Converged ab initio calculations of heavy nuclei

We propose a novel storage scheme for three-nucleon (3N) interaction matrix elements relevant for the normal-ordered two-body approximation used extensively in ab initio calculations of atomic nuclei. This scheme reduces the required memory by approximately two orders of magnitude, which allows the generation of 3N interaction matrix elements with the standard truncation of E3max = 28, well beyond the previous limit of 18. We demonstrate that this is sufficient to obtain the ground-state energy of 132Sn converged to within a few MeV with respect to the E3max truncation. In addition, we study the asymptotic convergence behavior and perform extrapolations to the un-truncated limit. Finally, we investigate the impact of truncations made when evolving free-space 3N interactions with the similarity renormalization group. We find that the contribution of blocks with angular momentum Jrel > 9/2 to the ground-state energy is dominated by a basis-truncation artifact, which vanishes in the large-space limit, so these computationally expensive components can be neglected. For the two sets of nuclear interactions employed in this work, the resulting binding energy of 132Sn agrees with the experimental value within theoretical uncertainties. This work enables converged ab initio calculations of heavy nuclei.

Automated summary

This study proposes a new storage scheme for three-nucleon interaction matrix elements used in ab initio calculations of atomic nuclei. The scheme significantly reduces the required memory and allows for the generation of interaction matrix elements with improved convergence. The study also explores the impact of truncation and approximation on the ground-state energy.