Partial Dynamical Symmetry in Deformed Nuclei

Abstract

We discuss the notion of partial dynamical symmetry in relation to nuclear spectroscopy. Explicit forms of Hamiltonians with partial $SU(3)$ symmetry are presented in the framework of the interacting boson model of nuclei. An analysis of the resulting spectrum and electromagnetic transitions demonstrates the relevance of such partial symmetry to the spectroscopy of axially deformed nuclei.Comment: 12 pages, Revtex, 1 uuencoded figure, Phys. Rev. Lett. in pres

Partial dynamical symmetry and odd-even staggering in deformed nuclei

“…The essential idea is to relax the stringent conditions of complete solvability, so that only part of the eigenspectrum retains all the DS quantum numbers. Various types of bosonic and fermionic PDS are known to be relevant to nuclear spectroscopy [4][5][6][7][8][9][10][11][12][13]. In the present contribution we demonstrate the relevance of PDS to the odd-even staggering in the γ-band of 156 Gd [13].…”

“…Two-body Hamiltonians of this class have been shown to play a role in diverse phenomena, including spectroscopy of rare-earth nuclei [5][6][7], quantum phase transitions [17,18] and mixed regular and chaotic dynamics [18,19]. The two classes of SU(3)-PDS Hamiltonians demonstrate the increase in flexibility obtained by generalizing the concept of DS to PDS.…”

Partial Dynamical Symmetry in a Fermion System

“…Implications of the structural differences between the various resonance bands for giant monopole and quadrupole transitions remain to be investigated. The occurrence of partial symmetries for fermions, as shown in this work, and for bosons, as presented in previous works [3], highlights their relevance to dynamical systems and motivates their further study.…”

“…Partial Dynamical Symmetry (PDS) [2] corresponds to a particular symmetry-breaking for which the Hamiltonian is not invariant under the symmetry group and hence various irreps are mixed in its eigenstates, yet it possess a subset of 'special' solvable states which respect the symmetry. This new scheme has recently been introduced in bosonic systems and has been applied to the spectroscopy of deformed nuclei [3] and to the study of mixed systems with coexisting regularity and chaos [4]. It is the purpose of this Letter to demonstrate the relevance of the partial dynamical symmetry concept to fermion systems.…”

“…The solvable states then form rotational bands and since their wave functions are known, one can evaluate the E2 rates between them [10]. It is of interest to note that both the fermion Hamiltonian presented here and the boson Hamiltonian of [3] exhibit partial SU(3) symmetry and involve a SU(3) tensor of the form [(2, 0)…”