Pade-resummed high-order perturbation theory for nuclear structure calculations

TL;DR

This paper demonstrates that Pade resummation of high-order perturbation series enables accurate and rapidly converging calculations of nuclear ground-state energies, overcoming divergence issues in traditional perturbation methods.

Contribution

The study introduces a Pade resummation technique applied to high-order perturbation theory for nuclear structure calculations, achieving improved convergence and accuracy.

Findings

Perturbation series up to 30th order computed for nuclei.

Pade approximants effectively resummate divergent series.

Results closely match exact no-core shell model calculations.

Abstract

We apply high-order many-body perturbation theory for the calculation of ground-state energies of closed-shell nuclei using realistic nuclear interactions. Using a simple recursive formulation, we compute the perturbative energy contributions up to 30th order and compare to exact no-core shell model calculations for the same model space and Hamiltonian. Generally, finite partial sums of this perturbation series do not show convergence with increasing order, but tend to diverge exponentially. Nevertheless, through a simple resummation via Pade approximants it is possible to extract rapidly converging and highly accurate results for the ground state energy.