The dynamical symmetries in the algebraic shell model and the collective Interacting Vector Boson Model (IVBM) realized in terms of fermion and boson creation and annihilation operators are investigated. The obtained analytic eigen-energies in both models are compared with the experimental ones and the strengths of the corresponding terms of the model Hamiltonians are evaluated in both cases. In the algebraic realization of the Pairing plus Quadrupole Shell Model the correlations and transition between the quadrupole and pairing phases—dynamical symmetries are investigated in application to nuclear systems in the first few light shells. In the symplectic extension of the IVBM the spectra of heavy even-even nuclei with transitional between rotational and vibrational character is well reproduced. The algebraic connections between dynamical symmetries of the nuclear collective spectra and the ordering of the low-lying states with fixed angular momentum permits a reasonable and experimentally proved prediction of the position of the 0+ band heads of the collective bands. The models based on dynamical symmetries give an elegant and simple way to describe the complex spectra of nuclei with different shapes.

We present Algebraic Microscopic Pairing-plus-Quadrupole Shell Model results for negative-parity states in the upper sd-shell nuclei S-32, Si-32 and Ar-36. The Hamiltonian of the system consists of isoscalar pairing, isovector pairing, quadrupole-quadrupole interaction as well as single-particle terms. The outcome for the energy spectrum calculated in two-oscillator shell model space is compared with the experiment and the results obtained in another theoretical approach. The addition of the second shell to the model space allows us to include the description of the negative-parity states on the same footing for the chosen nuclei which gives a better and more complete picture of their nuclear spectra and other characteristics of interest.

Results obtained for the energy spectra and the low-lying positive-parity energy eigenstates of the upper p f -shell nuclei 64Ge and 68Se with the use of the effective interaction JUN45 are reported. We address the question of how appropriate is the possibility to construct a symmetry-adapted shell model in a single oscillator shell using a Pairing-plus-Quadrupole Hamiltonian. Specifically, we study the goodness of the symmetries pseudo SU(3) and O(6) in the structure of the energy eigenstates. Finally, we relate our results to a proposed mixed-symmetry approach which is able to simultaneously account for the presence of both the pairing and the quadrupole modes as the most important ingredients in the effective interaction while using a restricted part of the full model space.

We present results for the phase transition phenomenon in sdand pf -shell nuclei from calculations performed in the symmetry-adapted basis of the Algebraic Microscopic Pairing-plus-Quadrupole Shell Model. Besides the quadrupole and the pairing (isoscalar plus isovector) interactions, the Hamiltonian also includes the spin-orbit interaction as single-particle terms of the studied systems. Comparison is made between the description obtained for the low-lying excitation energy spectra when these terms are present or not in the Hamiltonian.

The dynamical symmetries of the microscopic shell model appear as the limiting cases of a symmetry adapted Pairing Plus-Quadrupole Model /PQM/, with a Hamiltonian containing isoscalar and isovector pairing and quadrupole interactions. We establish a correspondence between each of the three types of pairing bases and Elliott's SU(3) basis, that describes collective rotation of nuclear systems with quadrupole deformation. It is derived from their complementarity to the same LS coupling chain of the shell model number conserving algebra. The probability distribution of the S U(3) basis states within the pairing eigenstates is also obtained through a numerical diagonalization of the PQM Hamiltonian in each limit. We introduce control parameters, which define the phase diagram of the model and determine the role of each term of the Hamiltonian in the correct reproduction of the experimental data for the considered nuclei.

We explore the dynamical symmetries of the shell model number conserving algebra, which define three types of pairing and quadrupole phases, with the aim to obtain the prevailing phase or phase transition for the real nuclear systems in a single shell. This is achieved by establishing a correspondence between each of the pairing bases with the Elliott’s SU(3) basis that describes collective rotation of nuclear systems. This allows for a complete classification of the basis states of different number of particles in all the limiting cases. The probability distribution of the SU(3) basis states within theirs corresponding pairing states is also obtained. The relative strengths of dynamically symmetric quadrupole-quadrupole interaction in respect to the isoscalar, isovector and total pairing interactions define a control parameter, which estimates the importance of each term of the Hamiltonian in the correct reproduction of the experimental data for the considered nuclei.

