Pigmy resonance in monopole response of neutron-rich Ni isotopes ?

The RPA monopole strength as well as the unperturbed particle-hole excitation strength is studied, in which the strength in the continuum is properly treated without discretizing unbound particle spectra. The model is the sef-consistent Hartree-Fock calculation and the RPA Green's function method with Skyrme interactions. Numerical examples are the Ni-isotopes, especially $^{68}_{28}$Ni$_{40}$, in which an experimental observation of low-lying socalled "pigmy resonance" with an appreciable amount of monopole strength at 12.9 $\pm$ 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 $^{68}$Ni in that energy region. Instead, a broad shoulder of monopole strength consisting of neutron excitations to non-resonant one-particle states (called "threshold strength") with relatively low angular-momenta $(\ell, j)$ is obtained in the continuum energy region above the particle threshold, which is considerably lower than that of isoscalar giant monopole resonance. In the case of monopole excitations of $^{68}$Ni 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.