Extrapolation uncertainties in the importance-truncated No-Core Shell Model

TL;DR

This paper analyzes the uncertainties in extrapolating importance-truncated No-Core Shell Model calculations for Li-6, comparing them to full NCSM results, and investigates the effects of various parameters and methods on these uncertainties.

Contribution

It introduces a detailed analysis of extrapolation uncertainties in IT-NCSM for Li-6 and compares different extrapolation techniques and parameters to full NCSM results.

Findings

Extrapolation uncertainties increase with Nmax, from a few keV to about 50 keV.

Differences between IT-NCSM and NCSM ground-state energies can reach 100-250 keV.

Uncertainty depends on the extrapolation method, harmonic oscillator energy, and SRG scale.

Abstract

We report on Li-6 calculations performed with the IT-NCSM and compare them to full NCSM calculations. We employ the Entem and Machleidt chiral two-body N3LO interaction (regulated at 500 MeV/c), which has been modified to a phase-shift equivalent potential by the similarity renormalization group (SRG) procedure. We investigate the dependence of the procedure on the technique employed to extrapolate to the complete Nmax space, the harmonic oscillator energy, and investigate the dependence on the momentum-decoupling scale (\lambda) used in the SRG. We also investigate the use of one or several reference states from which the truncated basis is constructed. We find that the uncertainties generated from various extrapolating functions used to extrapolate to the complete Nmax space increase as Nmax increases. The extrapolation uncertainties range from a few keV for the smallest Nmax spaces to about 50 keV for the largest Nmax spaces. We note that the difference between extrapolated IT-NCSM and NCSM ground-state energies, however, can be as large as a 100-250 keV depending on the chosen harmonic oscillator energy. We also present the extrapolation of IT-NCSM results to Nmax infinity and compare these to similarly extrapolated full NCSM results.