Title: Zero-pairing and zero-temperature limits of finite-temperature Hartree-Fock-Bogoliubov theory

Abstract

Recently, variational Hartree-Fock-Bogoliubov (HFB) mean-field equations were shown to possess a mathematically well-defined zero-pairing limit, independently of the closed- or open-shell character of the system under consideration. This limit is non-trivial for open-shell systems such that HFB theory does {\it not} reduce to the Hartree-Fock (HF) formalism in all cases. The present work extends this analysis to finite-temperature HFB (FTHFB) theory by investigating the behavior of this more general formalism in the combined zero-temperature and zero-pairing limits. The zero-pairing and zero-temperature limits of the FTHFB statistical density operator constrained to carry an arbitrary (integer) number of particles A on average is worked out analytically and realized numerically using a two-nucleon interaction. While the FTHFB density operator reduces to the projector corresponding to a pure HF Slater determinant for closed-shell nuclei, the FTHFB formalism does not reduce to the HF theory in all cases in the zero-temperature and zero-pairing limits, i.e. for open-shell nuclei. However, the fact that a nucleus can be of open-shell character in these joint limits is necessarily the result of some symmetry restrictions. Whenever it is the case, the non-trivial description obtained for open-shell systems is shown to depend on the order with which both limits aremore » taken, i.e. the two limits do not commute for these systems. When the zero-temperature limit is performed first, the FTHFB density operator is demoted to a projector corresponding to a pure state made out of a linear combination of a finite number of Slater determinants with different (even) numbers of particles. When the zero-pairing limit is performed first, the FTHFB density operator remains a statistical mixture of a finite number of Slater determinants with both even and odd particle numbers. While the entropy (pairing density) is zero in the first (second) case, it does not vanish in the second (first) case in spite of the temperature (pairing) tending towards zero. The difference between both limits can have striking consequences for the (thermal) expectation values of observables. For instance, the particle-number variance does not vanish in either case and has limiting values that differ by a factor of two in both cases. In conclusion, while in the textbook situation associated with closed-shell nuclei Hartree-Fock-Bogoliubov (finite-temperature Hartree-Fock) theory reduces to Hartree-Fock theory in the zero-pairing (zero-temperature) limit, the present analysis demonstrates that a non trivial and unexpected limit is obtained for this formalism in open-shell systems. This result sheds a new light on certain aspects of this otherwise very well-studied many-body formalism.« less

Authors:

Duguet, Thomas  ^[1];

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Ryssens, Wouter  ^[2]

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• Search DOE PAGES for ORCID "0000-0002-4775-4403"

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1. Univ. Paris-Saclay, Gif-sur-Yvette (France); KU Leuven (Belgium)
2. Yale Univ., New Haven CT (United States)

Publication Date:

Tue Oct 27 00:00:00 EDT 2020

Research Org.:

Yale Univ., New Haven CT (United States)

Sponsoring Org.:

USDOE Office of Science (SC), Nuclear Physics (NP)

OSTI Identifier:

1691460

Grant/Contract Number:  

SC0019521

Resource Type:

Accepted Manuscript

Journal Name:

Physical Review. C

Additional Journal Information:

Journal Volume: 102; Journal Issue: 4; Journal ID: ISSN 2469-9985

Publisher:

American Physical Society (APS)

Country of Publication:

United States

Language:

English

Subject:

73 NUCLEAR PHYSICS AND RADIATION PHYSICS; Nuclear many-body theory; Nucleon-nucleon interactions; Thermal & statistical models; 20 ≤ A ≤ 38; 6 ≤ A ≤ 19; Mean field theory