 9151046. 1451 062. 8851121.2051 197. 8251214.4051259. 7651314. 9951328. 7851332.0051367. 9651406. 8451422.5251425.0551454.0751479. 3751498. 0251500. 0151523. 6651537. 0951559. 6351 561. 1951 580..8651584. 0951584.6251610.4451611. 8151625.9251 628. 2251653. 1251654.1651661.2051662. 8151668.0651689.0551 689. 90
2-22-12-12-11-01-1
0-1
1-21-21-1
1-01-11-21-21-11-01-11-21-21-11-01-21-21-21-11-01-21-11-01-21-11-01-21-21-11-01-21-21-11-01-21-21-11-01-21-21-11-01-21-21-21-11-21-01-21-1
1-21-01-21-1
2.77272.77662.77862. 78622.54332.5438
2. 1181
2.58072.58232.5844
2.60142. 60172. 62672. 62812.62952.64172. 64192. 65892.66062.66172.67072.67092.68392. 68462. 68532.69212.70162.70312. 70842.71532.71682. 72102.72612. 72742.72772.73102.73462.73612. 73632.73902.74142.74312. 74332.74562. 74682. 74892. 74912.75102.75132.75132.75382.75392.75522. 75552. 75782.7579
2. 75882.75932. 76132.7614
TABLE I (Continued).
Wave UpperWavelength number Transition Levelc
Comm.a Int.b (A, vac) (cm'1) J" J' At
33145
3313s5
311
3s5
2814
2718*
*
2518*
*
2517*
*
251
241
240
220
23240
220
201918181717151413121095876543443221
Q
1934. 4051934. 1651933. 4991933.4721933. 3301933. 0861932. 5221932. 4911932. 3921932. 1621931. 6651931. 6451931. 5721931. 3581930. 9221930. 8511930. 6511930. 2671930. 2671930. 2161930. 0381929. 6971929. 6971929. 6591929. 4871929. 1891929. 1891929. 1641929. 0011928. 7221928. 5771928. 3251928. 1901927. 9671927. 8451927. 6441927. 3521927. 2581927. 0871926. 9901926. 8451926. 6251926.4241926.2381926. 0691925. 9121925. 7671925.6331925. 5091925. 3921925. 2841925. 1851925. 1391925. 0921925. 0031924. 9211924. 8451924. 7721924. 7041924. 6401924. 5801924. 5241924.4691924.4201924. 370
51695.4951 701. 951 719. 751720.4251 724.2451 730. 7651 745. 8651 746. 6851 749. 3451 755.551 768. 851 769. 3551 771. 3051 777. 0551 788. 7451 790. 6451 796. 0051 806. 351 806.351 807. 6851812.4451 821.6051821.6051822.6451 827.2651835.2551 835.2551 835. 9351 840. 351 847. 8151 851. 751858.4751 862. 151 868. 1051871.451 876. 8051 884.6551 887.251 891.7951894.451 898. 3151904.2551 909. 6651 914. 6651919.2351923.4651 927.3651 930. 9851 934. 3351 937.4751940.3851 943. 0751944.2951945.5851947. 9751 950. 1951952.2451954.2051956.0551 957. 7851959.3051960.9051962.3951963.7251 965. 06
1-21-01-21-11-21-01-21-11-21-01-21-11-21-01-21-21-01-21-11-21-01-21-11-21-01-21-11-21-01-21-01-21-01-21-01-21-21-01-21-01-21-21-21-21-21-21-21-21-21-21-21-20-21-21-21-21-21-21-21-21-21-21-21-21-2
2. 76192.76252.76422. 76432. 76472.76532. 76672. 76682.76712.76772. 76902.76902.76922. 76982.77092.77112. 77162. 77262.77262.77272. 77322. 77412.77412.77422.77462. 77542. 77542.77552.77592. 77662. 77702. 77772. 77802. 77862.77892. 77952. 78022. 78052. 78092. 78122. 78162.78222. 78272. 78322.78362.78402. 78442. 78482. 78512.78542.78572.78602.23562. 78622. 78652.78672. 78692. 78712.78732. 78742.78762. 78772. 78792. 78802. 7881
1242 J. Opt. Soc. Am., Vol. 67, No. 9, September 1977 Brown et al. I1242
TABLE I. (Continued).
Wave UpperWavelength number Transition Levelc
Comm. a Int.b (A, vac) (cmnt) J1 , J ' n
060'
500cd
Q 105
30080
Q 2400
Q 420
200300
Q 1N 2
150d
250N 3
125N 1
2405C
N 5115
N 2220
N 3s11030
N 10200
N 1S
100N 8
175N Os
95N 10
16090
N 1215090
N 15150
85N 18
13585
N 15135
80N 12
130ld
77N 10
12075
N 75
1924.3241924.2791924. 2381924. 1521904. 7981903. 7831898. 9751892. 1491886. 0171868. 7691824. 7551820. 4901812. 9671806. 3521805. 5581794. 6761766. 6381763. 0521756. 3771756. 1711740. 3021740. 0031733. 5501733. 4461723. 7781723. 2491722. 6411718. 9191718. 8641712. 3671712. 0091708. 9591708. 9281705. 0831704. 3311704. 0941701.8641701. 8461698. 4781698. 3081696. 6321696. 6161694. 0731693. 9481692. 6421690. 6741690. 5801689. 5511687. 9981687. 9241687. 0991685. 8511685. 7931685. 1201684. 1031684. 0551683. 5001682. 6601682. 6211682. 4031682. 1581681. 4561681. 4221681. 0321680.441
51966.3051 967. 5251968. 6151970. 9452 499.52 52752 66052 849. 9753 021. 8053 511. 1554 801. 8854 930.2755 158. 1955 360.1955 384.5555720.3656 604. 7056 719. 8156 935. 3856 942. 0557461. 357471. 1757 685.1057 688.5558 012. 1058 029. 9358 050.3958176.0958 177. 9758 398.7158 410.9058 515. 1658 516.2258 648. 1858 674. 0458 682.2058 759. 158 759.7358 876.2458 882.1458940.358940.8759 029.3459 033. 6859 079.2459 148. 0259 151.3059187.3359 241. 7959244.3659 273.3559 317.2459319.2759342.9559378.7959380.4759400.0659429.7059431.1059438.859447.4659472.2759473.4659487.2859508.20
1-21-21-2
0-1
0-2
0-1
0-20-10-2
0-10-10-20-00-1
0-10-0
0-10-20-1
0-00-10-20-10-0
0-1
0-20-10-00-10-20-10-00-10-20-10-10-20-10-10-20-10-10-20-10-10-20-10-10-20-1
0-10-20-10-10-2
2.78832.78842. 7885
2.2644
2.2832
2.3199
2.40512.41972.4328
2.45682.51892. 52732.54332.5438
2.58442.60142.60172.62812.6295
2.64172. 64192.66062.66172.67072.6708
2.68462. 68532.69212.69222.70262.70312. 70842.70842.71652. 71682.72102.72742. 72772.73102.73612.73632.73902.74312.74332.74562.74892.74912.75102.75382.7539
2.75552.75782.75792. 75932.7613
TABLE I. (Continued).
