The nucleus can be considered a relativistic system, In particular, we focus on heavy nuclei with zero spin and utilize the relativistic core-cluster model to investigate their structure properties. A zero-spin nucleus is assumed to consist of a core and a cluster, core and cluster spins are zero. We will solve the Klein–Gordon equation, which is a relativistic equation optimized for studying zero-spin systems, with the new phenomenological potential. Then, we will calculate the binding energy and charge radius of the zero-spin heavy nuclei by employing the wave function obtained from the Klein–Gordon equation.

[Formula: see text]C is a beta decay isotope, its beta decay is very slow reflecting the stability of this nucleus and emitted from medium and heavy mass nuclei. The [Formula: see text]C result is in excellent agreement with the favored ground-state-to-ground-state transition according to the cluster model of Blendowske et al. We study nuclear structure properties of spin-1/2 heavy nuclei in the relativistic core-cluster model, that its cluster is [Formula: see text]C. According to this model for spin-1/2 heavy nuclei and for obtaining its wave function, we solve the Dirac equation with the new phenomenological potential by parametric Nikiforov–Uvarov method and then calculate the binding energy and charge radius.