Generalized Heisenberg Uncertainty Principle applied to isospin symmetry breaking operators in atomic nuclei

Abstract

Based on Sandro Stringari’s article Heisenberg Uncertainty Inequality and Breaking of Isospin Symmetry in Atomic Nuclei [1], the generalized Heisenberg’s uncertainty inequality is used to find a lower bound to the breaking of isospin symmetry. To do this, we employ the lowering isospin operator and the isovector giant monopole resonance operator (IVGMR) instead of the original position and linear momentum operators to set up the new uncertainty principle. As an original development of our thesis, we modify the IVGMR operator in order to eliminate the contribution of the isobaric analogue state (IAS). We find, within the Hartree-Fock plus Random Phase Approximation method applied to a sound nuclear effective interaction (Skyrme-type), that the IAS isolates the main contribution to the generalized Heisenberg’s uncertainty principle presented here