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Title: Scaling properties of the pairing problem in the strong coupling limit

We study the excited states of the pairing Hamiltonian providing an expansion for their energy in the strong coupling limit. To assess the role of the pairing interaction we apply the formalism to the case of a heavy atomic nucleus. We show that only a few statistical moments of the level distribution are sufficient to yield an accurate estimate of the energy for not too small values of the coupling G and we give the analytic expressions of the first four terms of the series. Further, we discuss the convergence radius G{sub sing} of the expansion showing that it strongly depends upon the details of the level distribution. Furthermore G{sub sing} is not related to the critical values of the coupling G{sub crit}, which characterize the physics of the pairing Hamiltonian, since it can exist even in the absence of these critical points. -- Highlights: •We study the excitation spectrum of the pairing Hamiltonian. •We provide an analytic expansion around the strong coupling limit. •We discuss the convergence radius of the expansion. •We connect the radius with the critical points of H.
Authors:
 [1] ;  [2] ;  [1] ;  [2]
  1. Dipartimento di Fisica Teorica, Università di Torino, Istituto Nazionale di Fisica Nucleare, Sez. di Torino, Torino (Italy)
  2. Dipartimento di Fisica, Università di Genova, Istituto Nazionale di Fisica Nucleare, Sez. di Genova, Genova (Italy)
Publication Date:
OSTI Identifier:
22224221
Resource Type:
Journal Article
Resource Relation:
Journal Name: Annals of Physics (New York); Journal Volume: 337; Other Information: Copyright (c) 2013 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
73 NUCLEAR PHYSICS AND RADIATION PHYSICS; CONVERGENCE; COUPLING; EXCITATION; EXCITED STATES; HAMILTONIANS; NUCLEI; PAIRING INTERACTIONS; RICHARDSON EQUATION; SPECTRA; STRONG-COUPLING MODEL