Uncertainty quantification of transition operators in the empirical shell model

TL;DR

This paper quantifies the uncertainties in transition operators within the empirical shell model, focusing on effective parameters for various nuclear transitions, providing insights into the precision of these models for interpreting experimental data.

Contribution

It provides the first detailed statistical error analysis of effective transition operator parameters in the empirical shell model, especially for the $sd$ valence space.

Findings

Quenching factor for Gamow-Teller transitions is tightly constrained.

Isoscalar E2 coupling is more constrained than isovector.

Effective M1 couplings show more constraint in isovector components.

Abstract

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 $sd$ ($1s_{1/2}$-$0d_{3/2}$-$0d_{5/2}$) 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. We find the quenching factor for Gamow-Teller transitions relative to free-space values is tightly constrained and that the isoscalar coupling of E2 is much more tightly constrained than the isovector coupling. For effective M1 couplings, we found isovector components more constrained than isoscalar, but that to get any sensible result we had to fix one of four couplings. This detailed quantification of uncertainties, while highly empirical, nonetheless is an important step towards interpretation of experiments.