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

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$\%$.

Figure 1

Predictions from the linear Walecka models for the saturation density, binding energy, and incompressibility coefficient at saturation. Model parameters were generated according to the distribution $\exp (-\Delta {\chi }^2/2)$. Both of the covariance ellipsoids were generated by limiting the models to the region $\Delta {\chi }^2\le 1$.

Figure 2

Color-coded plot of the 21 independent correlation coefficients between the 7 model parameters of the FSUGold effective interaction.

Figure 3

Color-coded plot of the 55 independent correlation coefficients between 11 physical observables as computed with the FSUGold effective interaction.