Improving Predictions with Reliable Extrapolation Schemes and Better Understanding of Factorization

TL;DR

This paper advances nuclear physics calculations by developing reliable extrapolation methods for oscillator basis truncation effects and analyzing the scale dependence of factorization in knockout reactions, enhancing predictive accuracy.

Contribution

It introduces new extrapolation formulas for oscillator basis truncation and systematically studies the scale dependence of factorization in nuclear reactions using SRG transformations.

Findings

Finite oscillator basis acts as a hard-wall boundary condition.

Derived accurate extrapolation formulas for energy and observables.

Scale dependence of factorization varies systematically with kinematics.

Abstract

We investigate two distinct sources of uncertainty in low-energy nuclear physics calculations and develop ways to account for them. Harmonic oscillator basis expansions are widely used in ab-initio nuclear structure calculations. Finite computational resources usually require that the basis be truncated before observables are fully converged, necessitating reliable extrapolation schemes. We show that a finite oscillator basis effectively imposes a hard-wall boundary condition. We accurately determine the position of the hard-wall as a function of oscillator space parameters, derive extrapolation formulas for the energy and other observables, and discuss the extension of this approach to higher angular momentum. Nucleon knockout reactions have been widely used to study and understand nuclear properties. Such an analysis implicitly assumes that the effects of the probe can be separated from the physics of the target nucleus. This factorization between nuclear structure and reaction components depends on the renormalization scale and scheme, and has not been well understood. But it is potentially critical for interpreting experiments and for extracting process-independent nuclear properties. We use similarity renormalization group (SRG) transformations to systematically study the scale dependence of factorization for the simplest knockout process of deuteron electrodisintegration. We find that the extent of scale dependence depends strongly on kinematics, but in a systematic way. Based on examination of the relevant overlap matrix elements, we are able to qualitatively explain and even predict the nature of scale dependence based on the kinematics under consideration.