Sensitivity analysis of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>β</mml:mi></mml:math>-decay half-life predictions for Ge, As, Zr, and Mo nuclei within the mapped interacting boson model

We analyze parameter sensitivities of the mapped interacting boson model (IBM) and boson-fermion-fermion model (IBFFM) in the description of $\ensuremath{\beta}$-decay properties of the even-mass neutron-deficient Ge and As, and neutron-rich Zr and Mo isotopes. Based on the self-consistent mean-field calculations with a given energy density functional and a pairing interaction, the IBM Hamiltonian for even-even nuclei, single-particle energies, and occupation probabilities for unpaired nucleons, which are necessary building blocks of the IBFFM Hamiltonian and Gamow-Teller and Fermi transition operators, are completely determined. A few coupling constants of the boson-fermion and residual neutron-proton interactions are only phenomenological parameters fitted to reproduce low-energy spectra of odd-mass and odd-odd nuclei. It is found that the calculated ${log}_{10}ft$ values for the ${\ensuremath{\beta}}^{+}$ decays $^{68}\mathrm{As}\ensuremath{\rightarrow}^{68}\mathrm{Ge}$ are particularly sensitive to the quadrupole-quadrupole boson interaction strength used for the parent $(^{68}\mathrm{As})$ nucleus. We further incorporate higher-order terms in the one-nucleon transfer operators in the boson system, and find that, while their effects are non-negligible, they do not significantly alter qualitative features of $\ensuremath{\beta}$-decay properties. We report a novel application of the mapped IBM framework to compute $\ensuremath{\beta}$-decay half-lives, and show that the observed trend along isotopic chains are reasonably reproduced.