A determination of the angular distribution parameter beta of the 3d and 4s main lines of atomic scandium in the resonance region of the 3p-- \u3e nd,ms excitations has been carried out using electron spectrometry in conjunction with monochromatized synchrotron radiation., These measurements reveal strong variations of beta8 throughout the entire resonance region, highlighting the complicated nature of the ionization process for this first and seemingly simple 3d transition metal. The beta values-of the photoelectrons resulting in 4s subshell, ionization deviate significantly from 2.0 in qualitative, but not-quantitative, agreement with recent many-body perturbation-theory calculations

Bjelland, M.

Jiménez-Mier, J.

Krause, M. O.

Myers, T.

Olalde-Velasco, P.

Wehlitz, R.

Whitfield, S. B.

English

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University of Central Florida STARS Faculty Bibliography 2000s Faculty Bibliography 1-1-2002 Angular distributions of the atomic scandium 3d and 4s photoelectrons in the region of the 3p - > 3d giant resonance S. B. Whitfield T. Myers M. Bjelland R. Wehlitz J. Jiménez-Mier See next page for additional authors Find similar works at: https://stars.library.ucf.edu/facultybib2000 University of Central Florida Libraries http://library.ucf.edu This Article is brought to you for free and open access by the Faculty Bibliography at STARS. It has been accepted for inclusion in Faculty Bibliography 2000s by an authorized administrator of STARS. For more information, please contact STARS@ucf.edu. Recommended Citation Whitfield, S. B.; Myers, T.; Bjelland, M.; Wehlitz, R.; Jiménez-Mier, J.; Olalde-Velasco, P.; and Krause, M. O., "Angular distributions of the atomic scandium 3d and 4s photoelectrons in the region of the 3p - > 3d giant resonance" (2002). Faculty Bibliography 2000s. 3545. https://stars.library.ucf.edu/facultybib2000/3545 Authors S. B. Whitfield, T. Myers, M. Bjelland, R. Wehlitz, J. Jiménez-Mier, P. Olalde-Velasco, and M. O. Krause This article is available at STARS: https://stars.library.ucf.edu/facultybib2000/3545 Angular distributions of the atomic scandium 3d and 4s photoelectronsin the region of the 3p\3d giant resonanceS. B. Whitfield,1,* T. Myers,1 M. Bjelland,2 R. Wehlitz,3 J. Jime´nez-Mier,4 P. Olalde-Velasco,4 and M. O. Krause51Department of Physics and Astronomy, University of Wisconsin-Eau Claire, Eau Claire, Wisconsin 547022Department of Chemistry, University of Wisconsin-Eau Claire, Eau Claire, Wisconsin 547023Synchrotron Radiation Center, University of Wisconsin, Stoughton, Wisconsin 535894Instituto de Ciencias Nucleares, UNAM, 04510 Mexico City, Mexico5Department of Physics, University of Central Florida, Orlando, Florida 32816~Received 31 July 2002; published 5 December 2002!A determination of the angular distribution parameter b of the 3d and 4s main lines of atomic scandium inthe resonance region of the 3p→nd ,ms excitations has been carried out using electron spectrometry inconjunction with monochromatized synchrotron radiation. These measurements reveal strong variations of bthroughout the entire resonance region, highlighting the complicated nature of the ionization process for thisfirst and seemingly simple 3d transition metal. The b values of the photoelectrons resulting in 4s subshellionization deviate significantly from 2.0 in qualitative, but not quantitative, agreement with recent many-bodyperturbation-theory calculations.DOI: 10.1103/PhysRevA.66.060701 PACS number~s!: 32.80.Fb, 32.80.DzThe experimental determination of the angular distribu-tion parameter b of photoelectrons provides a crucial test fortheoretical methods beyond that provided by partial crosssections alone. This is because b depends on the relativephases of the outgoing partial waves in addition to the tran-sition matrix elements. Open-shell atoms add yet anotherlayer of complexity, because there are typically three differ-ent terms that characterize the final state of the ion plus pho-toelectron; while for closed shell atoms there is only one, a1P term ~we restrict our discussion to dipole transitionsonly!. Even for the photoemission of a single partial wave,the presence of these additional terms can lead to interestingeffects in the photoionization process, which cannot occur inclosed-shell atoms. A prime example is the s-subshell photo-ionization where even in the absence of relativistic effects bof the photoelectrons can deviate significantly from 2.0@1–5#. For s-subshells of closed-shell atoms in the absence ofrelativistic effects, b is always 2.0. Despite such intrinsicallyinteresting effects that can arise in the photoionization ofopen-shell atoms, there are still relatively few studies ofthem as compared to what has been done on closed-shellatoms, chiefly the rare gases, and far fewer involving angulardistribution measurements. This can largely be attributed tothe difficulty in producing a usable atomic beam of open-shell atoms.Atomic Sc with a lone 3d electron, @Ar#3d4s2(2D3/2), isin principle the simplest open-shell atom to have a partiallyfilled d subshell. This makes detailed studies of atomic Scparticularly attractive both theoretically and experimentally.Following our recent experiments of the partial cross sec-tions of the 3d and 4s main and satellite lines of atomic Scin the region of the 3p→3d giant resonance @6#, we reporthere b measurements of the 3d and 4s main lines in thesame photon energy region. These measurements were partlymotivated by recent many-body perturbation theory ~MBPT!calculations of the 4s angular distributions in the 3p→3dresonance region @7#.The experiment was conducted at the University of Wis-consin Synchrotron Radiation Center on the plane gratingmonochromator with an undulator photon source @8#. Energyselected photons from the monochromator are directedthrough a glass capillary into a resistively heated Ta crucible,where Sc atoms are produced by evaporation of the solid.The crucible used in this experiment differs from that usedpreviously @6#, in that it has two slits in it to allow the pho-toelectrons to pass directly from the oven into two analyzersthat are mounted perpendicular to the photon beam at 0° and90° with respect to the polarization vector of the synchrotronradiation. For additional details of the experimental setup seeRefs. @6,9#. At typical oven temperatures of 1170 °C, ther-mal excitation produces 56% of the target atoms in the 2D5/2excited state and 44% in the ground state.The angular distribution parameter b can be determinedfrom the ratio R of the measured intensities at 0° and 90° ifthe degree of linear polarization, p, of the incident photonbeam is known @3#. We measured p to be 0.993~5!. R wascorrected for possible differences in the source volume asseen by the two analyzers as well as for differences in thedetection efficiency of the two analyzers as determined fromNe 2s and 2p calibration spectra. Once b has been obtained,then the relative partial cross section s can be derived fromeither the 0° or the 90° spectrum. Spectra were recordedprimarily in the constant ionic state ~CIS! mode in which aphotoelectron line is scanned synchronously with the photonenergy. The resolution of a CIS spectrum depends solely onthe bandpass of the monochromator. The resolution of theelectron spectrometer only plays a role insofar as it must becapable of isolating single final states of the ion. In this mea-surement we used the same slit settings as previously @6#,where a bandpass of 20~3! meV at 47.7 eV was determined.As in our earlier partial cross section measurements @6#,five different CIS spectra were recorded for each main line ata given angle to cover the photon energy range from 29.0 to40.4 eV. The step size was 10 meV. A detailed explanation ofthe analysis procedures involving the raw CIS scans is givenin Ref. @6#.*Electronic address: whitfisb@uwec.eduRAPID COMMUNICATIONSPHYSICAL REVIEW A 66, 060701~R! ~2002!1050-2947/2002/66~6!/060701~4!