Emission processes in a self-consistent field

We present a microscopic description of cluster emission processes within the Cluster–Hartree–Fock (CHF) self–consistent field (SCF) theory. The starting point is a Woods–Saxon (WS) mean field (MF) with spin–orbit and Coulomb terms. Pairing is treated through standard Bardeen–Cooper–Schrieffer (BCS) quasiparticles. The residual two–body interaction is given by a density–dependent Wigner force having a Gaussian shape with a center of mass (com) correction located in a region of low nuclear density slightly beyond the geometrical contact radius of a system comprised from a nucleus and a surface cluster. We show that such a description adequately reproduces the ground state (gs) shape of a spherical nucleus while the surface correction enhances the radial tail of single particle orbitals, thus allowing for an adequate description of the $\alpha$-decay width for unstable systems.