= Solution
In <near-edge X-ray absorption fine structure>, a <photon> promotes a core <electron> into an unoccupied molecular or solid-state level. Near an oxygen K-edge this is principally an O $1s$ excitation. Bound or resonant final states, orbital symmetry, local bonding and multiple scattering shape the edge. A monochromatic tunable X-ray beam can measure transmission through a thin specimen, or fluorescence or <electron> yield as an absorption proxy. In <scanning transmission X-ray microscopy>, a focused spot is scanned while transmitted intensity is recorded; <energy> stacks across an edge distinguish regions with different chemistry even when their thicknesses are similar. A zone plate or another suitable X-ray optic sets spatial resolution, while <energy> resolution and reference spectra control chemical discrimination.
The dipole transition amplitude contains $\mathbf e\cdot\mathbf r$, so the incident electric-field direction selects final-orbital orientations. For an approximately free diatomic molecule with axis $\mathbf n$, the axial $\sigma^*$ transition has strength proportional to $|\mathbf e\cdot\mathbf n|^2$. Summing the two perpendicular $\pi^*$ directions gives strength proportional to $1-|\mathbf e\cdot\mathbf n|^2$, with separate radial matrix-element factors for the two resonance families. This <NEXAFS orientation dependence of a diatomic molecule> explains the complementary <polarization> behavior; the molecular axis is not itself the direction of a $\pi^*$ orbital.
In the supplied geometry, normal incidence has <electric field> parallel to the surface, whereas near-grazing incidence with the illustrated <polarization> has a large surface-normal field component. The single-layer curves show a stronger $\pi^*$ resonance and much weaker $\sigma^*$ structure in the latter geometry. This is consistent with oxygen axes lying largely parallel to the surface: a normal <electric field> is perpendicular to those axes and excites $\pi^*$ efficiently, while suppressing the axial $\sigma^*$ transition. For flat molecules with random in-plane azimuths, the ideal axial factor is $1/2$ for a tangential field and zero for a normal field.
The multilayer curves instead have a strong $\pi^*$ peak at normal incidence and substantially stronger relative $\sigma^*$ response at grazing incidence. Their axes therefore have a substantial surface-normal component, consistent with the proposed tilted, more upright packing. The distinction supports a different orientation distribution in the multilayer and monolayer, rather than one isotropically oriented molecular population in both.
\Image[/past-exam-of-the-frontiers-of-experimental-condensed-matter-physics-course-of-the-university-of-cambridge/2013/paper-1-diatomic-nexafs-polarization.png]
{title=Ideal dipole orientation factors for flat and tilted diatomic molecules}
For illustration, a molecular polar tilt $\beta$ and random azimuth give $\langle|\mathbf e\cdot\mathbf n|^2\rangle=\cos^2\beta\cos^2\alpha+\tfrac12\sin^2\beta\sin^2\alpha$, where $\alpha$ is the electric-field angle to the surface normal. The original diagram plots these ideal factors for two chosen tilts; it is not a reconstruction or fit of the supplied spectra. Quantitative tilt extraction would additionally need intensity normalization, <polarization> purity, azimuthal distribution and substrate-induced changes of the resonances. The spectra alone do not determine unique bond lengths or every adsorption site.
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