Microscopic studies in heavy nuclei are very scarce due to large valence spaces involved. This computational problem can be avoided by means of the use of symmetry based models. Ground-state, γ and β-bands, and their B(E2) transition strengths in 160−168 Dy isotopes, are studied in the framework of the pseudo-SU(3) model which includes the preserving symmetry Q · Q term and the symmetry-breaking Nilsson and pairing terms, systematically parametrized. Additionally, three rotor-like terms are considered whose free parameters, fixed for all members of the chain are used to fine tune the moment of inertia of rotational bands and the band-head of γ and β-bands. The model succesfully describes in a systematic way rotational features in these nuclei and allows to extrapolate toward the midshell nucleus 170 Dy. The results presented show that it is possible to study full chain of isotopes or isotones in the region with the present model.

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The hadronic spectrum obtained in the framework of a QCD-inspired schematic model, is presented. The model is the extension of a previous version, whose basic degrees of freedom are constituent quarks and antiquarks, and gluons. The interaction between quarks and gluons is a phenomenological interaction and its parameters are fixed from data. The classification of the states, in terms of quark and antiquark and gluon configurations is based on symmetry considerations, and it is independent of the chosen interaction. Following this procedure, nucleon and ∆ resonances are identified, as well as various penta-and hepta-quarks states. The lowest pentaquarks state is predicted at 1.5 GeV and it has negative parity, while the lowest hepta-quarks state has positive parity and its energy is of the order of 2.5 GeV.PACS numbers: 12.90+b, 21.90.+f I. INTRODUCTIONIn previous papers [1, 2, 3], we have proposed a schematic model aimed at the description of the non-perturbative regime of QCD. The main concepts about the model can be found in [1], together with the applications to the meson spectrum of QCD. Along this line, Ref.[2] deals with the appearance of phase transitions and condensates. A preliminary set of results, about the energy and parity of systems of the type q 3 (qq) (pentaquarks), and q 3 (qq) 2 (heptaquarks), was presented in [3].As it was discussed in [1], this model describes reasonable well the main features of the meson spectrum of QCD. This is a nice result since it shows that, also in the conditions of low energy QCD, e.g.; large coupling constants and non-conservation of particle number, the use of simple models may be very useful. The model of [1] belongs to the class of models [4] which may be solved by algebraic, group theory and symmetry-enforcing techniques, and that describe the interaction between fermions and bosons. Some examples of this class of models can be found in [5], [6], and [7]. Concerning the use of symmetry principles, the work of [8] shows how the ordering of levels of many gluon states may be understood. In [8], the predictive power of the model, based on the microscopical treatment of gluons configurations, was tested by means of the spectrum related to exotic quantum numbers.The purpose of this work is to extend the model of Ref.[1] to describe the main structure of the hadronic spectrum of QCD. The essentials of the model are the following: a)color, flavor and spin degrees of freedom are taken explicitly into account to built the configurations, both in the quark and gluon sectors of the model; b)the quarks and antiquarks are placed in a s-state; c)the interaction of the quarks with the gluons proceeds via gluon pairs coupled to spin and color zero, only. Other possible gluon states are considered as spectators.The present work is organized as follows. Section II gives a brief description of the model. We shall avoid as much as possible the repetition of details which can be found in the already published papers [1,2,3], and concentrate in the aspects which are relevant for the ...

Isovectorial pairing in solvable and algebraic modelsToAbstract. Schematic interactions are useful to gain some insight in the behavior of very complicated systems such as the atomic nuclei. Prototypical examples are, in this context, the pairing interaction and the quadrupole interaction of the Elliot model. In this contribution the interplay between isovectorial pairing, spin-orbit, and quadrupole terms in a harmonic oscillator shell (the so-called pairing-plus-quadrupole model) is studied by algebraic methods. The ability of this model to provide a realistic description of N=Z even-even nuclei in the fpshell is illustrated with 44 Ti. Our calculations which derive from schematic and simple terms confirm earlier conclusions obtained by using realistic interactions: the SU(3) symmetry of the quadrupole term is broken mainly by the spin-orbit term, but the energies depends strongly on pairing.

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