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 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 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)PRLTAO0031-900710.1103/PhysRevLett.61.1930], supplemented with the newly proposed -value-based preformation factor for the cluster with mass . The penetration probability is calculated from the interaction potential using the Wentzel-Kramers-Brillouin (WKB) approximation. The nucleon-nucleon () 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 values of the cluster decays. The nonlinear RMF Lagrangian from which the effective relativistic R3Y potential is derived using the 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 values are used as input in the PCM to obtain the half-lives () of isotopes in their ground and intrinsic excited states.

Results: The calculated half-lives () for relativistic R3Y potential and 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 is required for R3Y potential due to its repulsive nature, whereas the value is 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 . 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 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.