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

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 nonminimal 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. 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 interband 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.