Multiconfigurational nature of 5f orbitals in and plutonium intermetallics

C.H. Bootha,1, Yu Jianga, D.L. Wangb, J.N. Mitchellc, P.H. Tobashc, E.D. Bauerd, M.A. Walle, P.G. Allene, D. Sokarasf, D. Nordlundf, T.-C. Wengf, M.A. Torrezd, and J.L. Sarraog

aChemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720; bNuclear Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720; cMaterials Science and Technology Division, Los Alamos National Laboratory, Los Alamos, NM 87545; dMaterials Physics and Applications Division, Los Alamos National Laboratory, Los Alamos, NM 87545; eCondensed Matter and Materials Division, Livermore National Laboratory, Livermore, CA 94550; fStanford Synchrotron Radiation Lightsource, SLAC National Accelerator Laboratory, Menlo Park, CA 94025; and gScience Program Office-Office of Science, Los Alamos National Laboratory, Los Alamos, NM 87545

Edited by* Zachary Fisk, University of California, Irvine, Irvine, CA, and approved May 4, 2012 (received for review January 13, 2012)

Uranium and plutonium’s 5f are tenuously poised be- and orbital components of the angular momentum (11)—impor- tween strongly bonding with ligand spd-states and residing close tant quantities for understanding the absence of magnetism in to the nucleus. The unusual properties of these elements and their plutonium (12). These results rely on fractional f-occupancies compounds (e.g., the six different allotropes of elemental pluto- especially in the delocalized channel. Recent Dynamical Mean- nium) are widely believed to depend on the related attributes of Field Theory (DMFT) calculations by Shim, Haule, and Kotliar f-orbital occupancy and delocalization for which a quantitative (13) suggest that, whereas the average f-occupancy is an impor- measure is lacking. By employing resonant X-ray emission spectro- tant quantity, the actual ground state in elemental plutonium scopy (RXES) and X-ray absorption near-edge structure (XANES) may require a more complete description. In particular, they spectroscopy and making comparisons to specific heat measure- find that unlike cerium and ytterbium intermetallics that are de- ments, we demonstrate the presence of multiconfigurational scribed as dominated by two valence configurations (f 0 and f 1 for f-orbital states in the elements U and Pu and in a wide Ce4þ and Ce3þ and f 13 and f 14 for Yb3þ and Yb2þ), a description range of uranium and plutonium intermetallic compounds. These of elemental plutonium actually requires three valence configura- results provide a robust experimental basis for a new framework tions, f 4,f5, and f 6. Here, we present both X-ray absorption near- toward understanding the strongly-correlated behavior of actinide edge structure (XANES) and resonant X-ray emission spectro- materials. scopy (RXES) data collected at the actinide L3 edge in a wide variety of uranium and plutonium intermetallics that not only local moment magnetism ∣ intermediate valence ∣ strongly correlated point to the necessity of a multiconfigurational ground state for systems understanding elemental plutonium but also demonstrate the wide applicability of such multiconfigurational ground states in