Wave UpperWavelength number Transition Leveic
Comm.a Int.b (A, vac) (cm-1) J" J' n
11073
N 7s11570
N 5s10068
N 3s9565
N 259563
N Is9061
N Os9060
N Os90585
N Os8557
N Os85
q 1
55N Os
8552
N Os8551
N os8550
N Os854880457545704268406840683566336030562852264925
1680.4111680. 0781679. 5771679. 5501679. 2651678. 8351678. 8101678. 5631678. 1921678. 1701677. 9551677. 6341677. 6131677. 4251677. 1461677. 1251676. 9591676. 7131676. 6951676. 5481676. 3311676. 3141676. 1831676. 0831675. 9941675. 9751675. 8571675. 6931675. 6721675. 6261675. 5661675. 4181675. 4001675. 3051675. 1711675. 1551675. 0691674. 9521674. 9331674. 8561674. 7501674. 7321674. 6621674. 5501674. 4851674. 3831674. 3231674.2311674. 1751674. 0911674. 0401673. 9621673. 9161673. 8441673. 8011673. 7341673. 6941673. 6331673. 5961673. 5381673. 5041673. 4511673. 4191673. 3691673. 341
59 509.2459521.0359 538. 8059 539. 7759 459. 8859 565. 1359 566.0059 574. 7559 587. 9259 588. 7159 596.3459 607. 7459 608.5059 615.1859 625. 159 625. 8659 631. 7559 640.559 641. 1559646.3759 654. 159 654. 6959 659. 3659662.9059 666. 159 666.7659 670. 9559 676. 859 677. 5559 679.259 681.3159 686. 659687.2559 690. 6359 695.459 695.9659 699. 0459 703.259 703. 8759 706. 6459 710.459 711. 0359 713. 5659 717. 5459 719. 8659 723.4959 725. 6259 728.9259 730. 9059 733. 9259 735. 7259 738. 5259 740. 1659 742. 7459744.2759746. 6659748.0859 750.2659 751. 5859 753. 6359 754. 8559 756.7759 757. 8859759. 6759 760. 69
0-10-10-20-10-10-20-10-10-20-10-10-20-10-10-20-10-10-20-10-10-20-10-1
0-20-10-10-20-1
0-10-20-10-10-20-10-10-20-10-10-20-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-1
2. 76142.76252.76422. 76432. 76532.76672.76682. 76772. 76902.76902.76982.77092.77092.77162. 77262. 77262.77322. 77412. 77412. 77462. 77542.77542. 7759
2. 77652. 77662. 77702. 77762. 7777
2.77802.77852.77862. 77892.77942. 77952.77982.78022.78022.78052. 78092.78092.78122. 78162. 78182. 78222. 78242. 78272.78292. 78322.78342. 78362. 78382. 78412. 78422. 78442.78462. 78482. 78492.78512.78522.78542.78552.78572.7858
1243 J. Opt. Soc. Am., Vol. 67, No. 9, September 1977
-
Brown et al. 1243
TABLE I. (Continued).
Comm.' Int.b
4323432240213819S3618s3417s32l6s30l6s29
1 5 s2714s2613s2423222120191817161615151413121110987
El 200Al 100E2 250A2 10E3 70A3 5dEl 150Al 40E2 100A2 40E3 10A3 10A 20E1 100Al 30E2 60A2 10E3 15A 50"A 30E1 100E2 80E3 25
Wavelength(A, vac)
1673. 2941673. 2681673. 2221673. 1981673. 1561673. 1341673. 0951676. 0731673. 0361673. 0171672. 9811672. 9631672. 9301672. 9121672. 8811672. 8661672. 8341672. 8211672. 7921672. 7781672. 7511672. 7381672. 7131672. 6761672. 6421672. 6091672. 5781672. 5481672. 5221672. 4941672. 4691672. 4441672.4211672. 3991672. 3771672. 3571672. 3381672. 3191672. 3011672. 2861672. 2681672. 2521661. 101659. 011633. 591615.771586.041880.031507. 951505. 801499.251495.331478.521476. 671445.751445. 001441. 611438. 991432.661431. 601416. 9461415. 531415. 071411.851407. 36
UpperTransition LevercJ," J, n'
0-1 6.2341-
1244 J. Opt. Soc. Am., Vol. 67, No. 9, September 1977 Brown et al. 1244
Wavenumber(cm'1)
59 762.3659 763.2959 764. 9359 765.7859 767.2859 768. 0959 769.4859 770.2659 771. 5959 772.2759 773. 5559774.2059775.3759 775. 9959 777. 1259 777. 6559 778. 7859779.2759 780.3159 780.7859 781. 7559 782.2259 783. 1359784.4459 785. 6759 786. 8559 787. 9459 789. 0359 789.9659 790. 9359 791. 8459792.7359 793. 5559794.3459 795. 1359 795. 8359 796. 5359 797. 1959 797. 8659 798.4059 799.0359 799. 6160 20160 2776121561 89063 05063 29066 31566 41066 70066 87567 63567 72069 16869 20469 3676949369 80069 85270574. 3270 64570 66870 82971 055
TransitionJ" J,0-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-1
0-10-10-10-1
Upperlevel'nt Comm..'
2. 7860 A32.7861 q2. 7862 El2. 7863 E22. 7865 E32. 7865 A32. 7867 E12. 7868 Al2. 7869 E22.7870 E32. 7871 A32. 7871 E12. 7873 Al2. 7873 E22. 7874 E32. 7875 A32. 7876 E12. 7876 Al2. 7877 E22. 7878 E32.7879 A32. 7879 E12.7880 Al2. 7882 E22. 7883 A22.7884 E32.7885 A32. 7886 E12. 7887 Al2. 7888 E22. 7889 A22. 7890 A32. 7891 E12. 7891 Al2. 7892 E22.7893 A22. 7894 A32. 7894 E12. 7895 Al2. 7895 E22. 7896 A22. 7897 A32. 83 E1
Al2. 941 E2
A2A3
3.216 E13.803 Al3. 827 E23.90 A2
A3E1
4.2137 AlE2
4. 8337 A2A3
4. 9897 E15. 1731 Al
E2A2A3
5. 8264 E15. 9771 Al
E2
WavelengthInt.b (A, vac)
5 1406.921 1401.420
120 1397.753100 1395. 8720 1392.9715 1392.83
100 1386.83810 1386.7575 1385. 61710 1383. 66310 1383.5980 1379. 5068 1379. 444
60 1378.6738 1377.2998 1377. 240
75 1374.3407 1374. 297
50 1373.7435 1372. 7487 1372. 689
65 1370.5626 1370. 520
45 1370. 1184 1370. 0324 1369. 3876 1369. 325
60 1367. 7154 1367. 684
40 1367.3774 1367. 2806 1366. 768
55 1365. 5154 1365. 487
35 1365. 2514 1365. 1685 1364. 770
50 1363. 7801363. 755
33 1363.5704 1363. 5125 1363. 191
45 1362.3871362. 364
30 1362. 2184 1362. 1664 1361. 906
32 1361. 2531361. 230
29 1361. 1135 1361. 0704 1360. 855
25 1360. 3161360. 294
28 1360. 2004 1360. 1593 1359. 985
23 1359. 5331359. 511
26 1359.4354 1359. 4033 1359. 257
20 1358.8721358. 852
25 1358. 789
Wavenumber(cm-l)
71 07771356.2271543. 471 64071 78971 79672 106. 572 11172 170. 072 271.9272 27672 489. 772 493. 072 533. 572 605. 9072 60972 762.272 764. 572 793. 872 846.5672 849. 772 962.7572 96572 986.472 99173 025.3973 028.773 114. 6473 116. 3073 132. 773 137. 9373 165.373 232.4373 233. 9473 246.673 251. 0573 272.473 325.6073 326.9573 336. 973 34073 357.373 400. 5673 401. 8073 409.6873 412. 573 426. 573 461. 7573 462. 9973469.2773 471.673 483.273 512.3573 513.5373 518.5973 520. 8173 530.273 554.6873 555. 8573 559. 9573 561. 773 569.673 590.4773 591.5373 594.92
0-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-1
6. 82306. 9672
7.22087. 8205
7. 9629
8.21868. 8190
8. 9592
9.21739. 8179
9. 9571
10. 218510. 8168
10. 9558
11.218411. 8158
11. 9540
12. 216112. 8150
12. 9531
13. 216413.8142
13. 9520
14.211514. 8134
14. 9504
15.213215. 8124
15. 9496
16. 213516. 8111
16. 9478
17. 21117. 8099
17. 9471
18. 20718. 8094
18. 9303
TABLE I. (Continued).
UpperTransition LevelcJ", J' n
TABLE I. (Continued).
