Measurement and isobar-model analysis of the doubly differential cross section for the. pi. /sup +/ produced in. pi. /sup -/p. -->. pi. /sup +/. pi. /sup -/n

The doubly differential cross section d/sup 2/sigma/d..cap omega..dT for ..pi../sup +/ mesons produced in the reaction ..pi../sup -/p ..-->.. ..pi../sup +/..pi../sup -/n was measured at 203, 230, 256, and 358 MeV with a single-arm magnetic spectrometer. A set of five previous measurements at 254, 280, 292, 331, and 356 MeV was reanalyzed with the new measurements. Integrated cross sections were calculated for the combined data set with unprecedented accuracy for this energy range. The chiral-symmetry-breaking parameter was determined to be epsilon = -0.03 +- 0.26 by extrapolating the mean square modulus of the matrix element to threshold and comparing the threshold matrix element with the prediction of soft-pion theory. This value of epsilon is consistent with zero as required by the Weinberg Lagrangian. Measurements at the three highest energies were compared with the results of an isobar-model analysis of bubble-chamber events by an LBL-SLAC collaboration. After allowing for an overall normalization difference, the measurements at 331 and 358 MeV were in excellent agreement with the results of their analysis. The measurement at 292 MeV required variation of the PS11(epsilonN) amplitude, as well as the overall normalization, which could be due to the limited number of bubble-chamber events available for the LBL-SLAC analysis at this energy. A partial-wave analysis of the measurements was also carried out with the VPI isobar model. Within this model, the matrix element contains a background term calculated from a phenomenological ..pi..N Lagrangian that is consistent with the hypotheses of current algebra and PCAC. The reaction was found to be dominated by the initial P11 wave. Production of the ..delta.. isobar from initial D waves was found to be significant at the two highest energies