Accurate calibration of relativistic mean-field models: Correlating observables and providing meaningful theoretical uncertainties

Abstract

Theoretical uncertainties in the predictions of relativistic mean-field models are estimated using a chi-square minimization procedure that is implemented by studying the small oscillations around the chi-square minimum. By diagonalizing the matrix of second derivatives, one gains access to a wealth of information-in the form of powerful correlations-that would normally remain hidden. We illustrate the power of the covariance analysis by using two relativistic mean-field models: (a) the original linear Walecka model and (b) the accurately calibrated FSUGold parametrization. In addition to providing meaningful theoretical uncertainties for both model parameters and predicted observables, the covariance analysis establishes robust correlations between physical observables. In particular, we show that whereas the correlation coefficient between the slope of the symmetry energy and the neutron-skin thickness of Lead is indeed very large, a 1% measurement of the neutron radius of Lead may only be able to constrain the slope of the symmetry energy to about 30%.

Giant monopole energies from a constrained relativistic mean-field approach

“…Finally, the two insets display the cumulative sums relative to their corresponding sum rules computed from the constrained RMF approach as indicated in Eqs. (7) and (8). The insets indicate that the RPA response accounts for about 90% of the corresponding sum rules.…”

“…For example, one could ask whether certain linear combinations of model parameters remain poorly constrained by the choice of observables. We find this to be particularly true in the case of the isovector sector that is hindered by the unavailability of highly accurate data on neutron skins [8].…”

“…Until recently, once the minimum was found, one proceeded to validate the model against observables not included in the quality function [6]. Lately, however, a few studies have been devoted to map the landscape around the χ 2 minimum [7][8][9]. Among the wealth of information revealed by such detailed statistical studies is the degree of correlation among various observables.…”

Pure Neutron Matter Constraints and Nuclear Symmetry Energy

“…[25] and its power has been recently illustrated in Refs. [18,19,24]. In a nutshell, one can describe it as follows.…”

“…Since the number of experimental observables is usually larger than the number of free parameters, the problem of optimizing these EDFs is generally overdetermined, and this results in a significant degeneracy among parameter sets. Fortunately, one can use the covariance analysis techniques [18,19] to study correlations between predicted observables from a particular EDF in its model space. We use the linear regression method to optimize the two pure isovector parameters of RMF and SHF models by using the results from the ab initio theoretical calculations of the PNM EoS as our 'experimental' constraints.…”