$^{13}$C and $^{19}$F Nucleus-Electron Correlation and Self-Energies

TL;DR

This paper investigates electron-nucleus correlations for $^{13}$C and $^{19}$F using RPA and Green's function methods, highlighting the importance of vertex corrections and self-interaction error mitigation.

Contribution

It introduces a theoretical framework connecting RPA with perturbation theory and evaluates $GW$ self-energies for nuclear densities, advancing quantum treatment of these nuclei.

Findings

RPA effectively captures correlation energies for $^{13}$C and $^{19}$F.

Self-interaction errors significantly affect results, requiring vertex corrections.

The work establishes a foundation for future quantum mechanical studies of these nuclei.

Abstract

We present a theoretical and numerical study of the correlation between electrons and the fermionic $^{13}$C and $^{19}$F nuclei. We use the random-phase approximation (RPA) as a valuable tool in obtaining these correlation energies. A special connection between the RPA and second-order perturbation theory for the inter-fermionic interaction is outlined. Subsequently, Green's function based $GW$ self-energies are evaluated for the nuclear densities. The strong influence of self-interaction errors is outlined, and vertex corrections are shown to be strictly necessary to obtain reasonable results. The theoretical and technical requirements for a quantum mechanical treatment of $^{13}$C and $^{19}$F nuclei are also addressed in this work, thereby facilitating further research in this area.