Rearrangement of valence neutrons in the neutrinoless double-$\beta$   decay of $^{136}$Xe
  A quantitative description of the change in ground-state neutron occupancies between $^{136}$Xe and $^{136}$Ba, the initial and final state in the neutrinoless double-$\beta$ decay of $^{136}$Xe, has been extracted from precision measurements of the cross sections of single-neutron adding and -removing reactions. Comparisons are made to recent theoretical calculations of the same properties using various nuclear-structure models. These are the same calculations used to determine the magnitude of the nuclear matrix elements for the process, which at present disagree with each other by factors of 2 or 3. The experimental neutron occupancies show some disagreement with the theoretical calculations. 
S. V. Szwec, B. P. Kay, T. E. Cocolios, J. P. Entwisle, S. J. Freeman,   L. P. Gaffney, V. Guimar\~aes, F. Hammache, P. P. M...
nucl-ex nucl-th