JOURNAL OF THE OPTICAL SOCIETY OF AMERICA Interferometric Measurements of Cesium * HERBERT KLEIMANt Department of Physics, Purdue University, Lafayette, Indiana (Received July 24, 1961) Sixty-four lines in the arc spectrum of cesium have been measured interferometrically by utilizing several different light sources, to obtain, in general, wavelengths with an uncertainty of ±t0.001 A, and energy levels with an uncertainty of -40.001 cm-'. The energy levels of the individual series have been rep- resented by extended Ritz formulas with a root-mean-square deviation of less than 0.004 cm-'. The value of the series limit derived from these formulas is (31 406.450±t0.030) cm-'. Eight terms of the 2 F series have been represented by a two-parameter polarization formula with a rms deviation of 0.04 cm-'. INTRODUCTION ONLY two sets of precision interferometric meas- 0 urements of the cesium spectrum have been pub- lished. Meissner,i in 1921, reported interferometric measurements of 26 cesium lines. In 1937, Meissner and Weinmann 2 measured interferometrically the first member of the fundamental series. The goal of the present investigation, which was initiated under the direction of Meissner was to obtain interferometric wavelengths of all the strong cesium lines in the range 3800-11 000 A. The plan was to make use of several different light sources to evaluate the effects of external perturbations and thence to derive an energy-level scheme which would be characteristic, as nearly as possible, of that of the unperturbed atom. It was hoped to fit these experimental levels with extended Ritz formulas and also to represent the nonpenetrating 2 F series by a polarization formula, in accordance with the methods of analysis pioneered by Edlen's group at Lund. One motive was to provide a more stringent test of the polarization formula with the improved inter- ferometric wavelength measurements. Jackson 3 has shown that the hyperfine splitting factor of an unresolved upper state can be obtained from the measured line splitting of a transition involving that state and a knowledge of the relative intensities of the hyperfine components of the transition provided the splitting of the lower state is known. In the present work a number of hyperfine splittings have been investigated for the first time, and this method of analysis has been used to obtain the splitting factors for the states involved. These values of the splitting factors were then compared to the values predicted on the basis of the Fermi-Segre-Goudsmit formula. The paper is presented in three sections. The first *This work supported by a grant from the Office of Naval Research. t Present address: Physics Department, Univeristy of Califor- nia, Berkeley, California. I K. W. Meissner, Ann. Physik 65, 378 (1921). 2 K. W. Meissner and W. Weinmann, Ann. Physik 29, 758 (1937). 3 D. Jackson, Proc. Roy. Soc. (London) A147, 500 (1934). The hyperfine components of the 6 2 S 1 , 82Si, and 6PI levels have been resolved. By making use of the theoretically predicted dipole intensity relations, rough values of the splitting factors in the unresolved S and D states have been obtained which agree with the values predicted on the basis of the Fermi-Segre-Goudsmit formula. In the forbidden transitions n 2 D, -62Si, the theoretical quadrupole intensity relations were used to obtain the splitting factors of the n 2 D3, states. These splitting factors differed markedly from those predicted )y, the Fermi-Segre-Goudsmit formula. section deals with the experimental techniques involved. Next the experimental results of the investigation are presented, and in the third section these results are analyzed. EXPERIMENTAL TECHNIQUES Inasmuch as one of the primary objectives of this work was to obtain energy levels equal, as nearly as possible, to those of the unperturbed atom, several different light sources were used. Thus it was possible to evaluate and, in some cases, to correct for the different perturbations introduced. The first light source used was an electrodeless discharge tube made by sealing a few tenths of a gram of cesium metal in a short length of quartz tubing which was thoroughly outgassed and sealed under high vacuum. No carrier gas was necessary. The