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The Generalized Coherent State Model, proposed previously for a unified description of magnetic and electric collective properties of nuclear systems, is extended to account for the chiral like properties of nuclear systems. To a phenomenological core described by the GCSM a set of interacting particles are coupled. Among the particle-core states one identifies a finite set which have the property that the angular momenta carried by the proton and neutron quadrupole bosons and the particles respectively, are mutually orthogonal. All terms of the model Hamiltonian satisfy the chiral symmetry except for the spin-spin interaction. The magnetic properties of the particle-core states, where the three mentioned angular momenta are orthogonal, are studied. A quantitative comparison of these features with the similar properties of states, where the three angular momenta belong to the same plane, is performed.

Using an angular-momentum-projected single-particle basis, a proton-neutron quasiparticle random-phase approximation approach is used to study the 2νββ properties of 10 isotopes, exhibiting various quadrupole deformations. The parent and daughter nuclei exhibit different quadrupole deformations. Since the projected basis enables a unified description of deformed and spherical nuclei, situations where the nuclei involved in the double β decay process are both spherical, both deformed, or one spherical and the other deformed can be treated through a single formalism. Dependence of single β − and β + strength distribution on atomic mass number and nuclear deformation is analyzed. For the double β decay process, the Gamow-Teller transition amplitudes and half-lives are calculated. Results are compared with experimental data as well as with predictions of other theoretical approaches. The agreement between the present results and experimental data is fairly good.

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The phenomenological generalized coherent-state model Hamiltonian is amended with a many-body term describing a set of nucleons moving in a spherical shell-model mean field and interacting among themselves with pairing, as well as with a particle–core interaction involving a harmonic quadrupole–quadrupole, an anharmonic hexdecapole–hexdecapole and a spin–spin interaction. The model Hamiltonian is treated in a restricted space consisting of the core projected states associated to the bands ground, and and two proton-aligned quasiparticles coupled with the states of the ground band to a total angular momentum. The chirally transformed particle–core states are also included. The Hamiltonian contains two terms which are not invariant to the chiral transformations relating the right-handed trihedral and the left-handed ones , , where are the angular momenta carried by fermions, proton and neutron bosons, respectively. The energies defined with the particle–core states form four chiral bands, two of them being degenerate. The electromagnetic properties of the chiral bands are investigated and the results are compared with the experimental data of 138Nd.

A set of interacting particles are coupled to a phenomenological core described using the generalized coherent state model. Among the particle-core states a finite set which have the property that the angular momenta carried by the proton and neutron quadrupole bosons and the particles, separately, are mutually orthogonal are identified. The magnetic properties of such states are studied. All terms of the model Hamiltonian exhibit chiral symmetry except the spin-spin interaction.There are four bands of the type with two-quasiparticle-core dipole states, exhibiting properties which are specific for magnetic twin bands. An application is presented, for the isotopes 188,190 Os.

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