Heisenberg Uncertainty Inequality and Breaking of Isospin Symmetry in Atomic Nuclei

TL;DR

This paper uses the Heisenberg uncertainty inequality to establish bounds on isospin impurities and symmetry violations in atomic nuclei, linking physical observables to symmetry breaking effects.

Contribution

It introduces a rigorous lower bound on isospin impurities based on measurable nuclear properties and connects isospin violation to the isovector dipole moment.

Findings

Derived a lower bound on isospin impurities in N=Z nuclei.

Connected isospin symmetry breaking to measurable charge exchange strengths.

Provided an upper bound on the isovector dipole moment related to isospin impurities.

Abstract

The Heisenberg uncertainty inequality is used to derive a rigorous lower bound to the amount of isospin impurities in $N=Z$ atomic nuclei, caused by the violation of isospin symmetry. The bound is fixed by the difference between the neutron and proton radii and the sum of the charge exchange monopole strengths. It can be used to check the consistency of advanced many-body calculations accounting for the breaking of isospin symmetry. The uncertainty inequality is also employed to derive an upper bound to the isovector dipole moment in terms of the amount of isospin impurities, providing an insightful connection between the violation of parity and isospin symmetries.