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

TL;DR

This study measures proton configuration changes in neutrinoless double-beta decay of specific isotopes, revealing discrepancies between experimental data and theoretical models crucial for understanding decay rates.

Contribution

It provides experimental measurements of valence proton configurations in neutrinoless double-beta decay, highlighting significant differences with existing shell-model and interacting-boson-model calculations.

Findings

Measured cross sections of ($d$,$^3$He) reactions at 101 MeV.

Identified discrepancies between experimental data and theoretical models.

Implications for nuclear matrix element calculations in decay rate predictions.

Abstract

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.