Effective field theory for vibrations in odd-mass nuclei

TL;DR

This paper develops an effective field theory to describe vibrations in odd-mass nuclei, coupling a fermion to an even-even core, and successfully predicts various observables with quantified uncertainties.

Contribution

It introduces a novel EFT framework for odd-mass nuclei that relates their properties to even-even neighbors, including uncertainty quantification.

Findings

The EFT accurately describes energy levels and transition strengths within uncertainties.

Predictions for observables in rhodium and silver isotopes are consistent with experimental data.

The approach provides a systematic way to include uncertainties in nuclear structure calculations.

Abstract

Heavy even-even nuclei exhibit low-energy collective excitations that are separated in scale from the microscopic (fermion) degrees of freedom. This separation of scale allows us to approach nuclear vibrations within an effective field theory (EFT). In odd-mass nuclei collective and single-particle properties compete at low energies, and this makes their description more challenging. In this article we describe odd-mass nuclei with ground-state spin $I=\sfrac{1}{2}$ by means of an EFT that couples a fermion to the collective degrees of freedom of an even-even core. The EFT relates observables such as energy levels, electric quadrupole ($E2$) transition strengths, and magnetic dipole ($M1$) moments of the odd-mass nucleus to those of its even-even neighbor, and allows us to quantify theoretical uncertainties. For isotopes of rhodium and silver the theoretical description is consistent with data within experimental and theoretical uncertainties. Several testable predictions are made.