Convergence Rates from Yukawa to Coulomb Interaction in the Thomas-Fermi-von Weizs\"acker Model

TL;DR

This paper proves explicit convergence rates of the Thomas-Fermi-von Weizs"acker Yukawa model solutions to the Coulomb model solutions, including force convergence, extending previous work and establishing new foundational results.

Contribution

It provides the first explicit convergence rates from Yukawa to Coulomb interactions in the TFW model for general nuclear configurations.

Findings

Uniform convergence with explicit rate established

Convergence of forces from Yukawa to Coulomb shown

New existence, uniqueness, and stability results for Yukawa ground states

Abstract

We establish uniform convergence, with explicit rate, of the solution to the Thomas--Fermi--von Weizs\"acker (TFW) Yukawa model to the solution of the TFW Coulomb model, for general condensed nuclear configurations. As a consequence, we show the convergence of forces from the Yukawa to the Coulomb model. These results rely on an extension of Nazar \& Ortner (2015) to the Yukawa setting. Auxiliary results of independent interest shown also include new existence, uniqueness and stability results for the Yukawa ground state.