2009/04/30 by Feng Pan, Ming-Xia Xie, Mingxia Xie +4
Chemistry · Mathematics · Physics and Astronomy · #Advanced NMR Techniques and Applications #Ansatz #Bethe ansatz #Boson #Eigenvalues and eigenvectors #Exact solutions in general relativity #Gauge (firearms) #Mathematical analysis #Mathematical physics #Mathematics #Nuclear physics research studies #Pairing #Physics #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Simple (philosophy) #Standard Model (mathematical formulation) #Subspace topology #Superconductivity #cond-mat.str-el #nucl-th #quant-ph
paper · pdf · doi:10.1103/physrevc.80.044306
published as Phys.Rev.C80:044306,2009 · 10 pages, Revtex4
arxiv created 2009/08/05 · openalex publication_date 2009/10/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A new step-by-step diagonalization procedure for evaluating exact solutions of the nuclear deformed mean-field plus pairing interaction model is proposed via a simple Bethe ansatz in each step from which the eigenvalues and corresponding eigenstates can be obtained progressively. This new approach draws upon an observation that the original one- plus two-body problem in a k-particle Hilbert subspace can be mapped onto a one-body grand hard-core boson picture that can be solved step by step with a simple Bethe ansatz known from earlier work. Based on this new procedure, it is further shown that the extended pairing model for deformed nuclei [Feng Pan, V. G. Gueorguiev, and J. P. Draayer, Phys. Rev. Lett. 92, 112503 (2004)] is similar to the standard pairing model with the first step approximation, in which only the lowest energy eigenstate of the standard pure pairing interaction part is taken into consideration. Our analysis shows that the standard pairing model with the first step approximation displays similar pair structures of the first few exact low-lying states of the model, which, therefore, provides a link between the two models.