Shape phase transitions in odd-A nuclei are investigated within the framework of the interacting boson-fermion model. The case of a single j = 9/2 fermion coupled to an even-even boson core is considered. This boson core transits from spherical to γ -unstable shapes depending on the value of a control parameter in the boson Hamiltonian. The effect of the coupling of the odd particle to this core along the shape transition and, in particular, at the critical point is discussed. For that purpose, the ground-state energy surface in terms of the β and γ shape variables for the even core and odd-even energy surfaces for the different K states coming from j = 9/2 are constructed. The evolution of each individual coupled state along the transition from the spherical [U(5)] to the γ -unstable [O(6)] situation is investigated. One finds that the core-fermion coupling gives rise to a smoother transition than in the even-core case.

Even-even nuclei in the A ∼ 100 mass region are investigated within the framework of the interacting boson model-1 (IBM-1). The study includes energy spectra and electric quadrupole transition properties of zirconium, molybdenum, ruthenium and palladium isotopes with neutron number N ≥ 52. A global parametrization of the IBM-1 Hamiltonian is found leading to a description of about 300 collective levels in 30 nuclei with a root-mean-square deviation from the observed level energies of 120 keV. The importance of the d 5/2 subshell closure at neutron number N = 56 is pointed out. The geometric character of the nuclei can be visualized by plotting the potential energy surface V (β, γ) obtained from the IBM-1 Hamiltonian in the classical limit. The parametrization established on the basis of known elements is used to predict properties of the unknown, neutron-rich isotopes 106 Zr, 112 Mo, 116 Ru and 122 Pd.

We investigate even-even nuclei in the A ∼ 70 mass region within the framework of the proton-neutron quasi-particle random phase approximation (pn-QRPA) and the interacting boson model-1 (IBM-1). Our work includes calculation of the energy spectra and the potential energy surfaces V(β, γ) of Zn, Ge, Se, Kr and Sr nuclei with the same proton and neutron number, N = Z. The parametrization of the IBM-1 Hamiltonian was performed for the calculation of the energy levels in the ground state bands. Geometric shape of the nuclei was predicted by plotting the potential energy surfaces V(β, γ) obtained from the IBM-1 Hamiltonian in the classical limit. The pn-QRPA model was later used to compute half-lives of the neutron-deficient nuclei which were found to be in very good agreement with the measured ones. The pn-QRPA model was also used to calculate the Gamow-Teller strength distributions and was found to be in decent agreement with the measured data. We further calculate the electron capture and positron decay rates for these N = Z waiting point (WP) nuclei in the stellar environment employing the pn-QRPA model. For the rp-process conditions, our total weak rates are within a factor two compared with the Skyrme HF+BCS+QRPA calculation. All calculated electron capture rates are comparable to the competing positron decay rates under rp-process conditions. Our study confirms the finding that electron capture rates form an integral part of the weak rates under rp-process conditions and should not be neglected in the nuclear network calculations.

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