Inadequacies of the New Form of the Strip Approximation for theπ−πScattering Amplitude

Abstract

The new form of the strip approximation is used to obtain mutually self-consistent trajectories with isopin $I=0\mathrm{}$ and $I=1\mathrm{}$ in the $\pi -\pi$ system. However, these trajectories do not correspond to those which are obtained from experiment, and violate unitarity in the asymptotic region. The trajectories obtained from experiment, which satisfy unitarity, are shown not to produce sufficient strength to bootstrap themselves. Also the $I=0\mathrm{}$ trajectory gives rise to a repulsive potential, and to obtain a solution of the $\frac{N}{D}$ equations we are impelled to the doubtful assumption that this repulsion is completely cancelled by other $I=0\mathrm{}$ trajectories that do not reach the right-half angular-momentum plane. It is concluded that both these difficulties stem from the fact that the potential is included only in the first Born approximation, and that more satisfactory results would be forthcoming if the potential were iterated in the way proposed by Mandelstam.