Collisional heavy ion double-charge-exchange (DCE) reactions, induced by second-order nucleon-nucleon interactions, are shown to provide access to the two-body transition densities of the complementary DCE transitions in the interacting nuclei. Corresponding two-body operators are introduced, treating the second-order distorted wave reaction amplitude in the $s$-channel interaction form. The theoretical results are applied to the reaction ${}^{18}\mathrm{O}+{}^{76}\mathrm{Se}\to {}^{18}\mathrm{Ne}+{}^{76}\mathrm{Ge}$ at $T_{\mathrm{lab}}=270\mathrm{MeV}$, being ${}^{76}\mathrm{Ge}$ a candidate for neutrinoless double beta decay.

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• Charge-exchange reactions
• Neutrinoless double beta decay
• Nuclear decay
• Nuclear many-body theory
• Nuclear reactions
• Nuclear structure & decays
• 59 ≤ A ≤ 89