tube was excited by a Raytheon Microtherm microwave generator at low power, with- out external heating. Cooling by a gentle air stream enhanced the spark spectrum as well as the transitions from the higher excited states, and, in addition, gave sharper lines. In general, lines emitted by this source produced interference fringes over path differences as large as 20 cm. The second light source used was an end-on Geissler tube previously described by Meissner.' Geissler tubes with helium and with argon as carrier gases were made and operated in an oven. A pressure of 2.5 mm Hg of carrier gas was used in both cases. The type of spectrum produced was stongly temperature dependent. For oven temperatures of less than 150'C, the spectrum of the carrier gas predominated. Between 150' and 200TCthe cesium spectrum took over the discharge. This tempera- ture range was particularly successful in exciting transitions from the higher members of the various series. Above 200'C the forbidden transitions n 2 D 1 , -62S,_ were excited. These transitions disappeared above 250'C, whereupon most of the emitted radiation appeared in the first two members of the principal series. The line profiles emitted by this source were considerably broader than those of the electrodeless discharge tube, but gave satisfactory fringes with a 30-mm etalon. 441 VOLUME 52, NUMBER 4 APRIL,, 962
Transcript
JOURNAL OF THE OPTICAL SOCIETY OF AMERICA
Interferometric Measurements of Cesium *HERBERT KLEIMANt
Department of Physics, Purdue University, Lafayette, Indiana(Received July 24, 1961)
Sixty-four lines in the arc spectrum of cesium have beenmeasured interferometrically by utilizing several different lightsources, to obtain, in general, wavelengths with an uncertaintyof ±t0.001 A, and energy levels with an uncertainty of -40.001
cm-'. The energy levels of the individual series have been rep-resented by extended Ritz formulas with a root-mean-squaredeviation of less than 0.004 cm-'. The value of the series limitderived from these formulas is (31 406.450±t0.030) cm-'. Eightterms of the 2F series have been represented by a two-parameterpolarization formula with a rms deviation of 0.04 cm-'.
INTRODUCTION
ONLY two sets of precision interferometric meas-0 urements of the cesium spectrum have been pub-lished. Meissner,i in 1921, reported interferometricmeasurements of 26 cesium lines. In 1937, Meissnerand Weinmann2 measured interferometrically the firstmember of the fundamental series. The goal of thepresent investigation, which was initiated under thedirection of Meissner was to obtain interferometricwavelengths of all the strong cesium lines in the range3800-11 000 A. The plan was to make use of severaldifferent light sources to evaluate the effects of externalperturbations and thence to derive an energy-levelscheme which would be characteristic, as nearly aspossible, of that of the unperturbed atom. It was hopedto fit these experimental levels with extended Ritzformulas and also to represent the nonpenetrating 2Fseries by a polarization formula, in accordance with themethods of analysis pioneered by Edlen's group atLund. One motive was to provide a more stringent testof the polarization formula with the improved inter-ferometric wavelength measurements.
Jackson3 has shown that the hyperfine splitting factorof an unresolved upper state can be obtained from themeasured line splitting of a transition involving thatstate and a knowledge of the relative intensities of thehyperfine components of the transition provided thesplitting of the lower state is known. In the presentwork a number of hyperfine splittings have beeninvestigated for the first time, and this method ofanalysis has been used to obtain the splitting factorsfor the states involved. These values of the splittingfactors were then compared to the values predicted onthe basis of the Fermi-Segre-Goudsmit formula.
The paper is presented in three sections. The first
*This work supported by a grant from the Office of NavalResearch.
t Present address: Physics Department, Univeristy of Califor-nia, Berkeley, California.
I K. W. Meissner, Ann. Physik 65, 378 (1921).2 K. W. Meissner and W. Weinmann, Ann. Physik 29, 758
(1937).3 D. Jackson, Proc. Roy. Soc. (London) A147, 500 (1934).
