Narrow Results

The shape evolution of even–even Mo isotopes from the line of stability up to the two-neutron drip-line is investigated within the self-consistent Hartree–Fock–Bogoliubov theory in both the axial and triaxial symmetries. The Skyrme energy density functional SLy4 has been considered in the particle-hole channel, while the zero range delta-interaction has been employed in the particle–particle channel. In order to correctly treat the pairing correlations, a particle-number projection was carried out by the Lipkin–Nogami (LN) method. The two-neutron separation energies and root-mean-square (rms) charge radii are investigated and compared with available experimental data. The evolution of the potential energy surfaces in the (β, γ) deformation plane is presented and discussed. In addition, the obtained ground state deformation parameters are compared to those obtained by other models.

A particle rotor model with a quasi-neutron coupled with a triaxially deformed rotor is applied to study signature splitting for bands with intruder orbital ν7/2⁺[633] and nonintruder orbital ν5/2^-[512] in ¹⁷³W. Excellent agreement with the observed energy spectra has been achieved for both bands. Signature splitting for band ν7/2⁺[633], and band ν5/2^-[512] before the onset of signature inversion, is satisfactorily reproduced by introducing the γ degree of freedom. The phase and amplitude of signature splitting in band ν5/2^-[512] are attributed to strong competition between 2f_7/2 and 1h_9/2 components. However, the self-consistent explanation of signature inversion in band ν5/2^-[512] is beyond the present one quasi-neutron coupled with a triaxially deformed rotor.

The nuclear potential energies of neutron deficient even–even rare earth nuclei ¹⁵⁸Er and ¹⁶²Hf for the spin range 0–60 are computed within the framework of cranked Nilsson–Strutinsky shell correction method. The potential energy surface diagrams are analyzed in terms of quadrupole deformation and triaxiality parameter. The shape evolution of these isotopes with respect to spin is studied. The spin dependence of nuclear equilibrium potential energy is also verified.

The phenomenological classification of collective quadrupole excitations by means of the Bohr–Hamiltonian (BH) is reviewed with focus on signatures for triaxility. The variants of the microscopic BH derived by means of the Adiabatic Time-Dependent Mean Field theory from the Pairing-plus-quadrupole–quadrupole interaction, the Shell Correction Method, the Skyrme Energy Density Functional, the Relativistic Mean Field Theory and the Gogny interaction are discussed and applications to concrete nuclides reviewed. The Generator Coordinate Method for the five-dimensional quadrupole deformation space and first applications to triaxial nuclei are presented. The phenomenological classification in the framework of the Interacting Boson Model is discussed with a critical view on the boson number counting rule. The recent success in calculating the model parameters by mapping the mean field deformation energy surface on the bosonic one is discussed and the applications listed. A critical assessment of the models is given with focus on the limitations due to the adiabatic approximation. The Tidal Wave approach and the Triaxial Projected Shell Model are presented as practical approaches to calculate spectral properties outside the adiabatic region.

In this paper, a transitional interacting boson model (IBM) Hamiltonian in both sd-(IBM) and sdg-IBM versions based on affine $SU(1,1)$ Lie algebra is employed to describe deviations from the gamma-unstable nature of Hamiltonian along the chain of Xe isotopes. sdg-IBM Hamiltonian proposed a better interpretation of this deviation which cannot be explained in the $sd$-boson models. The nuclei studied have well-known $\gamma$ bands close to the $\gamma$-unstable limit. The energy levels, $B(E2)$ transition rates and signature splitting of the $\gamma$ -vibrational band are calculated via the affine SU(1,1) Lie algebra. An acceptable degree of agreement was achieved based on this procedure. It is shown that in these isotopes the signature splitting is better reproduced by the inclusion of sdg-IBM. In none of them, any evidence for a stable, triaxial ground state shape is found.

Recently, from the study of the absolute $B(E2)$ values for the ($\gamma$–$g$) $E$2 transitions, the different roles of the triaxiality parameter $\gamma =(0^{\circ }\text{–}20^{\circ })$ and $\gamma =(20^{\circ }\text{–}30^{\circ })$ parts were pointed out. Here, the use of the triaxial rotor model expressions for the $B(E$2)s in producing the bell-shaped curve of $B(E2,2_{\gamma }-0_1^{+})$ is illustrated. The variation of certain ($\gamma$–$g$) $B(E2)$ ratios versus $\gamma$ for the states $2_{\gamma }$ and $3_{\gamma }$ are illustrated, reflecting the two regions of $\gamma$. The inter relation of the $\gamma$ and $\beta$ variables is illustrated for the Os isotopes.