/$20.00 ©2002 The American Physical Society66 060701-1A high-resolution photoelectron spectrum ~PES! of theatomic Sc main lines and nearby satellites recorded by the 0°and 90° analyzers at hn535.24(2) eV is shown in Fig. 1.This photon energy corresponds to the maximum value ofthe cross section of the 3d(1S) main line in the region of the3p→3d transitions. As in our earlier paper @6#, we will referto the main lines according to the subshell of the electronremoved in the photoionization process, and not by the ionicstate left behind: thus, the 3d(1S) designation refers to the@Ar#4s2(1S) final-ionic state, and 4s(3,1D) to the@Ar#3d4s(3,1D) final-ionic states. The binding energy scalewas established by setting the 3d(1S) photoline to 8.015 eVas derived from optical data @10#. The lower panel shows theb values for all lines in the spectrum. Both the 0° and 90°spectra have been corrected for background, source volumeasymmetries, and analyzer detection efficiencies. Clearly evi-dent for both 4s lines is a strong deviation from b52.0. Inthe absence of relativistic effects such a deviation from b52.0 is not possible for s-subshell photoelectrons of closed-shell atoms, even in the presence of autoionizing resonances.The significant difference in the b value of the two 4s linescan be attributed to the difference in their spin multiplicities.At this energy we obtain the following b values for the mainlines: b3d(1S)50.76(5), b4s(1D)50.63(5), b4s(3D)50.98(5).The dynamical behavior of b through a series of reso-nances is revealed in greatest detail by employing the CIStechnique. Panels ~a! and ~b! of Figs. 2–4 show the CISspectra of the 3d and 4s main lines recorded at 0° and 90°,respectively, while panel ~c! shows the resulting b curve.Panel ~d! shows our derived partial cross section, s , usingthe 0° spectrum and the b curve. A comparison of thesederived partial cross sections with those measured directly@6# shows excellent overall agreement, which gives us addedconfidence in the accuracy of our b curves. The positions oftwo of the five 3p thresholds, the 3P and the 3F @6#, areindicated in panel ~a! ~the other three thresholds lie above thephoton region shown here!. Also shown are five of the ion-ization thresholds associated with 3p ionization of a second-ary configuration @Ar#3d24s(2D) that mixes with the pri-mary @Ar#3d4s2(2D) ground-state configuration @6,11#. Allvalues of R used to derive the b curves for the main lineswere scaled such that they would yield the same b at hn535.24(2) eV as obtained from our PES results. Thus, sys-tematic errors associated with these PES results could shiftthe curves as a whole. However, the relative error within theb curve is given by the statistical scatter of the data points.These spectra are displayed without any correction to thephoton energy scale, which is estimated to have about a 20meV accuracy. Absolute peak positions of those resonanceslying between 29.0 and 32.0 eV can be found in Ref. @6#.The 3d b curve, Fig. 2, is essentially flat with frequentexcursions. The very noisy region between about 33.2 and 34eV is due to the very low statistics in both the 0° and 90°spectra due to a minimum in the 3d cross section at thisenergy. Perhaps surprisingly, there is almost no variation ofb across the large resonance feature at hn535.24 eV. Thelargest excursion occurs at about 36.7 eV and is due to aresonance that becomes quite prominent in the 90° spectrum,but is hardly seen in the 0° spectrum. The next largest ex-cursion occurs on the lower-energy flank of the resonancestructure that peaks at about 29.6 eV. Very recent calculations@12# of the total cross section of atomic Sc in this photonenergy region have identified this resonance as being com-posed primarily of the 2D3/2→3p54s23d2(1G)2F5/2 and the2D5/2→3p54s23d2(1G)2F7/2 transition, indicating the im-FIG. 1. Top panel, high-resolution photoelectron spectrum of the3d and 4s main lines and nearby satellite lines ~FWHM is 84 meV!recorded at at the maximum of the 3p→3d giant resonance. Thestep size is 15 meV. Bottom panel, b values of the photoelectronlines.FIG. 2. The 3d(1S) main line. ~a! CIS 0° spectrum; ~b! CIS 90°spectrum; ~c! b; ~d! derived partial CIS s spectrum. See text