# The Limitations of 5f Delocalization and Dispersion
## 4 ARPES of \(\alpha\)-U  
Metallic \(\alpha\)-U has been studied by [PERSON] et al. [24; 25], using angle resolved photoelectron spectroscopy [32], to probe a single crystal of \(\alpha\)-U. Examples of their data are shown in Figure 6. These spectra can be compared to those reported earlier in the 1970s and 1980s. It should be noted that [PERSON]'s spectra are significantly different than those for UO\({}_{2}\)[15; 33; 34], but quite consistent with those for \(\alpha\)-U [15; 33; 35]. This strongly suggests that their data are valid. Nevertheless, it is likely that the surface in these studies was not as clean as asserted. Here are three reasons. (1) XPS has a sensitivity problem with the O1s. This makes it difficult to accurately assess how clean or dirty a sample was based solely on the O1s XPS, because low coverage yet potentially significant levels of O contamination might not be detected (see Figure 6 of Reference [32]). (2) The peak at \(-\)5 eV binding energy (Figure 4 of Reference [25]) has been identified as oxygen derived (see Figure 7 of Reference [32]). There are also papers on U that have a similar assignment [15; 33; 34]. (3) The peak between the 6p\({}_{3/2}\) and 6p\({}_{1/2}\) is probably oxygen as well (see Figure 5 of Reference [24] and Figure 10 of Reference [32]). However, this level of oxygen contamination may not be sufficient to invalidate the ARPES experiment, only complicate it. Assuming that the sample is still clean enough and the band-mapping valid, an important conclusion can be drawn: the U 5f levels show little if any dispersion and exhibit no clear dependence upon symmetry points in the BZ. Consider what can be gleaned from Figure 6 (the Fermi energy is at 0 eV). First, examine the angle resolved spectra shown in Figure 6, for excitation with HeI (hv \(\sim\)21 eV) and HeII (hv \(\sim\)41 eV) radiation and with normal emission. It is well known that the 5f cross section rises dramatically between hv = 21 and 41 eV, as shown in the right panel of Figure 6, using data from the calculations by [PERSON] and [PERSON] [36]. Thus, any 5f derived peak should show a substantial rise between hv = 21 eV and hv = 41 eV. This only occurs for the peaks adjacent to the Fermi level. A careful examination of the spectra leads to two observations: (1) the peak immediately adjacent to the Fermi level (B\({}^{\rm F}\sim\)0 eV) is clearly of predominantly 5f character; (2) the peak at binding energy of \(\sim\) 1/3 eV does not rise as substantially, but still may be of 5f character. The assignment of these two peaks as 5f is supported by comparison with [PERSON]'s calculations in Figure 2, where a pair of peaks is observed below the Fermi energy, although extending away more from the Fermi energy than is reported experimentally. An important observation is that the two peaks near the Fermi energy, both of 5f character, do not disperse with hv and thus do not disperse with k\({}_{\perp}\). Under the conditions of normal emission, k\({}_{\parallel}\) = 0 and k\({}_{\perp}\) = k. Changing hv under these conditions keeps k\({}_{\parallel}\) constant and only varies k\({}_{\perp}\). Hence, this is a test, albeit a fairly rough and incomplete one, of the possible dispersion with k\({}_{\perp}\). The result is that no dispersion with k\({}_{\perp}\) is observed. The k\({}_{\parallel}\) dependence is addressed in the insets. A further consideration of the pseudo three-dimensional mapping in the upper insets clearly shows that the peaks nearest the Fermi level (1) do not disperse significantly or systematically with k\({}_{\parallel}\), (2) do not behave symmetrically around high symmetry lines in the BZ and (2) do not agree with theory. Thus, ARPES does not provide the desired fingerprint of 5f delocalization, even in single crystal \(\alpha\)-U.