The hyperfine components of the 62S1 , 82Si, and 6PI levelshave been resolved. By making use of the theoretically predicteddipole intensity relations, rough values of the splitting factors inthe unresolved S and D states have been obtained which agreewith the values predicted on the basis of the Fermi-Segre-Goudsmitformula. In the forbidden transitions n2 D, -62Si, the theoreticalquadrupole intensity relations were used to obtain the splittingfactors of the n2D3, states. These splitting factors differedmarkedly from those predicted )y, the Fermi-Segre-Goudsmitformula.
section deals with the experimental techniques involved.Next the experimental results of the investigation arepresented, and in the third section these results areanalyzed.
EXPERIMENTAL TECHNIQUES
Inasmuch as one of the primary objectives of thiswork was to obtain energy levels equal, as nearly aspossible, to those of the unperturbed atom, severaldifferent light sources were used. Thus it was possibleto evaluate and, in some cases, to correct for thedifferent perturbations introduced. The first lightsource used was an electrodeless discharge tube madeby sealing a few tenths of a gram of cesium metal in ashort length of quartz tubing which was thoroughlyoutgassed and sealed under high vacuum. No carriergas was necessary. The tube was excited by a RaytheonMicrotherm microwave generator at low power, with-out external heating. Cooling by a gentle air streamenhanced the spark spectrum as well as the transitionsfrom the higher excited states, and, in addition, gavesharper lines. In general, lines emitted by this sourceproduced interference fringes over path differences aslarge as 20 cm.
The second light source used was an end-on Geisslertube previously described by Meissner.' Geissler tubeswith helium and with argon as carrier gases were madeand operated in an oven. A pressure of 2.5 mm Hg ofcarrier gas was used in both cases. The type of spectrumproduced was stongly temperature dependent. For oventemperatures of less than 150'C, the spectrum of thecarrier gas predominated. Between 150' and 200TC thecesium spectrum took over the discharge. This tempera-ture range was particularly successful in excitingtransitions from the higher members of the variousseries. Above 200'C the forbidden transitions n2D1 ,
-62S,_ were excited. These transitions disappearedabove 250'C, whereupon most of the emitted radiationappeared in the first two members of the principalseries. The line profiles emitted by this source wereconsiderably broader than those of the electrodelessdischarge tube, but gave satisfactory fringes with a30-mm etalon.
441
VOLUME 52, NUMBER 4 APRIL,, 962
HERBERT KLEIMAN
.r
IES
* A Geissler Tube vs E. D. Tube+ He Geissler Tube vs E. D. Tube
2.5mm Argon Carriern=7nI
n=6 _t
+ +I
2.5mm Helium Carrier+
1=11
Transition
FIG. 1. Rare-gas shifts of the n2 F-5 2 D transitions. The plottedpoints represent the shifts of the transitions n2 F-52D, in cm',as determined by comparing the wavelengths emitted by aGeissler tube containing 2.5 mm Hg of a rare-gas carrier withthose same wavelengths as emitted by an electrodeless dischargetube which has no carrier gas. The intervals labeled n= 10 andn= 11 in the figure represent the total shift between the wave-lengths of these two transitions emitted by a helium-filled Geisslertube relative to those same wavelengths emitted by a Geisslertube containing argon as a carrier. These transitions were notobserved with an electrodeless discharge tube. The curve has beenextrapolated to fit these intervals.
Although the Geissler tube was the best source forthe excitation of the higher members of the variousseries, the presence of a carrier gas caused systematicwavelength shifts. Fig ire 1 is a plot of the wave-numbershift induced in the fundamental series by the presenceof a carrier gas. The shift is measured relative to thevalues obtained with the electrodeless discharge tube,which has no carrier gas. In the case of the n= 10 and
I D
. Z
. 'E -.01
.2 -. 022 e.