Wave UpperWavelength number Transition Levelc
Comm.a Int.b (A, vac) (cm-) J" J' n'Comm. a
A2A3ElAlE2A2A3ElAlE2A2A3ElAlE2A2A3ElAlE2A2A3ElAlE2A2A3ElAlE2A2A3ElE2A2A3ElE2A2A3ElE2A2A3ElE2A2A3ElE2A2A3ElE2A2A3ElE2A2A3ElE2A2A3El
Int.b
43
18
2332
15
2232
12
2032
10
16228
17225
15214
14213
102128212821182116210520051
0
0
5
Wavelength(A, vac)
1358. 7551358. 6371358. 3101358.2901358. 2391358.2101358. 1071357. 8251357. 8081357. 7651357. 7351357. 6521357. 4081357. 3901357. 3551357. 3281357. 2551357. 0441357. 0261356. 9971356. 9701356. 9111356.7251356. 7081356. 6841356. 6581356. 6051356. 4441356. 4261356. 4071356. 3811356. 3391356. 1941356. 1621356. 1381356. 1011355. 9741355. 9441355. 9201355. 8941355. 7731355. 7491355. 7271355. 6991355. 5971355. 5731355. 5511355. 5321355.4351355. 4161355. 3991355. 3751355. 2901355. 2731355. 2541355. 2361355. 1641355. 1451355. 1191355. 1021355. 0471355. 0281355. 0041354. 9921354. 931
TABLE I. (Continued).
33. 91
Wavenumber(cmi1)
73 596. 8173603.273 620. 9273 621. 9873 624. 7573 626.373 631. 973 647. 1773 648. 1273 650.4573 652. 0773 656. 673 669. 8473 670. 8073 672.6973 674. 1473 678. 173 689.5873 690.5873 692. 1573 693.6273 696. 873 706. 8973 707. 8273 709. 1373 710. 5773713.473 722. 1773 723. 1373 724.1873 725.6073 727.973 735.7973 737. 4873 738. 8373 740. 873 747.7273749.3873 750. 6673 752. 173 758. 6773 759. 9773 761. 1673 762. 773 768.2473 769.5273 770. 7273 771. 873 777.0773 778. 1073 779.073780.373 784.9573 785. 8573 786. 9373 787.9173 791. 873 792. 8673 794.2673795.273798.273 799.273 800. 5173 801.273 804.49
0-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-1
aComments in this column have the following meanings, q= questionable line; Q = electric quadrupole transition; N= nuclear-spin-induced transition; Al, A2, A3 = absorptionmaxima of Beutler-Fano profile while. El, E2, E3 =absorp-tion minima of Beutler-Fano profile (see Fig. 2).Intensities are visual estimates (see text). A d indicates adiffuse line, an s a shoulder measurement, and an * a blend.The intensity scales for the emissionlike features (absorptionminima) and the absorptionlike features are necessarily in-dependent, and in the opposite sense.
cThe upper level of the transitions is defined by its J' valueand n2* effective quantum number (see Table II and text).
3Z. 8Y characterized experimentally both in this work and in
33.22 the previous work of Wood and Andrew 3 together with33.78 the J, nt, and n* values (columns 2-4, respectively) for
each level. A numerical value in columns 5 or 6 of Ta-
1245 J. Opt. Soc. Am., Vol. 67, No. 9, September 1977
E219.207 A219. 8067 A3
E219. 9437 A2
E220. 207 A220. 8070 E2
A220.9430 E2
A221.205 E221. 8049 A2
E221.9408 A2
E222.206 A222.8018 A2
A222. 9419 E2
A223.202 E223. 7986 A2
E223.9374 A2
E224.208 A224.7964 E2
A224. 9372 E2
A225.204 E225. 8004 A225.9337 E2
A226.20 E226. 7879 A226.9345 E2
A227. 18 E227. 802 A227. 930 E2
A228.20 E228. 789 A228. 929 E2
A2Zi U. 10
29. 80029. 925
30.2030. 79830. 918
31.2031. 75231. 908
32.2632.73
1354. 9181354. 8961354. 8851354. 8241354. 7961354. 7331354. 7071354. 6501354. 6261354. 5751354. 5491354. 5051354. 4791354. 4371354. 4161354. 3751354. 3541354. 3201354. 2981354. 2651354. 2461354.2151354. 1951354. 1731354. 1541354. 1311354. 1101354. 0871354. 0701354. 0501354. 0321354. 0151353. 9981353. 9821353. 9661353. 9491353. 9431353. 9181353. 9061353. 8911353. 8761353. 8611353. 8501353. 8381353. 8261353. 8161353. 801
73 805. 273 806.4173 807. 073 810. 373 811. 8773 815. 373 816. 7173 819. 873821.0973 823. 973 825. 3273 827. 773 829. 1073831.473 832.5773 834. 873 835. 9273 837. 873 839. 0073 840. 873 841. 8373 843.573 844. 5973 845. 873 846. 8573 848. 173849.2373 850. 573 851.4473 852. 573 853. 5173 854.473 855. 3373 856.273 857. 1173 858. 073 858. 8573 859. 773 860.3873861.273 862. 0173 862. 873 863.4373 864. 173 864. 7173 865. 373 866. 12
0-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-10-1
34.2334.85
35. 86
36. 84
37. 81
38. 79
39. 81
40. 82
41. 79
42. 82
43. 82
44. 73
45.70
46. 78
47.74
48.7
49.7
50. 7
51. 8
52.7
53. 8
54. 8
55.7
.
Brown et al. l1245
TABLE II. Observed odd parity energy levels of Pb,. TABLE II. (Continued).
EnergyLevel(cm-') J,
34 959. 91b 0
35 287. 22b 1
45 443. 17" 2
46 060. 84" 2
46 068 . 44k 1
46 328 . 67k 3
48 188. 63" 2
48 686. 93b 1
48 726. 26b 0
49 439. 62 1
52 101. 66b 2
52 311. 32b 2
52 412. 32" 3
52 499. 64 1
53 475, 37b 0
53 511. 15 1
55 003. 29b 2
55 084. 14b 2
55143. 14b 3
55 158.19 1
55 416. 46b 3
55 417. 30b 45
55706. 17b 0
55 720. 36 1
56 526, 49b 2
56 563. 20b 2
56 600. 67b 3
56 604. 70 1
56 76 2 . 04b 3
56 935.33 0
56 942.05 1
57 424. 02 2
57 444. 52 2
57 469. 34 3
57 471. 17 1
57 573. 46b 3
57685.08 0
57 688.57 1
57 995.90 2
58 012.05 2
58 028. 50b 3
58 029.94 158100. lb 3
58 176.07 058 177.97 1
58 378.56 2
58398.71 2
58 409. 32b 3
58 410. 90 1
58 461.3 3
58 515.17 0
58 516.22 1
58 517.71 2
58 666.94 2.
58 674.04 2
72 n2?
