Collective0+excitations and their global properties

Abstract

A simple compact correlation of the energies of the lowest 0 ϩ excitation with the yrast energy ratio R 4/2 (g.s.)ϵE(4 1 ϩ )/E(2 1 ϩ ) is found to characterize all collective nuclei, regardless of structure. This correlation can be reproduced by interacting bosom approximation calculations. Collective signature observables for the states based on 0 2 ϩ excitations indicate a different structure than for the ground state configuration but systematic inconsistencies in their global behavior and discrepancies with calculations prevent a definite interpretation.Two recent areas of interest in the study of collective nuclei have been the evolution of structure with nucleon ͑especially valence nucleon͒ number, in particular the correlations of collective observables, and the structure of intrinsic excitation modes, in particular the nature of 0 ϩ modes. In the former case, recent work ͓1,2͔ has focused on the bilinear correlation of E(4 1 ϩ ) with E(2 1 ϩ ) or of the two neutron separation energies S 2n with E(2 1 ϩ ). Both these correlations basically pertain to the structural evolution of the equilibrium configuration, not that of intrinsic excitation modes. In the latter case, numerous studies of the 0 2 ϩ ͑first excited 0 ϩ state͒ have focused on possible interpretations in terms of multiphonon ͑double ␥-vibrational͒ ͓3-5͔, ␤-vibrational ͓6,7͔, or shape coexisting structures ͓8,9͔.It is the purpose of the present paper to link these two subjects by studying the correlation of the 0 2 ϩ excitation energies with the collective shape signature observable R 4/2 (g.s.)ϵE(4 1 ϩ )/E(2 1 ϩ ), and to compare the properties of the states based on the 0 2 ϩ state with those based on the ground state. The main results will be the discovery of robust simplicities in these poorly understood 0 2 ϩ excitations and evidence that their global properties are seemingly inconsistent and are not easily reproduced by model calculations.The first result is shown in Fig. 1͑a͒ for nuclei from Z ϭ8Ϫ98 where, to compare widely different nuclei, the 0 2 ϩ energies are given on the scale of E(2 1 ϩ ) values. The figure shows a remarkably simple and compact trajectory as a function of R 4/2 (g.s.). Note that the well known difficulties in attempting to understand the nature of 0 2 ϩ excitations in deformed nuclei are not resolved by this simplicity: they are still reflected in the wide range of values of the 0 2 ϩ energies for R 4/2 (g.s.)տ3.2. Nevertheless, the simplicity and robustness of the correlation argues for a simple underlying interpretation. Most of the handful of points above the main trajectory are for light actinide nuclei while the two isolated points below the trajectory are for nuclei ( 184 Hg and 98 Sr) where deformed intruder states have descended into the lowlying spectrum.To try to understand this correlation, we carried out an extensive mesh of interacting boson approximation ͑IBA͒ ͓10͔ calculations, as representative of a collective model approach. The calculations were done with the scaled Hamiltonian (2) . For 0рр1 and Ϫ...

Generic rotation in a collectiveSDnucleon-pair subspace

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