he magnetic and electronic properties of actinide (An) mate- actinide intermetallics in general. SCIENCES There are some advantages to using L3-edge spectroscopy for Trials have long defied understanding, where scientists prior to APPLIED PHYSICAL World War II (and even Mendeleev) placed the actinide series obtaining f-occupancies, especially for multiconfigurational underneath the 5d transition series in the periodic table. The states. At this X-ray absorption edge, a 2p3∕2 core is reason for such confusion is that the 5f orbital is intermediate excited primarily into a state of d symmetry where the number between localized, as generally are the 4f orbitals in the lantha- of unoccupied 6d states is only a weak function of the f-occupancy nide series, and delocalized, such as occurs in the d-orbitals of (Fig. 1A). If a multiconfigurational f-state exists, its otherwise- the transition metals. In those two limiting cases, well-defined degenerate components are split by the core-hole interaction as methodologies exist that account for their magnetic behavior the different number of f-electrons in each configuration screen such as Hund’s Rules, crystal-field theory, and quenched angular the core hole differently. Because the total number of unoccupied momentum theory. No similarly successful theory exists for the d-states is approximately fixed, the excitation amplitude into any intermediate localization that occurs in elemental U, Np, and Pu, split states is proportional to that particular configuration’s elec- and their intermetallic compounds; yet, the consequences are tronic occupancy. By associating a given peak with a particular likely fundamental toward understanding their complex behavior configuration, the relative weight to each configuration can be (1, 2). simply determined. For instance, in RXES results on Yb inter- Although the degree of f-electron localization is widely recog- metallics (14, 15), the integrated intensity I13 and I14 of features 13 14 nized as the dominant factor in determining the structural, mag- identified as due to the f and f configurations give the f-hole netic, and electronic properties of the , for instance, in occupancy nf ¼ I13∕ðI13 þ I14Þ. Similar methods have long been determining basic crystal bonding (3), experimental methods for applied in XANES spectroscopy (16). Whereas these measure- determining the f-orbital occupancy have generally failed to yield ments give the f-occupancy and configuration fractions in the quantitative measurements though some exceptions exist. For excited state, which includes the core hole and the outgoing example, elemental Pu is thought to have an f-orbital occupancy photoelectron, such final-state occupancies are within several near 5, close to that expected for a 5f 5 ground-state configuration percent of those obtained using more sophisticated treatments 3þ (Pu ) based on photoemission, N4;5-edge X-ray absorption, and for deep core-level excitations (17). electron-energy loss spectroscopy (4, 5). In addition to these ex- amples, several researchers have shown that so-called “two-fluid” “ ” Author contributions: C.H.B., Y.J., E.D.B., P.G.A., D.S., D.N., and T.-C.W. designed research; or dual nature models of the 5f orbitals, whereby some fraction C.H.B., Y.J., D.L.W., E.D.B., D.S., D.N., and T.-C.W. performed research; J.N.M., P.H.T., E.D.B., of the f-electrons contribute to delocalized behavior and the rest M.A.W., M.A.T., and J.L.S. contributed new reagents/analytic tools; C.H.B. and Y.J. analyzed contribute to the more localized local moment behavior, can suc- data; and C.H.B. and E.D.B. wrote the paper. cessfully describe some properties (6) such as coexistent antifer- The authors declare no conflict of interest. romagnetism and superconductivity in CeRhIn5 (7), the inelastic *This Direct Submission article had a prearranged editor. neutron scattering of UPd2Al3 (8), de Haas-van Alphen frequen- 1To whom correspondence should be addressed. E-mail: [email protected]. cies of UPt3 (9), and the photoemission spectra of PuCoGa5 and This article contains supporting information online at www.pnas.org/lookup/suppl/ PuIn3 (10). Such mixed behavior also manifests itself in the spin doi:10.1073/pnas.1200725109/-/DCSupplemental.

www.pnas.org/cgi/doi/10.1073/pnas.1200725109 PNAS ∣ June 26, 2012 ∣ vol. 109 ∣ no. 26 ∣ 10205–10209 Downloaded by guest on September 29, 2021 A B

CD

Fig. 1. Actinide L3-edge follows strongly correlated electron behavior. (A) Energy level diagram demonstrating the dominant transitions and the final state

splitting due to the generation of the core hole as well as the final states relationship to EI and ET for the RXES data. Note that other decay channels between the intermediate and final state configurations also occur (for instance, from a f4 intermediate state to an f5 final state); we have chosen only to illustrate the dominant channels for clarity. The intermediate states in the middle of the diagram represent the final state for the XANES data shown in (B). (B) Repre- sentative results from Pu L3 edge XANES spectroscopy. (C, D) Linear coefficient of the low temperature specific heat in the normal state (γ) as a function of the shift of the peak in the white line relative to the α-An sample. Many of the γ values come from the literature (12, 19, 31–48). These results are available in tabular form in SI Text together with individual references for the γ values.

