A density variational approach to nuclear giant resonances at zero and finite temperature

Abstract

We present a density functional approach to the description of nuclear giant resonances (GR), using Skyrme type effective interactions. We exploit hereby the theorems of Thouless and others, relating RPA sum rules to static (constrained) Hartree-Fock expectation values. The latter are calculated both microscopically and, where shell effects are small enough to allow it, semiclassically by a density variational method employing the gradient-expanded density functionals of the extended Thomas-Fermi model. In contrast to the widely spread fluid-dynamical approach, our method has the advantage of dealing with realistic density profiles with continuous surfaces and of allowing us to use realistic effective nuclear interactions including nonlocalities, such as effective mass and spin-orbit terms and the Coulomb interaction. We obtain an excellent overall description of both systematics and detailed isotopic dependence of GR energies, in particular with the Skyrme force SkM ∗. For the breathing modes (isoscalar and isovector giant monopole modes), and to some extent also for the isovector dipole mode, the A-dependence of the experimental peak energies is better described by coupling two different modes (corresponding to two different excitation operators) of the same spin and parity and evaluating the eigenmodes of the coupled system. Our calculations are also extended to hot nuclei (without angular momentum) and the temperature dependence of the various GR energies is discussed.