It has been found that the observed low-energy DCX cross-section
are in strong discrepancy with the predictions based on various nuclear models.
Also the strong forward peaking of the cross-section at the pion kinetic energy
remains in contrast with calculations.
A new model of the above processes based on proton-neutron
Quasiparticle Random Phase Approximation (pnQRPA) with realistic
two-nucleon forces generated by one-boson exchange potential of Bonn
type has been developed by Lublin-Tuebingen collaboration.
This model has already been successfully used to describe two-neutrino
double beta decay in heavier nuclei and at the
same time the DCX reaction due to similar
nuclear structure aspects of both processes.