Isotopic Dependence of Giant Monopole Resonance (GMR) in the $^{106-116}$Cd isotopes and the asymmetry term in nuclear incompressibility

The asymmetry term associated with the neutron excess, K$_{\tau}$, plays a very important role in the Equation of State (EOS) for neutron matter. The GMR studied over a series of isotopes provides a direct way to measure this term. We have measured GMR strength distributions in even A, $^{106-116}$Cd isotopes in an experiment performed at RCNP, Osaka University, Japan. Measurements were taken at forward angles, including 0\r{ }, using a 400 MeV $\alpha $ beam. The results affirm the conclusions of a recent experiment with the Sn isotopes. The constraints put by values of K$_{\tau}$ and K$_{\infty}$, obtained from this experiment on the effective interaction currently in use in nuclear structure and EOS calculations, will be discussed.