Change of nuclear configurations in the neutrinoless double-$\beta$   decay of $^{130}$Te $\rightarrow$ $^{130}$Xe and $^{136}$Xe $\rightarrow$   $^{136}$Ba
  The change in the configuration of valence protons between the initial and final states in the neutrinoless double-$\beta$ decay of $^{130}$Te $\rightarrow$ $^{130}$Xe and of $^{136}$Xe $\rightarrow$ $^{136}$Ba has been determined by measuring the cross sections of the ($d$,$^3$He) reaction with 101-MeV deuterons. Together with our recent determination of the relevant neutron configurations involved in the process, a quantitative comparison with the latest shell-model and interacting-boson-model calculations reveals significant discrepancies. These are the same calculations used to determine the nuclear matrix elements governing the rate of neutrinoless double-$\beta$ decay in these systems. 
J. P. Entwisle, B. P. Kay, A. Tamii, S. Adachi, N. Aoi, J. A. Clark,   S. J. Freeman, H. Fujita, Y. Fujita, T. Furuno, T. Ha...
nucl-ex nucl-th