Pion double charge exchange formalism

The behavior of the operator responsible for sequential pion double charge exchange (DCX) on nuclei has been investigated in the plane wave limit in order to study its extension in space especially the short-range part.

The DCX cross sections were calculated for Ca isotopes up to an incident pion energy of 300 MeV as two single-charge exchanges, using both the shell model and the seniority model. The effects of previously proposed modifications to the mechanism have been investigated at low energy, where a resonance-like structure in the energy dependence has been observed. One of the modifications that has been studied is the inclusion of pion true absorption in the pion optical potential, by extracting the coefficients which correspond to the calcium and carbon nuclei from existing data of pion absorption. The second effect studied is the removal of the delta function from the DCX amplitude (which originated from the idea of point-like pion-nucleon coupling), where the interaction extends over a finite region of space. This work was restricted to the sequential pion double charge exchange mechanism, which is generally believed to be dominant in many cases. These corrections have been studied in the plane wave and distorted wave modes.

The results of these calculations for calcium agree with the data for the energies above 200 MeV and partially agree below 200 MeV. The calculations were done for different pion-nucleon ranges (a= 800, 600, 300 MeV/c). The DCX cross sections were calculated for ^'^C up to 300 MeV of pion energy using two single charge exchange (SCX) scattering steps on the valence nucleons and at different ranges a. The results give a reasonable fit with data.