Subtraction of the spurious translational mode from the RPA response function

TL;DR

This paper develops a formalism to remove spurious translational modes from the RPA response function, ensuring more accurate physical quantities in many-body nuclear physics calculations.

Contribution

We introduce a formalism to subtract spurious translational contributions from the full RPA response function, improving the accuracy of response calculations.

Findings

Formalism successfully removes spurious modes from RPA response

Enhances accuracy of transition densities and strength functions

Applicable to many-body frameworks like particle-vibration coupling

Abstract

It is well known that within self-consistent Random Phase Approximation (RPA) on top of Hartree-Fock (HF), the translational symmetry should be restored. Due to approximations at the level of the practical implementation, this restoration may be only partial. As a result, one has spurious contributions in the physical quantities that are extracted from RPA. While there are several recipes in the literature to overcome this drawback in order to produce transition densites or strength functions that are free from spurious contamination, there is no formalism associated with the full RPA response function. We present such formalism in this paper. Our goal is to avoid spurious contamination when the response function is used in many-body frameworks like the particle-vibration coupling theory.