Abstract. We extend the Weinberg compositeness condition to partial waves of L = 1 and resonant states to determine the weight of meson-baryon component in theWe obtain an appreciable weight of N in the (1232) wave function, of the order of 60 % and we also show that, as we go to higher energies in the members of the decuplet, the weights of meson-baryon component decrease and they already show a dominant part for a genuine component in the wave function. We interpret the meaning of the Weinberg sum-rule extended to complex energies.

No abstract

No abstract

The Euclidean dynamical symmetry hidden in the critical region of nuclear shape phase transitions is revealed by a novel algebraic F(5) description. With a nonlinear projection, it is shown that the dynamics in the critical region of the spherical-axial deformed and the spherical-γ soft shape phase transitions can indeed be manifested by this description, which thus provides a unified symmetry-based interpretation of the critical phenomena in the region. PACS numbers: 21.60.Fw, 21.60.Ev, 21.10.Re, 64.70.Tg Dynamical symmetries (DSs) play an important role in elucidating the quintessential nature of quantum many-body dynamical structures, especially their evolution under changing conditions. Typical examples of DS are those associated with the interacting boson model (IBM) [1] for nuclear structure and the vibron model (VM) [2] for molecules and atomic clusters [3], where various DSs provide considerable insight into the nature of shape phases and shape phase transitions (SPTs) [4].