2y ago
3.02 MB
199 Pages
Last View : 3m ago
Last Download : 1y ago
Upload by : Halle Mcleod

zoo2,0BARC/1991/P/003oo 70Oo SPECTROSCOPY DIVISIONPROGRESS REPORT FOR 1990Edited byA. Sharma and S. M. Marathe1991


BARC/1991/P/003BIBLIOGRAPHIC DESCRIPTION SHEET FOR TECHNICAL REPORT(as per IS : 9400 - 19B0)01Security classi f ication :Unclcissi f ied02Distribution :Ex ternal03Report status :New04Series :BrtRC External05Report type :Progress Report06Report No. :BARC/1991/P/00307Part No. or Volume No. :08Contract No. :10Title and subtitle :Spectroscopy Division i progressreport for 199011Collation :196 p., figs., tabs.13Project No. :20Personal author(s) :21Affiliation of author(s) :Spectroscopy Division, Bhabha AtomicResearch Centre, Bombay22Corporate23Originating24Sponsor(s) Name :author(s)A. Sharma; S.M. Marathe «ds.):unit :Type:30Date ofsubmission :31Publication/Issue date :Bhabha Atomic Research Centre,Bombay - 400 085SpectroscopyDivision, BARC, BombayDepartment of Atomic EnergyGovernmentAugust 1991September 1991Contd. (ii)

(ii)413Publisher/Distributor :Head, Library and InformationDivision, Bhabha Atomic ResearchCentre, Bombay42Form of distribution :Hard Copy50Language of text :EngIish51Language of summary :Engli sh52No. of references :refs.53Gives data on :6(2Abstract : This report summeri ses the work done by members ofthe Spectroscopy Division both within BARC as well as inscientific insfcitutiens elsewhere during the calendar year 1990.Main tHruas of research activity include atomic spectroscopy forhyperfine structure and isotcpe shift determi nation, theoreticaland e? ;per imnnta 1 studies c-f diatomic molecules, infrared ndfabrication of be,?m line optics for INDUS-1synchrotronradiation source?, beam fail spectrascopy and laser spectroscopyof various atomic and molecular systems.Major experimentalfacilities that have been utilised include a fourier transformspectrometer, i\n c :cimer la or pumpsd dye-laser and a esthecpLctrcscapic analytical cervici; rendered fur vdr ious DAE unitsand de-scribes briefly some new analytical facilities like la&erenhenc3d i on i 2 r , h i on in f lamas and resonance ionization massspectroECopy using pulsed lasers which are being set up. The?above activities were reported by members of the SpectroscopyDivision via invited lectures, p spurs presented in variousnational and internationalconferences and publication inscientific journals. Details of these are given at the end ofthe report.70Keyi-srdsi/Descriptors : PROGRESS REPORT; EMISSION SPECTROSCOPY;X-r-:AY FLUORESCENCE ANALYSIS; TRACE AMOUNTS; INFRARED SPECTRA;RAKAN SPECTRA; RESEARCH PRDi AMB; LASER SPECTROSCDPY;ROTATIONAL STATES; DARC; THIN FILMS; VIBRATIONAL STATES;MOLECULAR STRUCTURE71Class No. :99Supplementary elements : The previous progress report coveringthe.- period January 1989-Dscember 1989was published as BARC—1536.INISubjact Category : A12.10; B11.20

