Compressibility of nuclear matter from shell effects in nuclei

The compressibility of nuclear matter has received significant attention in the last decade and a variety of approaches have been employed to extract this fundamental property of matter. Recently, significant differences have emerged between the results of relativistic and non-relativistic calculations of breathing mode giant monopole resonance (GMR). This is due to a lack of understanding of the dynamics of GMR and of its exact relationship to the compression modulus of the infinite nuclear matter. Here, I present an alternative approach based upon nuclear shell effects. The shell effects are known to manifest experimentally in terms of particle-separation energies with an exceedingly high precision. Within the framework of the non-relativistic density-dependent Skyrme theory, it is shown that the compressibility of nuclear matter has a significant influence on shell effects in nuclei. It is shown that 2-neutron separation energies and hence the empirical shell effects can be used to constrain the compressibility of nuclear matter.