A. -aW-.02
-a o
. -D
Wavelength ()
f* *f * 0
50;0';~- + .7000
Spacers Used toDetermine WavenumberCorrection
* 30mm; 8mm+ 55mm 8mmA 60mm 8 mmo 55mm
FIG. 2. Ratio of wave-number correction to free spectral rangeas a function of X. Here we have plotted the fraction of an order-number shift, relative to that of X5460.7532, induced by the phaseeffects upon reflection from the aluminum surfaces of the inter-ferometer. Each point was obtained from interferometric measure-ments with two different etalon values of the corresponding lineemitted by the same.light source. The values of these pairs ofetalons are indicated in the figure. The line at 8761 A wasmeasured only with a 55-mm etalon, thereby making it impossibleto determine the relative phase change at this point. However,by using the accurately known 62P fine-structure splitting andthe Ritz combination principle, one is able to predict the vavc-length value that would be measured in the absence of wavelengthcorrections due to phase effects, and this value was used inconjunction with the measured value to determine the point onthe curve.
n= 11 transitions of n2 F-5 2 D, which were obtainedonly with the helium-filled and argon-filled Geisslertubes, recourse was had to the following procedure.The wave-number difference of the He-A values,represented by the intervals labeled n=10 and n=11in Fig. 1, should be the separations of the two curves atthe corresponding abcissae. The curves were extrap-olated to fit these intervals, and then corrections weretaken from them to estimate the rare-gas shifts in thesetwo transitions. Since no source free of carrier gasexcited these transitions with sufficient intensity tomake measurements of the corresponding wavelengths,the best that could be done was to use the estimatedcarrier-gas shifts to correct the Geissler-tube wave-length values and obtain approximately unshiftedwavelengths. Although it seems probable that similareffects occur in the higher members of the other seriesemitted by Geissler tubes, no such systematic shiftswere found, although three nonsystematic deviationsbetween 0.001 and 0.003 A were obtained. Hence itshould be borne in mind that energy levels based onlyon measurements of wavelengths produced by Geisslertubes may be subject to shifts of several thousandthsof a cm-'.
The third light source used was an atomic jet,modeled after the mercury atomic beam apparatus ofMeissner and Barger.4 The original plan was to producea cesium atomic beam, the emitting atoms of which areessentially free, unperturbed atoms. However, theauthor was not successful in developing an electron guncapable of giving sufficient excitation to the atomicbeam. In order to obtain sufficient excitation with theelectron gun available, a higher density of atoms wasrequired than beam operation permitted. This higherdensity was obtained by heating the collimator ratherthan cooling it as in conventional atomic beam opera-tion. The greater density seriously destroyed thecollimation but brought about an increase in intensityof several orders of magnitude over conventional beamoperation. Interference fringes could be produced atpath differences of 40 cm, and the intensity of the lightsource was roughly 1/20 that of the electrodelessdischarge tube.
Interferometric measurements with these three lightsources were carried out by means of a Fabry-Perotinterferometer which was crossed with a glass prismspectrograph. The interferometer was used in bothexternal and internal mountings, and illuminatedwithparallel light. To insure constant conditions of tempera-ture and pressure during an exposure, the interferom-eter was housed in a pressure-tight, temperature-controlled chamber, containing dry air at atmosphericpressure. At the start of each exposure the temperatureand pressure of the air inside the housing were measured,and the housing was closed off from the atmosphere.
K. W. Meissner and R. L. Barger, J. Opt. Soc. Am. 48, 22(1958).
I , ^ .. ., . .
442 VSol. 52
INTERFEROMETRIC MEASUREMENTS OF CESIUM I
Light from the standard source, which was a water-cooled mercury 198 Meggers lamp with argon at apressure of about 2 mm Hg, was reflected off a glassplate through which the cesium light passed and wasthus passed through the optical system simultaneouslywith the cesium light. The green line of mercury,5460.7532 A, was used as the standard wavelength.Corrections for the dispersion of standard air and thereduction to standard conditions were made from theEdlen tables.
Corrections for the phase change upon reflectionwere carried out and are shown in Fig. 2. The ratio ofthe wave-number correction to the free spectral rangeof the interferometer [fractional order number shift=Av(1/2t)] is plotted as afunctionof wavelength.Pointson this curve were computed from the differences inwavelength obtained for a given line when measuredwith two different interferometer spacers. This wave-length difference was reduced to fractional order-number shift by the relation = (AX/X)211t2/(t2-11).