foradditional details.RAPID COMMUNICATIONSWHITFIELD et al. PHYSICAL REVIEW A 66, 060701~R! ~2002!060701-2portance of accounting for photoionization from the excitedstate of the neutral. This feature has a strongly negative bvalue at its minimum, in contrast to the other transitions thatare generally positive. The same sort of windowlike excur-sions also appear on the low-energy flanks of the ‘‘rabbitears’’ at 30.7 and 31.1 eV.The two 4s lines, Figs. 3 and 4, show dramatic deviationsfrom b52.0 throughout the entire resonance region, high-lighting the open-shell character of this atom. Both linesshow qualitatively similar behavior, which is, not surpris-ingly, quite distinct from what is observed for the 3d line.Detailed differences between the two 4s b curves are due tothe different spin multiplicities of the two lines. In both casesb dips substantially from a value of about 1.5 at 29 eV toalmost zero near the center of the feature at 29.6 eV. Whilethe 4s(1D) line continues to show strong modulations overthe next 1.5 eV, the 4s(3D) line essentially returns to itsinitial value of 1.5 before another strong set of modulationsbegin which are associated with the resonances beginning at30.7 eV and continuing to about 31.8 eV. For both 4s lines,and in particular the 4s(1D) line, there are substantial excur-sions in b from about 31.6 eV to about 34.0 eV. As can beseen from the CIS spectra, these are due to the very weakresonances that are scattered throughout this photon energyregion. Only a few of these resonances are visible in the 3dCIS spectra where only the feature just above 32.8 eV exhib-its a large excursion in the 3d b curve. It is worth noting thatthe 4s(3D) line very nearly approaches b52.0 at about 33.4eV. While the 4s(1D) line also reaches a local maximum atthis energy, it is closer to 1.8 than 2.0. In contrast to the 3dline there is a significant change in b for both 4s lines acrossthe large resonance located at 35.2 eV. The rather strongexcursion in b that is seen in both 4s lines near 39.0 eV,particularly the 4s(1D) line, may be due to the presence ofthe 3p(3F) ionization threshold.Figure 5 shows a comparison of our measured b values tothose calculated in Ref. @7#. A convolution procedure @13#using a 20-meV Gaussian profile has been applied to thetheoretical curves so that a direct comparison with experi-ment can be made. As can be seen, there is not particularlygood agreement between theory and experiment. This is notsurprising since these calculations are based on the sameMBPT formalism in LS coupling that was used to obtain thepartial cross sections of the 3d and 4s main lines @14#, whichwere shown earlier @6# to be at variance with experiment.Nevertheless, a detailed comparison does provide some use-ful information. For the experimental 4s(1D) line from 29.0to about 31.4 eV there is partial qualitative agreement withtheory from 29.0 eV to about 32.5 eV. Similarly, for theexperimental 4s(3D) line from 29.0 to about 30.5 eV there isagain partial qualitative agreement with theory from 29.0 to32.5 eV. This suggests that while the absolute magnitudes ofthe transition matrix elements for these excitations aregreatly over estimated @6,14#, their relative magnitudes andphases give b values that are in better agreement with ex-periment. It is also worth noting that the overall magnitudeof the excursions from b52.0 is very consistent betweenexperiment and theory ~most are between b52.0 and 0!,particularly for the 4s(3D) line. Above the large resonanceat 35.2 eV in the experimental CIS spectra, Rydberg excita-tions of the 3p electrons become energetically possible. Ascan be seen from the CIS spectra and the b curves, there isFIG. 