Universal properties of infrared oscillator basis extrapolations

TL;DR

This paper refines infrared extrapolation formulas in nuclear many-body calculations by studying two-body models and the deuteron, accurately determining effective box sizes and phase shifts, and exploring universal properties.

Contribution

It introduces improved infrared extrapolation formulas based on detailed two-body and deuteron studies, enhancing accuracy in nuclear calculations.

Findings

Accurate determination of effective box size as a function of model parameters

Effective approximation of energy shifts using asymptotic normalization coefficients

Universal properties demonstrated through deuteron calculations

Abstract

Recent work has shown that a finite harmonic oscillator basis in nuclear many-body calculations effectively imposes a hard-wall boundary condition in coordinate space, motivating infrared extrapolation formulas for the energy and other observables. Here we further refine these formulas by studying two-body models and the deuteron. We accurately determine the box size as a function of the model space parameters, and compute scattering phase shifts in the harmonic oscillator basis. We show that the energy shift can be well approximated in terms of the asymptotic normalization coefficient and the bound-state momentum, discuss higher-order corrections for weakly bound systems, and illustrate this universal property using unitarily equivalent calculations of the deuteron.