Here I, and 2 are the two etalon thicknesses used.Although corrections for these phase effects were takenfrom the plotted points rather than the smoothed curve,the plot is given to illustrate the rapid change withwavelength of the corrections for aluminum coatings inthe vicinity of 9000 A.
Nine spacers with separations varying from 8 to 200mm were used. The choice of spacers was to a largeextent dictated by the hyperfine components to beresolved. The spacers were determined from thenomogram of Meissner et al.5 The final wavelengthmeasurements are based to a large extent on the 30-,55-, and 58-mm spacer values.
Whenever possible a line was measured with allthree sources, and with at least three different spacers.For each combination of source and spacer at least twodifferent exposures were measured. Four to six fringediameters were measured on each interferogram. Themeasurements were done with a Zeiss-Abbe comparator,and the readings reduced to wavelength measurements
TABLE I. Cesium wavelengths and vacuum wave numbers.
a From measurements of I. Johansson, Arkiv Fysik 20, 135, (1961).
by the method of least squares described by Meissner,8
but programmed for a Burroughs 205 digital computer.It was found that e, the fractional part of the centralorder number, could be measured to :4:0.005, which
TABLE III. 62P Fine-structure splitting.
n Splitting (in cm-')
From n2 Su/2-62 P3/2, 12 transitions.
8 554.0399 554.038
10 554.03811 554.03912 554.036
From n2D3/2 - 62P3 /2,
78
1/2 transitions554.040554.039
Mean of seven determinations (554.0385±t0.0012) cm 1
6 K. W. Meissner, J. Opt. Soc. Am. 31, 405 (1941).
for the longest spacers gave rise to a wave-numberaccuracy of +40.0005 cm-'.
EXPERIMENTAL RESULTS
The experimental results are listed in a series oftables. The first table is a listing of the wavelengthsinstandard air and the vacuum wave numbers. In additionthe light source used to obtain this measured valueand the relevant Fabry-Perot etalon is given. Ifwavelength measurements from the atomic jet wereavailable, these were taken as the most reliable measure-ments. Electrodeless discharge tube values were thenext most desirable, and when neither of these lightsources produced a given line, the Geissler-tube meas-urement of the wavelength was used. In the last case,when a member of the fundamental series was involved,corrections for the presence of carrier gas were takenfrom Fig. 1. All wavelengths, with one exception, werecorrected for the effects of phase change upon reflection.In the case of the third member of the principal series,measurements with only one etalon were available, andthe correction was not determined.
For some 19 lines measured with both the atomic jetand the electrodeless discharge tube, the root-mean-square deviation between the two sets of values was0.0005 A. For 20 lines (excluding members of thefundamental series) measured with both the electrode-less discharge tube and the Geissler tube, the rmsdeviation was 0.0009 A. This larger rms deviation wasa reflection of the fact that only etalons up to 30 mmin length were used to measure lines emitted by the
TABLE IV. Hyperfine line splittings.
Experimental value of Spacers usedTransition line splitting (in cm-') (in mm)
Geissler tube, while, for the other sources, etalons of55 and 58 mm were employed.
Table II is the energy-level scheme derived from themeasurements of Table I. In most cases a level wasfixed relative to the ground state by two transitions.One of these two transitions was either the 62P-62Sor the 52D- 6'S transition, both of which were interfero-metrically measured for the first time. The levels werefor the most part accurately placed to t10.001 cm-l.Because of the previously mentioned correction for thepresence of a carrier gas, the higher 'F levels were fixedto only =t0.005 cm-'.
In Table III are seven measurements of the 62Pfine-structure splitting. The rms deviation from themean of these seven measurements is -t0.0012 cm-'.Since each of these measurements depends on thedifference of two transitions, this deviation indicatesthat the wave numbers have the accuracy claimed.