CONTENTSANALYSIS BY OPTICAL EMISSION SPECTROSCOPY1.1INDUCTIVELY COOPLEI) PLASMA-ATOMIC(ICP-AES)EMISSION1.1.1Determination of adjacent rare earths inby ICP-AESSPECTROMETRThighpurity11.1.2Determination of Aluminium in Niobium by ICP-AES31.2SERVICE ANALYSIS42.ATOMIC, MOLECULAR, SOLID STATE AND LASER SPECTROSCOFY2.1ATOMIC SPECTRA2.1.1Isotope shift studies in levels of 4 50*63 and 4f *5d6pconfiguration of Sml and confirmation of aoae tentativeassignments. Dependence of Isotope Shift3configuration of neutral Gadoliniuminthe4fv5d26s9Term shifts in odd and even parity levelsvariationinJiLncoupledstatesofconfiguration of Yb*and their4f* 5d6s2.1.4Esti mationofGaussianandDeconvolution of Airy Line Shapewidth2.2SODD STATE SPECTRA2.2.16-d Luminescence in O**:ThBr42.3ELECTRONIC SPECTRA AND STRUCTURE OF SIMPLE MOLECULES2.3.1On the Determination of Vibration Transition Dlpole Monontfrom Rovibrational Intensities: Application toCIO andHC1 as Test Cases.2.3.2Lorentzian611byRotation-Vibration Spectrum of Oxygen Moleculo: Estimationof Magnetic Dipole Contribution to Intensity.15181922 of Forbidden Transitions in Diatomic Spectra:Line Intensities in Intra-Multiplet Transitions.The Vibrational and Rotational Analysisoftho25A*nBands of SiSe282.3.5The Electronic Spectrum of Silicon Monotelluride (SIT )342.3.6Broad band emission spectrum of InBr at 52(5 nm.372.3.7Absorption Spectrum of InBr382.3.8Spectrum of Hfia392.3.9The 430 nm System of Indium Oxide402.3.10 The spectrum of the InO* molecule462.3.11 The spectrum of InCl*502.4INFRARED AND RAMAN SPECTRA2.4.1Low Temperature and Long path Multiple Reflectionfor diode laser and FTIR instruments.2.4.2Fourier Transform High Resolution studyGD3CGHofPerturbations in the v7 state of CDgCCH2.4.4Perturbations in the vibration-rotationalacetylene in the 2650-4100 cm" region. Resolution FTIRregionspectraofup542i j bandof582. bandsof66in9-11 M M68High Resolution Infrared Spectroscoplc measurementsthe Bomem DA3.002 Fourier Transform SpectrometerInfrared and Raman SpectroscopicSuperconductors & Related MaterialsStudiesofwith70high-Te74Double Resonance Study of Nil, with TEA CGfe Laser and DiodeLaser2.5LASER SFECTROSCOPY2.5.1Determination ofTritium in EfeODltratraceLevelsofDeuteriumand8081

2.5.2High man822.5.3Plasmei emission characteristics of laser ablated 3olids862.5.4Formation of thin films bysuperconducting ofhigh T(.Pulsed Laser induced hole burning in an aerosol medium:new technique for flow visualization in gases.Detection of Sub-PicoKram Concentrations of SodiumOne-Step Laser Enhanced Ionisation SpectrometryEffect of Laser Power on LEITwo-Photon Lines of SodiumSignalofOne-photonA89by96and100Effect of Low and High Ionisation PotentialLaser Enhanced Ionisation Signal of SodiumElementson105Molecular Photophysics1082.5.10 Two Poton Spectroscopy of Autoionising LevelsSulphur (3*50)ofSinglet1112.5.11 (2 1) REMPI Spectroscopy of Excited O 1 ) Sulphur Atom2.5.12 Laser power dependent studies inof BaMultiphotonionisation1232.5.13 Study of Roll of Collisions in MultiphotonBa2.5.14 Setting of a ResonanceFacility for the Ultraisotopes.118Ionisation126Ioniaation Masstrace DetectionSpectrometryof short-lived2.6SYNCHROTRON, BEAM-FOIL AND PLASMA SPECTROSCOPY2.6.1Progress report on the beam line forgasos in INDUS-IPESofofsolids129and1322.6.2High Resolution VUV Spectroscopic Facility at INDUS-I1352.6.3Design and evaluation of PES Beamline Optics1452.6.4Design and evaluationOpticsofHighResolutionVUVDoaraline151

2.6.5Beam-Foil Spectroscope1552.6.6Reinvestigation of some of the autoionizing lines of Cul1603.ELECTRONICS3.1.1Signal Detection and Processing for ICP Spectrometer1653.1.2Instruments Maintained and Serviced1694.FABRICATION AND MACHINE SHOP ACTIVITIES4.1.1Interfacing of RecordingPersonal ComputerFabry-PerotSpectrometer with1704.1.2Machine Shop Activities1715.POBLICATIONS5.1Papers published in scientific journals1795.2BARC Reports1805.3Papers presented in Conferences, Symposia, Seminars etc.1815.4Invited talks1846.OTHER ACADEMIC ACTIVITIES6.1Members registered for M.Sc/Ph.D degrees187DIVISIONAL STAFF CHART189

