# Local Field and Core-hole Effects (PMBSE, TDDFT)

### From FEFF

These are features of feff that are still under development. They are not reliable in this release of feff9.

Many-body effects such as local fields and the core-hole interaction can be significant in x-ray absorption spectra, even several hundred eV above an absorption edge. The treatment of these effects requires theories beyond the independent-particle approximation, e.g., the Bethe- Salpeter equation (BSE) or the time-dependent density-functional theory (TDDFT).

The projection-operator method Bethe-Salpeter equation (PMBSE) is used for core-hole absorption spectra calculations. The BSE is usually limited to low energies, while the TDDFT often ignores the nonlocality of the core-hole interaction. Time dependent density functional theory (TDDFT) is a general framework for studying non-stationary electronic processes. TDDFT is used for local-field absorption spectra calculations.

The approach being developed for feff is a combined approach for calculations of the x-ray spectra that include both of these effects, together with inelastic losses and self-energy shifts over a wide energy range.

Note that the TDLDA card accounts for some of the same effects, and is functional in this release of feff9.

See *Combined Bethe-Salpeter equations and time-dependent density-functional theory ap-*
proach for x-ray absorption calculations*; A.L. Ankudinov, Y. Takimoto, and J.J. Rehr, Phys.*
Rev. B 71, 165110 (2005)