Absorption spectrum of Ge I between 1500 and 1900 Å

Absorption spectrum of Ge I between 1500 and 1900 A

C. M. Brown and S. G. TilfordE. 0. Hulburt Center for Space Research, Naval Research Laboratory, Washington, D.C. 20375

Marshall L. Ginter t

Institute for Molecular Physics, University of Maryland, College Park, Maryland 20742(Received 9 August 1976)

The high-resolution absorption spectrum of Get is reported between 1500 and 1900 A. Transitions have beenobserved from the 4p2

3j and ID terms to levels with J< 3 associated with 4pns, 4pnd, and 4pngconfigurations. Levels with it values as high as 70 have been determined. Numerous perturbations amongRydberg levels have been analyzed by the Lu-Fano graphical method. A total of 989 spectral lines and 549energy levels are reported, most of which are new. Ionization energies of 63713.24 - 0.10 cm-' and65480.60-0.10 cm-' have been determined for the 2P 1/2 and 2P3/2 limits, respectively. Eigen quantumdefects, transformation matrix elements, and approximate dipole parameters from multichannel quantumdefect theory are presented.

I. INTRODUCTION

Since 1969, a simple yet elegant technique has been de-veloped for treating two-electron Rydberg series with acompleteness previously possible only for series as-sociated with one-electron (alkali) spectra. This tech-nique has its basis in Seaton's multichannel quantumdefect theory, 1 and is applied here to the two-limit case.Other applications to spectroanalysis include work byFano, 2 Lu and Fano, 3 Lee and Lu, 4 Herzberg and

567Jungen, Brown et al., 6 and Yoshino. 7 Fano8 has re-cently reviewed the technique and summarized othercurrent applications.

Our work on the high-resolution absorption spec-trum6' 9 of Sii associated with transitions to levels con-verging on the 2P3/2,1/2 ground state of Siii suggestedthat the homologous spectra for other atoms of the car-bon group are amenable to similar analyses. Althoughthe present work is confined to Ge i, current researchin our laboratory has confirmed this speculation for allmembers of the carbon group. 1U, 11

The electronic spectrum and structure of Gei were in-vestigated extensively prior to 1967. The high-resolu-tion emission spectra of Andrew and Meissner, 12 Kauf-man and Andrew, 13 and Humphreys and Andrew, 14

supercede previous listings of energy levels and spec-tral line positions in both accuracy and completeness.Precise g factors have been determined for many ofthese levels, 15 and a number of effects attributed15" 6 tointermediate coupling and configuration interactionshave been noted. Finally, Ge i has been observed pre-viously in absorption by Wilson'7 at lower dispersionand purity.

II. EXPERIMENTAL PROCEDURES

The experimental apparatus used in this work pre-viously has been described in detail. 18 The proceduresemployed to obtain spectra of Gei are similar to thoseused to obtain the above mentioned Sii spectrum, 6 andin recent studies183 2

1 on MgI, Cai, BI, Zni, and Cdi.Germanium22 was heated in an evacuable King furnacesystem to temperatures in the range 1100-1900 'C.Absorption spectra were obtained from a single passthrough the 122-cm-long hot zone of the furnace.Microwave-excited rare gas lamps23 provided back-

584 J. Opt. Soc. Am., Vol. 67, No. 5, May 1977

ground continua in the 1200-1950 A region, and a1000 W high-pressure xenon arc lamp was used for thecontinuum in the 1950-3100 A region. Spectra in theregion of principal interest in the present work, - 1520-1900 A, were photographed in the third order of a 6. 6m spectrograph with a reciprocal dispersion of -0.41A/mm. Most experiments were performed with flow-ing argon in the furnace at pressures less than -0. 1torr. In a few cases argon pressures as high as 14torr or as low as 10-4 Torr were employed.

Iron reference standards, 24 the method of plate mea-surement, and data reduction procedures are the sameas those described previously. 18 A short list of pro-visional vacuum-uv Ritz standards'1325' 26 for Ge i wasused to establish absolute values for wavelengths longerthan - 1625 A, whereas wavelengths shorter than 1625A were checked by the combination principle. The un-certainty in absolute wavelengths is estimated to be±0.001 A (±0.04 cm-' at - 1650 A). This estimate isbased on the observations (a) that all of our values forthe lines given as Ritz standards agree with the reportedvalues 2 6 to within ± 0. 05 cm-' (90% are within ± 0. 03cm-') and (b) that application of the Ritz principle to ourdata showed no systematic shifts. The uncertainties inthe relative positions of sharp, unblended lines appearto be -±0.03 cm-', although the uncertainties associatedwith weak, diffuse, or blended features are muchlarger.

III. DESCRIPTION OF THE SPECTRUM

A. Conventional approach

Although in subsequent sections we will abandonsuch notations, it is useful to review the configura-tions and associated LS and jj coupling labels which inprevious works have been correlated with the levels ofGe i. In conventional notation the levels in question be-long to one of the following possible groupings: (a) theground configuration 4s 2 4p2 (LS levels 3P2 ,1 0, 1D2 , IS);(b) the two-electron configurations 4s 24p nx (with x be-ing s, p, d, f, or g) which have the ground configura-tion of Ge ii as their core; or (c) 4s4p3 (LS terms5 '3 S0, 1'.p

0 3"D0 ). In Gei, as in Ci and Sii, only thegeneral dipole selection rules (even -odd, AJ= 0, ± 1,J= 0 4 J= 0) are observed to apply to transitions be-

Copyright O 1977 by the Optical Society of America 584

66

64 I

62

G e al2 0

Pa2

2p 0P/2

Ge I4P( 2 PO)n I 4P( 2 P3 )n I

15

2n

20

13

12

11 -

10

9

8

~~7

FIG. 1. Schematic diagram illustrating two hypothetical non-interacting Rydberg series of levels (channels), one converg-ing on each of the two lowest ionization limits of Gex, togetherwith their associated continua. The energy scale is k cm 1

above the 4p2 3PO ground level of Ge i.

tween states of 4p2 and the excited configurations.Hence for the spectra under discussion, considerationscan be limited to the odd-symmetry levels in (b) abovewith J s 3 which are 4pns lP3P°(J= 1,0, 1, 2),4pnd 1i3pO (J= 1, 0, 1, 2), 1,3D(J= 2, 1, 2, 3), 13Fp(J

=3, 2, 3), and 4png ", "F'(J=3, 2, 3), 3G°(J= 3). These19 odd parity series must converge on either the4S24p 2P /2 or the 4S24p 2P' /2 levels of Ge i (the 2poterm is regular with a 3 - separation 27 of 1767.36cm-'). Consideration of the jj-coupling terms produced

to 2by adding an ns, nd, or an ng electron to P 3/2 or 2p1/2indicates that four J= 3, four J= 2, three J= 1, and oneJ=0 series must converge on the 2P3/2 (upper) limit,whereas two J= 3, two J= 2, two J= 1, and one J= 0series must converge on the 'P1/ 2 (lower) limit. Ofthese 19 jj-coupled series, two J= 3 and one J= 2 serieswhich converge on 'P3/ 2 and one J=3 series which con-verges on 2P1/2 are from ng configurations. The re-maining 15 series result from ns or nd.

There are no unique correlations between the LS andjj labeling schemes just discussed, Although all cou-pling schemes predict the correct number of series ofeach J value, extensive interactions between the manylevels of the configurations in (b) and (c) above makeany pure configuration or pure coupling labels artificialfor all levels except those associated with the ground

n = (n1-) = [R/(Ei- En)]l/2, i=1, 2 (1)

where R is the Rydberg constant, Eio are the ionizationenergies, En the energy of the level in question, ni theprincipal quantum numbers assumed for the level, and6, the quantum defects, This step allows us to treat theproblem in an "effective quantum number space" (or,equivalently, quantum defect space), a two-dimensionalspace where n* lies along the Y axis and n* lies alongthe X axis, In this space an energy is mapped onto thepoint (n*, n*), and the energy levels belonging to Ryd-berg series occur as periodic patterns with unit periodin either n* or n* . In the presence of interactions,the levels of a series in n* will be perturbed periodical-ly with unit period in n2* (and vice versa).

The two effective quantum numbers belonging to eachenergy level are functionally related by the expres-sion3

n* = G(n*)= n* (1- n-*2A)1/2 (2)

where ni* and n2* are the two effective quantum numbers


configuration. We will continue to use pure configura-tions and LS notation throughout the remainder of thissection, but it should be emphasized that such designa-tions are retained temporarily only for the purposes oforienting the reader to several features of the elec-tronic structure of Gei.

The AJ selection rule limits the dipole transitionsfrom 4p2 3p to the 19 level series associated with 4pns,4pnd, and 4png to 35 spectral series. The Ge i groundterm 4p2 3P,- 3Po and 3P2 -'Po separations' 3 are 557. 13and 1409. 96 cm-', respectively; hence each of these 35spectral series from the 4p2 3p levels of Gei will con-verge to one of six apparent convergence limits be-tween 1527. 17 and 1605. 05 A, At temperatures ap-proaching 1900 0C, the 4p2 'D 2 level,' 3 7125.30 cm-'above 4p2 3 P0 , is populated sufficiently to permit ob-servation of 14 of the 17 spectral series from 4p2 'D 2to levels associated with 4pns, 4pnd, and 4png. Thesespectral series divide between two apparent serieslimits: 1713. 64 A (2P312) and 1767. 13 A ( 2 P112 ).

B. Multichannel, two-limit approach

As noted in the previous section, the two levels of4p 2 po in Geii give rise to two possible ionization en-ergies, El,, and E2 , for the removal of a 4p electronfrom the ground state of Ge i. In the absence of inter-actions between levels, all Rydberg series would con-verge regularly to one of these two limits, producingindependent one-electron-type series with constantquantum defects. Such a situation is illustrated sche-matically in Fig. 1, which turns out to be a first ap-proximation to the behavior of the two J= 0 level serieswhich converge on 4p 2 P0 of Ge ii. In reality, levelswith identical J value and parity interact with one an-other, especially when their energies are nearly de-generate. Fano2 recognized that such degeneracies andinteractions do not occur at random for level series(channels) converging to different limits, and that thesituation can be described most conveniently in termsof two effective quantum numbers, n4, for each level28 :

Brown et al. 585

(A)

n,

12

2 4 6 a n2'

7.88

0 (Dl7

I. 0

2 3 4 5 6 n2 7

(C) 0 f (D) e (o 1 i ( F

n2 mod I

FIGn 2. (A) Equation (2) as a function of nt and nT. The curvebecomes asymptotic to the line n*2 = 7. 88 as naxi approaches -o.(B) The function in (A) plotted modulo 1 in n i,- (C) The functionin (A) plotted modulo 1 in both Atl and n 2. (D) The effectivequnatum numbers for the levels of the two hypothetical nonin-teracting Rydberg series of Fig. 1 plotted modulo 1. Plots(E) and (F) are plots similar to (D) but for the cases of weakand strong channel mixing, respectively. In (G) plots (B) and(F) are superimposed, with the possible energy levels appear-ing as the points of intersection of the two functions (see text).

for the level and A = (E2,, - Eo,,)R-'. For the Ge I levelsunder discussion, E2,8 - El = 1767. 36 cm-' and R= 109 736. 49 cm-'. The specific form of this functionfor Gei is shown in Fig. 2(A). In this case, n* =7,88is the effective quantum number of a level at the lowerionization limit (i. e., n'= co). All levels of Ge i mustlie on the curve G(n*) in Fig. 2(A).

The key to practical applications of the multichannelapproach to the two-limit problems similar to the oneunder discussion is the existence2' 3 of an implicit func-tional relationship between n, and n* given by F(n*,n*) = 0. In general, the zeros of F are multivalued andperiodic in both ni and n* with unit periods which re-flect the Rydberg nature of the levels belonging to thevarious channels. A plot of both G and the solutionsof F= 0 [given by ni = f(n*)] in the effective quantumnumber plane is given for a similar situation in molec-ular hydrogen in Fig. 10 of Ref. 5. Other propertiesof f have been described in detail by Lu and Fano 3 andwill be mentioned only briefly here. (1) When plottedmodulo 1 (to match the periodicity of f), the effectivequantum numbers nl, n* of energy levels lie on sec-

0o


a

tions of thef curve. (2) The sections off are con-tinuous and monotonic. (3) Energy levels correspond tointersections of f and G in the effective quantum num-ber space. (4) When there are n channels belonging tothe upper (lower) limit, any horizontal (vertical) linedrawn in the (n'*, n'*)mod I plane will cut the f curves inexactly n places. (5) As a corollary, (4) holds for thetop and bottom edges and left and right edges of themodulo 1 plot. The periodicity of f requires that forevery curve that exits the modulo 1 plot on the left(top), another must enter at the corresponding point onthe right (bottom). (6) Finally, unless the levels arecompletely noninteracting, sections of f do not inter-sect in the modulo 1 plane. The sections off may ap-proach each other and then bend away in the mannerresembling an "avoided crossing" of molecular potentialenergy curves. The resulting curvature of f indicatesthe strength of interactions among channels and the ad-mixture of pure channel states contributing to a givenlevel. Simplified examples of these properties andsome of their applications are illustrated below. Thereader is referred to Refs. 1-5 and 8 for detailedmathematical treatments and further amplification of thesubject.

Empirical procedures for treating many-channel, two-limit problems take advantage of the periodic nature off by mapping the points (n*, n2*) belonging to each energylevel onto a unit square [a plot of (nfl)mod vs (n*)mod 1]for all observed levels of the same J and parity. Firstconsider the mapping of the function G(n2*) of Eq. 1 inFig. 2(A) onto (n'*),lw illustrated in Fig. 2(B). Fur-ther mapping of this function onto (n*)mod 1 superimposesthe contents of all six squares in Fig. 2(B) onto a singlesquare as in Fig. 2(C). To illustrate the periodicityand a few general properties of the functionf, considerthe two-channel (two-series) example of Fig. 1. If thelevels do not interact, the fractional parts of the n*effective quantum numbers of the series converging tothe lower limit will be approximately constant (con-stant quantum defects), whereas the fractional parts ofn* for these levels [computed from Eqs. (1) or (2)] willvary irregularly, In the example of Fig. 1, the levelslabeled n,= 11, 12, 13 have nl* values of S3 25, 9.25, and10. 25, respectively. On a plot of (n*1)mod 1 vs (n2)mod 1,

these points fall on a straight line parallel to the n*axis. Similarly, in Fig. 1 levels of the channel with2p3/2 as its ionic core have n* values with constantfractional parts and n* values which have variablefractional parts. In Fig. 2(D) the members of thisseries correspond to the points on the vertical line.Any interaction between the two channels will causedeviations from the simple pattern illustrated in Fig.2(D). In conventional perturbation theory, the greatestdepartures from the regularity of the simple pattern areexperienced when energy levels are nearly degenerate.In figures such as 2(D), these degeneracies occur wherethe horizontal and vertical lines cross. Conventionaltheories also lead us to expect that the magnitude of theperturbations will decrease in energy as n becomeslarge. However, as n becomes large, the n* valuesbecome more sensitive to changes in energy. Thesetwo effects compensate each other so that the perturba-

Brown et al. 586

tion, when observed in the effective quantum numberspace, is regular. Figures 2(E) and 2(F) illustrate theevolution of the periodicf function with progressivelyincreasing interaction between channels. In Fig. 2(E)the departure from the noninteracting channel picture(the dashed line portion of the figure) is relativelysmall, and such situations might be described by con-ventional methods involving perturbations between near-ly coincident levels. However, diagrams comparableto Fig. 2(F) result from sufficient channel mixing suchthat any attempt to identify individual channels (i. e.,assign levels to individual term series, etc.) is mean-ingless. Regardless of the failures of conventionallabeling procedures, the possible energy levels forsuch a two-channel system are given by the points ofintersection of f and G. Figure 2(G) is a superpositionof the functions determined in Fig. 2(F) on each n*2cycle of Fig. 2(B).

