Elastic Scattering of Positive and Negative Pions on Aluminum

Abstract

The elastic, plus nearly elastic, scattering of 80-Mev ${\pi }^{+}$ and ${\pi }^{-}$ mesons on aluminum have been measured as a function of scattering angle. The results are compared with optical model phase-shift calculations using a uniform nuclear model with $R=1.42\mathrm{}{A}^{\frac{1}{3}}\times {10}^{-13\mathrm{}}$ cm and various choices of constant complex potential $V=V_1+i{V}_2$ inside the nucleus. The experimental curves demonstrate clearly the destructive interference between nuclear and Coulomb scattering for ${\pi }^{+}$ mesons, and the corresponding constructive interference for ${\pi }^{-}$ mesons, near 20°. The experimental curves do not show the diffraction minimima present in the theoretical curves, and show a slow increase in the differential cross section beyond 90°. To the extent that the experimental curves for $\theta <\sim 50°$ can be compared with experiment, the best fitting values of $V_1$ and $V_2$ are $V_1=-20\mathrm{}$ Mev for ${\pi }^{+}$ and -30 Mev for ${\pi }^{-}$, corresponding to -25 Mev for nuclear effects alone, and $V_2\sim -20\mathrm{}$ Mev in each case. A value ${\lambda }_a\approx 4\times {10}^{-13\mathrm{}}$ cm is favored for this theoretical model used for comparison with experiment. The potential $V$ was treated as the fourth component of a four vector in a Klein-Gordon-type wave equation in analogy with the Coulomb interaction.