Self-consistent description of emission processes in axially-symmetric nuclei

We present a theory of cluster emission processes in terms of proton ($\pi$) and neutron ($\nu$) single–particle (sp) degrees of freedom within a self–consistent mean–field (SCMF) constructed from a two–particle interaction having relative (rel) and center of mass (com) terms centered on the nucler surface, the latter describing the interaction between the com of a pair of particles and the surface of an axially–symmetric nucleus. In this way the $\alpha$-clustering phenomenon becomes enhanced on the nuclear surface. We present applications for unstable nuclei that decay through the emission of $\alpha$–particles above ${}^{100}\text{Sn}$, ${}^{208}\text{Pb}$ and within the actinidies series.