Self-consistent Hartree-Fock and RPA Green's function method indicate no pygmy resonance in the monopole response of neutron-rich Ni isotopes

The random phase approximation (RPA) monopole strength and the unperturbed particle-hole excitation strength are studied, in which the strength in the continuum is properly treated without discretizing unbound particle spectra. The model is the self-consistent Hartree-Fock calculation and the RPA Green's function method with Skyrme interactions. Numerical examples are the Ni isotopes, especially Ni-68(28)40, in which an experimental observation of a low-lying peak with an appreciable amount of monopole strength at 12.9 +/- 1.0 MeV was recently reported. In the present study it is concluded that sharp monopole peaks with the width of the order of 1 MeV can hardly be expected for Ni-68 in that energy region. Instead, a broad shoulder of monopole strength consisting of neutron excitations to nonresonant one-particle states (called "threshold strength") with relatively low angular momenta (l, j) is obtained in the continuum energy region above the particle threshold, which is considerably lower than that of the isoscalar giant monopole resonance. In the case of monopole excitations of Ni-68 there are no unperturbed particle-hole states below 20 MeV, in which the particle expresses a neutron (or proton) resonant state. It is emphasized that in the theoretical estimate a proper treatment of the continuum is extremely important.