nuclear reaction dynamics, and the liquid-gas phase transition in nuclear matter, but also many critical issues such as properties of neutron stars and supernova explosion mechanism in astrophysics [@LiBA98; @Dan02; @Lat04; @Ste05; @Bar05; @LCK08]. In the past more than $30$ years, significant progress has been made in determining the EOS of symmetric nuclear matter from subsaturation density to about $5$ times normal nuclear matter density $\rho _{0}$ by studying the nuclear isoscalar giant monopole resonances (ISGMR) [@You99], collective flows [@Dan02] and subthreshold kaon production [@Aic85; @Fuc06a] in nucleus-nucleus collisions. On the other hand, the isospin dependent part of the nuclear EOS, characterized essentially by the nuclear symmetry energy $E_{\text{\textrm{sym}}}({\rho })$, is still largely uncertain [Bar05,LCK08]{}. Lack of knowledge on the symmetry energy actually hinders us to extract more accurately the EOS of symmetric nuclear matter. Therefore, to explore and narrow down the uncertainties of both the theoretical methods and the experimental data is of crucial importance for extracting more stringently information on the nuclear EOS.

During the past more than 30 years, it has been established that the nuclear ISGMR provides a good tool to probe the nuclear EOS around the nuclear normal density. In particular, it is generally believed 