Large-scale exact diagonalizations reveal low-momentum scales of nuclei

TL;DR

This paper extends exact diagonalization methods to large model spaces, enabling detailed nuclear structure calculations and IR extrapolations that reveal low-momentum scales governing nuclear properties.

Contribution

It introduces a scalable approach for no-core shell model calculations up to Nmax=22, and demonstrates IR extrapolation techniques to improve observable accuracy in nuclear physics.

Findings

Successfully performed NCSM calculations for 6Li with model spaces up to Nmax=22

IR extrapolations enhance the accuracy of energies and radii

Verified the small-momentum scale related to the first open decay channel

Abstract

Ab initio methods aim to solve the nuclear many-body problem with controlled approximations. Virtually exact numerical solutions for realistic interactions can only be obtained for certain special cases such as few-nucleon systems. Here we extend the reach of exact diagonalization methods to handle model spaces with dimension exceeding $10^{10}$ on a single compute node. This allows us to perform no-core shell model (NCSM) calculations for 6Li in model spaces up to $N_\mathrm{max} = 22$ and to reveal the 4He+d halo structure of this nucleus. Still, the use of a finite harmonic-oscillator basis implies truncations in both infrared (IR) and ultraviolet (UV) length scales. These truncations impose finite-size corrections on observables computed in this basis. We perform IR extrapolations of energies and radii computed in the NCSM and with the coupled-cluster method at several fixed UV cutoffs. It is shown that this strategy enables information gain also from data that is not fully UV converged. IR extrapolations improve the accuracy of relevant bound-state observables for a range of UV cutoffs, thus making them profitable tools. We relate the momentum scale that governs the exponential IR convergence to the threshold energy for the first open decay channel. Using large-scale NCSM calculations we numerically verify this small-momentum scale of finite nuclei.