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arXiv:2511.03161

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

Calvin W. Johnson, Keller, Austin

Published Nov 5, 2025• 0 citations
arXivHTMLPDF

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.

DOI
10.48550/arxiv.2511.03161

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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 nanbn_a n_bna​nb​ where nan_ana​ is the occupation of the single-particle orbital labeled by aaa. 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.
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A variational principle of maximal decoupling between the collective and noncollective subspaces has recently been proposed to pin down the collective degrees of freedom of the nuclear many-body problem. This maximal-decoupling variational principle is further utilized here to determine in an optimal way the auxiliary Hamiltonians to be used in severely truncated boson-space calculations for nuclear collective motions. In the present method one treats the spurious-state problem in truncated boson-space calculations by using appropriate auxiliary boson Hamiltonians. The viability of the method is demonstrated through its application to a simplified shell model containing only the monopole pairing interactions.
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