  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.
