Inelastic scattering from12 C has been measured at the extremely forward angles including 0• using 386 MeV α particles to study the α-cluster states around Ex ∼ 10 MeV, especially the 2 + state predicted by the α-cluster model. We have analyzed the (α,α ′ ) cross-section data using both the peak-fitting and the multipole decomposition techniques. A 2 + state at Ex = 9.84 ± 0.06 MeV with a width of 1.01 ± 0.15 MeV is found to be submerged in the broad 0 + state at Ex = 9.93 ± 0.03 MeV with a width of 2.71 ± 0.08 MeV. This 2 + state may be interpreted as the 2 + excitation of the Hoyle state and the α-condensate state.

The strength distributions of the giant monopole resonance (GMR) have been measured in the even-A Sn isotopes (A=112-124) with inelastic scattering of 400-MeV alpha particles in the angular range 0 degrees -8.5 degrees . We find that the experimentally observed GMR energies of the Sn isotopes are lower than the values predicted by theoretical calculations that reproduce the GMR energies in 208Pb and 90Zr very well. From the GMR data, a value of Ktau = -550 +/- 100 MeV is obtained for the asymmetry term in the nuclear incompressibility.

We have investigated the isoscalar giant resonances in the Sn isotopes using inelastic scattering of 386-MeV α-particles at extremely forward angles, including 0 • . We have obtained completely "background-free" inelastic-scattering spectra for the Sn isotopes over the angular range 0 • -9 • and up to an excitation energy of 31.5 MeV. The strength distributions for various multipoles were extracted by a multipole decomposition analysis based on the expected angular distributions of the respective multipoles. We find that the centroid energies of the isoscalar giant monopole resonance (ISGMR) in the Sn isotopes are significantly lower than the theoretical predictions. In addition, based on the ISGMR results, a value of K τ = −550 ± 100 MeV is obtained for the asymmetry term in the nuclear incompressibility. Constraints on interactions employed in nuclear structure calculations are discussed on the basis of the experimentally-obtained values for K ∞ and K τ .2

The isoscalar giant monopole resonance (ISGMR) in even-A Cd isotopes has been studied by inelastic α-scattering at 100 MeV/u and at extremely forward angles, including 0• . The asymmetry term in the nuclear incompressibility extracted from the ISGMR in Cd isotopes is found to be Kτ = −555±75 MeV, confirming the value previously obtained from the Sn isotopes. ISGMR strength has been computed in relativistic RPA using NL3 and FSUGold effective interactions. Both models significantly overestimate the centroids of the ISGMR strength in the Cd isotopes. Combined with other recent theoretical effort, the question of the "softness" of the open-shell nuclei in the tin region remains open still.The equation of state (EOS) of nuclear matter plays an important role in our understanding of a number of interesting phenomena such as the collective behavior of nucleons in the nuclei, the massive stellar collapse leading to a supernova explosion, nuclear properties including the neutron-skin thickness of heavy nuclei, and the radii of neutron stars [1, 2]. The nuclear incompressibility, K ∞ , is the curvature of EOS of nuclear matter at saturation density [3]. K ∞ is, thus, a measure of nuclear stiffness and thereby imposes significant constraints on theoretical descriptions of the effective nuclear interactions. However, even more stringent constraints emerge as one studies the evolution of the incompressibility coefficient as the system becomes neutron rich. Neutron-rich systems are sensitive to the poorly-known density dependence of the symmetry energy and the experiments reported here are of vital importance in this regard.The study of the isoscalar giant monopole resonance (ISGMR) provides a direct experimental tool to study nuclear incompressibility in finite nuclear systems. The centroid energy of ISGMR, E ISGMR , can be directly related to the nuclear incompressibility of finite nuclear matter, K A , as:where, m is the nucleon mass and < r 2 > is the mean square radius of the nucleus [4,5]. K A may be further