Parametric correlations in energy density functionals

Abstract

Parametric correlations are studied in several classes of covariant density functional theories (CDFTs) using a statistical analysis in a large parameter hyperspace. In the present manuscript, we investigate such correlations for two specific types of models, namely, for models with density dependent meson exchange and for point coupling models. Combined with the results obtained previously in Ref.[1] for a non-linear meson exchange model, these results indicate that parametric correlations exist in all major classes of CDFTs when the functionals are fitted to the ground state properties of finite nuclei and to nuclear matter properties. In particular, for the density dependence in the isoscalar channel only one parameter is really independent. Accounting for these facts potentially allows one to reduce the number of free parameters considerably.Since the early seventies, analogously to Coulombic quantum mechanical many-body systems, density functional theory (DFT) has played an important role in nuclear physics. In principle, it corresponds to an exact mapping of the complex many-body system to that of an artificial one-body system and therefore one with relatively small computational costs. It is universal in the sense that the form of the energy density functional (EDF) does not depend on the nucleus, nor on the specific region where it is applied, but only on the underlying interaction. Thus there is only one universal functional for the Coulomb interaction in atomic, molecular and condensed matter physics, but another one for nuclear phenomena determined by the strong interaction and the Coulomb force. In Coulombic systems the density functional can be derived in a microscopic way from the Coulomb force. On the contrary in nuclear physics, because of the complexity of the nuclear force such attempts are still in their infancy [2,3]. All the successful functionals are phenomenological. Their various forms obey the symmetries of the system, but in the absolute majority of the cases the parameters are adjusted to experimental data in finite nuclei and in homogeneous nuclear matter.Covariant density functional theories (CDFT) [3-7] are particularly interesting because they obey a basic symmetries of QCD. In particular, Lorentz invariance which not only automatically includes the spin-orbit coupling, but also puts stringent restrictions on the number of phenomenological parameters without loosing the good agreement with experimental data Nonetheless, over the years, the number of phenomenological functionals has grown considerably not only for non-relativistic Skyrme DFTs, but also for CDFTs, so that in recent years, questions have arisen about the reliability and predictive power of such functionals [8,9]. Apart from the systematic uncertainties which are connected with the analytic forms and the various terms in such functionals, there are so-called statistical uncertain-ties, connected with the procedures and strategies to adjust the various parameters to experimental data. Here we investigate whether the para...

New effective interactions for hypernuclei in density dependent relativistic mean field model

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Heavy Magnetic Neutron Stars

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