Threshold estimates of (π, 2π) on nuclei in the Fermi gas model: One-body mechanism

Abstract

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 ${\ensuremath{\eta}}^{4}$ dependence near threshold, where $\ensuremath{\eta}=\frac{({\ensuremath{\omega}}_{k}\ensuremath{-}2{m}_{\ensuremath{\pi}})}{{m}_{\ensuremath{\pi}}}$ for total incident pion energy ${\ensuremath{\omega}}_{k}$. In a simple eikonal approach incident pion attenuation is found to lead to a reduction of threshold estimates by a factor of \ensuremath{\sim} 10.