Covariance analysis for energy density functionals and instabilities

Abstract

We present the covariance analysis of two successful nuclear energy density functionals, (i) a non-relativistic Skyrme functional built from a zero-range effective interaction, and (ii) a relativistic nuclear energy density functional based on density dependent meson-nucleon couplings. The covariance analysis is a useful tool for understanding the limitations of a model, the correlations between observables and the statistical errors. We show, for our selected test nucleus 208 Pb, that when the constraint on a property A included in the fit is relaxed, correlations with other observables B become larger; on the other hand, when a strong constraint is imposed on A, the correlations with other properties become very small. We also provide a brief review, partly connected with the covariance analysis, of some instabilities displayed by several energy density functionals currently used in nuclear physics.

The Nuclear Symmetry Energy and Other Isovector Observables from the Point of View of Nuclear Structure

“…[25]. Here, we only focus on some illustrative findings that are of relevance in connection with our previous discussion on symmetry energy and other isovector observable.…”

“…Details and differences are highlighted in Ref. [25]. We now illustrate what happens to correlations between observables when one varies the fitting protocol.…”

“…We refer to our recent work [25] for better explanations, reminding also that many textbooks contain a more exhaustive treatment of the formalism (see e.g. [26]), and that an excellent introduction for nuclear theorists is given in Ref.…”

Statistical errors in Weizsäcker-Skyrme mass model

“…Unfortunately, it is difficult to accurately calculate the uncertainties of model predictions due to the complicated parameter space and limited computational power, and thus most nuclear mass models omit the theoretical estimation of errors and correlations between parameters. In recent years, estimates of extrapolation errors of theoretical models from different strategies such as least-squares fit, covariance analysis, variation of fit data, and so on, have attracted a lot of attention [31][32][33][34]. Covariance analysis is a useful tool for understanding the limitations of a model, the correlations between observables and the statistical errors, with which the statistical errors in the parameters of nuclear energy density functionals and in some predicted observables such as neutron-skin thickness of 208 Pb are investigated [33].…”

“…In recent years, estimates of extrapolation errors of theoretical models from different strategies such as least-squares fit, covariance analysis, variation of fit data, and so on, have attracted a lot of attention [31][32][33][34]. Covariance analysis is a useful tool for understanding the limitations of a model, the correlations between observables and the statistical errors, with which the statistical errors in the parameters of nuclear energy density functionals and in some predicted observables such as neutron-skin thickness of 208 Pb are investigated [33]. Although the statistical errors in the parameters of some energy-density functionals have been studied in the literature [35][36][37], a systematic study of statistical errors in the predicted masses of all bound nuclei, especially the unmeasured extremely neutron-rich nuclei and super-heavy nuclei, has not yet been performed based on the macroscopic-microscopic mass models.…”