Induced Isotensor Interactions in Heavy-Ion Double-Charge-Exchange Reactions and the Role of Initial and Final State Interactions

Abstract

The role of initial state (ISI) and final state (FSI) ion-ion interactions in heavy-ion double-charge-exchange (DCE) reactions $A(Z,N)\to A(Z\pm 2,N\mp 2)$ 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. %Please ensure meaning has been retained - corrected HL. The nuclear matrix element attains a form given by the products of two-body interactions directly exciting the $n^2p^{-2}$ and $p^2n^{-2}$ DCE transitions in the projectile and the target nucleus, respectively. %Please ensure meaning has been retained - corrected HL. 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.