Covariant density functional theory based on the relativistic mean field (RMF) Lagrangian with the parameter set NL3 has been used in the last ten years with great success. Now we propose a modification of this parameter set, which improves the description of the ground state properties of many nuclei and simultaneously provides an excellent description of excited states with collective character in spherical as well as in deformed nuclei. 24.10.Cn, 21.30.Fe, 21.60.Jz, 24.30.Gz Density functional theory is a universal and powerful tool for describing properties of finite nuclei all over the periodic table. In the non-relativistic framework the most successful density functionals are the ones based on density dependent forces, such as the Skyrme [1] or the Gogny [2] functional. Relativistic mean field (RMF) theory was first introduced as a fully fledged quantum field theory by Walecka [3,4]. However, it turned out very soon [5], that for a quantitative description of nuclear surface properties an additional density dependence is necessary. Nowadays RMF theory modified in this form is considered as a covariant form of density functional theory. Over the years it has gained considerable interest, in particular, for the description of nuclei at and far from stability [6,7,8,9,10]. Compared with non-relativistic density functionals covariant density functional theory has certain advantages. They are characterized by a new saturation mechanism obtained by a delicate balance between a strongly attractive scalar field and a strongly repulsive vector field. Moreover, the very large spin-orbit splitting, observed in finite nuclei, is a relativistic effect. Therefore, its treatment in relativistic models arises in a natural way without any additional adjustable parameters. In addition, time-odd mean fields which are important in systems with broken time reversal symmetry are uniquely defined in RMF theory because of the Lorentz covariance of the underlying Lagrangian [11].Pairing properties are essential for a description of nuclei with open shells. They have been included first in the constant gap approximation by occupation numbers of BCS-type [12]. Since this procedure requires the knowledge of the experimental pairing gaps, it cannot be applied in unexplored regions of the nuclear chart, where the binding energies are not known. In addition, it is noted that the BCS approximation breaks down in nuclei far from the valley of stability, where the coupling to the continuum is essential [13]. Therefore the constant gap approximation has been replaced by relativistic Hartree-Bogoliubov (RHB) theory [14] which includes a finite range particle-particle interaction of Gogny form. The details of this theory have been discussed in several review articles [6,7,8] and in the references given there.In any case the adopted functionals are considered universal in the sense that they can be used for nuclei all over the periodic table, where mean field theory is applicable. It is therefore very desirable to find a unique parameteri...

Relativistic mean field theory with the NL3 force is used for producing potential energy surfaces (PES) for series of isotopes suggested as exhibiting critical point symmetries.Relatively flat PES are obtained for nuclei showing the E(5) symmetry, while in nuclei corresponding to the X(5) case, PES with a bump are obtained. The PES corresponding to the Pt chain of isotopes suggest a transition from prolate to oblate shapes at 186 Pt.

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Time-series analysis allows one to quantify homeostasis in the optimal conditions of youth and health and the degradation of homeostasis or homeostenosis in the adverse conditions of ageing and/or disease, and may offer an alternative approach to diagnosis in clinical practice.