Toward extracting scattering phase shift from integrated correlation functions IV: Coulomb corrections

TL;DR

This paper extends a formalism to extract scattering phase shifts from correlation functions to include Coulomb interactions, addressing divergence issues and demonstrating reliability with an exactly solvable model.

Contribution

It introduces a modified formula that accounts for Coulomb interactions, enabling accurate extraction of phase shifts from correlation functions.

Findings

The modified formula removes divergence caused by Coulomb interactions.

The approach reliably extracts phase shifts in a model with Coulomb and short-range interactions.

The method shows rapid convergence to the infinite volume limit.

Abstract

The formalism developed in Refs.~\cite{Guo:2023ecc,Guo:2024zal,Guo:2024pvt} that relates the integrated correlation functions for a trapped system to the infinite volume scattering phase shifts through a weighted integral is further extended to include Coulomb interaction between charged particles. The original formalism cannot be applied due to different divergent asymptotic behavior resulting from the long-range nature of the Coulomb force. We show that a modified formula in which the difference of integrated correlation functions between particles interacting with Coulomb plus short-range interaction and with Coulomb interaction alone is free of divergence, and has rapid approach to its infinite volume limit. Using an exactly solvable model, we demonstrate that the short-range potential scattering phase shifts can be reliably extracted from the formula in the presence of Coulomb interaction.