Although useful for such purposes, diagrams likeFig. 2(G) are not limited to the correlation of existingenergy level data for interacting channels. They oftenprovide a powerful tool which can be used to extend en-ergy level and spectral assignments beyond the limitsimposed by conventional methods. It is essential tofirst identify a sufficient number of energy levels byconventional spectroscopic methods to sketch the gen-eral shape of f. These approximate functions can beused to estimate the energies of unidentified levels.As additional levels are identified, the f function is re-fined and the entire process iterated until no new en-ergy levels can be found.

Extensions to multichannel cases from the simplifiedtwo-channel example considered in Figs. 1 and 2 in-crease the complexity of the (nfln )mocI VS (n2*)mad 1 plotsbut require no new principles. For example, if a sec-ond noninteracting series converges on U2 of Fig. 1,the energy levels would lie on two horizontal and onevertical line in Fig. 2(D). If three noninteractingseries converge on P1/2 and two converge on P3/2,the energy levels in Fig. 2(D) would lie on three hori-zontal and two vertical lines. When the various chan-nels interact, deviations from straight-line behavioroccur in the vicinities of the intersections of the hori-zontal and vertical lines (two such intersections in thethree-channel case and six in the five-channel case).In the multichannel approach the magnitudes of thesedeviations are directly dependent on the extent of chan-nel mixing.

Breakdowns in the two-limit multichannel behaviordescribed in the preceding paragraphs are expectedwhenever there are appreciable interactions with levelsfrom configurations outside the channels under con-sideration (e.g., 4s4p3 in Ge i). Deviations also occurat low n where the electron ni has an appreciable in-teraction with the core.

C. Parametric fitting in the multichannel approach

Lu29 and Lee and Lu4 have shown in their analysis ofthe spectra of Xe and Ar that the observed propertiesare expressible in terms of a relatively small set ofparameters. Briefly, a set of parameters (designated

,icl, Dol and Ui,, with the numbers of i's and u'sequal to the number of channels being considered) re-sult from separating the state representing the systemcomposed of Rydberg electrons plus a charged ion coreinto two regimes and matching the states appropriatein the two regimes at their common boundaries. In thefirst regime the Rydberg electrons are close to the ioncore, while in the second regime these electrons arefar from the core. Quantum mechanically, the situa-tion is quite different in these two regimes. In the first(close-coupled) regime, the Rydberg electrons arestrongly correlated with electrons in the core. In thesecond (loose-coupled) regime, the electrons are sub-ject mainly to attractions from a centralized chargedion core, and the eigenstates appropriate at these largeelectron-core separations are the Coulomb functions.The total state of the system is then a linear combina-tion of the above eigenstates with the coefficients in thecombination (i, e., the mixing coefficients) determinedby the boundary conditions at infinity and at some pointiro where the two solutions join. For this situation Leeand Lu4 give the following wave functions for r' ro:

41(0l)= ' [(0, It, r)E Usy(coS~rAJu)M",I i f cc(3)

where a and i label the close-coupled and loose-cou-pled representations, respectively. In Eq. (3), 0irepresents the ion core radial functions together with thespin and angular factors of the entire atom, f and g arethe regular and irregular Coulomb functions, the Uieyare matrix elements of the transformation between theclose-coupled and loose-coupled configurations, the ju

are eigenquantum defects of the close-coupled eigen-states, and the Ma (denoted u in Ref. 4 and A,, in Ref.29) are the coefficients of the linear combinations ofclose-coupled states making up a given level, Lu29 hasshown that the boundary condition on Eq. (3) at r=leads to the condition

det I Uia sin7r(n* - g,, ) I = 0 . (4)

For the two-limit case of Gei considered here, nt isnt or n* depending on which state of the ion the ithloose-coupled state is built upon. Equation (4) is aspecific rendering of the implicit relationship betweennH and n* written above as F(n*, n>*)= 0.

The constant quantumn defect (i.e., noninteractingseries) cases mentioned previously can occur only whenthe angular momentum coupling case for the Rydbergelectron n is independent of n. In such cases, a singlecoupling scheme can be used in both the close- andloose-coupling regimes. The resulting Uic matrix is aunit matrix, which reduces Eq. (4) to z i 1 sinir(n* - ,)-0 with solutions (nT)mod 1A= i for each of the m non-interacting channels. Such simple situations can be ex-pected only for alkali-type atoms, where the 'S coreground state is widely separated from excited corestates, Atoms with cores exhibiting more complexelectronic structures can be expected to have perturba-tions among their Rydberg series. Such perturbations

587 J. Opt. Soc. Am., Vol. 67, No. 5, May 1977 Brown et al. 587

+ g(n* , ii, r) E Ui .. (sin7rA .. )M,,,i a I I

FIG. 3. Spectrogram and den-sitometer trace of GeI absorp-tion spectrum in the 1.525-1545

a A region. This figure con-,O ll tains a portion of the autoion-

1528.0 'ri1j ized 3 P0 -J=l spectrum. ThisI kf 1| spectrum consists of two series

7b p! of relatively sharp absorptionfeatures, and a series of

11 'A Beutler-Fano profiles each[ having an emissionlike peak

(feature a, which is actuallya minimum in the absorptioncross section) and an absorp-tion feature (feature b). Allthree of these series converge

_ _ _ _ _ _ __ : :-|regularly on the 2P;/ 2 limit

3Po -4s24p[2P34]flX 3pi -&4pf3 nlX near 1528 A.

can be divided into two categories: those due to the exis- with the continuous portions of J= 1 channels associatedtence of different angular momentum coupling schemes with 4p 2Pj1°2. This mixing produces a variety of ef-in the close- and loose-coupling regimes within a given fects commonly associated with levels which autoionize.30

electron configuration and those due to configuration Autoionization effects observed in the present work in-interactions. Both types of perturbations are evident elude diffuse and asymmetric spectral lines. For thein Ge I . two most prominent absorption series, at wavelengths

r .i < 1540 A in Fig. 3, the lines associated with one chan-For transitions between a ground-state level and a nlaedfuebtsmercwielnsascaeRydberg level, the transition probability depends on net are diffuse but symmetric while lines associateddipole integrals between the two states. Since the with the other are broadened asymmetrically. Themajor portion of the ground-state wavefunction extends spectrum associated with the third channel appears inonly a few angstroms from the nucleus, it is the close Fig. 3 as a series of Beutler-Fano profiles.3 0 In Fig.onplyaew pantro fhe brom thve nunclusitisn thicloskes 4, similar effects are apparent in transitions to levelscoupled part of the Rydberg wave function which makes p.'p

the largest contributions to the transition probability. in all channels above the 4P2 P 1 2 limit. The diffuseIf the ath close-coupled eigenstate has a dipole integral spectral features associated with the autoionizing levelsDIf with a given ground level, the oscillator strength is converge regularly on the 4p2 P'1 ,2 limit. An initialgiven 4 by value of E2,, = 65 480. 60 ± 0. 10 cm- was estimated by

requiring that the quantum defects of the two narrowerf =N ( MCD) , (5) features combining with 3P0 (see above) become con-

0\ ( stant as n becomes large. By subtracting the 1767.36where N is a normalization factor. Since each point on cm' 2pO splitting of Geiia El.. of 63713.24±0.10 cm'the diagonal of a Lu- Fano plot [i. e., levels with (nz*)mo was obtained.

(f* )mo, 1 = li j has only one4 nonvanishing mixing coef-ficient, one can learn much about the properties of theapparentficintonecan ear muh abut he ropetie ofthe series convergences on the 2P°. 2 limit give inconsistententire manifold of Rydberg states by examining transi- sitions involving a few levels lying near the diagonal. If values for Elt.. In the multichannel treatment, the con-the magnitudes of the D.'s can be wimt by examin- stant quantum defect condition is replacedby the periodicestiae f(n*) condition and the inconsistencies disappear.ing the strengths of the lines associated with the levels 1 2

For Ge i, thef(n*) curves are sensitive to errorsnear the diagonal, the general behavior of the remain- cm in E. The ionization energiesder of the spectrum can be predicted (see below). Be- lage tha X0 m'i l h oiaineegederso the spetru ca n bepeictedsee belo) determined above were consistent with the results fromcause the Mh ts depend only on n, intensity patterns aare observed to be periodic in n2* and extend in a smooth f2(n X within this error limit and have been adoptedfashion from the discrete levels into the autoionizationregion Transitions to levels below the 2P1/2 limit, such as

the series which converge to the 3P0- [2 PI12]n,,x limitIV. ENERGY LEVELS AND IONIZATION LIMITS in Fig. 4, produce spectral lines which are narrow and

symmetric but which exhibit a number of intensity andAs discussed above, six apparent convergence limits wavelength irregularities attributable to channel mixing.

exist for the various dipole-allowed spectral series Below the 4p 2P1/2 limit, the multichannel interactionsfrom 4p 3P2,1 0 to channels converging on the 4p 2P1/2 are sufficiently severe that conventional series analysesand 4p 2p, 2 states of Ge ii. The shortest wavelength and labelings are meaningless, or at the very bestspectral limit is approached by transitions from 4p2 3 P0 highly artificial, even for levels with relatively low n*to levels in three odd-parity, J= 1 channels which are values, We have, therefore, employed the two-limit,associated with 4p 2P3/, (see Sec. IIIA and Fig. 3). multichannel techniques described in the preceding sec-Above the 4p 2Pj'2 limit, these three channels can mix tions in the present analysis.

588 J. Opt. Soc. Am., Vol. 67, No. 5, May 1977 Brown et at 588

FIG. 4. Spectrogram and densito-meter trace of the 1557-1576 Aregion. The 2 P1/2 limit of the3 P 0 -J=1 spectrum can be seennear 1570 A. See Fig. 6, for anenlarged view of the 1570 A regionand the text for a discussion ofthe relationship between the des-crete and autoionized portions ofthe J= 1 spectrum.

3p 'Po2 [-p 1 4S24p[ PP]X

Once a list of observed Ge i lines had been prepared(see Table I), the initial phase of the analysis pro-ceeded conventionally. The energy differences betweenthe 4p2 3P0, 3 P1, 3 P2, and 'D 2 levels, and the AJ selec-tion rules were used to determine the J values and en-ergies of as many levels as possible. These levelswere sorted by J and used to construct preliminaryplots of (n1 )mod 1 vs (n*' )mod 1 for each J value. Althoughincomplete, sufficient data were available to sketch the(flt)modj1f=f(n)mod1 curves for each diagram. The itera-tive graphical procedure described in Sec. HIB above

.0 . .) .

0

,0 (n )t 1.

was then applied to complete the analysis. All observedspectral features in Table I were successfully identifiedexcept two weak lines at 1749. 5 and 1572. 25 A.

Table II lists all of the odd-parity energy levels ofGe i which have been characterized experimentally. Thefirst four columns of Table II list the energy, J, n*,and n* , respectively, for each observed level. A nu-merical value in any one of the next four columns in-dicates that a transition from 4p2 3 Po,1,2 or 'D2 to the

level in question has been observed in the present

Ina 9 W20

0 To5 3 .. n 7o

2 700A

J= 1

J 20

OLZJ..S

.0 I AI , T , , , , X .' AFIG. 5. Lu-Fano plots for the odd energy levels of Gei from the 4 pns and 4pnd configurations observed below the 2P1/2 limit.Plots of (nil)mod IVS (n*).d land (nl*i).d v Vs n* are presented for the observed energy levels. The function nl =G(n'*) is also indi-cated on the (n~i),d I vs n* plots with the principal part of no indicated at the top of the first figure (i. e., the curve labeled 5 cor-

responds to 5 -n0 -- 6). The large diamonds indicate the positions of the 4s4p3 interloper levels (see text), while the point n*2 =7.88marked with a triangle indicates the 2PI/2 ionization limit.


1576.6A 1I; I f

Brown et al. 589

TABLE I. Observed absorption lines of Gei. TBEI Cniud

Classification'g J' ,1i'2

Int. a

4050352

20402010505

3030

0015

40001115

2502

202

1530

535

1303420

303001

3535

130303222101010101

30

0

Classification"'Wavelength(A)

1895. 1981874. 2581865. 0531861. 0961860. 0881853. 1331849. 6361846. 9581845. 8731844. 4111842. 4111841.3291838. 3231837. 5311836. 6801824. 6601824. 3031822. 4291820. 9131820. 8441820. 5181816. 7301815. 1311813. 9091810. 6151810. 6021810. 1031809. 1841805. 1301804. 4531803. 3801802. 6251801. 6751801. 4321801. 0781796. 4071795. 6671795. 2831793. 0701791. 9551791.3611790. 8211786. 8691786. 0691785. 0451784. 4311784. 3371782. 7621782. 5881782. 5531781. 0701780. 0871779. 1961778. 8131777. 8081777. 6291776. 7501776.5671775. 8311775. 6531775. 0321774. 8721774. 3371774. 1751773. 728

Brown et al. 590

Wave number(cm-f)

52 764. 9353 354.4453 617. 7753 731. 7953 760. 9053 962. 6754 064. 7054 143. 0754 174. 9054 217. 8654 276. 7054308. 6154397.4054 420. 8654446. 0654 804. 7354 815. 4654 871. 8254 917.5154 919.5754 929. 4255 043. 9555 092.4455 129.5555 229. 8555 230.2555 245.4855 273.5355 397. 6755 418. 4755 451.4355 474. 6755 503. 9255 511.3955 522.3055 666.6855 689. 6155 701.5155 770. 2655 804. 9755 823.4755 840.3155 963. 8255 988. 8856 020. 9956 040.2756 043. 2356 092. 7456 098. 2056 099.3056 146. 0256 177. 0356 205. 1856 217. 2656 249. 0556 254. 7256 282.5356 288.3456311. 6556 317.3056 337. 0156 342.1056 359. 0756 364.2256378.42

3P2 -1

'122-1'D22-33 P2 -2

32P0 -1

'D22-33p22_I

'1D2-13 P' -2'122-1

122-2'D2 -1

'122-1'1D2-33p22-3

'02 -1

312I_1

'D2-3

1D2 121D2 -3

'D,2-1

102 -1'D22-3

'D22-3'D22-3'D22-3

1D22-1

'122-3' 2-21

'1D2-1'1D2-3'122-1

'1D2-1

'1D2-3

'D2 -.