.1 —1.1.1DETERMINATION OF ADJACENT RARE EARTHS WHIGHPURITVEU20.BVICP-AESS.S.Bisnas,I.J.Machado*nd P.S.MartyHigh purity Ei O, was analysed for Pr, Nd, Sm, Gd,Dy by ICF'-AES.Samples containing1 ing/ml of EuwereTbandnebulizedinto the plarma generated by a 5 6 MHz R.F. generator delivering m forward power of1.3 KW.Calibrationstandardsa b o v e six rare e a r t h s in the concentration rangewith1 mg/ml of Eu were used.Scanningchosen for calibration was donemonochromatorgiven inarecomparedemployed(Model no. JY-38 THRTabledeterminableby1.InTableof2,the ig/mlanalytelineslm-Czerny-Turn»rThe analyticallowestin ourTable n Limits*aqueousmatrixsolutionsolution ng/ml)limitsRSDb 7.)(ng/ml Pr 422.29328387.5NtJ 406. 1098182.7Sm 446.7348153.4Gd 303.2847153.5Tb 370.39220451.6Dy 364.5408302.0"Calculated using the method given in Ref.1for the R E concentration r a n g e 0.05-1.0 fjg/mlmethodpreviouslylaboratory.Analyte wavelengths and detectiondata isquantitatively(LQD) concentrations obtained by the ing

Table 2:Comparison o-f LQD ConcentrationsElementLQD 5050Tb100150100Dy10060200"Present Workcfrom Re-f.3References:1.R.K. Winge, V.J. PetersonandV.A.Fassel, Appl.Spectrosc., 33, 206 1979).2.P.S. Murty and S.M. Marathe, Z. Anal. Chem., 272, 341U974)3.R.M. Dixit and S.S. Deshpande, BARC Report No. 1275, 1985.

31.1.2DETERMINATIONor AmMtNturt ttt NIOBIUM BV JCP-AESP.S. Hurty *nd B.K. AnkushA preliminary method was developed for the determination ofAl in niobium byICP-AES.Niobiumsamplewasdissolvedaquaregia and HF and the solution containinglmg/mlused -fur- ICPMasanalysis.Al 396. 152n nlinoofscannedmonochroniator (Model No. JY-?B THR K36N9) using aqueousfor calibration.The average background intensityAl 396.152 nn line in Nb matrix, wasstandards.onwasastandardsUsing this method Al at More than 0.IX could bedetermined in Nb.about i.SNbincomparedtoDue to thisthebackgrounddifferencenecessary to enploy matrixThis is being ecalibration.

1.2SERVICE ANALYSISS.H. MaratheOur Division has been regularlycarryingUranium and a wide range of other materials.outanalysisThetableofshowsbreak-up of analysis of samples carried out in 1996) received fromdifferent divisions of BARC and from other units of DAE.TheICPSpectrometerregularly employed in theinstalledplasmamaterials like LagO,, T O,,Go O,,traces of other rare earths.inmode1987toEu 2 0,,isanalyseDy 2 0,andbeingraraearthY208Rare-earths separated fromby solvent extraction by the UMP are now analysed inmode.nowtheforUraniumplasmaPreviously these were being separated by column extractionand caprecipitation analysedspectrographically.Uranium(asU 3 0 a ) samples are analysed for B, Cd etc., in the DC arc modeonthe same spectrometer.Steel and stainless steelemission for C,S,P ectrometer.Other types of samples ware analysed spectrographically, using DCarc excitation.

-5 - Break up of Service Analysis carrl«tl out in 1990BaurcmType of SamplesA BARC UnitsUMPRE oxides,(UED)No. ofSamp leiUF4 ,No. ofdeterminationi7203588390268459314362201792Mg, RE nitrateY20gV DM water, U-ore,Calcium nitrate,carbon, graphite.AFDU, Stainless steel,Carbon steel.Metal-Y-Ba-Cu-D,Al-ZrtlurgySnO2, s t a i n l e s sWD9J1 Cu, V, Sn, NiO.OtherStainless Steel,Units o-f SnDj,, RE Oxide, Ti,BARCGraphite powder,Ag-Cu alloy, BaC0 9 ,CuO, Y 2 0 3 ,B80.B) DAE UnitsIREY20a, EUjsQa, Bd O,(Udyog-Trichromaticmandal phosphor.NPCCATCarbon steel3Stainless steel3Total12246904Chemistry Division, Chem. Engg. Division, NtPD, ChemicalEngg.Group, Powder Metallurgy Division, Applied Chemistry Division,TP&PED.