In Table IV a listening is made of all the hyperfineline splittings measured in this investigation, alongwith the spacers used to obtain these splittings.
ANALYSIS OF RESULTS
Analytic Representation of TermsTwo types of analytic representation of the term
values were tried, the extended Ritz formula and theformula for the term value as a function of the polariza-tion of the ion core. The importance of the extendedRitz formula has been pointed out by Edlen.7 It canbe expressed in terms of the energy levels by theformula
E,,=E,,,-R1(n-a-bt,-cn 2 . . .)2,
where E,, is the series limit and t is equal to (Eo-En)/R= Tn/R. The parameters E.., a, b, * * * may be foundfrom the experimental energy levels by the method ofleast squares as was done by Risberg,' who used threeparameters to represent the 'G series of Mg ii. In thisway a value of the series limit may be also obtained.The present work used five parameter formulas, (E,,,a, b, c, d), to fit eight levels of 'F, nine levels of ID andsix levels of 2S. The numerical work was done on adigital computer using a program written by R. R.Kenyon and K. L. Andrew of Purdue. The results aresummarized in Table V. In all cases the rms deviationof the predicted levels from the experimental levels is
I B. Edl6n, Proceedings of the Rydberg Centennial Conference,Lund (1954).
8 P. Risberg, Arkiv Fysik 9, 483 (1955).
0.003 to 0.004 cm-l. The value of the series limitaveraged over all the series is 31 406.450ht0.030 cm-l.
For the nonpenetrating series nF it is possible touse the following formula given by Bockasten' for theterm values in terms of the polarization of the ion corein the field of the valence electron,
Tn-R/n' = Ark (n,l)+BJ' (n,l),
where T. is a hydrogen-like term value, A and B areconstants proportional to the dipole polarizability andquadrupole polarizability, and , and Ai, which containall of the (nl) dependence, are tabulated functionsproportional to (r-4) and (r-6 ), respectively. Here r isthe distance from the nucleus to the valence electron,and (n) is the average of r-n taken over hydrogenicwave functions. Bockasten9 has given tables of 4 andt6. If we use the 42F and 5'F term values to determineA and B we get A = 1.65203X 106 cm-l and B= 1.84750X 107 cm-'. Table VI is a table of the residuals betweenthe observed terms and the terms of the F seriescalculated from these constants. The terms are predictedwith an rms deviation of 0.04 cm-l. This is an order ofmagnitude greater than the experimental error of:40.005 cm-'. A part of this error might be due to theuncertainty in the series limit. If the series limit werein error by as much as 0.03 cm-l, it would introduce anerror which varied from 0.006 cm-' for the n=6 termto 0.025 cm-l for the n= 11 term. However, this onlypartially explains the discrepancy. Two other possiblecauses are the presence of higher (i.e., octupole)
TABLE VI. Deviations of the term values predicted by the polari-zation formula from the observed term values of 2F.
moments of polarizability of the ion core, or pertitions due to the penetration of the valence eleiinto the ion core. It is not possible at this time to mmore definite statement as to the cause of disagreer
Analysis of Hyperfine StructureFrom the hyperfine splittings listed in Table IV
splitting factors listed in column 3 and 4 of Tablewere calculated. The splitting in the 62P1 and 8S swas resolved, and led to a direct measurement osplitting factors in these states. In both cases, b3of the Land6 interval rule, the splitting factor isfourth of the splitting of the state.
In all other cases the method outlined by Jac]was used to obtain the splitting factor. Here onethe relative intensities of the hyperfine componena given transition, and a known value for the splitti:the lower state of the transition to estimate the spliin the upper state. Figure 3 illustrates this for the gof transitions n2SI-6 2
PI. The hyperfine splittinthe 62P 1 state, as can be seen by examination ofhfs of the higher members of the diffuse serie(0.03914-0.0005) cm-'. In a transition of the sseries, if the upper S-state splitting cannot be resobut the lower P-state splitting can be resolved, one actually measures is a doublet which has cornents with centers of gravity given by
This means that the measured splitting (c.g.)2 - (c.g.)lwill equal 0.0391 cm-'+ 1.33a(n 2S,).
