Energy dependence of the nucleus-nucleus potential close to the Coulomb barrier

Abstract

The nucleus-nucleus interaction potentials in heavy-ion fusion reactions are extracted from the microscopic time-dependent Hartree-Fock theory for the mass symmetric reactions ${}^{16}\mathrm{O} + {}^{16}\mathrm{O}$, ${}^{40}\mathrm{Ca} + {}^{40}\mathrm{Ca}$, and ${}^{48}\mathrm{Ca} + {}^{48}\mathrm{Ca}$ and the mass asymmetric reactions ${}^{16}\mathrm{O} + {}^{40, 48}\mathrm{Ca}$, ${}^{40}\mathrm{Ca} + {}^{48}\mathrm{Ca}$, ${}^{16}\mathrm{O} + {}^{208}\mathrm{Pb}$, and ${}^{40}\mathrm{Ca} + {}^{90}\mathrm{Zr}$. When the c.m. energy is much higher than the Coulomb barrier energy, potentials deduced with the microscopic theory identify with the frozen density approximation. As the c.m. energy decreases and approaches the Coulomb barrier, potentials become energy dependent. This dependence indicates dynamical reorganization of internal degrees of freedom and leads to a reduction of the ``apparent'' barrier felt by the two nuclei during fusion of the order of 2--3% compared to the frozen density case. Several examples illustrate that the potential landscape changes rapidly when the c.m. energy is in the vicinity of the Coulomb barrier energy. The energy dependence is expected to have a significant role on fusion around the Coulomb barrier.