3. 11553. 07983. 11554. 87184. 88723. 29493. 31175. 10413. 11555. 15003. 34733. 35285. 26565. 28135. 29825. 55943. 29495. 61273. 31175. 65165. 65975. 75675. 79933. 34735. 92545. 92595. 94035. 96746. 09123. 56136. 14733. 31176. 20373. 58066. 22386. 38876. 41616.43043. 63606. 55966. 58356. 60556. 77393. 68.493.69226. 88486. 88936. 96436. 97276. 97447. 04777. 09777. 14407. 16427. 21807. 22787. 27617. 28647. 32787. 33797. 37367. 38327. 41433. 5806

7. 4505


Int. a

0000000000

352525

00

30

2535

00

20

0d

4000

150000

25

2020

500010

304020

0010

00

1210

0010

00

0d

0C0d

000

0

00

TABLE I. (Continued)

Wavelength(A)

1773. 5931773. 1951772. 7231772. 3031771. 9291771.5951771. 2941771. 0241767. 11766. 4341766. 0641765. 2841764. 81764. 1841763. 611759. 2711758. 2791755. 21753. 91753. 021750. 71750. 0441749.51748. 8571747. 11746. 21746. 0651745.501744.2541744. 0531742. 1961741.21740.51739. 9631739. 1021738. 4801738. 1191736. 61736. 161735. 7511733.21732. 9601732. 801732. 4801730.41730. 151729. 8871728.21728. 011727. 7921726.481726.271726. 0801725. 061724. 821724. 6641724.3081723. 771723. 611723. 4771722. 7221722.5811722.471722. 4141721. 80

Wave number(cm-i)

56 382. 7456 395. 3956 410.3856 423. 7756 435. 6656 446.3256 455. 9056 464.5156 59056 611. 2456 623. 0856 648. 1156 66556 683. 4256 702. 056 841. 7356 873. 8056 97257 01757 044.357 12057 141.4357 16057 180. 2057 23757 26857 271. 6557 290. 157331. 0957 337. 7057 398. 8357 43257 45557472.4857 500. 9357521.5157 533.4557 58357598.357 611. 9457 69757 704. 7457 709. 957 720. 7257 79057 798.457 807. 2457 86357 869. 957 877.3557 921. 257 928. 557 934. 7357 969. 057 977. 157 982. 3057 994. 2958 012.558 017. 958 022. 2658 047. 6958 052.42S8 056. 258 058. 0658 078. 8

g J'

'122-3

'122-3'1D2-3'D22-3'D22-3

'D2 -3

'D22-33p 2 _3'122-13 P2 -13P1 -23122-3

3 P0 -1

'D22-3P1 2 -0

'12 -13P2 -2

3 p 0 -1'D22-3

'D22-13 P2 -13P2 -2

3122-1'D22-3

1D2 -31D2 -3

3122-3'D2 -3

P1D -2

'02 -33p2 -i'D2 -3112 -3

1D2-3

n 27. 45887. 48277. 51157. 53737. 56067. 5 8187. 60097. 61817. 883. 63343. 63603. 84508. 053. 85428. 1473. 68493. 69228. 869. 069. 146

3. 9796

3. 63609. 88

10. 053. 7870

10. 144. 03524. 03713. 6849

10. 8911. 04811. 1463. 84504. 09344. 0971

11. 8712. 04612. 14812. 864. 1519

13. 04413. 14713. 8614. 04214. 14714. 8015. 04215. 14815. 8716. 04016. 14816. 8617. 04017. 1473. 9796

17. 89718. 03418. 14718. 8819. 03419. 1473. 8450

19. 88


Wavelength Wave number ClassificationbInt. a (A) (cm1i) I J' I I*2

11

od

0oc

od

2020

oc00ocOc00oc

0

0Ococ

00

30i.50000000

1oo0

0000

40000000000000

iO507

i5io3030

5

253040

2002050

730

640

1i721. 708

1721. 61i.721. 061720. 961720. 871720. 7461i720. 406i.720. 3061720. 2261719. 8817i9. 7361719. 671719. 31719. 241719. 183i.718. 851i71i8. 801718. 751718. 6881718. 4931718. 41i01718. 07171i8. 021717. 75417i7. 4741717.2261716. 9917i.6. 785i716. 60017i6. 421716. 271716. 14i715. 9991715. 8361715. 7717i5. 661715.561715. 4681715. 3831715. 3001715. 2311715. 1601715. i01715. 0401714. 981714. 931714.7491713. 0811707. 7221702. 3871698. 9381696. 7161695. 8591695. 1041694.3421691. 8661691. 6261691. 0901690. 9031690. 0351687. 8161685. 2221682. 1661681 343

58 081 i8658085. 158103. 858107.258110.258114.3358 125. 8058 129. 2058i31. 9i58 143. 658 148.4758 150. 658I6258 165. 258 167. 1558178.458 180. 158181.958 183. 9158 190. 5358193.3358205. 05 8 206. 558 215.5458 225. 0558233.4458 241. 358 248. 4158254. 6958 260. 858 265. 858 270. 358 275. 1158 280. 6458282. 858286.758 290. 058293.1158 296. 0158298. 8458301. 1958303.6058 305. 658307. 6958309. 658 3.1. 458317.5758 374. 3558 557.5658 741 0358 860. 2958937.3958 967. 1558993.4459 019. 9659 i06. 3559114.7359 133.4659140. 0059 170.3759248. 1759 339.3759447. 1659 476. 25

'D 2-31 D2 -]D2,-31 D2 -3'D2 -1

1D2 -31 D2-31D2 -1

'D 2 -3'D2 -13

1D, -3

1D2 -3

1D2 -31D2 -31D2 -1

1D2 - 3

1D2 -3

iD2 -3

1D2 -31D2 -3

3Pi-i

aPi-i

iD 2 -3a1D -3

pD2-3

iD2 - 3iD2 - 3

3P 2 -i3D2-3

tD2 - 3'D2 -3'D2 - 3'D2-3

'D2 - 3'D2 - 3'D2 -3'D2 - 3'D2--31D2-3'D2-33P2-13p, -23

3P2-2

3P, -03P, - 2

3P2-2

3P2-33p2 - 2

3Pi -2'P2 -13p, - 13P2 - 3P2 -1P2 -13P2-3

20. 034

20. 14520. 8821.03121. 1434. 2923

21.87122. 03022. 14822. 85423. 04223. 14723. 86924. 02624.13424. 86925. 02925. 1424. 03524.0371

26. 02627. 02027. 13828. 04729. 04230. 01531. 039

4. 34]i433. 04434. 07635. 03536. 0137. 0364. 3535

39.0440.0541. 0542. 0343.0544.1045. 0346. 0747.0848.0649. 1150. 11

4. 36744. 09344. 15194. 03524.58924. 28164. 29234. 64904.66124. 70164. 15194. 35354.71764. 36744. 77024. 81604. 87184. 8872


Wavelength Wave number ClassificationbInt. a (A) (cm-i) g J' nI

25401512502530253525'

8352035754030

0353035

51830602035

06

4025203525152830404070

15

504065609

g

550

453060452050120

654530152565

1679. 9881675. 56i1675. 2831674.6751674. 2711673. 8531671. 0111670. 9491670. 6071670. 595i668. 5241667. 8021666. 8661665. 2761663.5391662. 9871662. 8901662. 1911661.3441660.7951658. 3751654.5531652.5511652.3441651. 9551651. 6851651. 5291650.5551650.5141650. 2951649. 2131648. 9471647.5321647. 1231646. 1081645. 8391645. 1151644.5261644. 1181643. 1931640. 8191640. 8061640.3971639. 8281639.7321639. 638

1638. 9611638. 6011638. 1381637. 7911636. 3131636. 0831635. 7091635.2591634. 8731633. 8641633.4721633. 3121633.2071632. 9811631. 5331630. 173

59524.2359 68.i5159691.4159713. 0959 727.5059 742. 4059 844. 0359 846. 2359858.4759 858. 9359933.2159 959. 1659 992. 8360 050.1260 112. 8060 i32. 7660 136. 2860 161.5460192.2460212. 1260300. 0i60 439. 2860512. 5160520.0860 534.3560 544. 2360 549. 9560 585. 6860587. i960595.2360634.9760 644.7660 696. 8560 711. 9260 749. 3660 759.3060 786. 0160 807. 7960 822.8860 857. 1160 945. 1960 945. 6560 960. 8460 981.9960 985.5960 989.07

61 014. 2761027. 6761044.9061057. 8461 113. 026i121 6061135. 5761152.3961i166. 8561204. 6161219. 2861225. 2761229. 2361237. 7061292. 0661343. 19

ape-i3P2-23P2 -1

3p,-23p,_i

3P2 -1

3p 2 -23P1-23P2 -33P2 -23P2 -1

3PI-2

3Pi-i

3 p 0 -i0

3P2 -33P2-2

3P2 -1

3P2 -1

3p,-3

3P,-1

3P2 -23P2-23P2 - 33p,-2

3pe-i.

3p_1-

3P 2-33P2 -1

3P,-1

3P2-13P 2 -23Pi-23P,-23po-I

3P2-i

ap1i

3P2 - 33P2-2

3po-1

3P2 -

3P2 - 3

3P2 - 3

3PI-2

3P, -1

3P2-1

3p,-

3P2 - 33P2-23P2 -1

3P2-3

3P2-23P2 -23po-I

3P2 -1

3P2-3

3P2 - 33P2-23P2 -1

3P2 -1

3P, -2

3Pi -255 1629.585 61365.34

4.29235. 00025.00584. 58924.36745.03525. 09544.64905. 10415. 10455. i5004. 70164. 71764. 74535. 26565.27895. 28i.35. 29824. 81604. 82624. 87185.49725.55355. 55945.00025.00584. 71765. 6155. 61275. 03525. 65165.65975. 09545. 10454. 81605.75675. 15005. 79935. 81284. 87185.92545. 92595.94035.27655.27895.28135.96745.29826.00526. 02236. 03526.09126. 10016. i1i465.03526. 14736. 18786.20376.21026.21456. 22385.49725.15005.5535


-

Brown et al. 591l


Wavolongth WavO number Cl asificationbInt. a (A) (cm-1) g J ' '

45350

18205035304025350

45283255154520'25800

2540103533g

0121040383015200

183050354022202840354010400

4040'

0103530120

3510

of5030

1629. 1421629. 1001628. 7881628.5341628. 2181627. 6041626.4311626. 3381626. 0791625.5911625.4801624. 9501624. 7941624.5481624. 2271624. 1301623.7541623. 0561622. 7581622. 7461622. 6571622.4231621. 9721621. 7141621.3821621. 2931620. 6461620.554

1620.2471619. 5251619.2871619. 2081618.7381618. 1741617. 9111617. 7691617. 7391617.4891617.2531617. 2261617. 0431616.5181616. 0091615. 9421615. 9221615. 7091615. 6331615.5681615. 2601615.2301614. 9741614. 8031614.7861614. 6571614. 1371613. 8311613. 7971613. 7451613.6821613.5691613. 2041613. 1911612. 9761612. 959

61382. 0161383. 6061395.3661404.9461416. 8561440.0161484. 3261487. 8461497. 6261516.1061520. 2961540.3461546.2561555.5861567. 7661571.4261585.6861612.1661623.5061623.9361627.3061636.2161653.3561663.1661675.7761679. 1761703. 8061707.30

61718.9861746.5161755.5961758.5761776.5161 798. 0461808.1161813.5361 814. 6861824. 2261833.2461 834. 2961841.2861861.3561880. 8361883.4061884.1861892.3561895. 2561897.7361909. 5361910.6761920.5061927.0761927. 7061932.6661952. 6061964.3761965.6761967.6461 970. 0961974.4461988.4661 988. 9661997.2261997. 85

3P2 -33P2 -23 P2 -33P2-1'P2-1

3P0-1

3Pi-23 P2 -23 P2 -33P2 -33

Po-23P 2 -1

3 p2 -30

3Pi -1

3P 2 -2

3P2 -1

3P2 -1

3P2 -23P2 -33P 2-23P2-3

3P2 -1,Pi -2P2-2

3P2 -33 pi-23P 2-2

3P2-2P 2-1

3P 2-1

3P2 -3P 2-23p, _1

3P2-13P2 - 33P2 - 3P2-1

3P2-23P2-1'P2 - 33P2 -1

3P2-23P2 - 33P2-23 pl-23P2-23PI-13P2-13P2-33P2-23P2-13P2 -23P2-33P2 -23P2-1

3P2 -13 pl-23Pi-23P2-2

3P2-3

6.38876.39066.40466. 41616.43045.61275.64875.65165.65976.55426.55966. 58555. 28136. 60555.71855. 29826.64535.75676. 69656.69716. 70176.71386.73776. 75145. 81286.77396.80915.84136.81416.83096. 87146.88486.88936. 91615.92546.96436.97276.97446.98925. 95917. 00497. 01597.04777. 07917. 08317.08447.09777.10246.02237. 12596.03527.14407. 15507.15647.16427.19797.21807.22027.22377.22786. 10016. 11467.26055.61277. 2761


Wavelength Wave numberInt. a (A) (cm-i)

25105

3045g

g

100

320

35gg

1080

30gg

400

38gg

2528g

g

00Og

23g

000g0

00

0g

0

2109

03

190

20

1030190

15g

100

25g

0

08g9

00

0

30

390

1612. 9401612. 8661612. 8071612.3931612. 199

1612. 1121612. 0571611. 7351611. 6871611. 543

1611. 4581611. 4061611. 0891610. 972

1610. 8751610. 8451610. 772

61998.5962 001.4462 003.7062 019.6162 027. 10

62 030.4262 032.5762 044. 9362 046. 7762 052.33

62055.6262057.5962 069.8362074.33

62 078.0862 079.2262082. 02

1610.553 62 090.461610.471 62 093.62

1610. 4041610. 3541610. 1231610. 031

1609. 9731609. 9241609. 7061.609. 642

1609. 5871609. 5391609. 3651609.296

1609. 2511609. 2061608. 987

1608. 9051608. 7111608. 6361608. 5121608. 4631608. 3931608. 2401608. 1711608. 0361607. 9741607. 858

62 096.2462 098. 1662 107. 0562 110. 60

62 112. 8662 114. 7462 123.1362 125. 62

62 127. 7462 129. 6062 136.3262 1.38. 97

62 140. 7162 142.4562 150. 89

62 154.0862 161.5862 164.4662 169.2462 171. 1762 173. 8462 179.7762 182.4462 187. 6662 190. 0762 194.54

1607.793 62 197. 061607. 688 62 201. 14

1607.5321607. 3911607.2671607. 1671606. 8501606. 7761606. 680

62 207. 1562212. 6362217. 4062 221.3062 233.5562236.4262 240.13

Classificationbg J' *2

3P2-2 7.27743P2-1 7.2824'P2 -1 7.28643P - 1 6. 14733P2-3 7.32783P2-2 7.32843P2 - 1 7. 33403P2 -1 7.33793p,- l 5. 65163P2 -2 7.36353P2-2 7.37363P2-3 7.3736'P2 - 1 7.3794'P2 -1 7.38323P2-2 7.40573P2 - 2 7. 41383P2-3 7.41433p, - 2 6.21023P2 -1 7. 42333 Pj-O 6. 21453Pi- l 6.21453p, _1 6. 22383P2 -2 7.4497'P2 - 3 7.45053 P2-1 7.45523P2-1 7.45883 P2 -2 7. 47633P2-2 7.48183P2-3 7.48273 P2 -1 7. 48713P2 -1 7.49023P2-2 7. 50653P2 - 2 7.51063P2-3 7.51153P2 - 1 7.51553P2 - 1 7.51893P2-2 7.53203P2 - 2 7.53633P2-~3 7.53733P2.- 1 7.54083P2-1 7.54403P2-2 7.55973P2 -3 7.56063P2-1 7.56703P2-3 7.5818P2 - 1 7.58753po-1 5.75673P2-3 7.60093P2 -1 7.60613P2-3 7.61813P2-1 7.62343P2-3 7.63403P2-1 7.63893Pi - 2 6.34133P2 - 2 7. 64783P2 - 1 7. 65313P2-3 7.66173P2 -1 7. 66183P2 -3 7.6733P2-3 7. 68513P2-3 7. 69503P2-1 7.70283P2-2 7.72873pf -2 6.39063P2 -2 7. 7425