2.1.1ISOTOPE SHIFTCONFIGURATIONASSIGNMENTS.STUDIES IN LEVELS OF4F S 5D*6SANDOF S M I AND CONFIRMATIONOFSOMES.H. Afzal, S.G. Hakhate, Pushpa Rao, A. Venugopalan,mnd G.D. SaksenaTheconfigurations4f B 5d z 6stentatively assigned earlierneutral samarium atom (SmI)C13andstudies which could confirm thesebeen reported so far.4f s5d6pandtoa-fewisotopelevelIsotope shift (4-F m havemeasured presently in transitions involving some of thesetentatively assigned.The tentative assignment ClDconfiguration to some of the levels of Sm arebasis of the present isotope shift studies.the type 4f 5d 6s — 4f nsitionbeen4f 5d 6»or*thetransitionsofIS.Thisexpected, for the change in the electron charge densityat mAhmad4f 5d 6sA f 0) 4f 6sisA -fow lDvot-es- oiyneJ lu tftf )B2 is—negligible,Afew levels assigned to 4ftfSd6p are not pureand—isthereissomeconfiguration mixing as is evident from the small value of IS for4f*5d6p - 4f**6s2 transitions( \Tbe levelsbelongingto4f*5d*6sconfiguration whi-ch have been confirmed from the presentalong with levelsbelongingto4f*5d6p« are- shown—i**-—Fig.4-.Assuming a level shift of Xmk in the level at4f 6s0.0belongingconfiguration, the term shifts are evaluated.belonging to 4ftfSd6p configuration exhibitandtheextentofmixinghasadditional studies are taken ted,forwhichFurther studies Otf in progress.

-7-Reference:1.W.V. Martin, R. Zalubas and L. Hagan, Atomic anargythe rare-earth elements NSRDS-NBSStandards, Washington (1978).60National1avalsBureauof

-9-(M.i.) ffj.

2.1.24*'5d*6*TERM DEPENDENCE OF ISOTOPE SHIFTS IN THECONFIGURATIONOF NEUTRAL G A D O U N I U MA. Vwnugopalan,S.A. Ahmad and G.U. SalcsenaIn the first-order approximation, isotope shift IS [SpecificM ss Shift (SMS) and Field Shift(FS) 1 in heavy elements t.assame value for all terms of a pure configuration.it was found nd-orderFSisformainlytermsThis has been explained as(CSO)effect.dependent FS as the termsTheofaCSOpureslightly different electronic chargeExperimentallypredominantdifferentd.ieoftoef ensitiestonatermhavevary y(0 atthestudythenucleus.We have carried out extensive investigationstoterm dependence of isotope shift in the 4f J d 6s configurationneutralgadolinium.Theconfiguration of Gdl haveIBbeeninariousevaluatedtermsby4f 7 5d 2 6sconfiguration.isotopic samples *s *Gd and '""GdwereThetheexperimentalpublication As could be seen,1OofF , *F,1OP andBDthethefourcoreconf igur at ionwith the 6s electron causing the parent term (156-160) for eight terms of the 4f75d*6s configurationgiven in Table 1.4f 5d 6smeasuringseveral spectral lines involving transitions withGdl assigned to rms,commbin*intotwo

--JoRussel-Saundorsterms;eg. ,theFparental4f 7 5d z iO F) combining with 6s gives risa to41termF and *Vfromtermsandsimilarly -for other parent terms.Table1: TermShiftsforvarioustermsofthe4f 5a 6sconfiguration of Bdl lmk lB cm" 1 )TermAT(156-16 )TermAT(156-160)C4f 7 5d 2 ( 1O F)6s,"FD86 mKC4f7 5d Z (1OF)6s,PF376 mKC4f 7 5d 2 ( lo F)6s, P FJ68 mKC4f7 5d 2 (1 F)6s,11F365 mKC4f 7 5d 2 ( lo P)6s,"P388 mKC4f7 5d 2 (iOP)6s,PP376 mKC4f 7 5d 2 ( 8 D)6s, P D370 mKC4f75d2( D)6s,7D378 mKThe CSQ effect, which is due tothefai—off—configurationmixing results in different values of y(0) two terms arising out of the same parentfor eachterm.ofAT,proportional to y(0) , is thus different for thesethesewhichtwoisterms.No calculations are presently available for the y((3) values ofdifferentoftermsofthe4f 5d 6sconfigurationHartree—Fock calculation is available for the y((3) valuesvarious ter.ns of the 5d 6s configuration of LaIC23 thevariation in y(0) r to the ones observed presently in Gdl.References1.S.A. Ahmad, 6.D. Saksena and A. Venugopalan,366 (1976).2.M. Wilson, Phys. Rev. A3, 45 (1971).Physica81C,