2.1010 1.67872.1150 1.6858
2.7628 1.9637
2.8241 1.9854
2.8249 1.9857
2.8520 1.9950
3.0716 2.0659
3,1396 2.0862
3.1452 2.08783.2515 2.1181
3.7707 2.2437
3.8230 2.2545
3.8490 2.2598
3.8719 2.2644
4.1590 2.3179
4.1708 2.3199
4.7733 2.4098
4.8139 2.4149
4.8442 2.4187
4.8520 2.4197
4.9923 2.4366
4.9927 2.4366
5.1651 2.4559
5.1740 2.4568
5.7727 2.5132
5.8051 2.5158
5.8388 2.5186
5.8424 2.5189
5.9909 2.5304
6.1682 2.5433
6.1754 2.5438
6.7682 2.5807
6,7974 2.5823
6.8332 2.5843
6.8358 2.5844
6.9897 2.5925
7.1702 2.6014
7.1760 2.6017
7.7572 2.6267
7.7918 2.6281
7.8275 2.6294
7.8306 2.6295
7.9888 2.6354
8.1713 2.64178.1760 2.6419
8.7266 2.6589
8.7882 2.6606
8.8212 2.6615
8.8262 2.6617
8.9884 2.6660
9.1722 2.6707
9.1758 2.6708
9.1811 2.6709
9.7573 2.6839
9.7875 2.6846
ObservedCombinations" Level
n2 J"-=I J"-0 No.bn,
ObservedCombinations' LevelJ"=1 J"=0 No.'b 1
b b 2
b 3
b 4
b b 5
6
b 7
b b 8
b 9
b 5 10
b 11
b 12
13
b 500 14
b 15
b 300 16
b 17
b 18
19
b 400 20
21
22
b 23
b 200 24
b 25
b 26
27
b 300 28
29
3 2 30
2 150 31
2 32
5 33
34
b 250 35
36
3 3 37
2 125 38
1 39
7 1 40
41
6 240 42
43
3 5 44
1 115 45
8 46
6 2 47
48
7 220 49
s0
Designation'Designation0
75s (2.f)C
7s (1. 4),
6d IL2152Gd 4113126d a[l],
6d 1111,]
6d 2[113
7s 11,1),
8s (f, I)
8s (4, -21)0
7s ( 3,')I
7d 12512
7d 42112
7d I1111 37d A[ll]7d 212]1
gs (1.4)0
8d 2 1112
8d 12 1.12
8d 21[13
8d 111],
5g 1 123
5g 2' 12]24 5
lOs (4,4)e
lOS (21 , 2)
9d 4 [213
9d 4[13
9d 21213
9d 4111,
6g 41+13
lls (4,f),lls (,1),
led 41112
lOd {112]
led 21213
lad 24121,
7g [ 1]3
12s (4,A)0
12s (2,2)I
lid 121112
lid 4[111
lid 2211 3
lid 1 [1],
8g a4[T]3
13s ( ,4)a
13s (4,2)t
12d 11513
12d 4111t
9g [213
14s (4,4),14s (4,4)I
6d R121
EnergyLevel(cm-') J58 680. 17b 3
56682.20 1
58 719, 5" 3
58759.17 0
58 759. 73 1
58 865.40 2
58 876.24 2
58 879. 21b 3
58 882. 14 1
58 940.46 0
58 940.87 1
59 017. 08 2
59 029.34 2
59 033.67 1
59 079.02 0
59 079.24 1
59 134.25 2
59 148.04 2
59 151. 28 1
59 186. 62b 3
59 187.22 0
59 187.33 1
59 226.10 2
59241.79 2
59 244. 34 1
59 273. 33 0
59 273. 35 1
59 298. 63 2
59 317.25 2
59 319.27 1
59 342. 92 0
59 342. 95 1
59 356. 35 2
59 378. 84 2
59 380. 46 1
59 400.06 1
59400.12 0
59 403.35 2
59 403. 89 2
59 429. 70 2
59 431.09 1
59445.18 2
59 447.46 1
59447.48 0
59 472.31 2
59 473.45 1
59 482. 07 2
59 487. 28 1
59 487.32 0
59 508.25 2
59 509.20 1
59514.75 2
59 521.03 1
59 521.2 0
59 538.80 2
9.8138 2.6851
9.8226 2.6853 8
9.9877 2.688610.1728 2.6921 4
10.1755 2.6922 ...
10.7242 2.7016 5
10.7856 2.7026 *
10.8026 2.7028
10.8195 2.7031 9
11.1726 2.7084 4
11.1752 2.7084 ...
11.6938 2.7153 2
11.7842 2.7165 ...
11.8166 2.7168 12
12.1730 2.7210 3
12.1749 2.7210 ...
12.6541 2.7261 9
12.7833 2.7274 1
12.8143 2.7277 8
13.1672 2.7309
13.1734 2.7310 3
13.1745 2.7310 ...
13.5981 2.7346 17
13.7815 2.7361 1
13.8120 2.7363 9
14.1738 2.7390 3
14.1740 2.7390 ...
14.5139 2.7414 25
14.7804 2.7431 2
14.8102 2.7433 10
15.1732 2.7456 3
15.1737 2.7456 ...
15.3916 2.7468 2015.7794 2.7489 215.8085 2.7491 1016.1736 2.7510 ...
16.1747 2.7510 2
16.2373 2.7513 25
16.2477 2.7513 40
16.7771 2.7538 3
16.8071 2.7539 9
17.1204 2.7552 30
17.1728 2.7555 * *
17.1733 2.7555 1
17.7766 2.7578 3
17.8059 2.7579 8
18.0318 2.7588 32
18.1726 2.7593 -
18.1737 2.7593 1
18.7747 2.7613 3
18.8034 2.7614 6
18.9738 2.7619 33
19.1723 2.7625 * *
19.1778 2.7625 1
19.7698 2.7642 4
175
05
95
10
160
90
12
150
90
15
150
85
18
135
85
15
135
80
12
130
77
10
120
75
78
110
73
19d 1 [31,
21s (21,2),
21s (,42)0
20d 4111,
22s (1 , 1f)i
22s (a4, *),
21d 1 [11,
23s (4,4),
23s (42,12)
22d 411],
24s (4,41)I
24s (4,4)D
78
1246 J. Opt. Soc. Am., Vol. 67, No. 9, September 1977
19
21
20
4
15
12
1
54 13d 11123
200 55 13d 4ND],56 lOg f1[213
15 15s (1,4)0
100 15s (2,4)I
8
57 14d (1213
14d 4211]
16s (12,)0
16s (2,2)1
15d 12[1,
17s (2,4)0
17s (4,4)t
16d 41[],
58 6d 31113
18s (2,2)0
18s (4,4)I
17d 412],
19s (4, 2)0
19s (,42),
18d I [22]
20s (2,2)0
20s (4, a)1
3*
110 51
52
53
10
Brown et al 1246
TABLE II. (Continued).
Energy ObservedLevel Combinationsa Level(cm-') J' n* n 2* J" =1 J"=0 No.b Designationc
1 115 23d 2-[2
70
59 539.75
59 543.50
59549.88
59 550.02
59 565. 1
59 566.00
59 568. 60
59 574. 7
59 574.75
59 587. 9
59 588.71
59 590.56
59 596.21
59 596. 34
59 608. 00
59 608.50
59 609. 90
59 615. 18
59 615.26
59 625.1
59 625. 86
59 626.94
59 631.70
59 631.75
59 640.5
59 641. 15
59 641.90
59 646.37
59 646.52
59 654. 1
59 654.69
59 655. 19
59 659.36
59 659. 6
59 666. 1
59 666.72
59 667.07
59 670.95
59671.0
59 676.8
59 677.55
59 677.73
59681.3
59 681.31
59686.6
59 687.25
59 687.36
59 690. 63
59 690.7
59695.4
59 695.96
59 696.06
59 699.04
59 703.2
59 703. 87
19.8033 2.7643 5
19.9373 2.7647 33
20.1718 2.7653 ...
20.1770 2.7653 1
20.7663 2.7667 3s
20.8031 2.7668 5
20.9106 2.7671 31
21.1694 2.7677 1
21.1716 2.7677 ...
21.7641 2.7690 35
21.8023 2.7690 5
21.8902 2.7692 28
22.1653 2.7698 1
22.1718 2.7698 ...
22.7745 2.7709 4
22.8015 2.7709 ...
22.8775 2.7711 27
23.1711 2.7716 * *
23.1756 2.7716 1
23.7547 2.7726 8*
23.8013 2.7726 *
23.8679 2.7727 25
24.1684 2.7732 1
24.1716 2.7732 ...
24.7551 2.7741 8*
24.8002 2.7741 *
24.8525 2.7742 25
25.1711 2.7746 **
25.1820 2.7746 1
25.7524 2.7754 7*
25.7984 2.7754 *
25.8376 2.7755 25
26.1717 2.7759 ...
26.1913 2.7759 1
26.7402 2.7765 ...
26.7944 2.7766 **
26.8251 2.7766 24
27.1730 2.7770 **
27.1776 2.7770 1
27.7241 2.7776 **
27.7973 2.7777 ...
27.8149 2.7777 24
28.1717 2.7780 0
28.1727 2.7780 ...
28.7276 2.7785 * *
28.7981 2.7786 ...
28,8101 2.7786 22
29.1731 2.7789 * *
29.1810 2.7789 0
29.7282 2.7794 ...
29.7954 2.7795 ...
29.8075 2.7795 23
30.174 2.7798 * *
30.708 2.7802 ...
30.797 2.7802 ...
