a complete treatment of the particle continuum. In the present work, we study the ISGMR of nuclei by using a microscopic HF + continuum-RPA calculations with Skyrme interactions [@Ham96]. The RPA response function is solved in the coordinate space with the proton-neutron formalism including simultaneously both the isoscalar and the isovector correlation. In this way, we can take properly into account the coupling to the continuum and the effect of neutron (proton) excess on the structure of the giant resonances in nuclei near the neutron (proton) drip lines [@Ham96].

The RPA strength distribution of ISGMR of nuclei $$S(E_{x})=\sum_{n}|<n|Q|0>|^{2}\delta (E_{x}-E_{n})  \label{RPAStrength}$$can be obtained by using the isoscalar monopole operator $$Q^{\lambda =0,\tau =0}=\frac{1}{\sqrt{4\pi }}\sum_{i}r_{i}^{2}.
\label{ISGMROperator}$$Furthermore, one can define the *k*-th energy moment of the transition strength by $$m_{k}=\int dE_{x}E_{x}^{k}S(E_{x}).  \label{RPAmoment}$$The average energy of ISGMR can be defined by the ratio between the moments $m_{1}$ and $m_{0}$, i.e., $$E_{ave}=m_{1}/m_{0}.  \label{Eave}$$In addition, the so-called scaling energy of ISGMR can be expressed as $$E_{sca}=\sqrt{m_{3}/m_{1}},  \label{Esca}$$while the ISGMR energy obtained from the constrained HF approach can be written as $$E_{con}=\sqrt{m_{1}/m_{-1}}.  \label{Econ}$$The ISGMR energies defined by Eqs. (\[Eave\])-(\[Econ\]) will become identical in the case of a sharp single peak exhausting $100\%$ of the sum rule. In practice, 