SU3lib: A C++ library for accurate computation of Wigner and Racah coefficients of SU(3)

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We present the C++ library SU3lib for accurate computation of SU(3) Wigner coupling and Racah recoupling coefficients. It is built on the efficient mathematical algorithm originally proposed by Draayer and Akiyama [1]. The presented library extends the reach of this algorithm towards large SU(3) irreducible representations and outer multiplicities that were heretofore inaccessible due to floating-point precision errors. As large irreducible representations of SU(3) play an important role in medium- and heavy-mass atomic nuclei, SU3lib expands the scope of approaches to nuclear structure and reactions that rely on available SU(3) coupling-recoupling coefficients. Program summary: Program Title: SU3lib CPC Library link to program files: https://doi.org/10.17632/j977v8v5fp.1 Developer's repository link: https://gitlab.com/tdytrych/SU3lib Licensing provisions: BSD 2-clause Programming language: C++ External libraries: WIGXJPF [3], Boost Nature of problem: Accurate calculation of SU(3)⊃SO(3) and SU(3)⊃SU(2)×U(1) Wigner coupling and Racah recoupling coefficients for arbitrary couplings and multiplicity. Solution method: We adopt the mathematical procedure proposed by Draayer and Akiyama [1], who also provided its implementation as a FORTRAN library [2]. The challenge is to avoid the loss of precision due to cancellation in sums of large alternating terms in transformation between SU(3)⊃SO(3) and SU(3)⊃SU(2)×U(1) schemes, and to compute SU(3)⊃SU(2)×U(1) Wigner coefficients accurately for large outer multiplicities. The present library tackles these challenges by implementing key formulas and data structures as C++ templates and utilizing floating-point data types with extended precision provided by the Boost.Multiprecision library as template arguments. This permits an efficient and accurate computation of SU(3) coefficients even for large SU(3) irreps and outer multiplicities that were heretofore inaccessible. References: [1] J. P. Draayer and Y. Akiyama, J. Math. Phys. 14, 1904 (1973). [2] Y. Akiyama and J. P. Draayer, Comp. Phys. Comm. 5, 405 (1973). [3] H. T. Johansson and C. Forssén, SIAM J. Sci. Comput. 38(1), A376 (2016).

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Computer Physics Communications

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