Pion double charge exchange and nuclear correlations

Single- and double-charge-exchange reactions of pions on nuclei are analyzed by means of an elementary model based on the first- and second-order impulse approximations. The model is applied to the description of transitions induced between the isobaric analog states of ${}_{}{}^{14}{}_{}{}^{}\mathrm{C}$ and ${}_{}{}^{14}{}_{}{}^{}\mathrm{O}$ and ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ at 50 MeV incident pion energy. We find that the model, with only the familiar nuclear orbital wave functions as input, successfully explains the angular distributions observed in both the single and double analog state transitions. In the case of the double-charge-exchange reaction a particularly significant role in the process is played by the position correlation of the two valence neutrons in ${}_{}{}^{14}{}_{}{}^{}\mathrm{C}$. Double-charge-exchange measurements, we show, furnish a direct means of detecting this correlation, which is an important feature of any nuclear shell model. Calculating the effect of this correlation requires summing the nuclear transition amplitudes over all accessible intermediate states. To restrict the summation to the intermediate analog state is to omit the effect of correlation. The double-charge-exchange probability also has some sensitivity to the spatial dependence of the pion-nucleon interaction at short distances. We find that it indicates an approximate radius for the interaction of about 0.7 fm. We have evaluated corrections to the impulse approximations due to nuclear scattering and absorbtion and find that they make only modest quantitative changes in the analysis based on plane waves.