Isoscalar Giant Monopole Resonance in Relativistic Continuum Random Phase Approximation

The isoscalar giant monopole resonance (ISGMR) in nuclei is studied in the framework of a fully consistent relativistic continuum random phase approximation (RCRPA). In this method the contribution of the continuum spectrum to nuclear excitations is treated exactly by the single particle Green's function technique. The negative energy states in the Dirac sea are also included in the single particle Green's function in the no-sea approximation. The single particle Green's function is calculated numerically by a proper product of the regular and irregular solutions of the Dirac equation. The strength distributions in the RCRPA calculations, the inverse energy-weighted sum rule m_-1 and the centroid energy of the ISGMR in ¹²⁰Sn and ²⁰⁸Pb are analysed. Numerical results of the RCRPA are checked with the constrained relativistic mean field model and relativistic random phase approximation with a discretized spectrum in the continuum. Good agreement between them is achieved