-ii2.1.3TERM SHFTS IN ODD AND EVEN PARITY LEVELS AND THEIRJ»Ln COUPLED STATES OF4F* 5D6SVARIATIONWCONFIGURATION OF YB*Pushpa H. Rao, S.A. Ahmad and G.D. SaksanaIsotope shift studies by earlier workers inytterbiuminvolving(Yb* are confined to onlythegroundstatefoursingly—ioni sdlines,all4f 1 4 6s (configurationtransitions of the type 4f1 46p - 4f4 *6s were studiedofthornandthreaC13.Thisdid not not allow the evaluation of term isotope shifts (AT)the levels of Yb*, and for most of the levelsassignments exist [23.theconfigurationTheoretical calculation ofodd and even parity levels also exist C33 but somostfarofthaevaluationof term shifts (AT) of the levels of Y b % which could confirmconfiguration assignments had not been made.theth»The present studiesconcern the measurement of IS in transitions in Yb* spectrumthe evaluation of AT values forforlevelsofalltheandknownconfigurations of Yb*.The IS studies were carried out in 32 spectral lines of Yb*in highly enriched samples ofnitrogencooledhollowYb andcathodesandYbexcitedusingintheFabry-Perot spectrometer with etalons coated ).The term isotope shifts (AT) for the oddandwere evaluated from the experimentally measured isotope shifts inthe transitions. valuatedforThe AT values for various configurations of Yb*thefirstsummarised in Table 1.timeinthepresentstudiesareThese AT values are compatible with the

-12AT values of the odd and even configurations o-f neutral(Ybt)C43.YbThis could be checked as most of the AT valuescould be eva. ted using the screening parameters andatomofATYbvaluesof various configurations of Yb .The first example of JjLu coupling scheme was found inlevels of 4f 13 5d6s odd configuration of Yb* by Racah C53.theFro.nthe present studies we have attempted to check whether the levelsbelonging to 4f 13 5d6s electronic configuration couldbeaccording to their different JtLtl termdesignations.found that thebelongATvaluesoflevelssomewhat different from those levels oftoWehaveCJ1Ltl3armThisshowsthat there is a small difference in * (fl) values oftheleveldepending on their multiplicity M.shiftsof levels3Cll/23 ,**C9/23 configurations are slightly1Cll/23 , 9/23 etch DfThat is, the termetc.,largerEJ1L113.groupedthanof4f 19 2FVy,z 5d6s 3D thatfor4f i3 (2F7//2 5d6s(1D )This observation is being reported for theATfirstthelevelsconfiguration.timeinthistype of coupling scheme.The term isotope shifts of levels belonging to theconfiguration is given belaw.4f* 5d6s

-JS-ParityAT 172Yb - *7 *Yb xl0 *ci» *ConfigurationEven4f**6sS3 24fi36s6p145 104f**7sOdd10 34fi-*6d- 04f 13 6s 2255 1 04f i3 5d6s145 204f**6p10 5The configuration assignments of oddYb oreticalcalculations are mostly confirmed by the AT C172Yb-17 IYb)forthe odd parity level of 4f195cJ6s configuration38342.02cm"1atis AT 125 mk, which indicates a configuration mixing, as forpure 4f 5d6s configuration the value is 145 mk.The value offor this level is not compatible with the configurationaATassignedto it on the basis of the theoretical calculations in Table 2.

