Optimization of the number of intrinsic states included in the discrete Generator Coordinate Method

TL;DR

This paper introduces an efficient method for selecting the optimal number of intrinsic states in the discrete Generator Coordinate Method, improving stability and reducing computational effort in nuclear structure calculations.

Contribution

It proposes a new pre-selection mechanism based on a natural basis that avoids non-diagonal kernel evaluations, enhancing the GCM's efficiency and stability.

Findings

Reduces numerical instabilities in GCM calculations.

Effective in describing ground and excited states of selected nuclei.

Applicable with Gogny energy density functional.

Abstract

We present a mechanism to efficiently pre-select the number of intrinsic many-body states that are used to define the many-body wave functions within the discrete Generator Coordinate Method (GCM). This procedure, based on the proper definition of a natural basis of orthonormal states, does not require the evaluation of the non-diagonal Hamiltonian kernels to do the selection and helps to reduce the numerical instabilities. The performance of the method is analyzed in detail in the ground state and $0^{+}$ excited states of some selected nuclei computed with the Gogny energy density functional.