In this study, the An L3-edge XANES data collected from α-U, in SI Text.) As shown in Fig. 1 C and D, there is a strong correla- α-Pu, and δ-Pu (1.9 at% Ga) along with 17 other uranium and tion between ΔEα and the degree of localization of the 5f elec- nine plutonium intermetallic samples delineate the correspon- trons, as measured by γ. This correspondence is explained by dence between the edge position and localization of the 5f elec- considering that the higher f-occupancy (i.e., larger γ) implies trons. Pu L3-edge XANES data are shown for typical Pu materials more localized f-electrons are available for screening the 2p3∕2 from this study in Fig. 1B. Similar U data are in SI Text. The posi- core hole generating a more negative ΔEα, as observed. tion of the main peak, known as the “white line” position, is These XANES results indicate that the final-state shifts of the shown in Fig. 1 C and D as a function of the shift from the white- white line correlate well with a ground-state measurement of the line position of the α-phase of the actinide (i.e., α-U or α-Pu), density of states. Whereas individual peaks are not observed in ΔEα. Large shifts in ΔEα are observed as are broadened the white lines (Fig. 1B), there appears to be a correspondence white-line features for some compounds. Individual peaks are not between the width of the white line and the overall energy shift observed and so obtaining state configuration fractions is not pos- consistent with two or more configurations, though possibly also sible from these data. The Sommerfeld coefficient to the linear indicating a broader 6d band. Focusing on the U intermetallics, component of the low-temperature specific heat (γ) is used as a ΔEα > 6.5 eV between the end-point samples UCd11 and α-U. measure of the degree of localization. The value of γ often is the Using energy shifts between known oxidation states, for instance, defining quantity for heavy-fermion behavior because it is pro- between U3þ and U4þ oxides, a change of one electron corre- portional to the effective carrier mass; that is, it is proportional sponds to about 4 eV. A similar value is found between Pu oxides to the density of states at the Fermi level. In this sense, the flatter (20). A 6.5 eV shift implies a change in f-occupancy of nearly 1.5 bands have a large linear specific heat and are considered to have electrons. Whereas this is possible, we point out that a ∼1.5 eV 2 more localized character due to a higher f-orbital occupancy (18). shift is observed between UPd3, which has an f configuration This higher occupancy could be due to f-orbital hybridization with and is one of the few An intermetallic materials measured with the conduction band, as in a Kondo model, or due to direct in- a relatively well-known f-occupancy (21) and UO2, which is also volvement of the f-band at the Fermi level that is uncommon in f 2. We contend that such a shift is due to greater screening of the . In the case of samples with magnetic transitions the core hole in UPd3 due to conduction electrons (22). Such (many of the more localized materials are antiferromagnetic in conduction electron screening reduces the Coulombic attraction their ground state), γ is determined at temperatures above any between the core hole and the photoelectron and may also affect transitions to remove the effect of changes in magnetic degrees excitations into the lower unoccupied d-states just above the of freedom (19). Some of these transition temperatures are as Fermi level. Although this effect will be roughly constant between high as 30 K and so large errors are reported due to the larger metals, it makes determining f-occupancy from the measured contribution of phonon vibrations to the specific heat at such edge shifts less reliable. temperatures. (More information regarding the specific heat in- To gain quantitative information about the valence in elemen- cluding all the values of γ and transition temperatures is available tal U and Pu and their compounds, U and Pu L3-edge RXES

10206 ∣ www.pnas.org/cgi/doi/10.1073/pnas.1200725109 Booth et al. Downloaded by guest on September 29, 2021 data (23–26) were collected at the An Lα1 emission line (3d5∕2 → continuum. To determine the individual contributions to that line 2p3∕2 corresponding to an emission energy EE of about 14.2 keV shape, we follow standard procedures set forth by Dallera et al. for Pu and 13.6 keV for U) (Fig. 1A). Fig. 2 shows the RXES (14, 15) and find a Lorentzian line shape for the fluorescence and and the X-ray emission spectra (XES) for UCd11 and α-Pu at sev- the discrete excitation contributions. In general, three excitations eral incident energies EI as a function of the transfer energy, are required to fit most of the data. Although ET varies by 1 or 3 6 ET ¼ EI − EE. Data on PuSb2, UCoGa5, and δ-Pu are available 2 eV with EI for the lowest-ET excitation (the f UL3 and the f in SI Text. Because excitations into the continuum imply that for Pu L3), these three excitations remain well separated by about states are always available above a threshold energy and EE has 4eVinET , consistent with a difference of one electron occu- a constant distribution for these states, ET ∝ EI for fluorescence pancy for each state. The relative weights of each configuration lines. Excitations into unoccupied states with discrete energy le- and the fluorescence peak are shown in Fig. 3 as a function of EI . vels, on the other hand, have a distribution with a constant ET as The total configuration fractions are then obtained by integrating a function of EI. Fig. 2 (Top) shows data collected well below the these results over EI (Table 1). Absolute errors are estimated fluorescence threshold with excitations that are at approximately by altering the line shape for the standard discrete excitation fixed ET as EI is increased in Fig. 2 (Bottom), though the ampli- and are about 10% (see SI Text). Relative errors between these tude of the three individual features varies with EI . It is important measurements are about 2%. (Unfortunately, the PuSb2 data do to note that excitations into states below the fluorescence thresh- not allow for such a determination because the bandwidth-related old are not, in fact, discrete in these materials but have a finite shifts in ET are too large) (see SI Text). Whereas these below- bandwidth and so ET is expected to vary as much as a few eV. threshold excitations allow for a measurement of the state config- Fig. 2 B and D show the fluorescence line as a dominant feature uration fractions and the overall f-occupancy, the RXES data also with a ET that will increase linearly as EI increases further. allow for the determination of the fluorescence threshold energy These RXES data clearly show changes in line shape due to shifts. These shifts (Fig. 3 C and F) indicate differences in the total multiple excitation features as a function of incident energy— screening of the core hole and include the effect of differences in made possible by the improved resolution of this technique (27), the conduction electron density. which is set here by the 3d5∕2 orbital (about 4 eV) rather than the These results have important implications for understanding 2p3∕2 (7–10 eV) and the ability to separate excitations into the the nature of the ground states for all the measured actinide

