Elastic Scattering of 78-Mev Pions from Copper

The angular distributions of 78±5 Mev ${\pi }^{-}$ and ${\pi }^{+}$ mesons scattered elastically from copper have been measured. The experimental results are compared with the distributions found from a range of exact optical model phase shift calculations using a complex attractive square well potential for $r<\mathrm{}{R}_0$ (where $R_0=1.4\mathrm{}{A}^{\frac{1}{3}}\times {10}^{-13\mathrm{}}$ cm) and the Coulomb potential for $r>\mathrm{}{R}_0$. The effect of adding to the potential a term depending upon the gradient of the nuclear density, and thereby introducing a discontinuity in the matching of logarithmic derivatives at $r=R_0$, is also explored. The optical model as well as several modified Born approximation calculations show reasonable agreement with the experimental curve in the forward direction and in the region of the first diffraction maximum. At backward angles the calculated curves show pronounced maxima and minima which do not appear experimentally, perhaps because incoherent transitions at these angles mask the true coherent distribution in the experimental measurement.