A simple formula for ground state nuclear masses based on the microscopic-macroscopic approach is proposed. Considering a set of 2353 nuclei with Z >= 8 and N >= 8, the formula yields an rms deviation of just 266 keV. A few applications, including the loosely bound proton rich nuclei, superheavy nuclei, and cluster emitters, are presented and discussed, establishing the reliability of the proposed formula. The present investigation has a major advantage: it allows one to reliably parametrize the fluctuating part of the ground state energy. This result is very interesting and important, since the fluctuating part of the energy is related directly to the trace formula, which in turn encodes the interaction itself.
The emissions of a particles and protons are the dominant decay channels in the neutron-deficient nuclei corresponding to the sdg major shell. The possibility of cluster emission is explored here. It is shown that the cluster decay mode has a small yet sizable branching ratio.
Systematic investigation of the known even-even transactinide cluster emitters has been carried out by considering the cluster as a point particle and using the exact quantum mechanical treatment of the decay process. It is shown that the cluster decay phenomenon can be described reasonably well using a simple Woods-Saxon mean field. Sensitivity of the half-lives on various aspects of the mean field has been investigated in detail.