A new single-particle basis for nuclear many-body calculations

TL;DR

This paper introduces a new single-particle basis for nuclear many-body calculations, directly linked to the nucleon-nucleon interaction, with better asymptotic behavior and comparable computational cost to harmonic oscillator basis, improving energy estimates.

Contribution

A novel orthonormal, complete single-particle basis linked to the nucleon-nucleon interaction, addressing limitations of harmonic oscillator functions in nuclear calculations.

Findings

Lower energies for ${}^6He$ and ${}^6Li$ using the new basis

Comparable computational cost to harmonic oscillator basis

Proper asymptotic behavior at large distances

Abstract

Predominantly, harmonic oscillator single-particle wave functions are the choice as a basis in ab-initio nuclear many-body calculations. These wave-functions, although very convenient in order to evaluate the matrix elements of the interaction in the laboratory frame, have a too fast fall-off at large distances. In the past, in alternative to the harmonic oscillator, other single-particle wave functions have been proposed. In this work we propose a new single-particle basis, directly linked to the nucleon-nucleon interaction. This new basis is orthonormal and complete, has the proper asymptotic behavior at large distances and does not contain the continuum which would pose severe convergence problems in nuclear many body calculations. We consider the newly proposed NNLO-opt nucleon-nucleon interaction, without any renormalization. We show that unlike other basis, this single-particle representation has a computational cost similar to the harmonic oscillator basis with the same space truncation and it gives lower energies for ${}^6He$ and ${}^6Li$.