Rearrangement of valence neutrons in the neutrinoless double-$\beta$ decay of $^{136}$Xe

TL;DR

This study measures neutron occupancy changes in $^{136}$Xe and $^{136}$Ba to inform neutrinoless double-beta decay models, revealing discrepancies between experimental data and theoretical predictions that impact nuclear matrix element calculations.

Contribution

It provides the first precise experimental determination of neutron occupancies in the decay process, challenging existing nuclear-structure models used for decay rate predictions.

Findings

Experimental neutron occupancies differ from theoretical models.

Discrepancies impact nuclear matrix element estimates.

Results highlight need for improved nuclear structure calculations.

Abstract

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.