Normal-ordered k-body approximation in particle-number-breaking theories

Autor: Alexander Tichai, J. Ripoche, Thomas Duguet
Přispěvatelé: Direction des Applications Militaires (DAM), Commissariat à l'énergie atomique et aux énergies alternatives (CEA), Département de Physique Nucléaire (ex SPhN) (DPHN), Institut de Recherches sur les lois Fondamentales de l'Univers (IRFU), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay, Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay
Rok vydání: 2020
Předmět:
Zdroj: Eur.Phys.J.A
Eur.Phys.J.A, 2020, 56 (2), pp.40. ⟨10.1140/epja/s10050-020-00045-8⟩
European Physical Journal A
European Physical Journal A, EDP Sciences, 2020, 56 (2), pp.40. ⟨10.1140/epja/s10050-020-00045-8⟩
ISSN: 1434-601X
1434-6001
DOI: 10.1140/epja/s10050-020-00045-8
Popis: The reach of ab initio many-body theories is rapidly extending over the nuclear chart. However, dealing fully with three-nucleon, possibly four-nucleon, interactions makes the solving of the A-body Schr\"odinger equation particularly cumbersome, if not impossible beyond a certain nuclear mass. Consequently, ab initio calculations of mid-mass nuclei are typically performed on the basis of the normal-ordered two-body (NO2B) approximation that captures dominant effects of three-nucleon forces while effectively working with two-nucleon operators. A powerful idea currently employed to extend ab initio calculations to open-shell nuclei consists of expanding the exact solution of the A-body Schr\"odinger equation while authorizing the approximate solution to break symmetries of the Hamiltonian. In this context, operators are normal ordered with respect to a symmetry-breaking reference state such that proceeding to a naive truncation may lead to symmetry-breaking approximate operators. The purpose of the present work is to design a normal-ordering approximation of operators that is consistent with the symmetries of the Hamiltonian while working in the context of symmetry broken (and potentially restored) methods. Focusing on many-body formalisms in which U(1) global-gauge symmetry associated with particle number conservation is broken (and potentially restored), a particle-number-conserving normal-ordered k-body (PNOkB) approximation of an arbitrary N-body operator is designed on the basis of Bogoliubov reference states. A numerical test based on particle-number projected Hartree-Fock-Bogoliubov calculations permits to check the particle-number conserving/violating character of a given approximation to a particle-number conserving operator. Using the presently proposed PNOkB approximation, ab initio calculations based on symmetry-breaking and restored formalisms can be safely performed.
Comment: 27 pages, 12 figures, 6 tables, submitted to EPJA
Databáze: OpenAIRE
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