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

The role of initial state (ISI) and final state (FSI) ion–ion interactions in heavy ion double charge exchange (DCE) reactions A(Z,N)→A(Z±2,N∓2) are studied in the context of double single charge exchange (DSCE) reactions given by sequential actions of the isovector nucleon–nucleon (NN) T–matrix. The second order DSCE reaction amplitude is investigated in momentum representation in a formulation, focused on the extraction of nuclear matrix elements under the conditions of strong initial state (ISI) and final state (FSI) interactions. In closure approximation and using the momentum representation, the reaction amplitude is finally separated into ISI/FSI distortion coefficients and reaction kernels and nuclear matrix elements. The ISI/FSI reaction kernels emerge as the result of the repeated scattering on the avoided volume, introduced by the imaginary parts of the ion–ion optical potential and acting as sinks for the quantal probability current. The closure approximation allows derive a set of induced effective two–body isotensor interactions, given by products of spin–scalar, spin–vector central and rank–2 spin–tensor interactions. The intermediate propagator plays a key role in establishing correlation between the DCE transitions in the projectile and target nucleus. The presented approach emphasizes the special features of DSCE reaction dynamics as proceeding like a system of two coupled isospin dipoles whose strengths are determined by the momentum-space form factors of the NN isovector interaction. The properties of the DSCE interaction form factors are investigated and the approach is applied to data.