Analysis ofπ−He4scattering andHe4(π−,n)H3reactions at 290 MeV

This study evauates the amplitude for the pion absorption reaction ${}_{}{}^4{}_{}{}^{}\mathrm{He}({\pi }^{-},n){}_{}{}^3{}_{}{}^{}\mathrm{H}$ to first order in the pion absorption operator for a pion laboratory kinetic energy of 290 MeV and the associated angular distribution of emitted neutrons is compared with recent experimental results. The pion absorption amplitude requires the full elastic scattering wave functions for the ${\pi }^{-}-{}_{}{}^4{}_{}{}^{}\mathrm{He}$ and $n-{}_{}{}^3{}_{}{}^{}\mathrm{H}$ systems and the bulk of this study is the generation of the ${\pi }^{-}-{}_{}{}^4{}_{}{}^{}\mathrm{He}$ full elastic scattering wave function in the effective channel approach. The effective channel approach expresses the ${\pi }^{-}-{}_{}{}^4{}_{}{}^{}\mathrm{He}$ full elastic scattering state in terms of explicit elastic and inelastic channel wave functions. The input to the effective channel approach is a phenomenologica $\pi N$ separable interaction which satisfactorily accounts for the $\pi N$ 33 resonance and a complex local Gaussian potential which, in conjunction with the separable interaction, produces the approximate spin and isospin averaged $\pi N$ phase shifts and charge exchange cross section. A judicious choice of the form factor of the separable interaction allows an exact evaluation of the pion-nucleus potentials occurring in the application of the effective channel approach. These potentials are nonseparable and couple each partial wave to itself and to its two next neighbors as well as to the partial waves of the other channel. The complex local $\pi N$ Gaussian potential also allows the analytic construction of the associated terms of the effective channel approach. The resulting two-channel system of integrodifferential equations is solved by iteration. The parameters of the $\pi N$ potential are then varied to produce the observed total and inelastic ${\pi }^{-}-{}_{}{}^4{}_{}{}^{}\mathrm{He}$ cross sections and an angular distribution in reasonable accord with experiment to study pion absorption.