Introduction

Abstract

Our understanding of the ground state and excited state properties of the atomic nuclei remains unsatisfactory even decades after establishing the existence of the nuclear force. A lot of theoretical effort has been made over the past many years to explain the experimental observations and, at the same time, consistent effort has been put forward to push the experimental frontiers. Nuclear matter is a theoretical construct of an infinite number of nucleons with a fixed neutron to proton ratio. Nuclear matter is a powerful tool from the point of view of improving our understanding of the nuclear many-body problem. The nuclear matter equation of state (EOS) is essentially a constitutive equation which provides a mathematical relationship between two or more state functions associated with a given system, such as its temperature, pressure, internal energy, density or particle number. The nuclear matter EOS is important for understanding many interesting phenomena such as the collective behavior of nucleons in nuclei, the massive stellar collapse leading to a supernova explosion, the radii of neutron stars, and nuclear properties such as the neutron-skin thickness of heavy nuclei. It thus becomes important to know the EOS for nuclear matter accurately. In order to probe the density dependence of the EOS one must study the response of the nucleus to external perturbations. The isoscalar giant monopole resonance is one such compression mode of oscillation where protons and neutrons oscillate in phase with each other around the equilibrium density. Thus the ISGMR measures the response of the nucleus to density fluctuations. The ISGMR centroid energy is directly related to the incompressibility of finite nuclei which in turn constrains the incompressibility, an important property of the EOS, of the infinite nuclear matter.