From twonucleon forces to light nuclei with the similarity renormalization group
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Author(s): 
Total Authors: 3

Affiliation:  ^{[1]} Univ Granada, Dept Fis Atom Mol & Nucl, E18071 Granada  Spain
^{[2]} Univ Granada, Inst Carlos Fis Teor & Computac 1, E18071 Granada  Spain
^{[3]} Univ Presbiteriana Mackenzie, Escola Engn, Ctr Radioastron & Astrofis Mackenzie, Sao Paulo  Brazil
^{[4]} Univ Estadual Campinas, UNICAMP, Grp Opt & Modelagem Numer GOMNI, Fac Tecnol FT, BR13081970 Campinas, SP  Brazil
Total Affiliations: 4

Document type:  Journal article 
Source:  Physics Letters B; v. 735, p. 149156, JUL 30 2014. 
Web of Science Citations:  4 
Abstract  
On a finite momentum grid with N integration points p(n) and weights w(n) (n = 1,..., N) the Similarity Renormalization Group (SRG) with a given generator G unitarily evolves an initial interaction with a cutoff lambda on energy differences, steadily driving the starting Hamiltonian in momentum space Hn,m(0) = p(n)(2)delta(n,m) + Vn,(m) to a diagonal form in the infrared limit (lambda > 0), Hn,m(G,lambda > 0) = Epi(n) delta(n),(m), where pi(n) is a permutation of the eigenvalues En which depends on G. Levinson's theorem establishes a relation between phaseshifts delta(p(n)) and the number of boundstates, n(B), and reads delta(p(1))  delta(p(N)) = n(B)pi. We show that unitarily equivalent Hamiltonians on the grid generate reaction matrices which are compatible with Levinson's theorem but are phaseinequivalent along the SRG trajectory. An isospectral definition of the phaseshift in terms of an energyshift is possible but requires in addition a proper ordering of states on a momentum grid such as to fulfill Levinson's theorem. We show how the SRG with different generators G induces different isospectral flows in the presence of boundstates, leading to distinct orderings in the infrared limit. While the Wilson generator induces an ascending ordering incompatible with Levinson's theorem, the Wegner generator provides a much better ordering, although not the optimal one. We illustrate the discussion with the nucleonnucleon (NN) interaction in the S1(0) and S3(1) channels. (C) 2014 The Authors. Published by Elsevier B. V. (AU)  
FAPESP's process:  11/182112  The nuclear force and the renormalization group 
Grantee:  Varese Salvador Timoteo 
Support type:  Regular Research Grants 
FAPESP's process:  14/049759  From twonucleon forces to light nuclei with the similarity renormalization group 
Grantee:  Varese Salvador Timoteo 
Support type:  Regular Research Grants 