We explore the dynamical symmetries of the shell model number conserving algebra, which define three types of pairing and quadrupole phases, with the aim to obtain the prevailing phase or phase transition for the real nuclear systems in a single shell. This is achieved by establishing a correspondence between each of the pairing bases with the Elliott's SU(3) basis that describes collective rotation of nuclear systems. This allows for a complete classification of the basis states of different number of particles in all the limiting cases. The probability distribution of the SU(3) basis states within theirs corresponding pairing states is also obtained. The relative strengths of dynamically symmetric quadrupole-quadrupole interaction in respect to the isoscalar, isovector and total pairing interactions define a control parameter, which estimates the importance of each term of the Hamiltonian in the correct reproduction of the experimental data for the considered nuclei.

Within the algebraic realization of the Pairing-plus-Quadrupole Model /PQM/ in the framework of the Elliott’s SU(3) Model,we present some particular applications for realistic nuclear systems. The probability distribution of the SU(3) basis states within the isovector, isoscalar and total pairing eigenstates is obtained through a numerical diagonalization of the PQM Hamiltonian in each limit. This allows the investigation of the interplay between the pairing and quadrupole interactions in the Hamiltonian of the PQM, containing all of them as limiting cases. The relative strengths of the dynamically symmetric quadrupole-quadrupole interaction with the considered types of pairing interactions are investigated systematically for systems like the 20Ne.

We explore the algebraic realization of the Pairing-Plus-Quadrupole Model /PQM/ in the framework of the Elliott's SU(3) Model with the aim to obtain the complementary and competing features of the two interactions through the relation between the pairing and the SU(3) bases. First, we establish a correspondence between the SO(8) pairing basis and the Elliott's SU(3) basis. It is derived from their complementarity to the same LST coupling chain of the shell-model number-conserving algebra. The probability distribution of the SU(3) basis states within the SO(8) pairing states is also obtained and allows the investigation of the interplay between the pairing and quadrupole interactions in the Hamiltonian of the PQM, containing both of them as limiting cases. The description of some realistic N similar to Z nuclear systems is investigated in a SU(3)-symmetry-adapted basis within a model space of one and two oscillator shells.

A symmetry adapted realization of the Pairing-plus-Quadrupole Model /PQM/ has been explored in the framework of the Elliott’s SU(3) Model. The aim is to obtain the complementary and competing features of the pairing and quadrupole interactions in the model Hamiltonian, containing both of them as limiting cases of dynamical symmetries. For the purpose, one or two control parameters are introduced which account for the relative importance of each term in the Hamiltonian and serve to describe the effect of phase transition. The calculations are performed for nuclei in a single oscillator shell. PACS codes: 21.60.Fw, 21.60.Cs, 21.60.Ev

We explore the algebraic realization of the Pairing-plus-Quadrupole Model /PQM/ in the framework of the Elliott’s SU(3) Model with the aim to obtain the complementary and competing features of the two interactions through the relation between the pairing and the SU(3) bases. First, we establish a correspondence between the SO(8) pairing basis and the Elliott’s SU(3) basis. It is derived from their complementarity to the same LS-coupling chain of the shellmodel number-conserving algebra. The probability distribution of the SU(3) basis states within the SO(8) pairing states is also obtained and allows the investigation of the interplay between the pairing and quadrupole interactions in the Hamiltonian of the PQM. Some particular examples based on this SO(8)-SU(3) basis correspondence are applied for the build-up of a more elaborated microscopic model that can be used in more realistic cases, which take into account the interactions between two shells and between a shell plus an orbital.

As a simpler version of an extended (pseudo-)SU(3) model which acts in a model space of more than one oscillator shells, an extended pairing-plus-quadrupole model is introduced. The Hamiltonian consists of quadrupole-quadrupole plus pp-, nn- and pn-isovector and isoscalar pairing terms as well as terms describing the pair-scattering between two shells. Energy spectra and shape parameters for two N = Z nuclear systems having the same nucleon content as the nuclei Ne-20 and Zn-60 which belong to two different areas of the nuclear chart (ds - fp or upper - fp - gds shells) are calculated and the role of the two parts in the interaction, depending on the parameter strengths, is discussed. Both extended models provide for a microscopic description of nuclei while being selective on the choice of the relevant model space.

