Effective theory for the non-rigid rotor in an electromagnetic field: Toward accurate and precise calculations of E2 transitions in deformed nuclei

TL;DR

This paper develops an effective theory framework for calculating electric quadrupole (E2) transitions in deformed nuclei, providing a systematic, model-independent approach with uncertainty estimates that aligns well with experimental data.

Contribution

It introduces a gauge-invariant effective theory for E2 transitions in deformed nuclei, enabling accurate predictions and uncertainty quantification at leading and subleading orders.

Findings

Effective theory describes ground-state band transitions within uncertainties.

Predictions for inter-band transitions match experimental data.

Framework applicable to molecules and nuclei with scale separation.

Abstract

We present a model-independent approach to electric quadrupole transitions of deformed nuclei. Based on an effective theory for axially symmetric systems, the leading interactions with electromagnetic fields enter as minimal couplings to gauge potentials, while subleading corrections employ gauge-invariant non-minimal couplings. This approach yields transition operators that are consistent with the Hamiltonian, and the power counting of the effective theory provides us with theoretical uncertainty estimates. We successfully test the effective theory in homonuclear molecules that exhibit a large separation of scales. For ground-state band transitions of rotational nuclei, the effective theory describes data well within theoretical uncertainties at leading order. In order to probe the theory at subleading order, data with higher precision would be valuable. For transitional nuclei, next-to-leading order calculations and the high-precision data are consistent within the theoretical uncertainty estimates. We also study the faint inter-band transitions within the effective theory and focus on the $E2$ transitions from the $0^+_2$ band (the "$\beta$ band") to the ground-state band. Here, the predictions from the effective theory are consistent with data for several nuclei, thereby proposing a solution to a long-standing challenge.