A 0.08 C 0.15 UCd 17,160 eV α -Pu 18,058 eV 0.06 11 0.10 0.04 0.05 0.02

0.00 0.00

0.08 17,166 eV 0.15 18,062 eV 0.06

0.10 SCIENCES 0.04

0.05 APPLIED PHYSICAL 0.02

0.00 0.00

0.08 17,168 eV 0.15 18,064 eV 0.06 0.10 0.04 0.05 0.02 Normalized emission Normalized emission 0.00 0.00

total fit total fit 0.08 17,177 eV 0.15 18,078 eV fluorescence fluorescence 0.06 peak at 3,548 eV 0.10 peak at 3,783 eV 0.04 peak at 3,552 eV peak at 3,787 eV peak at 3,556 eV 0.05 peak at 3,791 eV 0.02

0.00 0.00 3,530 3,540 3,550 3,560 3,570 3,580 3,760 3,770 3,780 3,790 3,800 3,810 3,820 E E T T B D

Fig. 2. XES and RXES data on actinide intermetallics. Representative XES (A) and RXES (B) for UCd11 as an example of a strongly localized An intermetallic. (C, D), Analogous data for α-Pu as an example of a more delocalized An intermetallic. The colors in the RXES data represent the normalized emission flux. Note the clearly sharper resonance in the XES and RXES (yellow peak) plots for the UCd11 compared to the α-Pu data. Similar results for UCoGa5, PuSb2, and δ-Pu are available in SI Text.

Booth et al. PNAS ∣ June 26, 2012 ∣ vol. 109 ∣ no. 26 ∣ 10207 Downloaded by guest on September 29, 2021 2.0 UCd 1.5 ααα-Pu 11 1.5 1.0 1.0 0.5 0.5 A D 0.0 0.0

2.0 UCoGa 1.5 δδδ-Pu 5 1.5 3,783 eV 3,548 eV 1.0 3,787 eV 1.0 3,552 eV 3,791 eV 3,556 eV 0.5 0.5 B E 0.0 0.0 1.2 1.2 Normalized peak coefficient peak Normalized coefficient peak Normalized 1.0 1.0 0.8 0.8 PuSb 0.6 UCd 0.6 2 11 δ-Pu 0.4 UCoGa 0.4 5 α-Pu 0.2 C 0.2 F 0.0 0.0 17,140 17,150 17,160 17,170 17,180 17,190 18,040 18,050 18,060 18,070 18,080 18,090 E (eV) E (eV) I I

Fig. 3. Multiconfigurational orbital weights. Relative weights of the principle components to (A, B) the discrete-state excitation and the (C) fluorescence spectra for the measured U intermetallic samples. (D–F) Analogous data from the Pu intermetallics. In the case of the U intermetallics, we assign the excitations at transfer energies of 3548 eV, 3552 eV, and 3556 eV to f3,f2, and f1 configurations based on comparisons to the oxide. Likewise, for the Pu intermetallics, the excitations at 3783 eV, 3787 eV, and 3791 eV are assigned to f6,f5, and f4 configurations. The threshold energy shift in (C) is about 2.2 eV, and in (D) is about 4.5 eV. Discrete-state peak coefficients for PuSb2 are somewhat different and are available in SI Text.

