Self-consistent random phase approximation and the restoration of symmetries within the three-level Lipkin model

2004/05/03 by D. S. Delion, P. Schuck, J. Dukelsky · 23 citations
Chemistry · Mathematics · Physics and Astronomy · #Advanced NMR Techniques and Applications #Basis (linear algebra) #Geometry #Goldstone #Homogeneous space #Mathematical physics #Mathematics #Nuclear physics research studies #Operator (biology) #Phase (matter) #Physics #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Random phase approximation #Scattering #Spectrum (functional analysis) #nucl-th

paper · pdf · doi:10.1103/physrevc.72.064305

published in Physical Review C 72(6) (American Institute of Physics)

arxiv created 2004/05/03 · openalex publication_date 2005/12/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We show that it is possible to restore broken symmetries associated with the Goldstone mode within the self-consistent random phase approximation (SCRPA) applied to the three-level Lipkin model. To do this, it is necessary to include the so-called scattering terms in the RPA operator. We determine one- and two-body densities as very convergent expansions in terms of the generators of the RPA basis. We show that SCRPA excitations correspond to the heads of some rotational bands in the exact spectrum.

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