-14Table 2:Term shifts 5145124125References1.2.A.R. Golovin and A.R. Striganov, Opt. and Spect. 19,(1965).W.F. Megsprus, J. Research NBS (USA), 71A, 396 (1967).4673.W.V. Martin, R. Zalubas and L. Hagan, Atomic Energy Levelsthe rare earth elements NSRDS-NBS 60 National Bureaul ofStandards, Washington (1978).4.S.A. Ahmad T t.J. Machado and G.D. Saksena,35B 215 U 9 B Q ) .5.G. Racah, J. Opt. Soc. Aram. 5 7 , 771 (1960).SpectrochimA ta

2.1.4ESTIMATION OF GAUSSIAN AND LORENTZIAN WIDTH BY DECONVOLUTIONAIRY LINE SHAPEOFS.G. Nakhate,. S.A. Ahnad and G.O. approximation is justified can be described by Voigt profile withLorentzilan half—width proportional to the atom densityandGaussian half-width corresponding to the temperature of theIn Fabry- D erot(FP) interfwrometer the observed linethegas.profiledescribed by Airy function which is the convolution of theisVoigtprofile and the instrumental profile of the FP interferometer.For the ideal FP interferometer thenumericallyexpression for this convolution is given by Ballik*convenientandithasthe form:IT(z) CF "*"n t00ZC— Zwhere2n iIT

A. Sharma; S.M. Marathe «ds.) 21 Affiliation of author(s) :Spectroscopy Division, Bhabha Atomic Research Centre, Bombay 22 CorporateBhabh author(sa Atomic Researc) :h Centre, Bombay - 400 085 23 OriginatingSpectroscop unit :y Division, BARC, Bombay 24 Sponsor(s) Name : Type : 30 Date of s

Related Documents:

1. Introduction to Spectroscopy, 3rd Edn, Pavia & Lampman 2. Organic Spectroscopy – P S Kalsi Department of Chemistry, IIT(ISM) Dhanbad Common types? Fluorescence Spectroscopy. X-ray spectroscopy and crystallography Flame spectroscopy a) Atomic emission spectroscopy b) Atomic absorption spectroscopy c) Atomic fluorescence spectroscopy

Visible spectroscopy Fluorescence spectroscopy Flame spectroscopy Ultraviolet spectroscopy Infrared spectroscopy X-ray spectroscopy Thermal radiation spectroscopy Detecting and analyzing spectroscopic outputs The goal of all spectroscopic systems is to receive and analyze the radiation absorbed, emitted, .

Spectroscopy Beauchamp 1 y:\files\classes\Spectroscopy Book home\1 Spectroscopy Workbook, latest MS full chapter.doc Basics of Mass Spectroscopy The roots of mass spectroscopy (MS) trace back to the early part of the 20th century. In 1911 J.J. Thomson used a primitive form of MS to prove the existence of isotopes with neon-20 and neon-22.

Organic Spectroscopy by William Kemp, 3rd Ed. ! Spectroscopy by Pavia, Lampman, Kriz, Vyvyan, IE. ! Application of absorption spectroscopy of organic compounds by John Dyer. ! Spectroscopic problems in organic chemistry, Williams and Flemings. ! Solving problems with NMR spectroscopy Atta-Ur-Rahman. ! Organic Spectroscopy by Jagmohan. 33

spectroscopy and fluorescence spectroscopy are used to accurately analyze light in both the visible and ultraviolet light ranges. Both photometric methods measure the same wavelength range, but they differ in the type of samples they UV-VIS Spectroscopy and Fluorescence Spectroscopy (Part 1 of 2) Fig. 1 Examples of Common Light Emission

5 nuclear magnetic resonance (nmr) spectroscopy 33 5.1 the physics of nuclear spins and nmr instruments 33 5.2 continuous wave (cw) nmr spectroscopy 37 5.3 fourier-transform (ft) nmr spectroscopy 39 5.4 chemical shift in 1h nmr spectroscopy 40 5.5 spin-spin coupling in 1h nmr spectroscopy 50

SPECTROSCOPY Absolute Optical Frequency Metrology ST Cundiff, L Hollberg 82 Fourier Transform Spectroscopy T Fromherz 90 Hadamard Spectroscopy and Imaging RA DeVerse, RM Hammaker, WG Fateley, FB Geshwind, AC Coppi 100 Nonlinear Laser Spectroscopy P Ewart 109 Raman Spectroscopy RWithnall 119 Second-Harm

Unit-1: Introduction and Classification of algae (04L) i) Prokaryotic and Eukaryotic algae ii) Classification of algae according to F. E. Fritsch (1945), G.W. Prescott and Parker (1982)