Cluster decay half-lives of Ba112–122 isotopes from the ground state and intrinsic excited state using the relativistic mean-field formalism within the preformed-cluster-decay model

Abstract

Background: The cluster radioactivity from the neutron-deficient trans-tin region of the nuclear landscape has given immediate attention in the nuclear structure studies. Recent prediction of the emitting clusters from the ground and intrinsic excited states of proton-rich Ba isotopes opens the direction to explore the corresponding decay characteristics. A theoretical probe is necessary for understanding the cluster decays of Ba isotopes.Purpose: In the present study, cluster-decay half-lives are calculated and their decay characteristics are investigated for even-even $^{112--122}\mathrm{Ba}$ isotopes in both ground and intrinsic excited states along the proton drip line.Method: The preformed-cluster-decay model (PCM) is employed for estimating the decay half-lives. The preformation probability $({P}_{0})$ of the cluster decay from the parent nuclei is calculated by using the well-known phenomenological formula of Blendowske and Walliser [Phys. Rev. Lett. 61, 1930 (1988)], supplemented with the newly proposed $Q$-value-based preformation factor for the cluster with mass ${A}_{c}>28$. The penetration probability is calculated from the interaction potential using the Wentzel-Kramers-Brillouin (WKB) approximation. The nucleon-nucleon ($NN$) potential and individual binding energy (BE) of the cluster and daughter nuclei are estimated from the microscopic relativistic mean-field formalism (RMF) and compared with those from experiments and the finite-range-droplet model for the estimation of the $Q$ values of the cluster decays. The nonlinear RMF Lagrangian from which the effective relativistic R3Y $NN$ potential is derived using the $\mathrm{NL}{3}^{*}$ parameter set is employed for the calculation of the nuclear matter densities. The R3Y and well-known M3Y potential are employed to obtain the cluster-daughter interaction potential using the double-folding procedure along with their corresponding RMF densities. The total potential along with their respective cluster decay $Q$ values are used as input in the PCM to obtain the half-lives (${T}_{1/2}$) of $^{112--122}\mathrm{Ba}$ isotopes in their ground and intrinsic excited states.Results: The calculated half-lives (${T}_{1/2}$) for relativistic R3Y $NN$ potential and $Q$ values are found to deviate slightly compared to the ones from the M3Y due to the difference in their barrier characteristics. We notice that at elongated neck configuration a minimum neck-length parameter $\mathrm{\ensuremath{\Delta}}R=1.0\phantom{\rule{4.pt}{0ex}}\text{fm}$ is required for R3Y potential due to its repulsive nature, whereas the value is $0.5\phantom{\rule{4.pt}{0ex}}\text{fm}$ is suitable for the M3Y case. However, the estimated decay half-lives for both the potentials are in reasonably good agreement with the experimental lower limit of $^{114}\mathrm{Ba}$. In contrast with the ground-state decays, the inclusion of intrinsic excitation reduces the corresponding half-life values considerably but does not rule out the role of magicity.Conclusions: The sensitivity of the decay half-lives to $Q$ values and neck-length parameter has also been demonstrated. The decay half-lives are predicted for various cluster decays from neutron-deficient Ba isotopes. Since none of the experimental half-lives for the examined clusters is precisely known yet, further studies with available observed half-lives will be needed to substantiate our findings.