Parameter dependence of the $β$-decay properties of neutron-rich Zr isotopes within the interacting boson model

Abstract

We investigate parameter dependence of the calculated $β$-decay properties, as well as low-lying states for the neutron-rich Zr isotopes within the neutron-proton interacting boson model (IBM-2) and interacting boson-fermion-fermion model (IBFFM-2). It is shown that the calculated $\log_{10}ft$ values for the transitions of the $0^+_1$ ground states of the parent even-even nuclei $^{96-102}$Zr into the $1^+_1$ states of the daughter odd-odd nuclei $^{96-102}$Nb consistently exhibit a strong dependence on those parameters associated with the quadrupole-quadrupole boson interaction, and with the residual interaction between an unpaired neutron and an unpaired proton in the IBFFM-2 Hamiltonian for the odd-odd Nb nuclei. By the reduction in magnitude of the quadrupole-quadrupole interaction strength by approximately a factor of 2, the calculated $\log_{10}ft$ values for the Zr$(0^+_1)\to$Nb$(1^+_1)$ transitions increase and agree with the experimental values. This points to a significant improvement over the previous study performed in the same mass region, that consists of the mapping from a relativistic energy density functional calculation onto the IBM-2 Hamiltonian.