In a similar way the transitions n2D 1-62Pj were
used to calculate the splitting factors of the 2D,states, and the forbidden transitions 2D1,,-
62S1
F
(c.g.), ( C-9 )2
-4(n2 S112)-3
FIG. 3. Hyperfine pat-tern of transition 2
Su/2-62Pi/ 2 . Here one hasused the theoretical in-tensities of the predicted
- 4 hyperfine pattern to cal-cr culate where the centers
9I cm of gravity of the ob-_ 3 served doublet should
lie. As a result of thiscalculation the differ-ence between the ob-served doublet splitting
Predicted and the known splittingOb- d of the lower state (0.0391Observed dnf') turns out to be
equal to +.33a(n 2 S1/2 ).
(c.9.)2-(c.9.)1z .0391 cmn . 33a(n2 S1 / 2)
K L EI MAN Vol. 52
- were used to calculate the splitting factors of then 2D1,1 states. For the allowed transitions the relativea intensities are just those listed in the tables of White
and Eliason."0 For the forbidden transitions two typesof radiation are possible, electric quadrupole radiationand enforced electric dipole radiation. The quadrupole-radiation relative intensity relations are given byGarstang as
I (F - F') = (2F+ 1) (2F'+ 1) I W (FJF'J'; I2) 12.
Here W(FJF'J'; 12) is an appropriate Racah coeffi-cient. These are the intensity relations used to calculatethe splitting factors in column four of Table VII. Thefact that the n=6 transition was considerably weakerthan the n = 5 transition is evidence against the presenceof any enforced electric dipole radiation, as was shownby Samburski.'2 Further, the sharpness of the linesindicates the absence of electric fields which could causesuch radiation. It should be noted however, asMillanczuk'3 has shown, that for the transition n2D1- 62S1 enforced electric-dipole radiation has the samerelative intensity relations as electric-quadrupole radia-tion, and therefore, even if enforced electric-dipoleradiation were present, it would have no effect on themeasured splitting.
In column 2 of Table VII are the splitting factorscalculated on the basis of the Fermi-Segre-Goudsmitformula with appropriate relativistic corrections. Thisformula should be accurate to a few percent as ex-perience with other atoms has shown. It is seen that, ingeneral, the splitting factors predicted on the basis ofthe dipole-intensity relations agree with the theoreticalvalues within experimental error. This is not true ofthe splitting factors based on the quadrupole-intensityrelations which present an interesting and as yetunexplained anomaly. For the D state in particular,where the presence of enforced electric dipole radiationas a perturbing influence has been ruled out, it is hard
TABLE VII. Theoretically and experimentally derivedsplitting factors.
10 H. E. White and Y. A. Eliason, Phys. Rev. 44, 753 (1933).11 R. H. Garstang, Proc. Cambridge Phil. Soc. 53, 214 (1957).12 S. Samburski, Z. Physik 76, 132 (1932). 1v13 B. Millanczuk, Acta Phys. Polon. 4, 65 (1935).
INTERFEROMETRIC MEASUREMENTS OF CESIUM I
to think of additional perturbations which might resolvethe discrepancy between the observed and predictedsplitting factors.
ACKNOWLEDGMENTS
The author desires to acknowledge a special debt tothe late Professor K. W. Meissner, who conceived this
JOURNAL OF THE OPTICAL SOCIETY OF AMERICA
work and directed it until his death. The iflucnce ofhis patient and skilled instruction and his enthusiasticinterest continued long after his sudden departure.
I should also like to thank Professor K. L. Andrewfor his aid in the analysis of the data. In particular,he is largely responsible for the success of the serieslimit calculations.
