  The theoretical approach to a sequential heavy ion double charge exchange
reaction is presented. A brief introduction into the formal theory of
second-order nuclear reactions and their application to Double Single Charge
Exchange (DSCE) reactions by distorted wave theory is given, thereby completing
the theoretical background to our recent work [1]. Formally, the DSCE reaction
amplitudes are shown to be separable into superpositions of distortion factors,
accounting for initial and final state ion--ion interactions, and nuclear
matrix elements. A broad space is given to the construction of nuclear DSCE
response functions on the basis of polarization propagator theory. The nuclear
response tensors resemble the nuclear matrix elements of $2\nu\beta\beta$ decay
in structure but contain in general a considerable more complex multipole and
spin structure. The QRPA theory is used to derive explicit expressions for
nuclear matrix elements (NMEs). The differences between the NME of the first
and the second interaction vertexes in a DSCE reaction is elucidated. Reduction
schemes for the transition form factors are discussed by investigating the
closure approximation and the momentum structure of form factors. DSCE unit
strength cross sections are derived.
