Properties of infrared extrapolations in a harmonic oscillator basis

TL;DR

This paper investigates the effectiveness of infrared and ultraviolet extrapolations in no-core shell model calculations, demonstrating successful methods for eigenstates and long-range operators with SRG-evolved Hamiltonians, while highlighting limitations of uv cutoff extrapolations.

Contribution

It extends previous work by showing that ir cutoff extrapolation is reliable for both eigenstates and expectation values, especially with SRG-evolved Hamiltonians, and clarifies the limitations of uv cutoff extrapolation.

Findings

Infrared extrapolation is successful for eigenstates and long-range operators.

Ultraviolet extrapolation below the ir scale is unreliable.

SRG evolution improves the robustness of extrapolations.

Abstract

We continue our studies of infrared (ir) and ultraviolet (uv) regulators of no-core shell model calculations. We extend our results that an extrapolation in the ir cutoff with the uv cutoff above the intrinsic uv scale of the interaction is quite successful, not only for the eigenstates of the Hamiltonian but also for expectation values of operators considered long range. The latter results are obtained with Hamiltonians transformed by the similarity renormalization group (SRG) evolution. On the other hand, a suggested extrapolation in the uv cutoff when the ir cutoff is below the intrinsic ir scale is neither robust nor reliable.