Structure of exotic nuclei and superheavy elements in a relativistic shell model

We have carried out a study of the structure of heavy exotic nuclei and superheavy elements in the framework of the relativistic mean field (RMF) theory, adopting a new relativistic force, (NL-RA1). Pairing correlations, are treated in the Bardeen-Cooper-Schrieffer formalism with a constant gap approximation, adopting a new model for the energy gap, where a Gaussian shape distribution depending on the particle numbers is assumed. This pairing model is found to successfully describe heavy open shell nuclei. The new relativistic force NL-RA1 successfully reproduced the ground state properties of finite nuclei as well as nuclear matter. This force is used to study the structure of Sn and Pb isotopic chains, while considering extreme values of isospin. It is found that the binding energies, neutron and proton rms radii, and neutron skins are fairly described. Furthermore, the charge rms radii, and the anomalous kind in the isotopic shifts of the charge radii of the Pb isotopic chain are also well described by the NL-RA1 force. In comparison with other relativistic forces like, TM1, NL-SH, and NL1 it is found that the TM1 force could describe the binding energy, while it overestimates the charge radii of Pb isotopes. The NL-SH produced larger binding in the lighter side of Pb-208 and smaller charge radii. The NL1 force shows systematic discrepancies in both the binding energies as well as the charge radii, due to their larger symmetry energies. Other relativistic forces, like NL-Z and NL-Z2, have also been tested and found to largely overestimate the charge radii of Pb isotopes. We also investigated the ground state properties of superheavy elements in the region Z greater than or equal to 98 and it is found that the NL-RA1 force fairly described the binding energy. The element (298)(184)114 is predicted to be the next spherically doubly magic superheavy nucleus to Pb-208, where a large stable two-proton gap for the Z=114 proton shell on the order of 3 MeV, depending on the effective interaction and pairing model, has been predicted. We also found strong evidence of other spherically doubly magic superheavy elements, such as the element (292)(172)120.