Infrared length scale and extrapolations for the no-core shell model

TL;DR

This paper precisely determines the infrared length scale in the no-core shell model (NCSM) and demonstrates how to perform accurate IR extrapolations for various nuclei, improving the understanding of NCSM calculations.

Contribution

The paper introduces a precise method to determine the IR length scale in NCSM and applies it to improve extrapolations for nuclear bound states.

Findings

IR length scale can be accurately determined using the hyper-radial well analogy.

IR extrapolations improve the accuracy of NCSM results for light nuclei.

Method applied successfully to nuclei up to $^{16}$O with chiral EFT interactions.

Abstract

We precisely determine the infrared (IR) length scale of the no-core shell model (NCSM). In the NCSM, the $A$-body Hilbert space is truncated by the total energy, and the IR length can be determined by equating the intrinsic kinetic energy of $A$ nucleons in the NCSM space to that of $A$ nucleons in a $3(A-1)$-dimensional hyper-radial well with a Dirichlet boundary condition for the hyper radius. We demonstrate that this procedure indeed yields a very precise IR length by performing large-scale NCSM calculations for $^{6}$Li. We apply our result and perform accurate IR extrapolations for bound states of $^{4}$He, $^{6}$He, $^{6}$Li, $^{7}$Li. We also attempt to extrapolate NCSM results for $^{10}$B and $^{16}$O with bare interactions from chiral effective field theory over tens of MeV.