Diffusion Chamber Study of Very Slow Mesons. III. Scattering of Negative Pions in Hydrogen

The elastic scattering in hydrogen of negative pions near 15 Mev is studied. In a path length represented by 8300 $\pi -\mu$ decays, twenty-six events were observed. At these low energies, the $S$-wave dominates the scattering. Treating the small $P$-wave and large Coulomb contributions as known, the data is found to be well represented by an $S$-wave phase shift proportional to momentum. Under this assumption, the phase shift parameters are given by the relation: ${\alpha }_3+2\mathrm{}{\alpha }_1=\frac{(0.25\mathrm{}\pm 0.05)p}{\mu c}$ in radians.