# Towards the Quantification of 5f Delocalization  
[PERSON]  
1 Departments of Physics and Chemistry, University of Wisconsin-Oshkosh, Oshkosh, WI 54901, USA 1  
[PERSON]  
2 SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA 2  
[PERSON]  
3 Lawrence Livermore National Laboratory, Livermore, CA 94550, USA; [EMAIL_ADDRESS]  
[PERSON]  
2 SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA 2  
[PERSON]  
2 SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA 2  
[PERSON]  
2 SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA 2  
[PERSON]  
2 SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA 2  
[PERSON]  
2 SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA 2  
Footnote 2: email: {[EMAIL_ADDRESS]}, {dsokaras@slac.  
Figure 1: The N4,5 X-ray Absorption Spectroscopy (XAS) of uranium dioxide and 8-Pu(Ga) are shown here. Note the significant reduction in the intensity of the Pu 4d\({}_{3/2}\) peak relative to that of the U in uranium dioxide. (The spectra are normalized with the 4d\({}_{5/2}\) level.) This has been shown to be due to the population of the 5f levels: n = 2 for UO\({}_{2}\) and n = 5 for Pu [2,10,11]. The UO\({}_{2}\) spectrum is courtesy of [PERSON], Lawrence Berkeley National Laboratory (LBNL).  
Figure 2: The N\({}_{4,5}\) XAS spectra of UF\({}_{4}\) and \(\alpha\)-U are shown here, analogous to Figure 1. UF\({}_{4}\) is a localized n = 2 system, very similar to UO\({}_{2}\)[2]. The data are originally from [PERSON], [PERSON], [PERSON] and [PERSON] [21]. The figure is reproduced from [27]. Note that the two spectra cannot be distinguished; they have the same BR.  
From other measurements and analyses, it has long been accepted that \(\alpha\)-U has three 5f electrons and that there is significant delocalization in the 5f states [10; 12; 17; 28]. An example of this is shown below in Figure 3. In Figure 3, the BIS of [PERSON] et al. [18] is compared to the calculations of [PERSON] [10; 29; 1]. The agreement between the BIS and the Unoccupied density of states (UDOS) derived from [PERSON]'s calculations is very good. Moreover, the underlying j-specific calculations demonstrate the admixture of the 5f\({}_{5/2}\) and 5f\({}_{7/2}\) states, consistent with strong delocalization.  
The essence of the problem is that the BR approach works very well for localized systems but cannot rule out the possibility of delocalization with a slightly different number of 5f electrons. However, there now appears to be a solution to this \"blind spot.\" Recently, it has been shown that the M\({}_{4,5}\) X-ray Emission Spectroscopy of UF\({}_{4}\)[30] exhibits results consistent with the Intermediate Coupling Model of [PERSON] and [PERSON] [22]. Normalizing to the 6p \(\rightarrow\) 3d peaks, it can be seen that there is a tremendous differential in the intensities of the 5f peaks in the two spectra, a factor of 5. Figure 4 (The X-ray Emission Spectroscopy (XES) results for UO\({}_{2}\) are very similar to those of UF\({}_{4}\)[30] and are omitted here.) It has been shown that this is consistent with the almost pure n\({}_{5/2}\) nature of the  
Figure 3: Comparison of the Bremstrahlung Isochromat Spectroscopy (BIS) results of [PERSON] and [PERSON] [18] with the Unoccupied density of states (UDOS) derived from the theory by [PERSON] [10]. In the lower panel, the unsmoothed 5f\({}_{5/2}\) calculation is shown in red, the unsmoothed 5f\({}_{7/2}\) calculation is shown in green, the partially smoothed total is the jagged black line and the UDOS is shown by the very smooth, heavier black line. The UDOS was derived by applying an inverse Fermi function and more extensive smoothing to the total.  
two 5f electrons in UF\({}_{4}\) and strong, albeit not complete, adherence to electric dipole select rules. It will be demonstrated here that this type of data will provide (1) a direct pathway to the experimentally driven discernment of the localized n = 2 and delocalized n = 3 cases in particular and (2) the degree of delocalization in 5f systems in general.