# On collisional free-free photon absorption in warm dense matter

## TL;DR

This paper derives a detailed formula for photon absorption rates in warm dense matter caused by free-free electron-ion collisions, considering non-relativistic bremsstrahlung and Fermi-Dirac electron distributions, valid for photon frequencies above the plasma frequency.

## Contribution

It provides a new closed-form expression for free-free photon absorption in warm dense matter, incorporating detailed balance and hypergeometric functions, extending previous approximate models.

## Key findings

- Derived a closed-form absorption rate formula depending on temperature, density, and photon energy.
- Numerically evaluated the formula across the full parameter space, including hypergeometric function representations.
- Compared results with existing asymptotic approximations to validate the model.

## Abstract

The rate of photon absorption in warm dense matter (WDM) induced by free-free electron-ion collisions is derived from Sommerfeld's cross-section for non-relativistic bremsstrahlung emission, making use of detailed balance relations. Warm dense matter is treated as a metal-like state in the approximation of a uniform degenerate electron gas and a uniform ion background. Total absorption rates are averaged over the electron Fermi distribution. A closed expression is obtained for the absorption rate, depending on temperature, density, and photon energy, that scales with ion charge Z. It is evaluated numerically for the full parameter space, which requires different representations of the hypergeometric functions involved. The results are valid for photon frequencies larger than the plasma frequency of the medium. They are compared with approximate formulas in various asymptotic regions.