3. The 4s(1D) main line. Otherwise as for Fig. 2. FIG. 4. The 4s(3D) main line. Otherwise as for Fig. 2.RAPID COMMUNICATIONSANGULAR DISTRIBUTIONS OF THE ATOMIC . . . PHYSICAL REVIEW A 66, 060701~R! ~2002!060701-3little evidence for any sharp well resolved Rydberg structurein this region, whereas theory predicts many sharp and wellisolated lines. This lack of Rydberg structure in the experi-mental spectra is not due to our bandpass, but is partly theresult of the decay of these excitations into continua associ-ated with the thresholds of the @Ne#3s23p53d24s ionic con-figuration @6,11#. This additional decay pathway causes asubstantial broadening of the Rydberg lines @15,16#. Thisbroadening, in addition to the close spacing of the Rydbergexcitations, leads to the large broad structures observed inthe spectra. A lack of the inclusion of these additional decaypathways is a primary reason the MBPT theory @7,14#predicts a very sharp, well isolated Rydberg structure. Inthe more recent calculations of Martins @12# the@Ne#3s23p53d24s final-ionic states, among many others, areincluded explicitly in the calculation of the photoabsorptioncross section and a much better agreement with experiment@6# is obtained.Finally, one of the interesting predictions made in Ref. @7#is the effect of the interchannel coupling on the 4s b valuesoutside the resonance region investigated here. We lookedfor such effects; unfortunately, the cross section of the 4sphotoelectrons is so small that it was not possible to obtainany off-resonance 4s b values.In conclusion, we have presented a detailed examinationof the angular distributions of the main lines of atomic Sc inthe region of the 3p→3d giant resonance. Our results, par-ticularly for the 4s lines, show strong variations of bthroughout the entire photon energy region examined. Dif-ferences between the two 4s lines arise from their differentspin multiplicities. A comparison of our CIS data with theonly existing angular distribution calculations reveals majordiscrepancies. It is hoped that these results will spur theoriststo make improved calculations for this seemingly simple 3dtransition metal.The authors would like to thank Dr. Zikri Altun and Dr.Steve Manson for making the numerical results of their cal-culations available to us. This work was supported by theResearch Corporation College Cottrell Grant No. CC5243.Support for J.J.M. and P.O.V. was provided by CONACyTProject No. 32204-E. The University of Wisconsin SRC isoperated under the National Science Foundation Grant No.DMR-0084402. Support by the staff at SRC is gratefullyacknowledged.@1# A.F. Starace, R.H. Rast, and S.T. Manson, Phys. Rev. Lett. 38,1522 ~1977!.@2# S.T. Manson and A.F. Starace, Rev. Mod. Phys. 54, 389~1982!.@3# S.B. Whitfield, K. Kehoe, M.O. Krause, and C.D. Caldwell,Phys. Rev. Lett. 84, 4818 ~2000!.@4# H. P. Saha, Phys. Rev. A 66, 010702~R! ~2002!.@5# Z. Felfli, N. C. Deb, D. S. F. Crothers, and A. Z. Msezane J.Phys. B. 35, 419 ~2002!.@6# S.B. Whitfield, K. Kehoe, R. Wehlitz, M.O. Krause, and C.D.Caldwell, Phys. Rev. A 64, 022701 ~2001!.@7# Z. Altun and S.T. Manson, Phys. Rev. A 61, 030702~R! ~2000!.@8# R. Reininger, S.L. Crossley, M.A. Lagergren, M.C. Severson,and R.W.C. Hansen, Nucl. Instrum. Methods Phys. Res. A 347,304 ~1994!.@9# M.O. Krause, T.A. Carlson, and A. Fahlman, Phys. Rev. A 30,1316 ~1984!.@10# J. Sugar and C. Corliss, J. Phys. Chem. Ref. Data Suppl., 14, 1~1985!.@11# H. E. Wetzel, Dissertation, University of Hamburg, 1987, un-published.@12# M. Martins, J. Phys. B 35, L223 ~2002!.@13# J.G. Childers, D.B. Thompson, and N.L.S. Martin, Phys. Rev.A 64, 062703 ~2001!@14# Z. Altun and S.T. Manson, Europhys. Lett. 33, 17 ~1996!;Phys. Rev. A 59, 3576 ~1999!.@15# C.D. Caldwell, M.O. Krause, R.D. Cowan, A. Menzel, S.B.Whitfield, S. Hallman, S.P. Frigo, and M.C. Severson, Phys.Rev. A 59, R926 ~1999!.@16# M. Martins, J. Phys. B 34, 1321 ~2001!.FIG. 5. Comparison of b between theory and experiment. Toptwo panels, 4s(1D); bottom two panels, 4s(3D).RAPID COMMUNICATIONSWHITFIELD et al. PHYSICAL REVIEW A 66, 060701~R! ~2002!060701-4

Angular distributions of the atomic scandium 3d and 4s photoelectrons in the region of the 3p - \u3e 3d giant resonance

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Angular distributions of the atomic scandium 3d and 4s photoelectrons in the region of the 3p - \u3e 3d giant resonance

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