VOLUME 52, NUMBER 4 APRIL, 1962
Interferometric Wavelengths of Thorium Lines between 2650 A and 3400 A*
A. DAVISON,? A. GIACCHETTI,t AND R. W. STANLEYPurdue University, Lafayette, Indiana
(Received May 19, 1961)
Interferometric wavelengths, suitable for use as secondary standards of class "B", are given for 68 thoriumlines in the range 2650 to 3400 A, as emitted by a thorium-iodide electrodeless discharge tube withoutcarrier gas. The rms deviation from the mean is 3X 10-4 A. The method of preparation of a reliable and veryintense thorium electrodeless tube is described.
INTRODUCTION
THE interferometrically measured thorium wave-lengths reported here are intended for use as
secondary standards of class "B" as defined by Edl6n.1The present measurements are an extension to shorterwavelengths of the earlier measurements of Meggersand Stanley.2 The two sets of measurements, takentogether, furnish 284 secondary standards between 2650and 7000 A with a root-mean-square deviation of0.0004 A or less.
A detailed discussion of the history of secondarystandards has been given by Stanley and Meggers.3
Before 1955 the source of secondary standards in mostcommon use was the iron arc in air. Beginning about1950 two practical, low-pressure, iron sources weredeveloped which produced sharper and more repro-ducible wavelengths than the iron arc. A completesummary of these developments with an extensive listof iron wavelengths has been given by Crosswhite.4 Formany purposes, especially the measurement of the veryrich rare-earth spectra, a source is needed which gives alarger number of standards, more evenly distributedthroughout the spectrum, than those furnished by theiron sources. Meggers suggested in 1955 that thorium
* This work was supported by a grant from the NationalScience Foundation.
t Present address: Baird-Atomic Inc., Boston, Massachusetts.t Fellow, Organization of American States. Present address:
Departmento de Fisica, Universidad Nacional de La Plata, LaPlata, Argentina.
1 B. Edl6n, Trans. Intern. Astron. Union 10, 211 (1960).2 W. F. Meggers and R. W. Stanley, J. Research Natl. Bur.
Standards 61, 95 (1958).3R. W. Stanley and W. F. Meggers, J. Research Natl. Bur.
Standards 58, 41 (1957).4 H. M. Crosswhite, Johns Hopkins Spectroscopic Rept. No. 13
(1958).
was eminently suited to this purpose.5 In addition tohaving a very large number of lines well-distributedbetween 2700 and 7000 A, thorium has a mass aboutfour times that of iron and, consequently, a Dopplerwidth only one half as great when excited at the sametemperature. In addition, thorium occurs naturally asa single, even-even isotope (Z=90, A= 232) so thatits lines are entirely free from hyperfine structure andisotope shifts. These expectations concerning the su-periority of thorium standards have been verified ex-perimentally in the paper cited above2 in which therelative error, AX/X, of thorium wavelengths is shownto be less than 1 part in 20 million. The present papergives interferometric wavelengths of 68 lines between2650 and 3400 A as emitted by an electrodeless dischargetube containing thorium iodide without carrier gas.
LIGHT SOURCES
The source of the thorium lines whose wavelengthsare reported here was an electrodeless tube preparedin this laboratory. The quartz tube was about 5 cmlong, had an internal diameter of 6 mm, and containeda small quantity of thorium iodide without carrier gas.The tube was excited at a frequency of 2450 Mc/sec bya Raytheon microwave generator operated at 90% to100% of full power.
Several procedures for obtaining discharge tubes havebeen described: Zelikoff et al.,6 give a method of makingsuch tubes in cases where the metallic element itselfhas a vapor pressure approaching 1 mm Hg at theoperating temperature of the lamp. Corliss, Bozman and
5 W. F. Meggers, Trans. Intern. Astron. Union 9, 225 (1955).6 M. Zelikoff, P. H. Wyckoff, L. M. Aschenbran(d, and R. S.
