Fusion barriers using the energy-density formalism: Simple analytical formula and the calculation of fusion cross sections

Fusion barriers are calculated within the sudden approximation, using the Skyrme interaction energy-density model. Both the closed and unclosed shell nuclei are considered and the role of spin-density term is studied in detail. For unclosed shell nuclei, the fusion cross sections are found to decrease by as much as ∼50 mb when spin-density effects are included. Very accurate, simple analytical expressions, in terms of only the masses and charges of the reacting nuclei, are obtained for the barrier heights and positions. This introduces a great simplification for the fusion barrier calculations