Wavelength Wave number ClassificationbInt. a (A) (cm-i) g J' n *2

Wavelength Wave number ClassificationbInt. a (A) (cm-1 ) g J' n*2

0

11.111if

3511111

g

00000000000000

25c102530looC

2835

20102540

3g

0

102

1525

0

35725

4045

g

520c30

10035

1606. 6061606.5371606. 4721606.4101606. 3501606. 2971606.2481606. 2261606. 1991606. 1561606. Ill1606. 0721606. 0361605. 999

1605. 9651605. 9331]605. 9041605. 8761605. 8471605. 8221605. 7961605. 7731605. 7511605. 7301605. 7101605. 6901605. 6711605. 6551605. 11603. 8691603. 7171603.3631602.91602.7811602. 5911602.5741602. 3821602.3491601.5781600. 8261600. 6191600. 60

1600. 2831599.5931599.5361599. 1841598.4641598. 1671598.0391597. 4621597. 3171597. 2321596. 6971596. 4461596. 2301.596. 2301595. 8921595. 61595.5221595.4821595.2251595. 049

1594. 632 62 710. 381594. 044 62 733.52


62 243.0162 245.7062 248.2062 250.5962 252. 9262 254. 9862 256.8962 257.7462 258. 7962260. 4662262. 2162 263. 7062 265. 1162266.54

62 267. 8562 269. 1062 270. 2162 271.3162272.4362273.4062274.4262275.3062 276.1762 276. 9762 277. 7462 278.5362 279. 2562 279. 8862 30362 349. 2462 355. 1362 368.9062 38862 391.5762 398. 9462 399. 6062 407. 0862 408.3962438.4162 467. 7662 475. 8462 476. 7

62 488. 9562515. 9162 518. 1362 531. 9162 560.0762571. 6862 576. 6962 599.2862 604.9662 608.3362 629.2862 639.1662 647. 6162 647. 6162 660.8662 67462675.4262 676.9762 687.0862694. 00

3 P2 -23P 2 -23p2 -23P2 -23P2 - 23P2 - 23P2 -2

3P2 - 23P2 - 23P2 -23P2 -23P2 - 2

3pi-1

3Pi-0

3po-23p2-23P2 - 23P2 -23 p2-23P2-2

3P2-23 p2 -23p2 -23 P2 -23P2 - 23P2 - 23P2 - 2

3P2-2

3P2 - 2

3P2 - 33Pi-2

3po-13pi-23p2 -33pi-i3po-13P2-2

3p,-o

3Pi -1

3Pi-2

3po-1

3Pi - o

3p, - 2'Pti-1

3Pi-2

3Pi-I

3Pi -1

3Pi - 23PO-i

3Pi - 0

3Pi-2

3po-1

3po-1

3Pi-2

3PI-1

3P2-3

3p1-0

3P -2

3Pi -1

7. 74877.75447.75987. 76487. 76977. 77427. 77826.41617.78237. 78607. 78977. 79287. 79606. 42677. 79907. 80187. 80467. 80717. 80947. 81167. 81407. 81627. 81817. 82017. 82187. 82357. 82527. 82687. 82837.886.52915. 92546. 55428.056.58355.96748. 10366. 60376. 60556. 64536. 03526.69586.69716. 69656.71386. 75146.75446.77396. 81416. 83096.14736. 87146. 87976. 88486.91616.21456. 22386.94396. 96438.866. 98676. 98927. 00497. 0159

3

39g

95C6060204010

10g

g

0404020

00

250

3515

000

301200

2510

00

2010

0

15

0

18

5gg

00

1518g

00

15120

god

15105f

2555033022

1594. 001593. 9771593. 9581593. 7061593. 6751593. 0351592. 846

1592. 2211591. 9811591. 8881591. 8381591. 8101591. 7771591. 6791591. 2981591. 0531590. 9821]590. 9461590. 9251590. 5131590. 3271590. 2491590. 2101589. 8351589, 6951589. 6151589. 5761589. 2541589. 1431589. 0651589. 0241588. 81588. 7481588. 6591588. 593

1588.5461588. 3051588. 2321588. 167

1588. 1231587. 9081587. 8541587. 7881587. 7481587. 651587. 5201587.4631587. 4231587. 4031587. 2191587. 1691587. 1291586. 9501586.9051586. 8671586. 7071586. 670

62 735. 462 736. 1762736. 9262 746. 8262 748. 0362 773. 2862 780. 70

62 805. 3462814. 8462 81]8. 4762 820. 4662 821. 5562 822. 8762 826. 7562 841. 7962 851.4762 854. 2562 855.6862 856.5362 872. 8162 880. 1362 883. 2362 884. 7762 899.6062 905. 1362 908.3062 909. 8462 922.6162 926. 9862 930.0862931.7062 94162942.6562 946. 1662 948. 81

62 950.6362 960. 1962 963.0962 965.69

62 967.4162975.9562 978.0962 980. 6962982.2762 986. 262 991.3362 993.5962 995. 1862 995.9963 003.2963005.2863 006. 8663 013. 9763 015.7463 017. 2563 023.6063 025.09

3p,-23P1-0

3P'1 -3P2-2

p 1-23Pi-2

3P-1 -]

3P - 2

ap1 23p,-23p 0 -1

ap1-3p,-2

3P, -I2ap1-

3p, - 23pi-2

3P 1 -1

3p1 -23p1 ..2

3p,-23p,-2

aPi

3P, -o

3P, - 2

3 Pai-3P2 - 2

3p, - 2

3p,-23Pi -2

3P,-o3P2 -233Pi - 2

3P, -03P2 -33P,-2

3Pi-13Pi -.2Pi-2

3P1 ..i3p,-23P-i-

7. 04177.07887.07919.067. 08317. 08449.10447.1 0247. 14407. 15647.157. 15687. 19796. 41617. 22027. 22377. 22557, 22786.43047. 26057. 27747. 28247.28497. 28647. 31527.32847. 33407. 33677.36357. 37367. 37947. 38227. 40577. 41387. 41967. 42269.887.44317. 44976. 58357. 45527. 45817. 47637. 48187. 48716. 60557. 49007. 50657. 51067.51557. 5187

10. 057. 53637. 54087.543810. 10487. 55977. 56377. 56677. 58087.58447. 58737. 60007. 6030

.

TABIE I. (Continued)

Brown et al. 593


Wavelength Wave number ClassificationbInt. a (A) (cm' ) g J' n*2

0000

00000

of00of00000000000000000

0

Of50o000000000000000000000

0

0

of

0

of

0o

00

0

1586. 6321586. 4881586. 4581586. 4171586. 3311586. 2881586.2691586. 2251586. 1811586. 1111586. 0951586. 0691586. 0451585. 9401585. 8921585. 7501585. 6681585. 6101585.5761585.4851585. 4601585. 4411.585. 4051585. 3761585. 3371585. 3201.585. 2731585. 2411585. 2191585. 1771585. 1531585. 1291585. 0891585. 0601584. 9901584. 9661584. 9181584. 8921584. 8511584. 8251584. 7861584.7601584.7231584. 7021584.6661584. 6441584. 6121584. 5921584.5611584.5461584. 5151584.4981584.4671584.4521584.4261584. 4111584. 3861584.3761584.3521584.3371584.3141584.3021584.2691584.237

63 026.6063 032.3263 033.4863 035. 1463 038.5363 040. 2463 041. 0263 042.7563044.5263 047. 2863 047. 9163 048. 9563 049. 9263 054. 0963056. 0063 061. 6563 064. 8963067.2163 068.5663 072.1863073.1763 073.9563075.3663 076.5163 078. 0763 078. 7763 080.6363 081. 8863 082. 7863 084. 4563 085.4063 086.3663087. 9463 089.0963091. 8763 092. 8463094.7463 095.7763 097.4363 098.4563 100. 0263 101. 0563 102.5363 103.3563 104.7963105.6463 106. 9363 107.7263 108. 9663 109.5763 110. 8063 111.4863 112. 7263 113.3263114. 3363114.9463 115.9263116. 3563 117.3163 117.8863 118. 8063119. 2763 120.5863 121.85

Jp1 -0

3p1-1

3p 1 -o

3pl - o

3PI-2

3p 1 -13pi-23pi-i3PI -13pi-2

3pi-03P, -1

3pi-i3 p 1 -0

3p 1 -o3p, -0

apo-13pi -1

3 p1 -_I3p 1-13p, -3o

3pi -03pi-i3p, _

api-i3P, -o

3PI-13pi-23p, - 0

3P1 -1

3 P1-2

3 pi-1

3P, - 2

3 PI-1

3Pt-i3Pi-2

3p,- i3pi-2

3P, -13p, -2

3pI3Pi-2

3P p-13p, -2

3Pi -13Pi1-23PI-13p p-2'Pt -13p,-23P, -13p,-23p,_l3P, -23Pi-23p,-2

7. 60607. 61757. 61997. 62327. 63007. 63357. 63517.63867.64227.64787. 64917.65127. 65327. 66187.66567.67737.68407.68887.69167. 69916. 75147.70287.7057.70817. 71137. 71287.71677.71937.72127.72477.72677.72877. 73216.77397.74037. 74257.74657.74877.75237.75447. 75787.75987.76307.76487. 76787. 76977. 77247.77427. 77677. 77827. 78077.78237.78477. 78607. 78827. 78977. 79167.79287.79477.79607. 79797.79907. 80187. 8046


Wavelength Wave number ClassificationbInt. a (A) (cm-i) g J' n 2

00000

0000000

25c2030100d

2025c5

257070

g

1015C458(d

155040

0351820c30158 0 d

12251010C

257

205

20c20

575d8

183

151

120

100

20c10

0

8

7 5 d

1584.2081584. 1801584. 1581584. 1281584. 1021584. 0801584.0561584. 0371584.0181583. 9971583.9791583. 9601583.61583.3691583. 1411582. 961582.7561582. 01581. 8271581. 4241580. 9961580. 9701580.54

1580. 0061580. 01579. 9451579. 401579. 2331579. 0191578. 8271578. 7181577. 8441577. 7841577. 11577.0031576. 9481576.631576.4951576. 2821576.2281576. 11575.6601575.6091575. 1201575. 0711574. 81574.6481574. 6011574.441574.3261574.2321574.1921573. 8681573. 8251573.5441573.5031573.2551573.211573. 01572. 9971572. 9581572.7661572.67

63 123. 0463 124. 1463 125.0363 126.2263 127. 2563 128. 1363 129. 0863 129. 8563 130. 6063 131.4263 132. 1663 132. 9163 14663 156. 4763 165.5663 172. 763 180. 9363 21063 218.0263 234.1663 251. 2663 252.3263 269. 6

63 290. 9063 29263 293.3363 315. 163 321. 9063330.4763 338. 1663 342.5263 377.6463 380. 0263 40863 411.4263 413.6363 426.363 431. 8463 440.4063442.5863 44963465.4763 467.5363487.2463 489.2063 50063 506.2663 508. 1463 514. 663 519. 2363523.0363 524. 6763 537.7563 539.4563 550.8363 552.4863562.5063564.363 57163 572. 9263 574.4963 582.2563 586.0

JP1 -23pi -23Pj -23PI -23PI-23PI-23p, -23p, -2p 1-23p1 -23p,-23p,-23P2 - 3

3Pi-1

3po-1

3P2 - 33P2-2

3p 0 -1

3P0 - 1

3 PO-13po-I3PI-23p 1

3P2 -3po-1

3p2 -3

3P2 - 33p2 -23PO-13PO-13po-1

3PO-1

3P2 -33P,-I3po-1P2 - 3

3p2.- 2

3PO -1

3P,-I3po-1

3p0.. 13po-1

3p 2 -33P0 -23PO-1

3P2-33P2-23po-1

3PO-13po-13PO-I3po-1

3P2 - 3

3po-13po-1

3P2 -3

7. 80717. 80947.81167.81407.81627.8181.7. 82017.82187. 82357. 82527. 82687. 8283

10.896. 87146.8848

11. 04811. 10527.9936.96436. 98927. 01598. 10368. 147

11.707.0791

11. 877. 0831

12. 04612. 10567. 14407. 15687.16427. 22377.2278

12.867.28247.2864

13. 04413. 10597.33407. 33798.727.37947.38327.41967.4233

13.867.45527.4588

14. 04214. 10637.48717.49027.51557.51897.54087. 54407. 56377.5670

14.807.58447.58757. 6030

15.042



Wavelength Wave number ClassificationbInt. a (A) (cm-1) g J, n *2

5f50

lof50

03

g

90101OC44

65e

4 f3555443322

1110

000000000OC000

65e505C

60e

5025c

60eof3C

50eof

3C

60e90C50d

2d

1572.5581572.5621572.521572. 3691572.3391572.251572.2021572. 045

1571. 7821571. 5571571. 6671571.4591571. 41571.3651571.2721571.231571. 1981571. 1511.571. 11.71571. 0441570. 9761570. 9121570. 8521570. 7971570. 7451570. 6941570. 6481570. 6041570. 5631570.5241570.4871570.4521570.4201570.3871570.3581570.3311570.3021570.2751570.2521570.2321570.231570. 211570. 191570. 171570. 031569. 9671569. 9221569.201569. 0291569. 9731568. 9381568. 8281.568.31.1568. 1811568. 1331567.5741567.4561.567. 4171566. 91566. 8331566. 81566. 7271566. 386

63589. 763590.5063592.363 598.2963 599. 5363603.063 605. 0663 611. 40

63 622.7063631.1763 626. 7363 635. 1263 63663 538.9563 642. 6963644,463645.7263 647.6063 648. 9863 651. 9563 654. 6963 657. 2963 659. 7163 661. 9563 664. 0863 666. 1163 667. 9863 669. 7663 671. 4563 673.0263 674.5163 675.9263 677.2463 678.5663679.7463680. 8463 682. 0363683.1163684. 0363 684. 8763684.963 685. 763 686.763687.463 693. 063 695. 6163 697.4463 726. 863 733.6863 735.9763 737.3763 741. 8563 763. 163 768.1563 770.1163 792. 8563 797. 6363 799. 2163 81963 823.0063 82563 827. 3263 841.24

3 P2 -2

3 p0 -1

3P1-1

3 p0 -_3 P0 -2

3 p0 -1

3P2-3

3 Pi -1,PO-],

3po-13 p0 -13 P2 -33p 0 -1

3 p0 -3

3 P -13

3 p0 -13P2 - 2

3 p0 -i

3p 0-I

3p 0 -13p 0 -_1

sPo-13Po-13p0 -13p,_-].

