# Nonlinear electronic stopping of negatively-charged particles in liquid water

## TL;DR

This study uses real-time density functional theory to analyze the nonlinear electronic stopping power of negatively charged particles in liquid water, revealing significant differences from traditional semi-empirical models and emphasizing the importance of nonlinear effects.

## Contribution

The paper introduces a first-principles nonlinear approach to calculating electronic stopping power for various charged particles in water, highlighting discrepancies with previous models.

## Key findings

- Nonlinear stopping power differs significantly from semi-empirical results.
- Discrepancies observed in maximum stopping power and Bragg peak position.
- Quantum effects of electron projectiles are crucial for accurate modeling.

## Abstract

We present real-time time-dependent density-functional-theory calculations of the electronic stopping power for negative and positive projectiles (electrons, protons, antiprotons and muons) moving through liquid water. After correction for finite mass effects, the nonlinear stopping power obtained in this work is significantly different from the previously known results from semi-empirical calculations based on the dielectric response formalism. Linear-nonlinear discrepancies are found both in the maximum value of the stopping power and the Bragg peak's position. Our results indicate the importance of the nonlinear description of electronic processes, particularly for electron projectiles, which are modeled here as classical point charges. Our findings also confirm the expectation that the quantum nature of the electron projectile should substantially influence the stopping power around the Bragg peak and below.