TART.P. TT (C-nfinsed-
55
100
68
3s
95
65
95
63
Vs
90
61Os
90
60
Os
90
58
Os
85
57
Os
85
55
Os
85
52
O.,
85
51
Os
85
25s (21. -2 1
25s (2'-2)0
24d 2 [21
26s (2', 200
26s (2- 2)
25d 2[2]t
27s (2 2)0
27s (2' I 2)
26d 2[b 2] t
28s (212 )
28s ( 2)0
27d 2[2] 1
29s (-2,2)0
29s (2-,-2)t
28d 2[;2t
30s (12 ),
30s (212) 0
29d 2[2]1
31s (2,2)1
31s (2, 2) 0
30d 2[2]1
32s (2 I2)1
32s (2, 2) 0
31d 2[21]1
33s (26. 2) 0
33s (2,2)1
32d 2[2]1
34s (2,2) 1
34s (12,) 0
33d -[211
35s (2,A2)t
34d 2[21 1
ObservedComblnationsa Level
nt ni J" -1 J" -=0 No, b Designation'
EnergyLevel(cm-
1)
59 703. 91
59706.4
59 706.64
59 710. 4
59 711. 03
59 711. 05
59 713.56
59 713.6
59 717. 54
59 717.57
59 719. 8659 723.49
59 723.51
59 725. 62
59 728.92
59 728.92
59 730.90
59 733. 92
59 733.92
59 735.72
59 738.49
59 738. 52
59 740. 16
59 742. 72
59 742.74
59 744.27
59 746.62
59 746.66
59 748.08
59 750.24
59 750.26
59 751.58
59 753. 59
59 753.63
59 754. 85
59 756.73
59 756.77
59 757. 88
59 759.64
59 759. 67
59 760. 69
59 762. 33
59 762.36
59 763.29
59 764.84
59 764. 93
59 765.78
59 767.23
59 767.28
59 768.09
59 769.45
59 769.48
59 770.26
59 771.50
59 771.59
J,
2
0
21
2
1
2
1
2
2
2
1
22
1
2
2
1
2
1
2
2
1
2
1
1
2
1
1
2
1
1
2
1
1.
2
1
1
2
1
30.802 2.7802 24
31. 139 2.7805 0
31.173 2.7805 ...
31.705 2.7809 **
31.797 2.7809 ...
31.800 2.7809 22
32.174 2.7812 ...
32.180 2.7812 0
32. 795 2.7816 ...
32. 800 2.7816 20
33.175 2.7818 ...33. 796 2.7822 ...
33.799 2.7822 19
34.177 2.7824 **
34. 793 2.7827 18
34.793 2.7827 *
35.179 2.7829 ...
35.794 2. 7832 18
35.794 2.7832 * *
36.176 2.7834 ...
36.789 2. 7836 17
36.796 2.7836 ...
37.174 2.7838 ...
37.788 2.7840 17
37.793 2.7841 ...
38.175 2.7842 ...
38.785 2.7844 15
38.796 2.7844 ...
39.179 2.7846 ...
39.785 2.7848 14
39. 790 2.7848 ...
40.175 2.7849 * *
40.782 2.7851 13
40.795 2.7851 ...
41.177 2.7852 ...41.789 2.7854 12
41.802 2.7854 *
42.176 2.7855 *
42.791 2.7857 10
42.802 2.7857 *
43.171 2.7858 *
43.785 2.7860 9
43.797 2.7860 *
44.157 2.7861 *
44.778 2.7862 8
44.815 2.7862 *
45.167 2.7863 *
45.789 2.7865 7
45.811 2.7865 *
46.170 2.7865 *
46.792 2.7867 6
46.806 2.7867 *
47.175 2.7868 *
47.779 2.7869 5
47.824 2.7869 * 36
1247 J. Opt. Soc. Am., Vol. 67, No. 9, September 1977
50Os
85
48
80
4575
45
70
42
68
40
68
40
68
35
66
33
60
30
56
28
52
26
49
25
43
23
43
22
40
21
36s (2', )O
36s 02,21)
35d 2'[T1
37s (A,2) 1
37s (2,2)0
36d 2[2]1
38s (2,-2) 1
37d 2'[31-
39s ( l , -2
38d 2[32]1
40s (2,2) 1
3gd 1[3]1
41s (2,2)1
40d 2[2]t
42s (21,2)
41d 12[21
43s (2,-2) 1
42d 1[13t
44s ( , )1
43d 12[21
45s (,2)t
44d -21[22
46s (2, 2) I
45d 2[2]t
47s (1,2)t
46d 2[2]
48s (, A)I
47d 1 [L1]1
49s (2,1)t
48d 21[]1
50s (1.)t
49d 2[2]t
51s (2, 'DI
51d 2'[]1
Brown et al. l1247
| * a * *s: 1.
38 50d 1[]I
l9, 52s (12-)t
. ,
EnergyLevel(cmn)
59 772. 27
59773.46
59 773.55
59 774. 20
59 775. 31
59 775. 37
59 775. 99
59 777. 04
59777.12
59 777.65
59 778.65
59 778.78
59 779.27
59 780. 16
59 780. 31
59780.78
59 781. 65
59781.75
59782.22
59782.98
59 783. 13
59 784. 32
59784.44
59 785.56
59 785. 67
59786.78
59 786. 85
59 787.87
59787.94
59789.03
59 789.96
59 790.93
59 791. 84
59 792. 73
59 793. 55
59 794. 34
59795.13
59795.83
59 796.53
59 797. 19
59 797. 86
59 798.40
59 799.03
59 799. 6160 201
61215
63 290
"t
48.167
48. 784
48. 832
49. 180
49. 793
49. 827
50. 18
50.80
50.84
51.16
51. 79
51. 87
52.18
52.77
52. 87
53.19
53.80
53. 87
54.20
54.76
54.88
55.80
55.89
56.80
56.90
57.8557.91
58.84
58.90
59. 94
60.88
61.90
62.91
63. 94
64.94
66.0
67.0
68.0
69.0
70.0
71.1
72.0
73.1
74.1
aThe combinations with the ground levels 6p2 (2,2), and (32,:T)observed in this work are indicated by intensity figures (fromTable I) in the J" =0 and J" =1 columns, respectively. Thecombinations observed by Wood and Andrew (Ref. 3) outsidethe wavelength range reported here are indicated by a "b" inthe appropriate column.
bIndicates data taken from Ref. 3.'Where possible, the levels have been given J or jk labels.In the case of the J=2 levels, the configuration mixing is seri-
ous enough to force the abandonment of this labeling for n > 11
1248 J. Opt. Soc. Am., Vol. 67, No. 9, September 1977
TABLE II. (Continued).
Brown et al 1248
.
n4
2.7870
2.7871
2.7871
2.78712. 7973
2.7873
2. 7873
2.7834
2.7874
2.7875
2.7876
2, 7876
2.7876
2.7877
2.7878
2.7878
2.7879
2.7879
2.7879
2.7880
2. 7880
2.7881
2.7882
2.7883
2.7883
2.7884
2.7884
2.7 885
2.7885
2.7886
2.7887
2.7888
2.7889
2.7890
2.7891
2.7896
2. 7892
2. 7893
2.7894
2.7894
2.7895
2.7895
2.789 6
2.78972.83
2. 941
3.216
. . .
.
.
.. .
.. .
.. .
.. .
.. .
.. .
.. .
.. .
.. .
.. .
.. .
.. .
.. .
