NEXAFS linear dichroism

Variation of absorption with incident electric-field direction. For a localized $1s\to {\pi }^{\ast }$ transition the dipole matrix element is proportional to the component of the field along the pi-orbital normal.

For a diatomic molecular axis $\mathbf{n}$ and unit electric-field polarization $\mathbf{e}$, the axial and summed two transverse dipole transition directions have the displayed geometrical factors. Radial matrix elements differ between resonances. If axes have polar tilt $\beta$ and random azimuth, with electric-field angle $\alpha$ to the surface normal, the mean axial factor is ${\cos }^2\beta {\cos }^2\alpha +\frac{1}{2}{\sin }^2\beta {\sin }^2\alpha$. Polarization-dependent near-edge absorption therefore constrains an orientation distribution, subject to substrate hybridization and instrumental normalization.