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Heavy ion double charge exchange reactions are described by sequentialmeson-exchange, corresponding to a double single charge exchange (DSCE)reaction mechanism. The theoretical formulation is discussed. The fully quantummechanical distorted wave 2-step calculations are shown to be reproduced verywell by approximating the intermediate propagator by its pole part. The role ofion-ion elastic interactions is discussed. As a first application, calculationsare performed for the reaction $^{40}$Ca $(^{18}$O $,^{18}$Ne $)^{40}$Ar at 15AMeV. Results are compared to the data measured at LNS by the NUMENCollaboration. The common aspects of DSCE reactions and double $\beta$- decayare discussed by a detailed comparison of the respective nuclear matrixelements (NME).

Sequential Heavy Ion Double Charge Exchange Reactions and the Link to Double $\beta$-decay