Isoscalar dipole strength in Pb-208(82)126: The spurious mode and the strength in the continuum

The isoscalar dipole (compression) mode is studied first using the schematic harmonic-oscillator model, and then the self-consistent Hartree-Fock (HF) and random-phase approximation (RPA) are solved in coordinate space. Taking Pb-208 and the SkyM* interaction as a numerical example, the spurious component and the strength in the continuum are carefully examined using the sum rules. It is pointed out that in the continuum calculation one has to use an extremely fine radial mesh in HF and RPA in order to separate, with good accuracy, the spurious component from intrinsic excitations.