Change of nuclear configurations in the neutrinoless double-$\beta$ decay of ${}^{130}$Te $\to$ ${}^{130}$Xe and ${}^{136}$Xe $\to$ ${}^{136}$Ba

Abstract

The change in the configuration of valence protons between the initial and final states in the neutrinoless double-$\beta$ decay of ${}^{130}$Te $\to$ ${}^{130}$Xe and of ${}^{136}$Xe $\to$ ${}^{136}$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.

Comments: 10 pages, 4 figures, 9 tables