Parallelizable approach for <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>S</mi><mi>D</mi></mrow></math>-pair shell model matrix elements and overlaps

Feng Pan; Si-Yao Zhang; Yan-An Luo; Bing-Cheng He; Lianrong Dai; Jerry Paul Draayer

doi:10.1103/lrcz-kyh9

Parallelizable approach for $S D$ -pair shell model matrix elements and overlaps

Feng Pan ^*

Si-Yao Zhang and Yan-An Luo^†

Bing-Cheng He

Lianrong Dai ^‡

Jerry Paul Draayer^§

Department of Physics, Liaoning Normal University, Dalian 116029, China and Department of Physics and Astronomy, Louisiana State University, Baton Rouge, Louisiana 70803-4001, USA

School of Physics, Nankai University, Tianjin 300071, China

Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, USA

Department of Physics, School of Science, Huzhou University, Huzhou, Zhejiang 313000, China

Department of Physics and Astronomy, Louisiana State University, Baton Rouge, Louisiana 70803-4001, USA

^*Contact author: daipan@dlut.edu.cn
^†Contact author: Luoya@nankai.edu.cn
^‡Contact author: dailianrong@zjhu.edu.cn
^§Contact author: draayer@lsu.edu

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Phys. Rev. C 112, 034328 – Published 23 September, 2025

DOI: https://doi.org/10.1103/lrcz-kyh9

Abstract

We propose a novel procedure for computing overlaps and matrix elements in the $M$ -scheme $S D$ -pair shell model. Our approach demonstrates that calculating the overlap or matrix element of a one- or two-body operator between two $N$ -pair states requires, at most, $N! (N + 1)! / 2^{N}$ products of one-pair overlaps. We also establish an upper bound on the number of independent one-pair overlaps involved. A major advantage of this method is its inherent parallelizability: the one-pair overlaps needed for $N$ -pair overlaps or matrix elements can be computed independently, enabling efficient parallelization to significantly accelerate the overall computation.

Physical Review C

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Parallelizable approach for $S D$ -pair shell model matrix elements and overlaps

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Parallelizable approach for SD-pair shell model matrix elements and overlaps

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Parallelizable approach for $S D$ -pair shell model matrix elements and overlaps