3 p0 -13 p0 -13p_3 po-13PO-13p2 -33p0_1

3PO-13 PO-13 P2 -33 p2 -33po-1

3 P2 -33p2 - 23P2 -13P2 -33P2 - 3

3p2 -33P2 -2

3p 2 -33p2 - 3

3 p2 -33P2 -33P2 -23

3P2 -33 p2 -33P2 -23

3pi-1aPo-13 p2 -3

15. 10537.61997.62347.63519. 1044

7. 64919. 1467.66187.68407.70287.69387.7113

15.877. 71937. 7267

16.0407.7334

16. 10597.74037.74657. 75237.75787.76307.76787.77247. 77677.78077.78477. 78827.79167. 79477. 79797.80077. 80367.80617.80857. 81117. 8137. 81547. 8173

16.867. 81917. 82137. 8228

17. 04017. 105117. 14717. 89718. 03418. 10518. 1479. 6369

18. 8819. 03419. 10619. 8820. 03420. 10520.8821. 031

9. 9968.147


Wavelength Wave number ClassificationbInt. ' (A) (cm-1) g J, z *2

40e

of40

od

od

30e

od

25eof

od

20eod

20eod

He

od

18e

od

15eod

12eof

12eof

1,0eof

10eof

5e

of5e

3e

36

2e2e2e2111

25c1111100

loo00

4000000002

50d

80e

1566.2941566.261566. 2031566. 01565. 9111565. 8241565.4841565.4121565.391565. 1121565.0471564. 7851564. 7251564.4881.564.4371564. 2241564. 1801563. 9901563. 9481563. 7781563. 7391563.5871.563. 5511563. 4121563. 3 801563. 2581563. 2251563. 1111563. 0831562. 9821.562. 9521562. 8321562. 7241562. 6221562.5301.562.4421562.3621562. 2871562. 2171562. 1501562. 1

1562. 0951562. 0371561. 9831561. 9321561. 8861561. 8401561. 8011561. 81561. 7611561. 7231561. 6821561. 6241561.5971561.5671561.5441561. 5161561.4921561.4671559. 7101559.41558.5861558.39

63 844. 9663 846. 363 848. 6863 85863 860.6063 864. 1263 878. 0363 880. 9463882.063 893. 2163 895. 8463906.5563 909. 0163 918. 6863 920.7563 929. 4563931.2863 939. 0363 940.7363947.6963949.3163955.5263 956. 9763 962. 6863963.9663 968. 9563 970.3263 974. 9863 976.1463980.2863981.4863 986.3963 990. 8363995. 0063 998. 7864002.3764005.6464008. 7164011.6164014. 326401664016.5964018.9864021.1864023.2664025.1864027.0464028.636403064030.2864031.8364033.5464035.8964037.0364038.2364039.2064040.3364041.3264042.3264114.496412764160.7464168.9

21.871 40 1558.250 64174.56

3P2 -3

3p 2 -23 p 2 -2

3P2 -3

3 P2 -33p2 -33 P2 -33P2 - 3

3P2 -13P2 -33P2 -33P2 -33P2 -33P2 -33P2 -33P2 -33P2 -33P2 -33P2 -33P2 --3

3p2 -33p2 -33P2 -33P2 -33P2 -33P2 -33P2 -33P2 -33P2 -33P2 -33P2 -3

3P2 -33P2 -33P2 -33P2 --33 P2 -33P2 - 33P2 --3

3P2 - 33P2 - 3

3 P2 -33P2 - 3

3P2-33P2 - 3

3P2-33P2 - 3

3P2-3

3P0 -1

3P2 -33P2 - 33Pt-23P2 --3

3P2-3

3p2 - 33P2-3

3p2 - 33p2 - 33p2 - 3

3Pt - 0

3Pt-1

3Pt-2

22. 03022. 10810. 10481.0.1.422. 85423.04223. 86924. 02624. 13424. 86925. 02925. 86026. 02626. 87227. 02027. 87828.04728. 87529. 04229. 87530. 01530. 87431. 03931. 86732. 05432. 85033.04433. 86934. 07634. 84835. 03536.0137. 03638. 04839. 0440. 0541.0542.0343. 0544.1010. 995245.0346.0747.0848.0649.1150.1151.118.72

52.1453. 1711. 105256.1957.1458.1859.0760.1761. 1862.2411.64689.00

11. 9959.146

12. 1056



Wavelength Wave number ClassificationbInt. a (A) (cm-1) g J' n0

od

260 d

60c4( e

od

15c1

40e40C

200

40C

140e

040d

50c25

00

40e40c25

015C

030e40c2030c40e70c2050d

030e40c15

025e30C

120

20e30C

121OC1l80

20612of

18f70c105

1518 d

50c20 d20d

20d

20d

2od

1558. 131556. 7371555. 861555.71555. 5851555.491554. 81554.4001553. 6881553. 61553.4721553. 3931553.221552.521552.4391552. 3651551. 9491551. 91551. 7711551. 7111551. 0001.550. 521550.51550. 3771550. 3291550.31549.7441549.3451549. 31.549. 2251548. 641548.3571548.31548. 2611548. 0531547. 8121547.5281547.51547.4421547.081546. 811546.81546. 7431546. 4191546. 2001546.21546. 1431546.11545.681545.71545. 6201545.381545.221545. 181545.171544. 911544. 8061544. 7621544.721544.451544. 131544. 111543. 8481543.83

64179.564 236. 9364 273.364 28064 284.5064288.464 31864333.5164 362. 996436564371.9364375.2364382.464411.464 414. 7564417. 8664 435. 126443764442.5264444. 9764474. 5364 494.56449664500.4364502.426450564526.7764543.4264 54564548.3964572.964584.606458564588.6064597.2564 607.3464 619. 1764 62064 622. 7764 637. 964 649. 064 65064 651. 9664 665.5364 674. 6764 67564 677. 0964 68064 696.664 69764 698. 9564709.264 715. 964717.564 717. 964 728.764 733. 0464 734.9164736.864 747. 964 761.264 762.364 773.2364 773. 9

3PI-1

3P, -2

3p_-1

3p, -2

3P, -1

3p1 -2

3Pi-i

3p,-13 p0-13 P1 -23p.-13 pi-1

3P1-2

3p,-2

3P,-1

3p,-1

3 p.-1

3Pj-2

3P, -23P,-2

3P, -23p, -2

3po-1

3p,-3P,-23p,-2

3P,-13p,-2

3P, -2

3P,-13p, -23P, -2

3PI - 13PI-23p, -23p, -2

3p,-23P,-13PI-1

3P,-13P,-13p,_

3p,-3p_

12. 14812. 642812. 990313.0513. 105913. 1479.72

13. 638413. 992814. 0114. 106314. 1479. 996

14. 63810.1414. 7314. 991815.0115. 105315. 14815. 634415. 993616. 0016. 105916. 14810.6016. 632016. 992617.0217. 105110. 995217. 995018. 0018. 10511. 14618. 63118. 99019.0119. 10619. 60119. 99520.0220. 10520. 62620. 99921.0021. 10411.7021.99622.0022. 10822.63223. 00111. 99523. 10223.7424. 00424.13412. 14825. 00426.00526. 10727. 00927. 138


Wavelength Wave number ClassificationbInt. a (A) (cmr-) g JI *2

20d

1 8d

5c1d

1d

25d14d40d35d35d30d30d

25e1015d108654332

000

20

0

1

0000000

16e

7c166

14e

4c136

663c

14256

46

56

56

2c

59

5e

Ie

1543.611543.3721543.21543. 171542.991542. 821542. 661542.521542.491542.401542.281542. 1731542. 1271542. 0771541. 9841541.911541. 821541. 7481541. 6801541.6171541.5581541.5031541. 4511541.4031541. 3571541.3141541.2741541. 2351541. 1991541. 1651541. 1341541. 1041541. 0741541. 0461541.0211540. 991540.971540. 951540. 931540.771540.3541540. 0691539. 11538. 6401538.4111537.611537.2421537. 0531536.41536. 0851535. 9311535.31535. 1151534. 9861534.51534.2961534. 1871533.81533.5981533.5071533.21532. 9971532. 9221532.6

64783.464793.206480064 801. 864809.464816.364822.964829. 164830. 264834.064839.064843.5764845.5264847.6264851.5064854.864 858.564861.4364864.2864866.9764869.4364871.7364873.9464875.9564877.9]64879.7164881.4064883.0264884.5664885.9764887.2964888.5764889.8064890.9964 892. 0364893.264894.064895.064895.964902.564920.1564932.146497564992.4465 002. 1565035.965 051. 5665 059.5665 08965100.5765 107. 1065 13265141.7165 147. 1665 16765176.4665 181. 0965 19965206. 1365 210. 0265 22565231.7065234.8865249

3Pi-13 pi-_I

'PO-i

a1pi-i3 p1 -13

P 1 -13p, _

3PO-1

3, 1-i3pi -'

3P, -i

3p-i-

3P -1 .

3Pi-I

3pi-i~3pi-I]

3pi -i

3pi-I

3p- 1.1

aPi-iapi-i

3p-1.3 p1_I3P,-l.

ap, -i.

3p-1.

3P 0 -1

api-i

3p 0 1.

api-i

3p_-1

3pi-i

3po-13P1-1

3PO-1

3PO-1

3PO-1

3PO-i

3PO-.

3po-1

3PO-1

28. 01529. 01712.6930. 03231. 03832.03333.04434. 04612. 990335. 05636.04537. 05213. 14738. 04339. 0340.0141,0142.0643.0244.0345.0346.0547.0648. 0249.1350. 0651.0652.0753.0554.0955.0756.0657.0858. 1259.0760. 1761.0162.1163.0713.7713. 99281.4. 14714.731.4. 991815. 14815.7115. 993616. 14816.7416. 99261.7. 14717.7417. 99501.8. 14718.7018. 99019. 14719.7419. 99520. 14520.7220.99921. 14321.76


-

Brown et al. 596


Wave length Wave number Classificationb- I.a , I -1E ,Int., (A) (cm-')

3e

2eod

2e2eod

].e

1.od

10od

1

ofod

1000

Of

00

of

000000000000000000000000000000000

1532. 4781532.41]01532. 11]532. 0231531. 9651531. 71531. 6251531. 5791531. 41531. 2751531. 2331531 .041530. 9641530. 9291530. 761530. 6861530. 6581530, 511530. 4381530. 4141530. 2711530. 21]61530. 1921530. 0701530. 0111529. 9911529. 881529. 8311529. 7131529. 6681529.561529. 5171529. 4231529. 3811529. 291529. 2551529. 181529. 1421529. 051529. 0361528. 971528. 9401528. 881528. 8511528. 81528. 7691528. 6931528. 6181528. 5541528. 4911528. 4331528. 3781528. 3311528. 2821528. 231528. 191528. 151528. 121528. 08

65 253. 8065 256. 6865 26865 273. 1865275.6565 28665290. 1265 292. 1065 30165305.0865 306. 8765315.065 318. 3465319. 8365 327. 165 330. 1765331.4065 337. 865 340. 7865 341. 7865 347. 9065 350. 2765 351. 2865 356. 5065 359. 0265 359. 8665364.465 366. 6965 371. 7465 373. 6665 378. 465380. 1065 384. 1365 385. 9365389.765 391. 3165394.665 396. 1465 399. 965 400. 6765403.565 404. 7865 407.365 408.5965 41165 412. 1265415.3865 418. 5965 421.3265 424. 0165 426.4965 428. 8665 430. 8565 432. 9565435.265 436. 865438.565 440.165 441.5

g .1

3 P0 -13Po-1

3po-1

3 PO-1

3po-13P0 -13po-l

3 P0 -1

3 P0 -13Po-1

3 P0 -i1

3 Po.- 13 P0 .-13Po-I

3po -I

3 P1 -13pI-i3PI-i1

3pI-i3Po-IaPI-i3P-_1

3P 1-13po-l

3Po-I3po-l

3po-1

3 PO-1

3po-1apI-i

3Po-i3Po-1

3PO-i3Po-i3po-l3 PO-13 Po-13Po-I3Po-i

3po-l

3 P1 -.13 Po-1

3 PO-1

3 PO-13Po-13po-l

21. 99622. 14822. 76223. 00123. 14723. 7424.00424. 13424. 71825. 00425. 14225.7426. 00526. 1 0726.7227. 00927. 13827. 71628. 01528. 13828. 75629. 01729. 13229. 73630. 03230. 15230. 72831. 03831. 74932. 03332. 76833. 04433. 72734. 04634. 74135. 05635. 72536. 04536. 87537. 05237. 72638. 04338. 69239. 0339. 7040. 0141.0142.0643. 0244. 0345. 0346. 0547. 0648. 0249.1350. 0651.0652.0753.05


lower level (from 4p2), the JI value of the upper level, and theeffective quantum number of the upper level (based on the 2p§/2ionization limit) appear in the last three columns.

CVery diffuse line.dDiffuse, unsymmetrical line.eUnsymmetrical.fShoulder measurement.9Blended line. The first entry in the table is the main contrib-utor to the line.

work, while the last column lists the level number forpreviously reported 12 ,1 levels. The n2* values in TableII serve to uniquely identify the upper states of thetransitions in the line assignments appearing in Table I.Figure 5 is a reproduction of the final plots of (nl).mod 1VS (n8* )mad 1 and (n )mod 1 VS n* for the f functions for theJ levels of Ge i observed in the present work. Beforeproceeding, we will discuss briefly a few features ofeach of the components of Fig. 5 starting with the J= 0levels.

As mentioned in Sec. IIIA above, there are only twoodd-parity, J= 0 channels associated with 4p 21,0, onewith each limit. From a comparison of the J= 0 por-tion of Fig. 5 with Fig. 2(D), it is apparent that thesetwo channels do not interact strongly. In this specificinstance, the two channels might be considered as slight-ly perturbed series with ancestries at lower n* valuesof 4pns 3PO (the horizontal line in Fig. 5, J= 0) and4pnd 3PO°. The J=O0 levels of SiI6' 9 behave in a similarmanner. For Ge i the J= 0 channels and the channelcorresponding to ns 3P2 are the only channels withJ- 3 for which approximate isolation of individual chan-nels seems to have any validity. Further evidence forthe weak interaction between the two J= 0 channels isthe relatively sharp symmetrical appearance of thetransitions from 4p2 3p to J= 0 levels in the autoioniza-tion region (see below).

There are five odd-parity, J= 1 channels which areassociated with 4p 2 po, two with the lower limit and threewith the upper limit. If there were no interactions be-tween these five channels, the (nl )mod 1 VS (fl*)mod I plotfor these levels would consist of two horizontal andthree vertical lines with six points of intersection. TheJ= 1 portion of Fig. 5 indicates that there is consider-able departure from this simple situation, which im-plies strong channel mixing. Additional configurationmixing arises from the presence of a J= 1 interloperlevel in the energy region under consideration. Thislevel presumably has 4s4p3 3D' ancestry and is dis-cussed below.

There are five odd-parity, Jo= 2 channels associatedwith configurations which have 4pns or 4pnd ancestors.With two of these channels associated with the lowerlimit- and three with the upper limit, the plots of (n*l )mod 1VS (n*)mod1 for noninteracting channels would be similarto the situation discussed above for the J= 1 channels.Figure 5 indicates that channel mixing is a dominantfeature for the Jo= 2 channels. Additional configurationmixing arises from three J= 2 interloper levels with4s4p 3 1"3D' and 4s4p 3 5 S ' ancestry.


'Relative intensities are based on visual estimates from photo-graphic emulsions and are intended only as a qualitative guideto the reader.

bThe breakdown of conventional notations is serious enough inthe case of Ge i to force their abandonment (see text). The

Brown et aL 597

TABLE 11. Odd energy levels of Ge i'.

