Isoscalar dipole strength in ^{208}_{82}Pb_{126}: the spurious mode and the strength in the continuum

Isoscalar dipole (compression) mode is studied first using schematic harmonic-oscillator model and, then, the self-consistent Hartree-Fock (HF) and random phase approximation (RPA) solved in coordinate space. Taking ^{208}Pb and the SkM* 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.