Background: The nuclear matrix element (NME) is an important quantity in studies of the neutrinoless double beta ($0\nu \beta \beta$) decay, for which the ${}^{76}\mathrm{Ge}$ nucleus is one of the candidate isotopes for direct searches. The NME might be experimentally constrained by heavy-ion double charge exchange (HI-DCE) reaction at relevant energies. However feasibility of the HI-DCE as a tool for the NME requires accurate analyses of the competing multisteps one-nucleon transfers that connects the same initial and final mass partitions.

Purpose: In this work we present the one-proton stripping and one-neutron pickup reactions in the ${}^{20}\mathrm{Ne}+{}^{76}\mathrm{Ge}$ system measured at 15.3 MeV/u. These one-nucleon transfer reactions are used to benchmark the direct reaction and nuclear structure models that will be used to compute the contribution of multinucleon transfers competing with the HI-DCE.

Methods: Experimental data of differential cross sections are compared with coupled reaction channel calculations using spectroscopic amplitudes as obtained from large-scale shell model. The validity of model space and interactions adopted to describe the target and the targetlike nuclei are further checked against (d,p) and (${}^3\mathrm{He}$,d) data available in the literature.

Results: We obtain an overall good description of experimental data for the one-proton stripping and one-neutron pickup transfer in the ${}^{20}\mathrm{Ne}+{}^{76}\mathrm{Ge}$ reactions. We also reproduce the behavior of the cross sections for channels in the ${}^{76}\mathrm{Ge}({}^3\mathrm{He},\mathrm{d}){}^{77}\mathrm{As}$ and the ${}^{76}\mathrm{Ge}\left(\mathrm{p},\mathrm{d}\right){}^{75}\mathrm{Ge}$ data.

Conclusions: The result obtained in this work fills some intermediate one-nucleon transfer steps in the intricate multitransfer paths that compete with the direct meson exchange mechanism for the heavy-ion double charge exchange.

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• Low & intermediate energy heavy-ion reactions
• Nuclear reactions
• Shell model
• Transfer reactions