Pi -40Ca elastic scattering.

Abstract

Elastic differential, total, and integrated reaction ${\mathrm{\ensuremath{\pi}}}^{\ifmmode\pm\else\textpm\fi{}}$${\mathrm{\ensuremath{-}}}^{40}$Ca cross sections are calculated in a semimicroscopic model for incident energies from 65 to 292 MeV. Kinematical and binding effects, as well as Pauli blocking of \ensuremath{\Delta} decay are calculated exactly on a shell-model basis, whereas shadowing due to multihole channels is represented by means of a phenomenological spreading potential with central and spin-orbit parts. Compared to lighter targets, the central \ensuremath{\Delta}-nucleus potential scales to a very good accuracy with the target mass number. The strength of the potential has smooth energy dependence up to ${\mathit{T}}_{\mathrm{\ensuremath{\pi}}}$=241 MeV. Below 100 MeV a repulsive S-wave ${\mathrm{\ensuremath{\rho}}}^{2}$ term in the optical potential is required in order to fit the experimental angular distribution. At 292 MeV comparison with the measured elastic cross section favors a strongly repulsive spreading potential. The distorted pion wave function is calculated and an interesting focusing effect is observed at low energies. The total ${\mathrm{\ensuremath{\pi}}}^{\ifmmode\pm\else\textpm\fi{}}$${\mathrm{\ensuremath{-}}}^{40}$Ca cross section is partitioned into elastic and reaction parts. Our calculation agrees well with an experimentally extracted ${\mathrm{\ensuremath{\pi}}}^{+}$${\mathrm{\ensuremath{-}}}^{40}$Ca elastic-scattering amplitude at \ensuremath{\theta}=0\ifmmode^\circ\else\textdegree\fi{}, but disagrees for ${\mathrm{\ensuremath{\pi}}}^{\mathrm{\ensuremath{-}}}$. Finally, a pion ``absorption'' cross section is calculated and its physical interpretation is discussed.