  We have constructed a Lagrangian model (SIG-OM) with coupling of sigma and
omega mesons in the relativistic mean-field theory. Properties of finite nuclei
and nuclear matter have been explored with the new Lagrangian model. The study
shows that with SIG-OM an excellent description of binding energies and charge
radii of nuclei over a large range of isospin is achieved. With an
incompressibility of nuclear matter K=265 MeV, it is also able to describe the
breathing-mode isoscalar giant monopole resonance energies appropriately. It is
shown that the high-density behaviour of the equation of state of nuclear and
neutron matter with the sigma-omega coupling is significantly softer than the
non-linear scalar coupling model.