materials in Fig. 1. In particular, Pu in the α- and δ-forms is best Materials and Methods described with partially delocalized and strongly multiconfigura- Sample Preparation. Metallic δ-and α-phase samples were first melted and tional f-orbitals to explain observed changes in the XANES and then high temperature annealed to remove any lattice defects and He gas the broad features in the RXES, each as compared to data from that accumulated while aging at room temperature. Subsequently, 2.3 mm diameter discs were punch pressed, lapped, and polished using a succession more localized samples such as UCd11 and PuSb2. Indeed, qua- of finer grit lapping films ending in a 1 μm surface finish and a final thickness litative agreement is obtained with DMFT calculations (13) for μ 4 5 6 of 70 m. The samples were then dip coated with liquid Kapton and cured at the configuration f ,f , and f fractions in δ-Pu that indicate 150 °C for 2 h. This encasement greatly reduces the oxidation of the metallic 5 about 60% f configuration compared to about 38 10% mea- Pu over time. The final curing at 150 °C also reverts any potential damage or sured here (see Table 1 caption for discussion of error estimates). phase due to the mechanical polishing process. All sample preparation/pro- In addition, DMFT predicts a difference in the total f-occupation cessing was done in an inert atmosphere glove box for safety and for the minimizing of the continuous oxidative nature of these materials. Δnf ¼ 0.2 between α—and δ-Pu, whereas the RXES results give Single crystals of all Pu intermetallic compounds were grown by the Δnf ¼ 0.12 0.02 (Table 1). Furthermore, within the estimated molten metal flux growth technique (28) as were single crystals of UCoGa5, absolute errors, a multiconfigurational ground state occurs even UM2Zn20 (M ¼ Fe, Co, Ru), USn3, UCd11, and U2Zn17. Polycrystalline samples for our most localized actinide sample, i.e., UCd11, raising the of UAuCu4,UAu3Ni2, UCu5, UPt3,UNi2Al3, URu2Si2, UPd2Al3, and UPd3 were 3þ fundamental question of whether any true U intermetallic synthesized by arc melting the elements on a water-cooled Cu hearth with a compound actually exists. Our results not only provide an accu- Zr getter under an ultrahigh pressure (UHP) Ar atmosphere. In some cases, rate measure of the f-occupancy in plutonium for the first time, the arc-melted samples were annealed under vacuum to improve crystallinity. they advance a new paradigm for understanding the light acti- XANES. nides based upon a 5f-electron multiconfigurational ground state Nearly all of the X-ray data were collected in fluorescence mode on “ ” single solid pieces of material. Exceptions are XANES data from PuCoGa5, that goes far beyond a dual nature scenario. PuGa3, and PuAl2. Each of these samples was ground with a mortar and pes- tle and passed through a 30 μm sieve. The resulting powder was mixed with Table 1. f-orbital occupancy and configuration fraction boron nitride or, in the case of PuAl2 only, brushed onto clear adhesive tape. measurements XANES data from these powder samples were collected in transmission Configuration fractions mode. The samples were loaded into a LHe-flow cryostat and data were col- lected with the samples near 30 K, though no changes with temperature have 1 2 3 Sample nf f f f been observed up to room temperature. All fluorescence data in Fig. 1 were measured on beamline 10–2or11–2 at the Stanford Synchrotron Radiation UCd11 2.71 0.07 0.15 0.78 Lightsource (SSRL) over a period of 10 y before and after the upgrade to that UCoGa5 1.92 0.32 0.44 0.24 facility that took place in 2003. All data were collected using a double-crystal f4 f5 f6 Si(220) monochromator half-tuned to remove unwanted harmonic energies from the X-ray beam. The fluorescence data were collected using a multiele- δ-Pu (1.9% Ga) 5.28 0.17 0.38 0.45 ment, solid-state, Ge detector and were corrected for dead time and were α-Pu 5.16 0.19 0.46 0.35 also corrected for self-absorption using the program FLUO (29). All mono- Values of the f-orbital occupancies, nf , are determined by the weighted chromator energies were calibrated to the first inflection point of the L3 edge sum of the integrated intensities from each configuration peak in Fig. 3A, absorption from UO2 at 17,166.0 eV (30) or PuO2 at 18,062.3 eV (20). B, D, and E. For example, nf ¼ð4I4 þ 5I5 þ 6I6Þ∕ðI4 þ I5 þ I6Þ where I4 is the 4 integrated intensity of the f peak, etc. Absolute errors are estimated by RXES. RXES data were collected at room temperature using the a seven-crystal altering the line shape for the standard discrete excitation and are about Johann-type X-ray emission spectrometer (25) at the wiggler beamline 6-2 10%. Relative errors between these measurements are about 2%. that incorporates a LN2 cooled double-crystal Si(311) monochromator and

