Relativistic many-body theory for unstable nuclei and astrophysics

We discuss the properties of unstable nuclei and the equations of state of nuclear matter in the framework of the relativistic many-body theory. We take the relativistic mean-field (RMF) theory as a phenomenological theory with several parameters, whose form is constrained by the successful microscopic theory (RBHF), and whose values are extracted by using the experimental values of unstable nuclei. We find the outcome with the newly obtained parameter sets (TM1 and TMA) is promising in comparison with various experimental data. We calculate systematically the ground-state properties of even-even nuclei up to the drip lines; about 2000 nuclei. We find that the neutron magic shells (N = 82 128) at the standard magic numbers stay at the same numbers even far from the stability line and hence provide the r-process nuclei. However, many proton magic numbers disappear at the neutron numbers far away from the magic numbers owing to the deformations. We also study the neutron star profiles with the equation of state of nuclear matter with the use of RMF with TM1. We find that the proton fraction at the neutron star centre is as large as 20%, which is much larger than the conventional number of less than 1%.