| Summary: | The role of initial state (ISI) and final state (FSI) ion–ion interactions in heavy-ion double-charge-exchange (DCE) reactions <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>A</mi><mo>(</mo><mi>Z</mi><mo>,</mo><mi>N</mi><mo>)</mo><mo>→</mo><mi>A</mi><mo>(</mo><mi>Z</mi><mo>±</mo><mn>2</mn><mo>,</mo><mi>N</mi><mo>∓</mo><mn>2</mn><mo>)</mo></mrow></semantics></math></inline-formula> are studied for double single-charge-exchange (DSCE) reactions given by sequential actions of the isovector nucleon–nucleon (NN) T-matrix. In momentum representation, the second-order DSCE reaction amplitude is shown to be given in factorized form by projectile and target nuclear matrix elements and a reaction kernel containing ISI and FSI. Expanding the intermediate propagator in a Taylor series with respect to auxiliary energy allows us to perform the summation in the leading-order term over intermediate nuclear states in closure approximation. The nuclear matrix element attains a form given by the products of two-body interactions directly exciting the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>n</mi><mn>2</mn></msup><msup><mi>p</mi><mrow><mo>−</mo><mn>2</mn></mrow></msup></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>p</mi><mn>2</mn></msup><msup><mi>n</mi><mrow><mo>−</mo><mn>2</mn></mrow></msup></mrow></semantics></math></inline-formula> DCE transitions in the projectile and the target nucleus, respectively. A surprising result is that the intermediate propagation induces correlations between the transition vertices, showing that DSCE reactions are a two-nucleon process that resembles a system of interacting spin–isospin dipoles. Transformation of the DSCE NN T-matrix interactions from the reaction theoretical t-channel form to the s-channel operator structure required for spectroscopic purposes is elaborated in detail, showing that, in general, a rich spectrum of spin scalar, spin vector and higher-rank spin tensor multipole transitions will contribute to a DSCE reaction. Similarities (and differences) to two-neutrino double-beta decay (DBD) are discussed. ISI/FSI distortion and absorption effects are illustrated in black sphere approximation and in an illustrative application to data.
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