10208 ∣ www.pnas.org/cgi/doi/10.1073/pnas.1200725109 Booth et al. Downloaded by guest on September 29, 2021 Rh-coated collimating and focusing mirrors. U Lα1 (13.6 keV) emission was mea- the width of each peak is due to the convolution of the spectrometer and the sured using Ge(777) analyzer crystals, and Pu Lα1 (14.2 keV) emission was mea- final-state lifetime. Difference cuts along EI showed the broadening by the sured using Si(777) analyzer crystals. The analyzer energy was calibrated using intermediate-state lifetime and the mono. the nearby elastic peak from the 999 reflection and the already-calibrated In addition, below threshold the fluorescence peak was held to zero am- monochromator energy. The resolution was measured from the elastically scat- plitude to avoid correlations with the other peaks, mostly the f4 peak for the tered beam to be 1.4 eVand 1.7 eV, respectively, at the An Lα1 emission energies. Pu L3-edge RXES data. This constraint is not required if ET is not allowed to Determination of the line shapes follows the methods of Dallera et al. vary as a function of EI, and such fits generate configuration fractions within (14). The intrinsic lifetime broadening (27) of any observed features is set the stated error estimates, though the fits are of poorer quality; however, the by the 3d5∕2 orbital (approximately 4 eV) rather than the 2p3∕2 (7–10 eV). fluorescence threshold in these fixed-ET fits is less well defined than shown in The fluorescence peak line shape and position were determined at an EI the floating-ET fit results in Fig. 3 C and F. An important improvement to E ¼ that was well above threshold. The U L3 edge data were fit using Lα1 these methods will be better defining the relationship between the fluores- 13;616.1 eV (UCd11) or 13,617.1 eV (UCoGa5) and a width ΓF ¼ 5.9 eV. The cence peaks and the below-threshold peaks. Pu L3 edge data were fit using E α1 ¼ 1;477.7 eV and a width ΓF ¼ 6.5 eV. L As a final note, an acceptable (but much lower quality) fit can be obtained The normalized emission line shape from the discrete excitations was ob- to the entire RXES spectra with the full Kramers-Heisenberg (KH) formula (23, tained well below threshold for the most localized samples measured, 25) using three discrete and three fluorescence peaks giving lower estimates namely UCd11 and PuSb2. These data were fit with a skewed Lorentzian: n n ¼ 5 2 δ α of f (e.g., f . for -Pu and 5.0 for -Pu). We attribute the low quality of 2 I Γ αðE − hE iÞ these fits to the bandwidth effects in determining ET (not accounted for in E ¼ W S 1 þ erf Tpffiffiffi T ; [1] 2 2 such fits) and the use of perturbation theory in deriving the KH formula. I0 π½ðET − hET iÞ þ ΓS 2ΓS ACKNOWLEDGMENTS. where W is the weight coefficient at fixed hET i for a given EI and erf is the error Work at Lawrence Berkeley National Laboratory supported by the Director, Office of Science, Office of Basic Energy Sciences function. The excitation width is ΓS ¼ 3.3 eV and the skew parameter is α ¼ 0.29 (OBES), of the U.S. Department of Energy (DOE) under Contract No. DE-AC02- for the U edge data and ΓS ¼ 4.7 eV and α ¼ 0.30 for the Pu edge data. 05CH11231. The authors acknowledge enlightening conversations with Once the line shape parameters were determined, an average hET i was J. A. Bradley, G. Kotliar, G. H. Lander, J.-P. Rueff, J. Seidler, J. D. Thompson, E found for each of the three discrete states as a function of I. These values and Z. Fisk. X-ray absorption and RXES data were collected at the Stanford E were then fixed for the reported results at all I except for the first peak (the Synchrotron Radiation Lightsource, a national user facility operated by Stan- 3 6 f peak for U edge and the f peak for the Pu edge data). As noted in the ford University on behalf of the DOE, Office of Basic Energy Sciences. Work at text, this energy shifts by 1–2 eV possibly due to a broad band for this Los Alamos National Laboratory (LANL) was performed under the auspices of configuration. This shift is severe enough in the PuSb2 data so as to make the U.S. DOE, OBES, Division of Materials Sciences and Engineering and it impossible to fit for individual f-configurations (see SI Text). Also, note that funded in part by the LANL Directed Research and Development program.

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