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Finite-temperature mean-field approximations for shell model Hamiltonians: the code HF-SHELL

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Abstract

We present the code HF-SHELL for solving the self-consistent mean-field equations for configuration-interaction shell model Hamiltonians in the proton–neutron formalism. The code can calculate both zero- and finite-temperature properties in the Hartree-Fock (HF), HF+Bardeen–Cooper–Schrieffer (HF+BCS) and the Hartree–Fock–Bogoliubov (HFB) mean-field approximations. Particle-number projection after variation is incorporated to reduce the grand-canonical ensemble to the canonical ensemble, making the code particularly suitable for the calculation of nuclear state densities. The code does not impose axial symmetry and allows for triaxial quadrupole deformations. The self-consistency cycle is particularly robust through the use of the heavy-ball optimization technique and the implementation of different options to constrain the quadrupole degrees of freedom.

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Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: All data presented here is included in the git repository.]

Notes

  1. Also known as the stationary phase approximation.

  2. At \(T=0\), we can use these definitions also in the canonical HFB basis. However, for \(T\not = 0\), a canonical basis generally does not exist.

  3. When pairing correlations vanish, this formula reduces to the Inglis moment of inertia [47].

  4. These purely numerical parameters are not to be confused with the chemical potential \(\mu _q\) and \(\alpha _q = \beta \mu _q\) that were introduced in Sect. 2.

  5. Also known as the imaginary time-step method.

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Acknowledgements

We thank P. Fanto for useful discussions and for comments on the manuscript. We also thank M. Bender for useful discussions, and in particular for pointing out the advantages of Brents algorithm for root finding, and providing an example subroutine. We thank P. Stevenson for providing an example of a Fortran module for the calculation of Clebsch–Gordan coefficients. This work was supported in part by the U.S. DOE Grant No. DE-SC0019521.

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Authors and Affiliations

  1. Center for Theoretical Physics, Sloane Physics Laboratory, Yale University, New Haven, CT, 06520, USA

    W. Ryssens & Y. Alhassid

  2. Institut d’Astronomie et d’Astrophysique, Université Libre de Bruxelles, CP 226, Brussels, 1050, Belgium

    W. Ryssens

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  1. W. Ryssens
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Correspondence to Y. Alhassid.

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Communicated by Michael Bender.

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Ryssens, W., Alhassid, Y. Finite-temperature mean-field approximations for shell model Hamiltonians: the code HF-SHELL. Eur. Phys. J. A 57, 76 (2021). https://doi.org/10.1140/epja/s10050-021-00365-3

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