ObservedComblnatlons' LevelJ" =- J"'O No.b
... 18'
4
... 34
... 175
3
... 32
*@ 16'
4
*- 30
... 16'
4
*-- 29
... 15'
3
... 27
... 14'
2
... 26
... 13'
2
... 24
Designation'
53s (2,2),
52d [32]1,
54s (L.-),
53d 2A11
55s (2.)1,
54d
56S (A.-A)
55d All1
57s (A ,A)
56d 2I [ff
58s (2.A 2)
57d 2[211
s9s (', *,2)1
58d 2All,
59d AllD,
60d 21[allt
61d Ali1,
62d Iffl,
63d 2Al21,
64d 2[J],
65d All],
66d A[l21,
67d A[ll1,
68d A2[],t
69d A[ll],
70d A2L],
71d Al,21
72d All],73d All],
74d 1Al],
75d Al[]1
76d A[3]1
77d All],E l"
E2e
A3S
23
22
21
20
19
18
17
16
16
15
15
14
13
12
11
10
9
8
7
200
250
5
(see Fig. 5). In the J= 0 and J= 1 cases, this labeling has beenextended to the series limits, however, the fact that levels canbe arranged into "series" with nearly constant quantum defectsshould not be taken to mean that configuration mixing is absentin the J= 0 and J= 1 channels. The evidence for this mixingis the appearance of the Beutler-Fano profiles in the autoionizedportion of the channel structure. It is fortuitous that theseries limits in the J = 0 and J= 1 cases occur in a region wherethe quantum defects are not changing rapidly (see Fig. 3).dThis "level" is actually the position of the first member of aseries of autoionized features (marked El in Fig. 2) with
0. 83. Since the wave number of the combination withthe J" = 0 level and energy of the autoionized "level" coincide.the remainder of this series is found in Table I with 2. 83 < n¶<33.78.eThe first member of a series of features (marked E2 in Fig. 2)with (nt).d I ; 0. 9. The remainder of these features are re-ported in Table I with 2. 94 < n4 < 55. 7.fThe first member of a series of features (marked A3 in Fig.2) with (nt44 ,d I - 0. 2. The remainder of this series with 3. 21< n4 < 34.23 are reported in Table I.
ble II indicates that a transition from 6p (2, 2) or (2 4)0to the level in question has been observed in the presentwork, with additional comments appearing in subsequentcolumns. The nz* and J values in Table II serve touniquely identify the upper levels of the transitions in theline assignments appearing in Table 1.
It should be emphasized that the intensities reportedin Tables I and II are visual estimates and are intendedonly as a rough guide to the relative intensities of theobserved features. Although attempts were made tomaintain a uniform scale, intensities for lines widelyseparated in wavelength could not be unambiguously cor-related. Further, spectra for transitions with 6p(2, 2Aas their lower level generally were observed under con-ditions quite different (i. e., higher temperatures andpressures) from those for trnnsitions involving the6p9(4, 2)0 ground level; thus t ensity scales for thesetwo sets of transitions should be regarded as unrelated.In addition, no relation could be established between theintensity scales for sharp spectral lines and for broadautoionized features. Hence, the intensity estimates inTables I and II should be used only when comparing sim-ilar transitions which occur within - 50 A of one another.
A. Odd parity, J= I channels
There are two J= 1" channels associated with the6p2plF/2 core level, with discrete portions which aremixtures of levels conventionally labeled 6pns(4, 4)0 and6pnd4[ A3R in j and jK notations. Below the 6pFP,/2limit, we have extended the series previously designated6p2(2, 2)0 -6pns(G, 412)f and 6p2(4, 42)0 -6pnd42[4t to n valuesof 59 and 77, respectively, and have observed the6p2(2, DIX 6pns(2, 2)f1 and 6p2(2, D)j-6pnd 2[ 2]71 transitions
for n= 11-1 3 and n= 10-3 0, respectively.
Above the 6p2plF,2 limit, the continuous portions of thetwo J= 1° channels mentioned above mix with the discreteportions of the three J= 1° channels associated with the6p2PIj/2 level, which are in turn mixtures of the levelsconventionally labeled 6pns(2, 2 ), s 6pnd 2[2],, and6pnd 4[ 4}1. A result of this mixing is that the absorp-
tion spectrum observed above the 6p2(4, 2)o-6pnd4[12
Pb I
Sn I
Gei
FIG. 1. Autoionized np2 3po-J= 1° transitions converging onthe2
P'312 ionic limit for Pbi, Sni, and Gei. The wavelengthscales have been adjusted to match the 14 n* '21 regions ofthe three spectra. Changes in the Beutler-Fano profiles fromsharp emissionlike windows in Pbi to asymmetrical absorptionprofiles in Gei are striking.
convergence limit consists of an intense continuum uponwhich are superimposed three series of Beutler-Fanoprofiles [see Figs. 1(a) and 2] which converge to a limitat 1353 A. As can be seen in Fig. 1, windows in theabsorption spectrum (emission like features) are morepronounced in Pb I than in Sn I or Ge I. Since the conceptof discrete series of energy levels breaks down in suchsituations, it should be emphasized that the data forautoionizing levels in Tables I and II are no more thancollections of energies and n* values for series of simi-lar spectral features. Analogous listings by Garton andWilson2 contain J= 1 ° features with n* values as high as26, while the present work extends such observations toa* values of 57.
A Lu-Fano plot for the J= 1° levels of Pb I under dis-cussion appears in Fig. 3. The main features of Fig.3 have been drawn using the J= 1° levels from Table IIlying below the 6p2Po/2 limit (points joined by solidlines) to locate the horizontal portions of the curve andthe approximate values of (n'*)modl for the main featuresin the autoionized portion of the spectrum [(n2*)mod1 valuesof 0.20, 0. 83, and 0. 94] to sketch the remainder of thediagram (dashed portion). Both channels associated with
0.0(a)
(b)
(c)
I 4§ 14.0
0.0 0.5 (n )mod .
FIG. 3. Lu-Fano plot for the J = 1° levels of Pb i. The thinsolid curves are the function nt = G(n*) from Eq. (1) plottedmodulo 1. The numbers on these curves indicate the principalpart of nt (i. e., the curve numbered 4 corresponds to 4 End- 5). The heavy solid and dashed curve corresponds to theexperimentally determined and estimated portions, respective-ly, of the function nt =f(n2*).
the 6p2Pl,/2 core contribute regular "series" that con-verge to the 2P1/2 ionization limit at n2* =2.79. In TableII, the J= 1° levels with (nt)mOdl = 0. 18 and - 0. 8 havebeen labeled 6pns(2, 2 and 6pnd [ l1, respectively,while the level at 49 439. 62 cm-' (nt = 3. 2515) has beendesignated 6p7s(2, 2)1. All such configuration and termlabels should be considered approximate because, insimilar situations, 10,11 levels in what appear to be regu-lar series are found to be admixtures of several chan-nels. The five eigenquantum defects for the J= 1 close-coupled states associated with 6p P3/2,1/2 can be esti-mated from Fig. 3, and are approximately 0. 1, 0. 2,0.80, 0.85, and 0.95.
The two ionization limits for levels converging on the2P levels of Pb II were evaluated by assuming that thequantum defects of the two J= 1 series converging on2 P1/2 and of the two charp emissionlike series (El andE2 in Fig. 2) converging on 2P3/2 become constant atlarge quantum numbers. Since we had no a priori rea-son to believe that the series limits should occur in aregion of constant quantum defects (in the case of theJ= 2 levels, exactly the opposite is true, see Fig. 4),the ionization potentials obtained were checked for con-sistency by requiring the following: (i) the values ob-tained must agree within experimental error; (ii) thequantum defects for the J= 2 levels must behave mono-tonically on Fig. 4; and (iii) the difference of the twolimits must correctly predict the 2po spacing of Pbii.All these criteria were met, and ionization limits of59 819. 57 i 0. 10 cm 1 and 73 900. 64 ± 0. 10 cm- 1 were ob-
tained for the 6p P1/2 and 6pP3°/2 levels of PbII, re-spectively. These should be compared with the best pre-vious values 3 of 59,819. 4 ± 0. 3 cm- 1 and 73 900. 5 ± 0. 3
cm-'. The difference of the limits if 14 081. 07 cm-', ingood agreement with the interferometrically measured1 2
6p P°/,-6P 3,/2 transition of PbII at 14 081. 074 cm'.
C0
0~
-00
cW
A2 tA 3 73028 Cm-'
FIG. 2. Densitometer trace of a portion of the np(2!,2)0-J=1autoionized spectrum of Pbi. Table I lists series of windowand absorption features which correspond to the features El,E2, E3 and A,, A2, A 3 , respectively, indicated in this figure.
1249 J. Opt. Soc. Am., Vol. 67, No. 9, September 1977
(wlT)modl
20.0 17.0 n 2
...........I............................. ... ................I.... ................. .... ....I.......I...........
E , .................I....I I
Brown et al. 1249
(fnl)mod 1
ON BI Y I
.0 0.5 ( n2) mod 1 1.0
FIG. 4. Lu-Fano plot for the J=20 levels of Pbi. See captionto Fig, 3.
The Rydberg constant used for lead was 109 737. 024 cm'based on an atomic weight of 207. 21 for the natural iso-topic mixture.
