Centroids of nuclear shell-model Hamiltonians, with optimization of energy-based truncation schemes

TL;DR

This paper introduces the TRACER code for efficiently computing energy centroids in nuclear shell-model Hamiltonians, enabling optimized truncation schemes to manage the exponential basis growth in nuclear many-body calculations.

Contribution

The paper presents a new Fortran90 code, TRACER, that efficiently computes energy centroids to optimize truncation schemes in nuclear shell-model calculations.

Findings

TRACER enables fast calculation of energy centroids in shell-model spaces.

Optimization of truncation schemes improves computational efficiency.

The method is applicable to both empirical and no-core shell models.

Abstract

The configuration-interaction shell model is an effective and widely-used approach to the nuclear many-body problem, whose main drawback is the exponential growth of the basis dimension. An useful way to character nuclear shell-model Hamiltonians is through traces, including traces in subspaces defined by orbital occupations. Such traces, or energy centroids, can be easily and efficiently computed through the monopole components of the nuclear interaction, that is, terms that go like $n_a n_b$ where $n_a$ is the occupation of the single-particle orbital labeled by $a$. These calculations can be carried out very quickly for both empirical (valence space) and no-core shell model spaces and interactions. In fact, they can be carried out so fast, one can use this to optimize an efficient, if approximate, many-body truncation scheme used in available nuclear shell-model codes such as BIGSTICK. To carry out both the traces and the optimization, we present the TRACER code, written in Fortran90 and described and available here. We give example results as well as discuss performance.