Dynamical symmetry of isobaric analog0+states in medium mass nuclei

Abstract

An algebraic sp(4) shell model is introduced to achieve a deeper understanding and interpretation of the properties of pairing-governed 0 + states in medium mass atomic nuclei. The theory, which embodies the simplicity of a dynamical symmetry approach to nuclear structure, is shown to reproduce the excitation spectra and fine structure effects driven by proton-neutron interactions and isovector pairing correlations across a broad range of nuclei.

Global properties of fp-shell interactions in many-nucleon systems

“…3), to find its optimal value (which is an exact solution) by maximizing the ζ correlation coefficient [50] between the model H M interaction and the pure two-body part H 0 (2) of each of the effective interactions under consideration. We do not alter the parameters of the Sp(4) model, which have already been shown in an appropriate domain of states to be valid for reproducing various quantities (such as binding energies and pairing gaps) and are in agreement with estimates available in literature [16,17].…”

“…[17] for parameter estimates). The sp(4) algebraic structure is exactly the one needed in nuclear isobaric analog 0 + states to describe proton-proton (pp), neutron-neutron (nn) and proton-neutron (pn) isovector pairing correlations (accounted by the pair annihilation (creation) operators ( †) +1,−1,0 ) and isospin symmetry.…”

“…where H sp (4) is an isoscalar Sp(4)-dynamically symmetric interaction [17] for a system of n valence nucleons (an eigenvalue ofN) in a 4Ω-dimensional space,…”

“…The latter is reflected by the isospin operatorT 2 and related to a J-independent isoscalar (T = 0) pn force. The most general model interaction with Sp(4) dynamical symmetry [17] has been found to provide for a reasonable microscopic description of the pairing-governed isobaric analog 0 + states in light and medium mass nuclei and to account quite well for the observed detailed structure beyond mean-field effects such as the N = Z anomalies, isovector pairing gaps and staggering effects [16]. In addition, the H sp(4) interaction (4) has been shown to strongly correlate, especially when the quadrupole term is introduced, with the "CD-Bonn", CD-Bonn+3terms and GXPF1 interactions in the 1f 7/2 orbit [18].…”

“…The likely success of the three interactions for reproducing pairing and rotational spectral features is examined in a comparison to a pairing-plus-quadrupole model interaction, which combines a Sp(4) dynamically symmetric model interaction [16,17] for description of like-particle and proton-neutron (isovector) pairing correlations with a SU(3) symmetric term that governs a shape-determined dynamics. If the model and effective interactions are strongly correlated, then the latter will reflect the characteristic properties of the simpler model Hamiltonian, which in turn may be used as a good approximation.…”