B. Odd parity, J = 0 channels
There are two J= 00 channels associated with the 6p2P0core, the discrete portions of which would be mixturesof levels conventionally labeled 6pns(2, X and6pnd 2[ 23 0. Of these, only the levels associated with theseries labeled 6pns have been identified with certainty.Values for 7s-13s are listed by Wood and Andrew. 3 Wehave observed the 6p2(z, 2)1-6pns(2, 2)O transitions forn= 11-36 and the forbidden transitions 6p2 (l, 26pns(I, 2 )O for n= 11-16. Since J= 0-J= 0 even-oddtransitions are forbidden for all types of radiation, theselines can be attributed to nuclear-spin-induced effectsin the 207Pb isotope (see Refs. 22-24 and Discussion).
A Lu-Fano diagram for the J= 0° levels is unnecessarybecause all of these levels (see Table II) fall on thestraight line with (nt)mod =I0. 2. We have not been ableto assign transitions which would allow us to sketch thevertical portion of the J= 0° diagram, although the ten-dency toward pair coupling in the close-coupled region(i. e., toward jj or jK coupling) suggests that the verticalJ= Oq portion will occur for (nf*)modI> 0. 8 as in the J= 1°case discussed above. For this situation the two eigen-quantum defects for J =0 would be approximately 0. 18and 0.8< Au<l.O.
C. Qdd parity, J= 2 channels
There are five J= 20 channels associated with the 6p 2po
core, the discrete portions of which would be mixturesof levels conventionally labeled 6pns(3, 2)2, 6pndz[]°6pnd-j[2, 6pnd{Fl[5], 6pnd3[3]°, and 6pnd@[ °. Woodand Andrew3 provide revised values for 6p7s(2, 22,6p6d3 [ ]° , 6pnd [ ]° for n = 6-13, and 6pnd2[ 3]° fori=6 6-12, while Moore's1 listing includes values for6p8s(, 2)° and 6p9s(3, ')°. In terms of these conven-
1250 J. Opt. Soc. Am., Vol. 67, No. 9, September 1977
tional labels we have observed the 6p 2(2, 1)1-6pnd {[ jotransitions for n = 10-62, the 6p2(3, 2)1-6pnd [3] transi-tions for n = 10- 13 and 16- 30, and the electric dipoleforbidden 6p2(, 22),-6pnd 2[! 2 transitions for n= 11-35.However, these conventionally labeled series exhibitmarked irregularities in both their energies and spectralline intensities, irregularities which vanish when viewedfrom the multichannel, two limit approach.
The data for the J= 2° levels in Table II appear aspoints in the Lu-Fano diagram illustrated in Fig. 4. Asindicated by the solid curves in Fig. 4, sufficient datawere available to construct a fairly complete diagram.The dashed vertical portion of the diagram is necessari-ly an estimate because it is based on the single datapoint for the level previously designated 6p7s(2, 2)2 atni = 3. 072, which is the only member of this channelappearing below the 6p 2P /2 limit. It should be notedthat the J= 20 level at 58 517 cm-' (the point at nt = 9. 18)belongs to the mixed ns, nd channel structures, whichagrees more closely with the classification of Wood andAndrew3 and the observed Zeeman pattern 4 than the6s6p3 5So classification suggested by Garton and Wilson. 2
The data for the J= 2° levels in Table II were used toevaluate the multichannel parameters appearing in Eq.(2), using least-squares iterative procedures similar tothose previously discussed. 10 The starting point for theiteration of the J=2' transformation matrix was the ma-trix for angular momentum recoupling between a loose-coupled jj and a close-coupled jK scheme, with ele-ments 2 0 calculated using formulas given by Cowan andAndrew. 21 Final values of /la and Ui,, are reported inTable III.
Mixing coefficients Ma for the close-coupled portionsof the J= 20 channels were calculated using Eq. (3) andthe data in Table III. Figure 5, which is a plot of M.vs (nfl)modl, summarizes the results of these calculations.
TABLE III. Transformation matrix Uj and eigenquantum de-fects p.u for the J = 2 odd parity levels of Pbi. a
d 2[22 [A d;1[112 di[A]. d2[ 2]
i 1 2 3 4
d (a, A)2 1 -. 385 78 .0. 883 93 0. 18916 0. 184 581
d(3,.)2 2 0. 684 67 - 0. 453 51 0. 538 32 0.18913
d(12, .)2 3 -0.314 43 - 0. 063 47 0. 013 70 0. 947 06
d(2, )2 4 -0. 532 48 0. 094 74 0. 821 12 - 0. 182 32 -
0.665 0.71 0.78 0.83
2<n' <36 N=60 a=0.015
aThe matrix elements Uia appear in the square brackets. Thens(2,-21) channel contributions have been neglected in ourparametric fitting because the channel is determined by asingle data point (see dashed portion of Fig. 4). The remain-ing matrix elements belong to the channels associated with thed electron. The jK labels on the columns and the jj labels onthe rows indicate the starting point of the iterative fitting pro-cedure (see text). Since the initial Ui elements were alteredconsiderably, these row and column level labels do not reflectthe properties of the a and i states. Included under the rowof p, values are the range of nt values considered, the actualnumber of energy levels used, and the standard deviation ofnt for the final fit.
Brown et al. 1250
(M)
(b)
0.5 -
0.0-0.0 (n0 ) 1 .0
FIG. 5. Plot of M2 vs (n').dt for J=2 levels of Pbi (-,ae =1; * .- a- ° °* -, = 2; ---- , Ue =3; --- , ca =4). Theupper figure corresponds to points on the branch A -B, B'-A' in Fig. 4 while the lower figure corresponds to points onthe curve X-Y, Y' -X'.
The composition (close- coupled portion) of the waveM2function of any J= 2° level in Table II is given by the Ma
values on a vertical line drawn through the level's(n*)modl value. Although a number of conventional desig-nations appear in Table II, it should be noted that theactual compositions of even the lower lying J= 2° levelsare those determined from Fig. 5.
DISCUSSION
As noted in the previous section, we have observed 31weak transitions which do not obey the electric dipoleselection rules. These transitions all originate from theground level 6p2(, DO and terminate on odd parity levelswith J values of either 0 or 2. They cannot be magneticdipole or electric quadrupole transitions because they in-volve changes in parity; however, they can result fromnuclear-spin-induced electric dipole effects.22,23 Mag-netic quadrupole effects are ruled out because of the ab-sence of other magnetic multipole transitions in our Pb Ispectrum and because such effects cannot produce2 2' 23 theobserved J " = 0- J' = 0° transition.
The nuclear spin effects under discussion mix23 levelswith the same parity and F values (the resultant of cou-pling electronic and nuclear spin angular momenta), butwith J values differing by ±1. The resulting mixed stateI J', nj) can be thought of as being approximately
JJnj) J,nj) (J, n 1l- /1. HIJ±l,n,) IJ+1,n,|J~nf= l~ni) Er, nj -EXJl, ni Jln)
where ,u is the nuclear magnetic moment and H is themagnetic field produced by the electrons.
Nuclear-spin-induced transitions can occur only inatoms with nonzero nuclear spins. The only stable iso-tope of lead with a nonzero spin is 207Pb which comprisesabout 23% of lead's natural abundance. Hence, the 31transitions (labeled with an N in the comment column inTable I) occur in the single isotope 207Pb. This observa-tion suggested24 a simple means of separating 207Pb viathe optical pumping of any of these transitions followedby either field or photoionization of the excited level.
There are intensity maxima in these series (see Ta-ble I) at intermediate n values. This effect is real andseems plausible if the general form of Eq. (4) holds forn < 30. In this situation the intensities of nuclear- spin-induced electric dipole transitions depend (a) on the mix-ing of levels with AJ= ± 1, which will tend to increasewith increasing n (as E0,n - EJkif values decrease withseries convergence) if the matrix elements are slowlyvarying functions of n, and (b) on the intensities of tran-sitions to the allowed portions of the resulting admix-tures, which normally decrease with increasing n. Be-cause effects (a) and (b) vary inversely with increasingn, their combination can explain the distribution of tran-sition intensities observed for these "forbidden" transi-tions in Pb i.
