Infrared and ultraviolet cutoffs in variational calculations with a harmonic oscillator basis

TL;DR

This paper discusses how to handle ultraviolet and infrared cutoffs in variational calculations using harmonic oscillator basis functions, providing methods for extrapolation to achieve converged results, demonstrated through triton ground state energy calculations.

Contribution

It introduces practical procedures for extrapolating variational calculations with harmonic oscillator bases to account for UV and IR cutoffs, enhancing accuracy in nuclear physics computations.

Findings

Established extrapolation procedures for UV and IR regulators.

Applied methods to calculate the triton ground state energy.

Validated the approach with Idaho N3LO nucleon-nucleon interactions.

Abstract

I abstract from a recent publication [1] the motivations for, analysis in and conclusions of a study of the ultraviolet and infrared momentum regulators induced by the necessary truncation of the model spaces formed by a variational trial wave function. This trial function is built systematically from a complete set of many-body basis states based upon three-dimensional harmonic oscillator (HO) functions. Each model space is defined by a truncation of the expansion characterized by a counting number (N) and by the intrinsic scale ($\hbar\omega$) of the HO basis. Extending both the uv cutoff to infinity and the ir cutoff to zero is prescribed for a converged calculation. In [1] we established practical procedures which utilize these regulators to obtain the extrapolated result from sequences of calculations with model spaces. Finally, I update this subject by mentioning recent work on our extrapolation prescriptions which have appeared since the submission of [1]. The numerical example chosen for this contribution consists of calculations of the ground state energy of the triton with the "bare" and "soft" Idaho N3LO nucleon-nucleon (NN) interaction.