Abstract The nuclear ground state properties of even-even $^{106-120}$Zr nuclei have been investigated within the framework of the relativistic mean field (RMF) approach. The RMF model with density-dependent DDME2 and DDPC1 interactions is utilized for the calculation of potential energy curves, the nuclear ground-state deformation parameters ($\beta_2$), {neutron} separation energies (S$_n$ and S$_{2n}$) and neutron skin thickness (r$_{np}$) of selected Zr isotopes. Later, the $\beta$-decay properties of Zr isotopes were studied using the proton-neutron {{quasi-particle}} random phase approximation (pn-QRPA) model. These include {Gamow-Teller} (GT) strength distributions, $\beta$-decay half-lives, and stellar electron emission/positron capture rates. The $\beta_{2}$ values computed from the RMF model were employed in the pn-QRPA model as an input parameter for the calculations of $\beta$-decay properties for even-even $^{106-120}$Zr nuclei. The stellar rates were computed {using} the pn-QRPA framework with three different types of deformation parameters. {Only at high temperature (T$_{9}$ $\ge$ $2$) and low density ($\rho Y_e \leq 10^{7}$ g/cm$^3$) values, the sum of electron emission and positron capture rates has a sizeable contribution (with positive exponents) to the stellar rates.
Read full abstract