The one-nucleon contribution to threshold pion production in pion-nucleus collisions is calculated using a Fermi gas model of the nuclear excitation spectrum in order to carry out the sum over final nuclear states. For the one-body input a threshold approximant to the production amplitude from the phenomenological Lagrangian theory is used. The cross sections are found to have an ${\eta }^4$ dependence near threshold, where $\eta =\frac{({\omega }_k-2\mathrm{}{m}_{\pi })}{m_{\pi }}$ for total incident pion energy ${\omega }_k$. In a simple eikonal approach incident pion attenuation is found to lead to a reduction of threshold estimates by a factor of ∼ 10.

NUCLEAR REACTIONS ${}_{}{}^{11}{}_{}{}^{}\mathrm{B}({\pi }^{-}, 2{\pi }^{-})$, ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}({\pi }^{-}, 2{\pi }^{-})$, ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}({\pi }^{-}, 2{\pi }^{-})$, ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}({\pi }^{+}, 2{\pi }^{+})$, ${}_{}{}^{31}{}_{}{}^{}\mathrm{P}({\pi }^{+}, 2{\pi }^{+})$; threshold pion production cross section calculated in the Fermi gas model with phenomenological Lagrangian input.

• Received 5 January 1983

DOI:https://doi.org/10.1103/PhysRevC.27.2150