We also have observed five weak transitions (markedQ in Table I) which obey the selection rules for electricquadrupole radiation. These transitions originate fromthe 6p2(l, ')o ground level and terminate on the even pari-ty levels 6pnp(-, 3)2 with n =8 and 9 and 6pnf '[ 5 2 withn= 5, 6, and 7.
There are 16 lines in Table I which remain unassigned.Of these the line at 51 970. 94 cmi1 mjay belong to the6p2(2, 2)1-6p6d 32[2] transition. Such an assignmentwould lead to an n2* value of 2. 7887 for the upper level,which would be in agreement with our estimates for thevertical portion of the J= 0° Lu-Fano diagram (seeabove). Aside from a few very weak lines of question-able existence, it is presumed that the remaining linesbelong to transitions involving levels in either the yet un-characterized 6s6p3 configuration or portions of the ns,nd channel structures associated with the 6p2
°3/ 2 corefor which combination lines are masked by the intense6p2(', 2)0 - J=1° autoionizing transitions. Without the aidof observable combinations we feel it is unwise to specu-late further on the possible assignments of these transi-tions.
*Ball Brothers Research Corporation.tPresent address: NASA Headquarters, Code SU, Washington,
D. C. 20546.
'C. E. Moore, Atomic Energy Levels, III, Natl. Bur. Stand.(U.S.), Circ. No. 467 (U. S. GPO, Washington, D.C.,1958), p. 211.
2W. R. S. Garton and M. Wilson, "Schumann region absorptionspectrum of lead vapour, " Proc. Phys. Soc. (Lond.) 87,841-851 (1966).
3D. R. Wood and K. L. Andrew, "Arc spectrum of lead," J.Opt. Soc. Am. 58, 818-829 (1968).
4 D. R. Wood, K. L. Andrew, A. Giachetti, and R. D. Cowen,
1251 J. Opt. Soc. Am., Vol. 67, No. 9, September 1977 Brown et al. 1251
"Zeeman effect and intensity anomalies in Pbi," J. Opt. Soc.Am. 58, 930-836 (1968).
5R. Heppinstall and G. V. Marr, "Vacuum ultraviolet absorptioncross-section measurements in lead vapor," Proc. Roy.Soc. (Lond.) A 310, 35-42 (1969).
OR. Assous, "Autoionized lines in arc spectra of lead andbismuth," J. Opt. Soc. Am. 62, 544-547 (1972).
7M. Kozlov, S. Mileshina, and G. P. Startsev, "Absorptionspectrum of lead vapor in ultraviolet and Schumann regions,"Opt. Spektrosc. 35, 158-160 (1973).
8U. Feldman, C. M. Brown, G. Doschek, C. E. Moore, and F.D. Rosenberg, "XUV spectrum of C I observed from Skylabduring a solar flare," J. Opt. Soc. Am. 06, 853-859 (1976).
9C. M. Brown, S. G. Tilford, R. Tousey, and M L. Ginter,"Absorption spectrum of Sii between 1500 and 1900 A," J.Opt. Soc. Am. 64, 1665-1682 (1974).
1°C. M Brown, S. G. Tilford, and M. L. Ginter, "Absorptionspectrum of Ge i between 1500 and 1900 J. Opt. Soc. Am.67, 584-606 (1977).C. M. Brown, S. G. Tilford, and M. L. Ginter, "Absorptionspectrum of Sni between 1580 and 2040 A," J. Opt. Soc.Am. 67, 607-622 (1977).
12 D. R. Wood, C. B. Ross, P. S. Scholl, and M. L. Hoke,"Interferometric measurement of Pbir spectrum," J. Opt.Soc. Am. 64, 1159-1161 (1974).
13U. Fano, "Unified treatment of perturbed series, continuousspectra, and collisions," J. Opt. Soc. Am. 65, 979 (1975).
4K. T. Lu and U. Fano, "Graphical analysis of perturbed Ryd-berg series," Phys. Rev. A 2, 81-86 (1970).
15K. T. Lu, "Spectroscopy and collision theory, The Xe ab-sorption spectrum," Phys. Rev. A 4, 579-596 (1971).
GC. M. Lee and K. T. Lu, "Spectroscopy and collision theory,II. The Ar absorption spectrum," Phys. Rev. A 8, 1241-121257 (1971).
7A set of parameters (designated pal D,, and Ui, with the num-bers of i's and at's equal to the number of channels being con-sidered) result from separating the state representing the sys-tem composed of Rydberg electrons plus a charged ion coreinto regimes and matching the states appropriate in the tworegimes attheircommon boundaries. In the first (close-coupled, short-range) regime, the Rydberg electrons arestrongly correlated with electrons in the core. In the second(loose-coupled, long-range) regime, the electrons are sub-
ject mainly to attractions from a centralized charged ioncore, and the eigenstates appropriate at these large electron-core separations are the Coulomb functions. The total stateof the system is then a linear combination of the above eilen-states with the coefficients in the combination (i. e., the mix-ing coefficients) determined by the boundary conditions at in-finity and at some point ro where the two solutions join. Forthis situation the wavefunctions for r- ro can be represented(see Ref. 15) as
z0l(n*) = Z; di [f(n*',i, r) FUie(cos7rp,)Ma
+g(nt, li, r) EUi,,,(sin7ry,,)MJ],
where a and i label the close-coupled and loose-coupledrepresentations, respectively. In this expression, the ioncore, spins, and angular parts are represented by 6i, f, andg are the regular and irregular Coulomb functions, the U1 aare matrix elements of the transformation between the close-coupled and loose-coupled configurations, the pa are eigen-quantum defects of the close-coupled eigenstates, and the Ma(denoted Ua in Ref. 16 and Ac, in Ref. 15) are the coefficientsof the linear combinations of close-coupled states making upa given level.
18C. M. Brown, R. H. Naber, S. G. Tilford, and M. L. Gin-ter, "High temperature furnace system for vacuum ultra-violet spectroscopic studies," Appl. Opt. 12, 1858-1864(1973).
"9Gallard-Schlesinger Chem., 99. 999% purity.20For row and column labelings identical to those in Table III,
the nonvanishing elements Ui are U - U 2 25, U33 = - U44, U2 = U2 = nd U43 = U34 = 5
2 1R. D. Cowan and K. L. Andrew, "Coupling considerations intwo-electron spectra," J. Opt. Soc. Am. 55, 502-516 (1965).
22 R. H. Garstang, "Theoretical and experimental forbiddenatomic transition probabilities," Mem. Soc. Roy. Sci. Liege,17, 37-48 (1969).
23R. H. Garstang, "Forbidden Transitions," Atomic and Mo-lecular Processes, edited by D. R. Bates (Academic, NewYork, 1962), pp. 1-46.
24C. M. Brown andM. L. Ginter, "Isotopic selection usingnuclear-spin-induced electric dipole transitions," Opt. Coin-mun. 21, 279-281 (1977).
The time-dependent physical spectrum of light*J. H. Eberlyt
Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627
K. WodkiewiczInstitute of Theoretical Physics, Warsaw University, 00-681 Warsaw, ul. Hoia 69 Poland
(Received 7 March 1977)
We investigate the time-dependent spectrum of light from an observational point of view and define a time-dependent "physical spectrum" of light based on the counting rate of a photodetector. The tunable element,the filter, that allows observation of different spectral components of the light is shown to play an essentialrole in the time-dependent spectrum. Its bandwidth cannot be taken arbitrarily narrow. We establish theconnection between our physical spectrum and other time-dependent spectra associated with Page, Lampard,Silverman, and Kolmogorov, as well as with the Wiener-Khintchine power spectrum. Also, we show theconditions under which these earlier definitions can be used as the first approximations to the completephysical spectrum, and give an expression for the correction terms.
I. INTRODUCTION Colours. "m It was not until one hundred years ago,however, that a proper mathematical framework began
The concept of spectrum has played a role in the in- to be constructed for the theoretical study of spectra.vestigation of light at least since the time of Newton and It was of interest to mathematicians and physicists suchhis observation of "the celebrated Phaenomena of as Schuster, Gouy, Poincar6, Michelson, and Lord
1252 J. Opt. Soc. Am., Vol. 67, No. 9, September 1977 Copyrio, it � 1977 by the Optical Society of America 1252
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