Energylevel(cm-,)

37 451.6937 702.3139117.9040 020.5641 926. 7348 480.0548 882.2648 962.7849 144.4050 068. 9550323.4650 786. 7951 437. 8051 705. 0251978.1552 148.7352 170.5152592.2452847.2153 911. 6054 174. 9055 372. 6155 474.6655 686. 6755 718.5656 828.4356 921.3557 168.3857 180.2157 398. 8557 430.9457 556. 1757 828. 7858058.0758 093.3758 551.4158 741. 0458 747.6658931.4958 943.4259114.7259494.5259524.2759 658.3859 690. 6059 727.5160270.2460403.3860 429. 9160 516.3060 549. 9660552.3760 607.2560 658. 1360 749.3660 769. 2560 857. 1260 886.2061091.4861101.3761152.3761253.9961268.4061269.0561343.1761522.7361539.1261542.7261546.2361571.4161 849. 2261 922.4761 930.0461 995.6461997.1462 041.4562 044.9362 054. 7362 124. 8962 125.2562 169.2662 217.75

Relative strength Previouslower level designa-

J n 'I nz 1D2 1P2

3P,

3Po tion Remarks

2.0442 1.97872.0540 1.9876 b2.1123 2.0402 b2.1521 2.0761 b2.2443 2.1585 b2.6840 2.5406 b2.7201 2.5712 b2.7276 2.5775 b2.7445 2.5918 b2.8360 2.6684 b2.8628 2.6907 b2.9136 2.73282.9899 2.7954 b3.0230 2.8224 b3.0580 2.85083.0804 2.8690 b3.0833 2.87133.1413 2.9179 b3.1779 2.9472 b3.3460 3.0798 b3.3919 3.1155 b3.6272 3.2949 b3.6496 3.3117 b3.6975 3.3473 b3.7049 3.3528 b3.9924 3.5613 b4.0196 3.5806 b4.0947 3.63344.0984 3.6360 b4.1688 3.6849 b4.1794 3.6922 b4.2217 3.72134.3184 3.78704.4051 3.8450 b4.4189 3.8542 b4.6108 3.9796 b4.6979 4.0352 b4.7010 4.0371 b4.7905 4.0934 b4.7965 4.0971 b4.8850 4.1519 b5.1002 4.28165.1183 4.2923 b5.2022 4.3414 b5.2230 4.3535 b5.2471 4.3674 b5.6456 4.5892 b5.7580 4.6490 b5.7812 4.6612 b5.8588 4.7016 b5.8899 4.7176 b5.8921 4.71885.9440 4.74535.9932 4.7702 b6.0848 4.8160 b6.1053 4.82626.1985 4.8718 26.2303 4.8872 206.4696 5.00026.4819 5.0058 **6.5461 5.0352 ...6.6800 5.0954 -6.6996 5.1041 106.7005 5.1045 ...6.8045 5.1500 57.0779 5.2656 07.1045 5.27657.1104 5.27897.1161 5.2813 07.1579 5.2982 17.6727 5.4972 ...7.8281 5.5535 **

7.8447 5.5594 57.9931 5.6115 **7.9966 5.6127 08.1019 5.64878.1103 5.65168.1342 5.6597 18.3119 5.71858.3129 5.71888.4305 5.7567 18.5661 5.7993 5

bbbbbbbbbb

bb

b

bbb40402030303030

303535

2530402020402012

201004010105

253020

730

640401525303525'8

75

4030

05

183006

2520

2840

bbbbbbbb

b

bbbbb

b503540

025

3035252535

2530

25301550

73030

200501225

3520

35

353035

60204035

2530

406560'552555

5035304032

45

1b 2

3b 4

4. 156

b 789

1010.111

b 1213

b 141517

b 1819

50 2021

35 222324262728

15 2950 30

313233

5 343536

15 37383940

40 4141.1

25 424344

50 4546474849

35 5050.150.2

15 51.151.2

70 525353.1

50 53.25454.555

65 5656.1

56.245 56.2355 56.25

50

32

30

56.3

5757.0557.1

Energy Relative strength Previouslevel lower level designa-(cm-,) J nX * n* ID2

3P2 'Pi

3P0 tion Remarks

62 232.8762 264.4362 355. 1562 355. 61

4s4p3 5

S2 62370.7962 390.3762 398. 9462 437.6362 454.8662 467.7962 522. 9862 531.5662545.5662 576.7462 614.6162 629.2362635.2262 639. 1562 639.1762 647.6162 751.6762 791.97

4s4p3 3Di 62 793.564s4p

3 3D2 62 805.324s4p

3 3D3 62 814. 8862 823.6762 826.7962 906.3762 926. 0562 930.2662 948.7662 950.3062 964.2162 965.5962995.5963 032.9763 033.4763 033.8963 037.2663 046.0863 063.3163 073.1163 075.2663 089.1063 113.7663 117.2363 128. 8163 156.4563 162.0963 165.5463 168.5363 1.86. 4463 204.74

6g 3° 63 218.0363 223.4963 224.6463 232.5563 234. 16

4s4p3 1D2- 63 244.22

63 251.2063 267.5163 271.3163290.6563 290.8663 293.3363 294.1063 302.3263 305.1963 319. 4963330.4563 337.0363337.8963 338.

8g 3° 63 338. 1663 342.5763 362.5263 374.3463 375. 6263 377.6163378.6863 380.0263 398. 92

8.6097 5.81288.7030 5.84138.9890 5.9254 08.9905 5.9259 29.0412 5.9403 209.1079 5.95919.1375 5.9674 29.2751 6.0052 -9.3383 6.0223 -9.3867 6.0352 ...9.6018 6.0912 159.6366 6.1001 -9.6942 6.1146 -9.8263 5.1473 59.9942 6.1878 ...

10.0614 6.2037 110.0893 6.2102 ...10.1078 6.214510.1079 6.2145 ...10.1478 6.2238 310.6828 6.3413 ...10.9140 6.3887 410.9234 6.3906 -10.9939 6.4046 ...11.0522 6.4161 211.1067 6.426711.1262 6.4304 011.6620 6.5291 **11.8069 6.5542 ...11.8386 6.5596 311.9810 6.5835 011.9931 6.585512.1039 6.603712.1151 6.6055 012.3657 6.645312.7009 6.695812.7056 6.696512.7095 6.697112.7411 6.701712.8251 6.7138 -12.9940 6.7377 -13.0931 6.7514 -13.1151 6.754413.2597 6.7739 113.5297 6.809113.5690 6.814113.7028 6.8309 014.0388 6.871414.1104 6.879714.1548 6.8848 114.1936 6.8893 314.4329 6.9161 -14.6903 6.9439 ...14.8861 6.9643 014.9688 6.9727 314.9865 6.9744 015.1093 6.986715.1346 6.9892 -15.2961 7.004915.4112 7.015915.6906 7.0417 ...15.7579 7.0477 316.1145 7.078816.1185 7.079116.1658 7.083116.1807 7.084416.3417 7.0977 216.3991 7.1024 -16.6942 7.1259 "I16.9315 7.1440 217. 0789 7.155017.0985 7.156417.10 7.1517.1046 7.156817.2061 7.1642 217.6887 7.1979 -17.9945 7.2180 118.028 7.2202 *-18.081 7.223718.110 7.225518.147 7.2278 018. 684 7.2605 --

401

550

04530604520120

6545

3015

45350

18

20

2535

..0

2815

20'25800

25

1035339

12

104038

15200

185035

40

222028403510

04040'

010353012

0of

4033'30

309 ...

4040

351030

25

35

40

35

4038'38' 4525 40'25

39

35 4022

... 251030

28 50'

2010 18'253

1g

0

10 02

15 50

2507 2025 30

4040'5 5

30 25

10035 703

3'' 10

60' 4560

40

10 50

100'

' 400

0

4020 3500 180

57.2

57.357.45858.1

59

59.56061

9g 3'

6g 3°

10g 3°

11g 3'

12g 3'

13g 3'

15g 3'


TABLE II. (Continued)

Brown et al 598


Energy Relative strength Previouslevel lower level designa-(cmi) J no n* ID2 3P2

3PI

3Po tion Remarks


Energy Relative strength Previouslevel lower level designa-(cm-') J nI n2 D2 i P2

3PI 'Po tion Remarks

63 407. 82 3 18. 955 7. 2761 1 30 63 613. 13 0 33. 108 7. 6656 063 408.58 2 18. 978 7. 2774 - 25 35 63 617.0 3 33. 767 7. 673 063 411.40 1 19. 067 7. 2824 - 10 15 30 63 618. 78 0 34.084 7. 6773 063 412. 81 0 19.111l 7. 2849 0 63 622. 05 1 34. 689 7. 6840.........0 063 413.65 1 19. 138 7.2864 0 5 0 15 63 622.57 3 34.789 7.6851 063 429.94 2 19.681 7.3152..... ....... 0 63 624.34 0 35. 133 7.6888 063 436. 95 3 19.929 7.3278 1 459 63 625.69 0 35.403 7.6916 063 437.27 2 19. 940 7. 3284 .. 45' 30 63 626. 76 1 35.622 7. 6938........0 053 440.39 1 20. 054 7.3340 .. 10 12 25 63 627.36 3 35.746 7.6950 063 441. 91 0 20. 110 7.3367 0 63 629.31 0 36. 159 7. 6991 063 442.57 1 20.135 7.3379 0 0 ... 10 63 631. 12 1 36.555 7.7028 0 0 163 456.73 2 20. 683 7.3635 .. 0 0 63 632.2 2 36.798 7.705 0-

636.9 2 20. 911 7.3736 - 35' 25 63 633. 64 0 37. 129 7.7081063 462.29 3 20. 911 7.3736 1 35' 63 635. 17 1 37.491 7. 7113........0 363 465.46 1 21. 044 7.3794 .. 10 10 25 63 635. 90 2 37.668 7.7128........063 466. 98 0 21. 109 7.3822 0 63 637.76 0 38. 129 7.7167 063 467.49 1 21. 131 7.3832 0 8 .. 7 63 638. 98 1 38.441 7. 7193......... .. 0 463 479.74 2 21. 678 7.4057 - 0 0 63 639. 91 2 38. 684 7. 7212......... .. 063 484. 12 2 21. 884 7. 4138 - 30' 20 63 641.58 0 39. 13 7. 7247 063 484. 37 3 21. 896 7.4143 1 30' 63 642.53 1 39.39 7. 7267..........

6472 1 2204 749.......10 20 63 643.50 2 39. 66 7. 7287 0.063 488. 83 0 22. 113 7.4226 0 63 645.07 0 40. 12 7. 7321 of63 489. 20 1 22. 131 7. 4233 .. 0 . 5 63 645. 72 1 40.31 7. 7334 4 f

63 499.78 2 22.673 7.4431....... ..... 0 63 648.99 1 41.32 7.7403 0 563503.29 2 22. 862 7.4497 - 28' 18 63 650. 03 2 41. 66 7. 7425 0 063 503. 72 3 22. 885 7. 4505 0 28' 63 651. 91 1 42.29 7.7465.......0 563 506. 23 1 23.024 7. 4552 0 0 0 35.9 2.5 77470 063 507. 77 0 23. 110 7.4581 0 63 654. 63 1 43.27 7. 7523........0 563 508. 13 1 23. 130 7. 4588 0 0 5 63 655.62 2 43.64 7. 7544 1 063 517. 32 2 23.666 7. 4763 0' o 0 63 657. 22 1 44.25 7. 7578 0 463 520. 23 2 23. 844 7.4818 - 23' 15 63 658. 17 2 44.63 7.7598 1 063 520. 69 3 23. 872 7. 4827 0 20' 63 659. 69 1 45.26 7. 7630........0 463 523. 00 1 24. 017 7. 4871 - 0 18' 18 63 660.52 2 45. 62 7. 7648 1..063 524.54 0 24. 115 7. 4900 0 63 661. 94 1 46.25 7. 7678..........0 363 524. 64 1 24. 121 7. 4902 0 .. 3 63 662. 83 2 46.65 7. 7697 1 063533.09 2 24.680 7.5065 0 0 63 664. 10 1 47.25 7.7724........0 363 535.22 2 24.828 7.5106 .. 22' 15 63 664. 90 2 47.64 7. 7742 1I 063535.68 3 24. 860 7. 5115 0 22' 63 666. 10 1 48.24 7. 7767..........0 263 537. 76 1 25. 007 7. 51.55 - 0 12 15 63 666. 78 2 48.60 7. 7782 if 063 539.41 0 25. 125 7.5187 0 63 667. 95 1 49.22 7. 7807............63839.50 1 25.1631 7.5189 0 163 668.68 2 49. 62 7. 7823 1 0

6863 2 2.3 7.30 0 63 669. 81 1 80.26 7. 7847........0 1638548.46 2 25. 806 7.5363 - 21' 15 63 670.44 2 50.63 7. 7860 1 063 549. 00 3 25. 848 7.5373 0 21' 63 671.46 1 51.24 7.7882........0 163 550. 78 1 25. 989 7.5408 .. 0 10 12 63 672. 12 2 .51. 65 7. 7897 1 063 552.31 0 26. 113 7.5438 Sf 63 673. 04 1 52.24 7. 7916........of 163 552.44 1 26. 123 7.5440 0 .. 0 63 673.57 2 52.59 7. 7928 1 063 560.43 2 26.797 7.5597 .. 20' 5 63 674.47 1 53.20 7.7947... ....... Of o63 560. 90 3 26. 839 7.5606 0 20' 63 675. 04 2 53.59 7. 7960 .. 1 063 562.46 1 26. 977 7. 5637 - 5 10 63 675. 93 1 54.23 7. 7979......... f 063 563. 99 0 27. 115 7.5667 0 63 676. 45 2 54. 61 7. 7990 ' 063 564. 13 1 27. 128 7.5670 .. 0 .. 0 63 677. 24 1 55.21 7. 8007...............063 571. 11 2 27.786 7. 5808............3 63 677. 76 2 55.61 7. 80180 063 571.58 3 27. 832 7.5818 0 20 63 678.56 1 56.25 7. 8036...........063 572. 90 1 27. 963 7. 5844............3 10 63 679. 02 2 56. 62 7. 8046 0 063 574.38 0 28.111l 7.5873 0 63 679. 74 1 57.23 7. 8061...........063 574.45 1 28. 118 7.5875 0 . 0 63 680.17 2 57.60 7. 8071 063 580. 74 2 28. 778 7. 6000 .......... 2 63 680.84 1 58. 19 7. 8085...........063 581. 16 3 28. 824 7. 6009 0 19 63 681.27 2 58.58 7. 8094 .. 0 063 582. 23 1 28. 941 7. 6030............2 8 63 682. 03 1 59.29 7. 8111.................063 583. 73 0 29. 108 7. 6060 0 63 682.28 2 59.53 7. 8116 0 063 583. 80 1 29. 116 7. 6061 0 .. .. 63 683. 1 1 60.33 7. 813.......... ..... 063 589.46 2 29.774 7. 6175.........0 63 683.36 2 60.60 7. 8140 0 063 589. 77 3 29. 812 7. 6181 0 iS 63 684. 03 1 61.29 7. 8154 -............ 063 590. 62 1 29. 915 7. 6199......... .. 0 5 63 684.39 2 61.67 7. 8162 .. 0 063 592. 27 0 30. 118 7. 6232 0 63 684. 87 1 62.19 7. 8173................63 592.40 1 30. 134 7. 6234 0 . 0 63 685. 26 2 62.62 7. 81810 063 595. 66 2 30.549 7. 6300........0 63 685.70 1 63. 12 7. 8191............063 597. 38 2 30.775 7. 6335........0 63 686.17 2 63.66 7. 8201 0 0

63 597.62 3 3.87 7630 1 63 686.70 1 64.30 7. 8213..............0639.5 1 30. 878 7. 6351........0 lo, 63 686.96 2 64.61 7. 8218 0 0

63 599. 89 0 31. 114 7. 6386 0 63 687.40 1 65. 16 7. 8228....... ....... 063 600. 03 1 31. 133 7. 6389 0 .. .. 63 687. 71 2 68 56 7. 8235 0 063 601. 65 2 31.359 7. 6422...........0 63 688.52 2 66.62 7. 8252 .. 0 0

63 604.41 2 3.74 7678 2'6 63 689.26 2 67.64 7. 8268 .. 0 0630.6 1 31. 849 7. 6491........0 3 63 689. 94 2 68.62 7. 8283 0 0

