Uncertainty quantification of transition operators in the empirical shell model

While empirical shell model calculations have successfully described low-lying nuclear data for decades, only recently has significant effort been made to quantify the uncertainty in such calculations. Here, we quantify the statistical error in effective parameters for transition operators in empirical calculations in the $sd$ ($1{s}_{1/2}\text{\ensuremath{-}}0{d}_{3/2}\text{\ensuremath{-}}0{d}_{5/2}$) valence space, specifically the quenching of Gamow-Teller transitions, effective charges for electric quadrupole ($E2$) transitions, and the effective orbital and spin couplings for magnetic dipole ($M1$) transitions and moments. We find the quenching factor for Gamow-Teller transitions relative to free-space values is tightly constrained. For effective $M1$ couplings, we found isoscalar components more constrained than isovector. This detailed quantification of uncertainties, while highly empirical, nonetheless is an important step towards interpretation of experiments.