# Resonant Inelastic X-Ray Scattering in Metals: A Diagrammatic Approach

## TL;DR

This paper introduces a diagrammatic formalism for analyzing RIXS responses in metals, emphasizing the importance of long-range Coulomb interactions and screening effects to better understand collective excitations like plasmons and electron-hole pairs.

## Contribution

It develops a new diagrammatic approach to study RIXS in metals, accounting for long-range interactions and dynamic screening, improving upon standard approximations.

## Key findings

- Single- and multi-plasmon peaks can be distinguished in RIXS spectra.
- Hybrid processes involving plasmon emission and electron-hole excitations are characterized.
- The formalism enables extraction of collective excitation information from RIXS data.

## Abstract

We develop a formalism to study the Resonant Inelastic X-ray Scattering (RIXS) response in metals based on the diagrammatic expansion for its cross section. The standard approach to the solution of the RIXS problem relies on two key approximations: short-range potentials and non-interacting conduction electrons. However, these approximations are inaccurate for charged particles in metals, where the long-range Coulomb interaction and dynamic screening effects are very important. In this work we study how to extract important information about collective excitations in the Coulomb plasma, plasmons and electron-hole pairs, from RIXS data. We find that single- and multi-plasmon excitations can easily be distinguished by positions of the corresponding peaks, singularities, and their intensities. We also discuss the hybrid processes, where plasmon emission is accompanied by excitation of electron-hole pairs, and study how they manifest themselves.