Investigation of ground state properties and shape evolution in Hf isotopes using the CDFT approach

The ground-state properties and shape evolution of even-even hafnium isotopes ranging from $N=80$ to the neutron dripline are thoroughly examined using Covariant Density Functional Theory (CDFT) with density-dependent effective interactions, specifically the parameter sets DD-ME1, DD-ME2, DD-PC1, and DD-PCX. Key nuclear properties, including binding energies, two-neutron separation energies ($S_{2n}$), two-neutron shell gaps ($\delta S_{2n}$), neutron pairing energies ($E_{pair,n}$), quadrupole deformation parameters ($\beta_2$), root-mean-square (RMS) charge and matter radii, and neutron skin thickness ($\Delta r_{np}$), are systematically computed and compared with available experimental results and predictions from various theoretical models. These include the Hartree-Fock-Bogoliubov (HFB) framework employing the Skyrme SLy4 interaction, the Finite Range Droplet Model (FRDM), the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) using the PC-PK1 functional, and the relativistic mean-field (RMF) approach with NL3 parameterization. Shell closures at $N=82$ and $N=126$, subshell effects at $N=108$ and $N=152$, and shape transitions with coexistence in $^{192}$Hf and $^{222-236}$Hf are observed. Neutron skin thickness increases with neutron excess, and potential energy surfaces show consistent trends, validating CDFT's reliability for nuclear structure predictions.