63 606. 08 2 32. 000 7. 6512........0 63 715. 3 7.'88 0. 25C

63 607. 02 1 32. 142 7. 6531 0 63 763. 1 1 7. 993 -- . 25'63 607. 08 0 32. 146 7. 6532 of 63 790. 3 8. 08 0' 100c

63 611. 21 3 32. 795 7. 6617.. 8' 63 809.51 2 8. 1036 - 25f 7063 611. 24 1 32. 800 7. 6618 - 8' 0 ' 63 827.3 1 8. 147 2 d

1 0ld 5 0 d

599 J. Opt. Soc. Am., Vol. 67, No. 5, May 1977 Brown et al 599


Energy Relative strength Previouslevel lower level designa-(cm-') J n * n* ID2

3P2

3p1

3Po tion Remarks

64 084.64 040.64 127.64 144.64 156.7264168.964 298. 9864 320.64 357.64382.464 3 96.64 405. 8864 415.64 505.64 556.64572.9064 581.664 590. 7864597.364 671. 6264 680.64 702.64717.964 724.464731.7864737.064 794.0664 800.64 818.64830.3064835.764 837.64 841.7264 845.864 890.6464 902.64 910.64 920.1464 922.64 924. 164 929. 1364932.364 968.564 975.64 980.64 992.3564 994.64995.664 999.6665 002.465 031.6665 036.65 045.65 051.6065 052.65 054. 165 057.5665 059. 865 083.9065 089.65 095.65 100.5665 102.65 102.765 105.5465 107.465 132.65138.065 141.7265 142.65 143.265 145.8365 147.465 164.4765 167.65 173.65 176.3265 177.65 177.7265179.9565 181.3065 195. 0

8.86 0'8.72 ...9.00 *--9.06 1'9.1044 -9.146 Id9. 63699.72 ...9. 88 0'9.996 -

10.05 0'10.1048 --10. 14 1d10.6010.89 0'10.9952 ...11. 048 1'11.105211. 146 id11.646811.7011.87 0'11. 995 --12. 046 1'12.1056 --12. 148 od

12.642812.69 ...12.86 0'12.9903 * -13. 044 1'13.05 *13.105913. 147 od13.638413.7713.86 0'13.9928 ...14.01 * *14. 042 1'14.1063 -14. 147 od14. 63814.73 ...14.80 0'14.9918 --15.01 ...15. 042 1d15.1053 -15. 148 od15. 634415.7115.87 0'15.9936 -*16.00 ...16. 040 1d16.1059 -16. 148 016. 632016.7416.86 0'16.9926 -17.02 *-17. 040 Id17.1051 -17. 147 017.74 *17. 897 0'17.9950 --18.00 ...18.034 od18. 105 -18. 147 018.63118.70 ...18.88 0'18. 990 * -19.01 *19. 034 od19.106 * *19. 147 019.601

20'

95'20

15'

90d

25

25'

;ood

20

15'

Sod

15

20'

1;2

20'

8

20'

75d

65'3

1';o

50

5'

60ie50

10' 100'*-- 50'

501' 80'2

... 15'

90' 40'

40od 40'

.*- 15'

25' 30'

40*- 50d

2... 10'

8 0 d 70'

40od 50'2

... 5'

60d 3 5 t

60'40'od 25'

6'

40' 20'40'

200 15'11 7'

4 0 d 18s50'

250 12'0

... 7c

40' 16'40'

250 10'0

... 6'

30' 14'40'

20... 8'

40' 13'70'

20.. 6'

0... 3c

,30' 12'40'

15... 5'

0

TABLE .I. (Continued)

Energy Relative strength Previouslevel lower level designa-(cm-

t) J n* n* ID2

3P2

3p,

3po tion Remarks

65 199. 165 203. 365 206.13 165 207. 265207.2 365 209.14 265210.2 165 222.66 065 225. 165 229. 365231.75 165 232. 265 232.5 365 234.22 265 235.12 165 249. 165251.2 365 253.80 165 254. 265 254.5 365256.09 265 256.9 165 266.37 065268.8 165270.5 365 273.18 165 273.93 365275.0 265 275.79 165 286. 165287.99 365 290.15 165 290.5 365 292.2 165 301.0 165 303. 17 365 305. 08 165305.43 365 307.0 165 315. 165 316.51 365 318.34 165318.6 365319.6 165 327. 165 328.64 365 330. 17 165 330.3 365331.6 165337.75 165 339.41 365 340.78 165341.1 365342.0 165 347.9 165 348.99 365350.27 165350.5 365351.3 165 356.50 165 357.65 365358.8 365358.93 165 359.9 165364.38 165 365.48 365366.69 165 366.7 365 371.74 165 372.54 365373.66 165373.8 365 378.40 165 378.91 365 380.1 365 380.10 165384.13 165 384.94 365 385.93 165386.1 365389.68 1

19.74 ...19.88 0'19.995 * -20.02 --20.034 od20.105 * *20. 145 020.62620.7220.88 0'20.99921.00 ...21. 031 od21.104 ...21. 143 021.76 *- -21. 871 O'21.996 ...22.00 ...22.030 022.108 ...22.148 022.63222.762 **22.854 O'23.001 * -23.042 023.102 ...23.147 023.74 -23. 869 O'24.004 -24.026 024.134 024.718 * *24. 869 025.004 -25. 029 025. 142 025.7425.86026.005 ...26. 026 026.107 ...26.72 ...26.872 ...27.009 ...27.020 027. 138 027.716 -27.878 ...28.015 **28. 047 028.138 -28.756 ...28.875 ...29.017 - -29. 042 029.132 ...29.736 -29.875 ...30. 015 030.032 * * -30.152 ...30.728 --30.874 ...31.038 -31. 039 031.749 --31.86732.03332.05432.76832.85033.044 033.044 **33.727 ...33.86934.04634. 076 034.741 -

3'

50'Of

3'

600

2d

40'of

Od

300

Od

25'Or

sod

120

Od

20e

Od

Od

100

Of

15'

l5e

25'30'

12

0

20'30'

12

18e

20'

12

..0

18'

10

2C

5e

4'

2C

5e

5'

3'

... 2'5 od

15 1'

1 8 d 1'... od

2 0 d 1

.. 0... od

2 0 d 1

2 0 d 0... od

2 0 d 1

2 0 d o1... .od

20d 0

... 0

... 0

1 8 d 0

... O0

..- 0

00'0

0

0

0

0

1 4 d 00-- 0

4 0 d 0

0-- 0

600 J. Opt. Soc. Am., Vol. 67, No. 5, May 1977 Brown et aL 600

v

16d

18d

15d

...


Energy Relative strength Previouslevel lower level designa-(cm-') J nl n 2 ID2

3P2

3Pt

3PO tion Remarks

65 390. 2465391.265 391.3165394.6265 396.65 396. 1465399.9065 400.665 400.6765 403.565 404.7865404. 865 407.365408.665 408.5965 411.065 412.0765 412.265 415.3865 415.565 418.565 418.5965 421. 3265421.465 424.0165 424.265 426.4965426.565 428.8665 428. 965 431.0765431.165 433.0265 433.165 435. 1565 435.165 436.8265436.965 438.5165438.665 440. 1365 440.2465 441.6265 441.7965443.165 444.4265445.6965 445. 8565 446. 9365 446. 9965 448. 1265 448. 1965 449.1665 449. 1665450.2965450.2965 451.1265 451.2865 452.1665 452.2865 453.02

34. 84835. 03535. 05635.72536.0136.04536. 87537. 03637. 05237. 72638. 04338. 0483 8. 69239.0439.0339.7040.0140.0541.0141.0542.0342.0643.0243.0544.0344. 1045.0345.0346.0546.0747.0647.0848. 0248.0649. 1349.1150.0650.1151.0651.1152.0752. 1453.0553.1754.0955.0756.0656.1957.0857.1458.1258.1859.0759.0760.1760.1761.0161. 1862.1162.2463.07

0

0o

0.

0

0

00

0

0

0

0

0

0

0

0

of

50

30

3-

20

. . .

2e

2

1

1

1

. . .I

1

. . .0

0

..0

0

11

...0

..0

0

0

0

0

0

0

35d

30d

30d

10

15d

8

6

5

4

3

3

2

2

1

1

0

0

.0

000

0

0

0

0

0

0

0

aThe third and fourth columns contain the effective quantumnumbers based on the 2

P, 12 = 63 713. 24 cm-' and the 2Pi 1 2=65 480. 60 cm-1 ionization limits, respectively. The next fourcolumns summarize the observed combinations of the reportedlevels with the levels of the 4p2 ID and 3P terms. A number inany of these columns gives the estimated intensity of the spec-tral line from Table I. An ellipsis in any of the four columnsindicates an allowed transition not observed in the present work.The level numbers in column nine are from Ref. 12. Severalenergy levels assigned to electronic configurations other than4pns or 4pnd have been designated in the remarks columns.In keeping with our multichannel quantum defect treatment, theeffective quantum numbers provide the most useful level labels.Using the fractional part of n* from this table, along with Figs.7, 10, 13, and 14, one can estimate the fraction, M2, of eachclose-coupled channel in the given energy level.

TABLE II (Continued)

bindicates transitions outside our wavelength region observedin emission (see Refs. 12, 13, and 14). If no transitionswere measured in this work, energy levels from Refs. 12 and13 have been included in col. 1 for completeness.

'Very diffuse line.dDiffuse, unsymmetric line.'Unsymmetrical.fShoulder measurement.913ended line (see footnote g to Table I).

There are three odd-parity, J= 3 channels with 4pndancestry, two associated with the upper limit and onewith the lower limit. If no interactions occurred be-tween these three channels, the resulting (nl )modlvs (nf*)md 1 plot would consist of one horizontal andtwo vertical lines. For the analogous channels6 in Si i,one of the three J= 3 channels were essentially unper-turbed while the other two interacted strongly. As canbe seen from Fig. 5, all three of the J=3 channels in-teract in Ge i. The J= 3 interloper level with 4s4p3 3DI'ancestry is discussed below.

We observe nine J= 3 levels which do not fit into thescheme for levels with 4pns, 4pnd, or 4s4p3 ancestry.These levels combine with the 'D2 and/or 3P2 of the 4p2configuration, but the transitions are among the weakestlines observed in the present work. Eight of theselevels can be arranged into a series converging on the2P J2 limit with nearly zero quantum defects (see TableII). We have tentatively identified these levels as the4png 3G' levels with 6-n' 15. A single level with n*= 6, 0052 seems to belong to the 2P3°/2 limit and may beeither 4p6g 1F3° or 4p6g 3FS.

The 4s4p3 configuration contributes 3'5 S0, 1,3P0 and1,3D' terms to the structure of Gei. These energylevels are expected to interact with other odd-paritylevels of the same J and must be taken into accounthere, Extra levels (indicated by large diamonds inFig. 5) occur in the Ge i structure and the energy levelpatterns deviate from the regularf curves in the vicinityof these levels. Many levels are affected by the in-terlopers and any attempt to identify a given level as4s4p3 is artificial. The level designations of 4s4p 3.5S0

and 1'3D' in Table II were based on the assumption thatall levels below the interloper are perturbed to lowerenergies and all levels above are perturbed upwards.Our designations of 4s4p3 3D,,2 3 levels differ from pre-vious designations. 12 We have observed the transitions

_- 5S and 3P1 -5S° in absorption at -2467,4 and

2416. 5 A, respectively, but the term value in Table IIis that previously reported. 13 The choice of 61101 cm-rather than 61091 cm-l as the 4s4p3 'D2 level is arbi-trary. We have not observed any discrete transitionsfor X<- 1500 A, nor have we observed any new transi-tions for X> ~ 1900 A.

An interesting comparison of the effects of channelmixing on discrete and continuous spectra is found inFigs. 3 and 6. Figure 6 shows the region where transi-tions from 3 P0 to J= 1 levels converge on the 2Pl12limit. In this region a J= 1 level associated with 2P3°r2

601 J. Opt. Soc. Am., Vol. 67, No. 5, May 1977 Brown et aL 601

FIG. 6. An enlargement of a portion of Fig. 4 near 1570 A,which contains the 3 PO-J=l transitions converging on the 2P!/ 2limit, is compared with the corresponding portion of the J= 1Lu-Fano diagram. For ease of comparison, the wavelengthsincrease from right to left on the spectrogram. The strongfeatures marked with triangles belong to unrelated transitions.A pronouced intensity minimum occurs at b112)mod I= 0. 63, andcorresponds to the minimum in the absorption cross sectionobserved in the autoionized portion of the spectrum (see textand feature a in Fig. 3).

(with n2* about 7. 7) interacts with many J = 1 levels withnH about 40. Since both the discrete and continuumlevels in each channel are solutions of the same Schr6-dinger equation, one expects (see below) similaritiesin the effects of configuration interaction in both thediscrete and continuous portions of the spectrum.These similarities are striking if the intensity fluctua-tion in Fig. 6 is compared with the features indicatedin Fig. 3O The quantum defects of the emissionlikefeatures (a in Fig, 3) are almost exactly the same asthat of the quantum defect for the intensity minimum inFig, 6, Likewise, the absorption maxima of the Beut-ler-Fano profiles (b in Fig, 3) correlate well with thereappearance of absorption lines in Fig, 6, In Fig. 6the spectral transition to the level associated with the2 P3/ 2 limit does not correspond to a single line, buthas its effect spread over all nearby transitions. Thequantum defects reveal the presence of an extra quan-tum state by rapidly rising 1 unit to incorporate an ex-tra level,

V. MULTICHANNEL PARAMETERIZATION

The data in Table II for levels existing below the 2Pl1 2level of the ion were used to evaluate the multichannelparameters appearing in Eq. (4). The procedure adopteto determine the best values of the pa and Uj, parame-ters was a least squares iterative procedure that variedthe individual parameters according to Newton's method.

For each energy level the value of Hi was calculated byfinding the solutions to Eq. (4), either explicitly in thecases of J=0 and J=3 levels, or by Newton's method inthe cases of J= 1 and J= 2. The parameters sar and Ui.were varied in order to minimize the quantity Z(ntobs- s . Data points were chosen with 4: n-' •63which were judged to be representative of the behaviorof the states near the E,,, limit. Energy levels per-turbed by the sp3 levels, whose quantum defects weresuspected of having significant energy dependence, orshowing any appreciable experimental scatter at highnl, were rejected. Increased weight was given tosome points in order to compensate for the high densityof data points in the region nearest the ionization limit.Starting values of Bela were estimated from the points ofintersection of the diagonals [lines defining the pointswhere (n*f )mod 1= (nf*)mod 1= Aa ] with the functions in theplots in Fig. 5. The LS to jj transformation matrixelements in Condon and Shortly3 l were chosen as start-ing values for the Ui,'s. The unitary properties of thematrix U were maintained throughout the variation pro-cess by setting U' = UV, where V is a general rotationmatrix (see Appendix B of Ref. 4) of proper dimension.

