Abstract
Neutron transfer reaction measurements, relevant to the neutrinoless double $\ensuremath{\beta}$ decay candidate $^{124}\mathrm{Sn}$ and its daughter $^{124}\mathrm{Te}$, have been performed. Precise measurements of both neutron addition $[(d,p),(^{4}\mathrm{He},^{3}\mathrm{He})]$ and removal $[(p,d),(^{3}\mathrm{He},^{4}\mathrm{He})]$ cross sections have been used to determine the occupation of valence orbitals pertinent to neutrinoless double $\ensuremath{\beta}$ decay in these two nuclei. This information could be used to constrain calculations of the nuclear matrix element for the neutrinoless double $\ensuremath{\beta}$ decay of $^{124}\mathrm{Sn}$. The change in the ground-state neutron vacancies in proceeding from $^{124}\mathrm{Sn}$ to $^{124}\mathrm{Te}$ is mainly found in the ${d}_{3/2,5/2}$ and ${h}_{11/2}$ orbitals. The occupancies of states near the Fermi level are in reasonable agreement with shell model calculations.
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