An extended SU(3) shell model that for the first time explicitly includes unique-parity levels is introduced. Shell-model calculations for the isotopes of $^{64}$Ge and $^{68}$Se are performed where valence nucleons beyond the N=28=Z core occupy levels of the normal parity upper-$fp$ shell ($f_{5/2},p_{3/2},p_{1/2}$) and the unique parity $g_{9/2}$ intruder configuration. The levels of the upper-$fp$ shell are handled within the framework of an m-scheme basis as well as its pseudo-SU(3) counterpart, and respectively, the $g_{9/2}$ as a single level and as a member for the complete $gds$ shell. It is demonstrated that the extended SU(3) approach allows one to better probe the effects of deformation and to account for many key properties of the system by using a highly truncated model space.

Microscopic models, which embody the simplicity and significance of a dynamical symmetry approach to nuclear structure, are reviewed. They can reveal striking features of atomic nuclei when a symmetry dominates and solutions in domains that may otherwise be unreachable.

Microscopic models, which embody the simplicity and significance of a dynamical symmetry approach to nuclear structure, are reviewed. They can reveal striking features of atomic nuclei when a symmetry dominates and solutions in domains that may otherwise be unreachable. 1. Overview of algebraic fermion models. A theory that invokes group symmetries is driven by an expectation that the wave functions of the quantum mechanical system under consideration can be characterized by their invariance properties under the corresponding symmetry transformations. But even when the symmetries are not exact, if one can find near invariant operators, the associated symmetries can be used to help reduce the dimensionality of a model space to a tractable size. Throughout the years, group-theoretical approaches have identified fundamental symmetries in light to heavy nuclei and achieved a reasonable reproduction of experimental data (for a review of fermion models, see 1). In addition, they provide theoretical predictions for nuclear systems including heavy unstable nuclei not yet explored, and 'exotic' nuclei, such as neutron-deficient or N ≈ Z nuclei on the path of the nucleosynthesis rp-processes. It is well-known that effective two-body interactions in nuclei are dominated by pairing and quadrupole terms. The former gives rise to a pairing gap in nuclear spectra, and the latter is responsible for enhanced electric quadrupole transitions in collective rotational bands. Indeed, within the framework of the harmonic oscillator shell-model, both limits have a clear algebraic structure in the sense that the spectra exhibit a dynamical symmetry. In the pairing limit the symplectic Sp(4) (∼ SO(5) 2,3) group together

. Shell-model calculations for isotopes of Ge and Se are reported where valence nucleons beyond the N = 28 = Z core occupy levels of the normal parity upper-fp shell (f 5/2 ,p 3/2 ,p 1/2 ) and the unique parity g 9/2 intruder configuration. Results are given for realistic interactions of the Kuo-Brown-3 type with various model space truncations that key in on the number of nucleon pairs allowed to occupy the intruder level. Electromagnetic (E2 & M1) rates as well as decay probabilities are calculated, some of which are key in determining the structure of “waiting point” nuclei that regulate certain nucleo-astrosynthesis processes. The role of the intruder level, which is treated on an equal footing with the normal parity levels, is shown to be important for reproducing structural details. The levels of the upper-fp shell are handled within the framework of a normal ls-coupled basis as well as its pseudo-SU(3) counterpart, and respectively, the g 9/2 as a single level and as a member for the complete gds shell. The second of these two approaches, namely, the SU(3) picture, allows one to better probe the effect of deformation.

Shell‐model calculations for upper fp‐shell nuclei using realistic interactions are reported. Valence nucleons beyond the N=28=Z core are considered to fill levels of the normal parity upper fp‐shell and the unique parity configurations that consists either of the g9/2 level or the whole gds‐shell. These two cases are handled within a standard M‐scheme approach and an SU(3) picture, respectively. Results for low‐lying energy spectra, single‐particle occupancies and symmetry properties of the eigenstates are reported. Various truncations are considered that key on the number of nucleon pairs allowed to occupy the unique‐parity space. The calculations demonstrate the importance of the unique‐parity space to the structure of upper fp‐shell nuclei.

Shell-model calculations for Cu-58 and Ge-64 in the pf(5/2)g(9/2) model space using a realistic interaction are reported and compared to those generated using an appropriately renormalized counterpart of the interaction in the truncated pf(5/2) subspace. The results suggest that reliable computations can be performed in a space that does not explicitly include the intruder level so long as the interaction as well as the transition operators are renomalized appropriately.