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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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