  The theory of heavy ion double charge exchange (DCE) reactions proceeding by
effective rank-2 isotensor interactions is presented. Virtual pion--nucleon
charge exchange interactions are investigated as the source for induced
isotensor interactions, giving rise to the Majorana DCE (MDCE) reaction
mechanism. MDCE is of a generic character, proceeding through pairs of
complementary ($\pi^\pm,\pi^\mp$) reactions in the projectile and target
nucleus. The dynamics of the elementary processes is discussed, where the
excitation of pion--nucleon resonances are of central importance.
Investigations of initial and final state ion--ion interactions show that these
effects are acting as vertex renormalizations. In closure approximation, well
justified by the finite pion mass, the second-order transition matrix elements
reduce to pion potentials and effective two-body isotensor DCE interactions,
giving rise also to two-body correlations in either of the participating
nuclei. Connections to neutrinoless Majorana double beta decay (MDBD) are
elucidated at various levels of the dynamics, from the underlying fundamental
electro-weak and QCD scales to the physical scales of nuclear MDBD and MDCE
physics. It is pointed out that heavy ion MDCE reactions may also proceed by
competing electro-weak charge exchange processes, leading to lepton MDCE by
electrons, positrons, and neutrinos.