In general there are insufficient data to uniquely de-termine all the Uir's and we have sought only one of themany possible solutions. Uniqueness of the Ui,,'s isnot necessary to our subsequent usage because theyserve only as intermediates in the calculation of quanti-ties which can be related to physical measurements.To demonstrate this property of the Uik's, for the J=3levels we obtained two quite different matrices whichfit the data equally well and which led to the same val-ues (within error limits) of all quantities of physicalsignificance calculated below. Table III gives the valuesof the matrix elements determined in this work alongwith the eigen-quantum defects, ,u,, for the close-coupled states. Because it was initially supposed (seepreceding paragraph) that the close-coupled stateswere LS coupled and that the loose-coupled states werejj coupled, these state labels are retained in Table IIIto orient the reader to the starting point of the calcula-tions. Since the final matrix elements are in mostcases quite different from the starting values, theselabels retain little of their original meaning. Theimportant fact is that there exist close-coupled eigen-states, a, and loose-coupled eigenstates, i, and thatthe actual states of the system at small r are linearcombinations of the a states with mixing coefficientsMa. The Ma's are computed from the expressions

Ma.= CC /(I Cla) (6)

where the Coa's, which are functions of n* and n*, arethe cofactors of the ith row and ath column of the de-terminant in Eq. (4). Although not essential to thepresent work, it should be noted that at large r theactual states are linear combinations of the i eigenstateswith different mixing coefficients (see the Zi's of Eq.2. 11 in Ref. 4).

As noted previously, if the s-d interaction betweenlevels with J= 0 were absent, the plot in Fig. 5 would

602 J. Opt. Soc. Am., Vol. 67, No. 5, May 1977 Brown et al 602

TABLE III. Transformation matrices U1a and eigen-quantum defects for Gei.a

J=o d 3Po s 3Po

A1. 22, 2) 1 0. 9980 0.06221 6<n*<39 N=382 2 0 2 L-.0.0622 0.9980j U 0. 0063

0.,690 0.113

J=1 d3D, d'Pl d3P1 s3 pi s p1

1 2 3 4 5

1 1 O. 0005 0.1848 0.5068 -0.7455 0.39142, 2 2 O. 0001 0. 8400 - 0. 2418 0. 1907 - 0.4467

0, A) 3 O. 00004 0. 3314 0. 7469 0.5758 - 0. 0269 4<n*<63 N=592 2 4 0.6434 0.2968 - 0.2727 0.2116 0.61552 21 5 0.7656 - 0.2497 0.2280 -0.1774 - 0.5174

ba 0.938 0.683 0.180 0.105 0.126

J=2 d 3P2 d 3D2 d 3F2 d 1Dj s 3P2

i\ 1 2 3 4 5

2 I'2 1 0.2478 -0.6500 0.4140 -0.5870 0(2 g)i 2 0.7169 0.0369 0.4181 0.5567 0 52 2 3 - 0.3781 -0.7148 - 0.0670 -0.5846 0 1

A,) 4 - 0.5307 0.2554 0.8058 0.0614 0 b rO.031(3 s ) 5 0 0 0 0 1b

pa 0.703 0.127 0.600 0.740 0.10

J=3 d IF3 d 3F3 d 3 D3

1i\ e ] 2 3

22 1 1 F 0.6652 - 0.0945 0.74061 3<nl<36 N=335)g 2 0.4573 0.7326 0.5042 u=0. 0352 3 -0. 5902 0.6741 - 0.4441-

JA 0.972 0.723 0.132

aThe matrix elements, Uia appear in the square brackets. The LS labels on the columns and the ji labels on the rows indicatethe starting point of the iterative fitting procedure (see text). Since the Uia's were adjusted considerably, these labels do notnecessarily reflect the properties of the a and i states. Included on the right are the range of nAj values considered, the actualnumber of energy levels used, and the standard deviation of ni' of the resultant fit. Our values of M. correspond to (i-Ma) ofRefs. 4 and 29.

bThe ns 3P2' levels were assumed to have negligible interaction with the nd J=2 levels.

consist of a horizontal and a vertical straight line thatcross freely. The nonzero off-diagonal elements in theJ= 0 matrix in Table III indicate that a small s-d in-teraction exists for these levels, which correlates withthe avoided crossing observed in Fig. 5. A plot of thesquares of the mixing coefficients computed from Eq.(6) and Table III versus (n*l)modl is given in Fig. 7.Plots such as Fig. 7 provide a representation of thedegree of mixing of the various channels [i. e., thecomposition of any level can be determined from allM2, values on a vertical line drawn through its (nf*)mod

value] and serve, with the n*2 values listed in Table II,to define the composition of all J= 0 levels which existbelow the 2P'/ 2 limit. In addition, the shape of theautoionized portion of the 3Pl-J= 0 spectrum immediate-ly above the 2P1/2 limit can be inferred from this figure.Because the level at n*= 6. 6958, whose character is al-most 100% a = 2 (see Fig. 7), is found to combine weakly

with 3 P1, we conclude that the D2 parameter in theJ= 0 expansion of Eq. (5) is small. Hence we expect the3 P1-J= 0 autojonization spectrum to consist of narrow,symmetrical peaks of relatively low intensity with(n*)mod l near 0. 70. Such features are observed (see

1.0.

0.04-0.0

FIG. 7. Plot of the squaresof the mixing coefficients, Ma(- a=1I ,. .a=2), vs(n*2)md I for the J=0 levels ofGe I.


Met

Brown et al. 603

o.o 0.5' (n2h md 1 0

FIG. 8. Calculated Lu-Fano diagram for the J=1 levels ofGei. The dashed curves were calculated using the LS-jj trans-formation matrices for Uj, (no s-d interaction) and the solidcurves are the result of numerically fitting the Uit to the ex-perimental data (see text and Table III). The . curvesrepresent the behavior expected for levels belonging to a purens channel and the ---- curves represent the behavior expectedfor the levels belonging to a pure nd channel. The observedavoided crossing at the upper right is a direct result of config-uration mixing between ns and nd configurations.

Table I) and the energies of these resonances were givenin Table II.

In Table III the five J= 1 channels labeled a = 1-5 arend3D', nd'P?, nd3P', ns 3Pp, and ns'P' in L-S nota-tion, while the loose-coupled states labeled i = 1-5 are(z, z 2 (2 ,1 (21 )1, (z z) and ( , 1)' in j-j nota-tion. If the pure L-S to j-j transformation matrix com-pletely described the situation (no s-d interaction), theU matrix for J= 1 would consist of only a 3X3 and a2 X 2 matrix in diagonal blocks, while the computed Lu-Fano plot would look like the dashed curves in Fig. 8.The effects of s-d interaction for the J= 1 levels are

0.0 0.5 0.0 0.51.0 (n*)mod 1

1.0

FIG. 9. Mixing coefficients, M, (---- ca=1,--*-- CY=2,.CY=3, -C1 = 4, -- a=5), fortheJ=1levels of GeIvS(tt 2)od -. The left half of the figure corresponds to points onthe branch of the Lu-Fano curve traced in going from A -B,B'-C in Fig. 8, while the right half corresponds to points onthe branch C'-D, DY-E, E'-A'.

1.0

M2

A'.n.-Id0. 0.5

FIG. 10. Plot of Mlf.1 vscaption to Fig. 9).

0.0 0.51 0 (f*l)mod I

1.0

(s2 Vmod 1 for J= I levels of Gel (see

evident from the form of U in Table HI and from theavoided crossings observed in Fig. 5. The solid curvein Fig. 8, which reproduces the corresponding curveobserved in Fig. 5, was calculated using the J= 1 ma-trix in Table HI. Figures 9 and 10 present the mixingcoefficients, Me, and their squares versus (n*)mod,,with the two cycles of (nfl)mod 1 necessary because twovalues of n0 exist for each value of n*. The left halfof Figs. 9 and 10 correspond to values of n* found onthe curve in Fig. 8 as one traces from A-B and B'-C,while the right half corresponds to the continued trac-ing from C'-D, D'-E, and E'-A'. As stated above, fora transition between discrete levels the oscillatorstrength is proportional to (E a Ma D )2 with the set ofcoefficients M,, chosen according to the branch of theLu-Fano plot on which the upper level lies. In theautoionization range, both branches of the curve willcontribute to the oscillator strength at any energygiven by n*2

The transitions 3 Po0 J= 1 represent an interestingopportunity to investigate the effects of channel inter-action on both the discrete and autoionized spectra.Since the J= 1 levels are the only levels which can com-bine with 3 Po in these experiments, the convergencesof these transitions on the 2P3°2 limit occurs in a regionwhere much of their structure is not overlapped by othertransitions (see Fig. 3). Similarly, with a few excep-tions, the 3 Po0 J= 1 transitions converging on 2p1 2 canbe examined with little confusion (see Figs. 4 and 6).Prominent in the discrete spectrum is an intensityminimum (see Fig. 6) which occurs on the B'-C sec-tion of the Lu- Fano curve at (n2 )od 1j=0. 63. An ex-amination of the mixing coefficients in Fig. 10 in theneighborhood of this feature reveals that the statesinvolved are nearly 100% a = 2. From this observa-tion we surmise that D2 is very small. Extrapolatingthese observations into the autoionization range, weobserve absorption minima near (nf )mod 1= 0. 63 (seefeature a in Fig. 3 for a representative sample). Si-milar strong correlations were found between strongdiscrete lines near (n )mod 1 = 0. 00 and 0. 16 and theseries of two relatively sharp autoionized features nearthe same (n* )moci values which are prominent in Fig. 3.These qualitative correlations encouraged initial at-tempts to determine the Da parameters more precisely.A densitometer trace of the range 14. 00-n2- 15.00of Fig. 3 is shown in Fig. 11 together with the function

(,! M. Da2ABBC+ (Za Me DQ)2 'DD'EA' as determined from


I/I. /I. "I

,III

i I.I'. JI

Brown et al. 604

I ,. , ^ .E ..

-v.

(a)

(b)

crZ,

CP

14.0 14.5 15.0 *n2

0.0

2(n )mod 11.0

FIG. 11. Top: Densitometer trace of the autoionized spectrumfor 3 P0 -J=- transitions with 14-n2 -15. Bottom: Calculatedrelative intensity for autoionized J= 1 channels. Ma values(see Fig. 9) and Dg parameters of 1. 03, -0. 34, 1 06, 0. 28,and 0.96 (a= -1-5, respectively) were used to fit the featuresabove.

the M,, values in Fig. 9 and relative Da values of 1. 03,- 0. 34, 1. 06, 0. 28, and 0.96 for a = 1, . . ., 5, re-spectively. The semiquantitative behavior of the cal-culated function indicates the potential of this techniquefor treating high-resolution intensity measurements.However, the reader is cautioned that these parame-ters reproduce only the qualitative features of a densi-tometer trace and will require revision. In particular,it seems that the value of D2 is too large, an errorwhich is traceable to uncertainties in the M<, coeffi-cients.

Before initial attempts were made at fitting the J= 2levels, it was recognized that several levels lying on

0.0 0.5 (n* 2mod 1.0

FIG. 12. Computed Lu-Fano diagram for J= 2 levels of Ge iusing the parameters in Table III. The as 3P2 levels were de-leted before fitting the data.


(a)

0.0 -0.0 (nfl)mod 1-0

1.0- 7''

(b)

2

0.0 ....... .10.0 (l) 1.0

mod 1

FIG. 13. M' parameters (. ... a =1, ---- a =2, - a =3,- =4) for the J=2 levels of GeIvs (n*2).d dl As in the

J=1 case, two cycles of (f12)mod I are required to present allthe Ma coefficients. The top figure corresponds to theA-B, B'-A' branch in Fig. 12 while the bottom figure cor-responds to the X-Y, Y' - X' branch.

the steep vertical curve near (n*) mod = 0. 10 in Fig. 5belong to the ns 3P2' channel. From the small devia-tions near the intersections of this line with the otherbranches of the Lu-Fano plot, it was judged that thes-d interactions were small and could be ignored.Thus the levels assigned to ns 3 P. were removed fromthe fitting procedure and the problem reduced to a four-channel problem. The ns 3 P2 levels can be noted amongthe J= 2 levels in Table II as a regular Rydberg serieswith (nf*)mOdi=10. 10. Above the 2P, 2 limit, this seriescontinues regularly with only slight diffuseness due toautoionization.

The fitted Lu- Fano curve for the remaining J= 2levels is shown in Fig. 12, while the correspondingM., coefficients are plotted in Fig. 13, As in the J= 1case, it was necessary to plot the M2 functions in twoperiods of (n* )mod 1, one for each branch of the Lu- Fanoplot. Since the transitions from 3 P and iD are over-lapped by transitions to other J levels, no attempt wasmade to fit the intensity patterns. However, it wasnoted that the levels having a large M2 coefficient had thestrongest transitions among the discrete J= 2 levels fromthe ground 3 Pl level (see, for example, the levels at63 294. 10 and 63 337. 89 cm-i in Table II). Since the M12function exhibits a broad maximum near (fl*)modi= 0. 1,we expect broad autoionized features near these posi-tions. Such features were found on densitometer tracesand, since no other assignment could be made, theywere assumed to belong to a strongly autoionized J= 2series. These features and the previously mentionedns 3P2 series were the only resonances associated withJ= 2 observed to converge on the 2

p3O 1 2 state of Ge ii.

For J= 3, the transformation matrix and the eigen-quantum defects are given in Table III, while the plot of

Brown et al. 605

0.000 ( ")od1

M' vs (nf*l)modl appears in Fig. 14. The autoionizedportion of the 3 P2 -J= 3 spectrum can be understood ifD1 vanishes, D2 is small, and D3 is large. Inspectionof Fig. 14 would lead to the prediction of a strong, nar-row resonance with (l*)mod 1 = 0. 1 and a weaker broadresonance near 0. 7 . Two such series of features areincluded in Table II as belonging to J=3.

In summary, using multichannel quantum defect the-ory, we have been able to correlate the line positionsin both the discrete and autoionization regions and givea qualitative interpretation of the intensity variationsfor the Ge I spectrum. The number of parameters usedin this approach is no greater than would be requiredin a conventional "constant quantum defect" treatment,For example, a conventional treatment of the J= Icase would require five quantum defects, five dipolematrix elements, and a large number of perturbationmatrix elements to describe the situation. We haveused only five eigen-quantum defects, b, five dipoleparameters, Da,, and ten independent rotation anglesin V (see above) to describe the entire manifold ofstates.

ACKNOWLEDGMENTS

The authors wish to thank R. H. Naber for his as-sistance with the experimental portions of this workand Dr. K. T. Lu and Dr. J. Armstrong for severalhelpful discussions.

*Present address: NASA Headquarters, Washington, D. C.20546.

tPartially supported by the E. 0. Hulburt Center for Space Re-search.

IM. J. Seaton, "Quantum Defect Theory I. General Formula-tion," Proc. Phys. Soc. London, 88, 801-814 (1966).

2U. Fano, "Quantum Defect Theory of 1 Uncoupling in H2 as anExampl of Channel-Interaction Treatment, " Phys. Rev. A 2,353-365 (1970).

3K. T. Lu and U. Fano, "Graphic Analysis of Perturbed Ryd-berg Series," Phys. Rev. A 2, 81-86 (1970).

4 C. M. Lee and K. T. Lu, "Spectroscopy and Collision TheoryII. The Ar Absorption Spectrum," Phys. Rev. A 8, 1241-1257 (1971).

5G. Herzberg and Ch. Jungen, "Rydberg Series and IonizationPotential of the He Molecule," J. Molec. Spectrosc. 41, 425-486 (1972).

6 C. M. Brown, S. G. Tilford, and M. L. Ginter, "Extendedidentifications of odd energy levels of Sii: Lu-Fano graphical

FIG. 14. Plot of M' (----z=1 ....... a =2, a =3)

VS 61*2).d I for the J=3 levelsof Ge I.


analysis," J. Opt. Soc. Am. 65, 385-388 (1975).7K. Yoshino and Y. Tanaka, " igh Resolution Absorption Spec-

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Brown et al 606

Absorption spectrum of Ge I between 1500 and 1900 Å

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