  The theory of heavy ion single charge exchange reactions is reformulated. In
momentum space the reaction amplitude factorizes into a product of projectile
and target transition form factors, folded with the nucleon-nucleon isovector
interaction and a distortion coefficient which accounts for initial and final
state ion-ion elastic interactions. The multipole structure of the transition
form factors is studied in detail for Fermi-type non-spin flip and
Gamow-Teller-type spin flip transitions, also serving to establish the
connection to nuclear beta decay. The reaction kernel is evaluated for central
and rank-2 tensor interactions. Initial and final state elastic ion-ion
interaction are shown to be dominated by the imaginary part of the optical
potential allowing to evaluate the reaction coefficients in the strong
absorption limit, realized by the black disk approximation. In that limit the
distortion coefficient is evaluated in closed form, revealing the relation to
the total reaction cross section and the geometry of the transition form
factors. It is shown that at small momentum transfer distortion effects reduce
to a simple scaling factor, allowing to define reduced forward-angle cross
section which is given by nuclear matrix elements of beta decay-type. The
response function formalism is used to describe nuclear charge changing
transitions. Spectral distributions obtained by a self-consistent HFB and QRPA
approach are discussed for $\tau_\pm$ excitations of $^{18}O$ and $^{40}Ca$,
respectively, and compared to spectroscopic data. The interplay of nuclear
structure and reaction dynamics is illustrated for the single charge exchange
reaction $^{18}O+^{40}Ca \to ^{18}F+^{40}K$ at $T_{lab}=270$ MeV.
