Heavy-ion fusion using a parabolic barrier with Coulomb interaction

Abstract

In this work, we describe the fusion mechanism between two heavy ions as penetration through a parabolic barrier in the presence of a proper Coulomb interaction with appropriate boundary conditions. The parabolic potential is matched to the Coulomb potential in order to avoid any discontinuity of the potential surface. The Schr\"odinger equations in the exterior and interior regions containing, respectively, the Coulomb and the parabolic potentials, are solved and the penetrability function is calculated from the logarithmic derivative at the matching radius. The theory is then applied to calculate the fusion cross sections for the reactions $^{16}\mathrm{O}$+$^{16}\mathrm{O}$, $^{12}\mathrm{C}$+$^{28,29,30}\mathrm{Si}$, $^{16}\mathrm{O}$+$^{24,26}\mathrm{Mg}$, $^{16}\mathrm{O}$+$^{28,29,30}\mathrm{Si}$, and $^{40}\mathrm{Ca}$+$^{40}\mathrm{Ca}$ and are found to reproduce the data quite well. The theory is valid for energies both below and above the barrier.NUCLEAR REACTIONS Heavy-ion fusion; effect of Coulomb interaction; analytic expression for the penetrability function; application to various reactions.